Locomotor Control Systems Laboratory

Publications

Prosthesis Design and Control

Exoskeleton Design and Control

Modeling and Measuring Human Locomotion

Control of Autonomous Legged Robots

Actuator Design, Optimization, and Control

Prosthesis Design and Control

Towards a Unified Approach for Continuously-Variable Impedance Control of Powered Prosthetic Legs over Walking Speeds and Inclines. A. Lee, C. Laubscher, T. K. Best, and R. Gregg. To appear in IEEE Int. Conf. Robotics & Automation, 2024. (Abstract, PDF)

Abstract: Research in powered prosthesis control has explored the use of impedance-based control algorithms due to their biomimetic capabilities and intuitive structure. Modern impedance controllers feature parameters that smoothly vary over gait phase and task according to a data-driven model. However, these recent efforts only use continuous impedance control during stance and instead utilize discrete transition logic to switch to kinematic control during swing, necessitating two separate models for the different parts of the stride. In contrast, this paper presents a controller that uses smooth impedance parameter trajectories throughout the gait, unifying the stance and swing periods under a single, continuous model. Furthermore, this paper proposes a basis model to represent inter-task relationships in the impedance parameters---a strategy that has previously been shown to improve model accuracy over classic linear interpolation methods. In the proposed controller, a weighted sum of Fourier series is used to model the impedance parameters of each joint as continuous functions of gait cycle progression and task. These weights are determined via convex optimization such that the controller best reproduces the joint torques and kinematics in a reference able-bodied dataset. Experiments with a powered knee-ankle prosthesis show that this simpler, unified model produces competitive results when compared to a more complex hybrid impedance-kinematic model over varying walking speeds and inclines.
Transfer Learning for Efficient Intent Prediction in Lower-Limb Prosthetics: A Strategy for Limited Datasets. D. Le, S. Cheng, R. Gregg, and M. Ghaffari. IEEE Robotics & Automation Letters, 2024, DOI: 10.1109/LRA.2024.3379800. (Abstract, PDF)

Abstract: This paper presents a transfer learning method to enhance locomotion intent prediction in novel transfemoral amputee subjects, particularly in data-sparse scenarios. Transfer learning is done with three pre-trained models trained on separate datasets: transfemoral amputees, able-bodied individuals, and a mixed dataset of both groups. Each model is subsequently fine-tuned using data from a new transfemoral amputee subject. While subject-dependent models, trained and tested using individual user data, can achieve the least error rate, they require extensive training datasets. In contrast, our transfer learning approach yields comparable error rates while requiring significantly less data. This highlights the benefit of using pre-existing, pre-trained features when data is scarce. As anticipated, the performance of transfer learning improves as more data from the subject is made available. We also explore the performance of the intent prediction system under various sensor configurations. We identify that a combination of a thigh inertial measurement unit and load cell offers a practical and efficient choice for sensor setup. These findings underscore the potential of transfer learning as a powerful tool for enhancing intent prediction accuracy for new transfemoral amputee subjects, even under data-limited conditions.
Automatic Stub Avoidance for a Powered Prosthetic Leg over Stairs and Obstacles. S. Cheng, C. Laubscher, and R. Gregg. IEEE Trans. Biomedical Eng., 2023, DOI: 10.1109/TBME.2023.3340628. (Abstract, Preprint, Video)

Abstract: Passive prosthetic legs require undesirable compensations from amputee users to avoid stubbing obstacles and stairsteps. Powered prostheses can reduce those compensations by restoring normative joint biomechanics, but the absence of user proprioception and volitional control combined with the absence of environmental awareness by the prosthesis increases the risk of collisions. This paper presents a novel stub avoidance controller that automatically adjusts prosthetic knee/ankle kinematics based on suprasensory measurements of environmental distance from a small, lightweight, low-power, low-cost ultrasonic sensor mounted above the prosthetic ankle. In a case study with two transfemoral amputee participants, this control method reduced the stub rate during stair ascent by 89.95% and demonstrated an 87.5% avoidance rate for crossing different obstacles on level ground. No thigh kinematic compensation was required to achieve these results. These findings demonstrate a practical perception solution for powered prostheses to avoid collisions with stairs and obstacles while restoring normative biomechanics during daily activities.
Data-Driven Phase-Based Control of a Powered Knee-Ankle Prosthesis for Variable-Incline Stair Ascent and Descent. R. Cortino, T. K. Best, and R. Gregg. IEEE Trans. Medical Robotics and Bionics, 2023, DOI: 10.1109/TMRB.2023.3328656. (Abstract, Preprint, Video)

Abstract: Powered knee-ankle prostheses can offer benefits over conventional passive devices during stair locomotion by providing biomimetic net-positive work and active control of joint angles. However, many modern control approaches for stair ascent and descent are often limited by time-consuming hand-tuning of user/task-specific parameters, predefined trajectories that remove user volition, or heuristic approaches that cannot be applied to both stair ascent and descent. This work presents a phase-based hybrid kinematic and impedance controller (HKIC) that allows for semi-volitional, biomimetic stair ascent and descent at a variety of step heights. We define a unified phase variable for both stair ascent and descent that utilizes lower-limb geometry to adjust to different users and step heights. We extend our prior data-driven impedance model for variable-incline walking, modifying the cost function and constraints to create a continuously-varying impedance parameter model for stair ascent and descent over a continuum of step heights. Experiments with above-knee amputee participants (N=2) validate that our HKIC controller produces biomimetic ascent and descent joint kinematics, kinetics, and work across four step height configurations. We also show improved kinematic performance with our HKIC controller in comparison to a passive microprocessor-controlled device during stair locomotion.
Improving Sit/Stand Loading Symmetry and Timing Through Unified Variable Impedance Control of a Powered Knee-Ankle Prosthesis. C. G. Welker, T. K. Best, and R. Gregg. IEEE Trans. Neural Systems and Rehabilitation Engineering, 2023, DOI: 10.1109/TNSRE.2023.3320692. (Abstract, Open Access, Video)

Abstract: Individuals using passive prostheses typically rely heavily on their biological limb to complete sitting and standing tasks, leading to slower completion times and increased rates of osteoarthritis and lower back pain. Powered prostheses can address these challenges, but have control methods that divide sit-stand transitions into discrete phases, limiting user synchronization across the motion and requiring long manual tuning times. This paper extends our preliminary work using a thigh-based phase variable to parameterize optimized data-driven impedance parameter trajectories for sitting, standing, and walking, with only two classification modes. We decouple the stand-to-sit and sit-to-stand equilibrium angles through a knee velocity-dependent scaling term, reducing the model fitting error by approximately half compared to our previous results. We then experimentally validate the controller with three individuals with above-knee amputation performing sitting and standing transitions to/from three different chair heights. We show that our controller implemented on a powered knee-ankle prosthesis produced biomimetic joint mechanics, resulting in significantly reduced sit/stand loading asymmetry and time to complete a 5x sit-to-stand task compared to participants' passive prostheses. Integration with a previously developed walking controller also allowed sit/walk transitions between different chair heights. The controller's biomimetic assistance may reduce the overreliance on the biological limb caused by inadequate passive prostheses, helping improve mobility for people with above-knee amputations.
Improving Amputee Endurance over Activities of Daily Living with a Robotic Knee-Ankle Prosthesis: A Case Study. T. K. Best, C. Laubscher, R. Cortino, S. Cheng, and R. Gregg. In IEEE Int. Conf. Intelligent Robots and Systems, 2023. IROS Best Application Paper Award Finalist. (Abstract, PDF, Video)

Abstract: Robotic knee-ankle prostheses have often fallen short relative to passive microprocessor prostheses in time-based clinical outcome tests. User ambulation endurance is an alternative clinical outcome metric that may better highlight the benefits of robotic prostheses. However, previous studies were unable to show endurance benefits due to inaccurate high-level classification, discretized mid-level control, and insufficiently difficult ambulation tasks. In this case study, we present a phase-based mid-level prosthesis controller which yields biomimetic joint kinematics and kinetics that adjust to suit a continuum of tasks. We enrolled an individual with an above-knee amputation and challenged him to perform repeated, rapid laps of a circuit comprising activities of daily living with both his passive prosthesis and a robotic prosthesis. The participant demonstrated improved endurance with the robotic prosthesis and our mid-level controller compared to his passive prosthesis, completing over twice as many total laps before fatigue and muscle discomfort required him to stop. We also show that time-based outcome metrics fail to capture this endurance improvement, suggesting that alternative metrics related to endurance and fatigue may better highlight the clinical benefits of robotic prostheses.
Controlling Powered Prosthesis Kinematics over Continuous Transitions Between Walk and Stair Ascent. S. Cheng, C. Laubscher, and R. Gregg. In IEEE Int. Conf. Intelligent Robots and Systems, 2023. IROS Best Student Paper Award. (Abstract, PDF, Video)

Abstract: One of the primary benefits of emerging powered prosthetic legs is their ability to facilitate step-over-step stair ascent by providing positive mechanical work. Existing control methods typically have distinct steady-state activity modes for walking and stair ascent, where activity transitions involve discretely switching between controllers and often must be initiated with a particular leg. However, these discrete transitions do not necessarily replicate able-bodied joint biomechanics, which have been shown to continuously adjust over a transition stride. This paper presents a phase-based kinematic controller for a powered knee-ankle prosthesis that enables continuous, biomimetic transitions between walking and stair ascent. The controller tracks joint angles from a data-driven kinematic model that continuously interpolates between the steady-state kinematic models, and it allows both the prosthetic and intact leg to lead the transitions. Results from experiments with two transfemoral amputee participants indicate that knee and ankle kinematics smoothly transition between walking and stair ascent, with comparable or lower root mean square errors compared to variations from able-bodied data.
Gait Event Detection with Proprioceptive Force Sensing in a Powered Knee-Ankle Prosthesis: Validation over Walking Speeds and Slopes. E. Keller, C. Laubscher, and R. Gregg. In IEEE Int. Conf. Robotics & Automation, 2023. (Abstract, Preprint)

Abstract: Many powered prosthetic devices use load cells to detect ground interaction forces and gait events. These sensors introduce additional weight and cost in the device. Recent proprioceptive actuators enable an algebraic relationship between actuator torques and ground contact forces. This paper presents a proprioceptive force sensing paradigm which estimates ground reaction forces as a solution to detect gait events without a load cell. A floating body dynamic model is obtained with constraints at the center of pressure representing foot-ground interaction. Constraint forces are derived to estimate ground reaction forces and subsequently timing of gait events. A treadmill experiment is conducted with a powered knee-ankle prosthesis used by an able-bodied subject walking at various speeds and slopes. Results show accurate gait event timing, with pooled data showing heel strike detection lagging by only 6.7 +/- 7.2 ms and toe off detection leading by 30.4 +/- 11.0 ms compared to values obtained from the load cell. These results establish proof of concept for predicting gait events without a load cell in powered prostheses with proprioceptive actuators.
Data-Driven Variable Impedance Control of a Powered Knee-Ankle Prosthesis for Adaptive Speed and Incline Walking. T. K. Best, C. Welker, E. Rouse, and R. Gregg. IEEE Trans. Robotics, 2023, DOI: 10.1109/TRO.2022.3226887. (Abstract, Preprint, Video)

Abstract: Most impedance-based walking controllers for powered knee-ankle prostheses use a finite state machine with dozens of user-specific parameters that require manual tuning by technical experts. These parameters are only appropriate near the task (e.g., walking speed and incline) at which they were tuned, necessitating many different parameter sets for variable-task walking. In contrast, this paper presents a data-driven, phase-based controller for variable-task walking that uses continuously-variable impedance control during stance and kinematic control during swing to enable biomimetic locomotion. After generating a data-driven model of variable joint impedance with convex optimization, we implement a novel task-invariant phase variable and real-time estimates of speed and incline to enable autonomous task adaptation. Experiments with above-knee amputee participants (N=2) show that our data-driven controller 1) features highly-linear phase estimates and accurate task estimates, 2) produces biomimetic kinematic and kinetic trends as task varies, leading to low errors relative to able-bodied references, and 3) produces biomimetic joint work and cadence trends as task varies. We show that the presented controller meets and often exceeds the performance of a benchmark finite state machine controller for our two participants, without requiring manual impedance tuning.
Data-Driven Variable Impedance Control of a Powered Knee-Ankle Prosthesis for Sit, Stand, and Walk with Minimal Tuning. C. Welker, T. K. Best, and R. Gregg. IEEE Int. Conf. Intelligent Robots & Systems, 2022. (Abstract, PDF, Video)

Abstract: Although the average healthy adult transitions from sit to stand over 60 times per day, the majority of powered prosthesis control research has only focused on walking. In this paper, we present a data-driven controller that enables sitting, standing, and walking with minimal tuning. Our controller comprises two high level modes of sit/stand and walking, and we develop heuristic biomechanical rules to control transitions. We use a phase variable based on the user's thigh angle to parameterize both walking and sit/stand motions, and use variable impedance control during ground contact and position control during swing. We extend previous work on data-driven optimization of continuous impedance parameter functions to design the sit/stand control mode using able-bodied data. Experiments with a powered knee-ankle prosthesis used by a participant with above-knee amputation demonstrate promise in clinical outcomes, as well as trade-offs between our minimal-tuning approach and accommodation of user preferences. Specifically, our controller enabled the participant to complete the sit/stand task 20% faster and reduced average asymmetry by half compared to his everyday passive prosthesis. The controller also facilitated a timed up and go test involving sitting, standing, walking, and turning, with only a mild (10%) decrease in speed compared to the everyday prosthesis. Our sit/stand/walk controller approaches clinical viability by enabling more activities of daily life with minimal tuning.
Stair Ascent Phase-Variable Control of a Powered Knee-Ankle Prosthesis. R. Cortino, E. Bolivar, T. K. Best, and R. Gregg. In IEEE Int. Conf. Robotics & Automation, 2022. (Abstract, PDF, Video)

Abstract: Passive prostheses cannot provide the net positive work required at the knee and ankle for step-over stair ascent. Powered prostheses can provide this net positive work, but user synchronization of joint motion and power input are critical to enabling natural stair ascent gaits. In this work, we build on previous phase variable-based control methods for walking and propose a stair ascent controller driven by the motion of the user's residual thigh. We use reference kinematics from an able-bodied dataset to produce knee and ankle joint trajectories parameterized by gait phase. We redefine the gait cycle to begin at the point of maximum hip flexion instead of heel strike to improve the phase estimate. Able-bodied bypass adapter experiments demonstrate that the phase variable controller replicates normative able-bodied kinematic trajectories with a root mean squared error of 12.66 deg and 2.64 deg for the knee and ankle, respectively. The knee and ankle joints provided on average 0.387J/kg and 0.212J/kg per stride, compared to the normative averages of 0.335J/kg and 0.207J/kg, respectively. Thus, this controller allows powered knee-ankle prostheses to perform net positive mechanical work to assist stair ascent.
Nonholonomic Virtual Constraints for Control of Powered Prostheses Across Walking Speeds. J. Horn and R. Gregg. IEEE Trans Control Systems Tech, 2021. (Abstract, PDF)

Abstract: This paper presents a method to design a nonholonomic virtual constraint (NHVC) controller that produces multiple distinct stance-phase trajectories for corresponding walking speeds. NHVCs encode velocity-dependent joint trajectories via momenta conjugate to the unactuated degree(s)-of-freedom of the system. We recently introduced a method for designing NHVCs that allow for stable bipedal robotic walking across variable terrain slopes. This work extends the notion of NHVCs for application to variable-cadence powered prostheses. Using the segmental conjugate momentum for the prosthesis, an optimization problem is used to design a single stance-phase NHVC for three distinct walking speed trajectories (slow, normal, and fast). This stance-phase controller is implemented with a holonomic swing phase controller on a powered knee-ankle prosthesis, and experiments are conducted with an able-bodied user walking in steady and non-steady velocity conditions. The control scheme is capable of representing 1) multiple, task-dependent reference trajectories, and 2) walking gait variance due to both temporal and kinematic changes in user motion.
Phase-Variable Control of a Powered Knee-Ankle Prosthesis over Continuously Varying Speeds and Inclines. T. K. Best, K. Embry, E. Rouse, and R. Gregg. In IEEE Int. Conf. Intelligent Robots & Systems, 2021. (Abstract, PDF)

Abstract: Most controllers for lower-limb robotic prostheses require individually tuned parameter sets for every combination of speed and incline that the device is designed for. Because ambulation occurs over a continuum of speeds and inclines, this design paradigm requires tuning of a potentially prohibitively large number of parameters. This limitation motivates an alternative control framework that enables walking over a range of speeds and inclines while requiring only a limited number of tunable parameters. In this work, we present the implementation of a continuously varying kinematic controller on a custom powered knee-ankle prosthesis. The controller uses a phase variable derived from the residual thigh angle, along with real-time estimates of ground inclination and walking speed, to compute the appropriate knee and ankle joint angles from a continuous model of able-bodied kinematic data. We modify an existing phase variable architecture to allow for changes in speeds and inclines, quantify the closed-loop accuracy of the speed and incline estimation algorithms for various references, and experimentally validate the controller by observing that it replicates kinematic trends seen in able-bodied gait as speed and incline vary.
Toward Phase-Variable Control of Sit-to-Stand Motion with a Powered Knee-Ankle Prosthesis. D. Raz, E. Bolivar, N. Ozay, and R. Gregg. In IEEE Conf. on Control Technology and Applications, 2021. (Abstract, PDF)

Abstract: This paper presents a new model and phase-variable controller for sit-to-stand motion in above-knee amputees. The model captures the effect of work done by the sound side and residual limb on the prosthesis, while modeling only the prosthetic knee and ankle with a healthy hip joint that connects the thigh to the torso. The controller is parametrized by a biomechanical phase variable rather than time and is analyzed in simulation using the model. We show that this controller performs well with minimal tuning, under a range of realistic initial conditions and biological parameters such as height and body mass. The controller generates kinematic trajectories that are comparable to experimentally observed trajectories in non-amputees. Furthermore, the torques commanded by the controller are consistent with torque profiles and peak values of normative human sit-to-stand motion. Rise times measured in simulation and in non-amputee experiments are also similar. Finally, we compare the presented controller with a baseline proportional-derivative controller demonstrating the advantages of the phase-based design over a set-point based design.
Effects of a Powered Knee-Ankle Prosthesis on Transfemoral Amputee Hip Compensations: A Case Series. T. Elery, S. Rezazadeh, E. Reznick, L. Gray, and R. Gregg. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 2020, DOI: 10.1109/TNSRE.2020.3040260. (Abstract, PDF, Video)

Abstract: Transfemoral amputee gait often exhibits compensations due to the lack of ankle push-off power and control over swing foot position using passive prostheses. Powered prostheses can restore this functionality, but their effects on compensatory behaviors, specifically at the residual hip, are not well understood. This paper investigates residual hip compensations through walking experiments with three transfemoral amputees using a low-impedance powered knee-ankle prosthesis compared to their day-to-day passive prosthesis. The powered prosthesis used impedance control during stance for compliant interaction with the ground, a time-based push-off controller to deliver high torque and power, and phase-based trajectory tracking during swing to provide user control over foot placement. Experiments show that when subjects utilized the powered ankle push-off, less mechanical pull-off power was required from the residual hip to progress the limb forward. Overall positive work at the residual hip was reduced for 2 of 3 subjects, and negative work was reduced for all subjects. Moreover, all subjects displayed increased step length, increased propulsive impulses on the prosthetic side, and improved impulse symmetries. Hip circumduction improved for subjects who had previously exhibited this compensation on their passive prosthesis. These improvements in gait, especially reduced residual hip power and work, have the potential to reduce fatigue and overuse injuries in persons with transfemoral amputation.
Design and Validation of a Powered Knee-Ankle Prosthesis with High-Torque, Low-Impedance Actuators. T. Elery, S. Rezazadeh, C. Nesler, and R. Gregg. IEEE Transactions on Robotics, 36(6): 1649-1668, 2020, DOI: 10.1109/TRO.2020.3005533. (Abstract, PDF, Video)

Abstract: We present the design of a powered knee-ankle prosthetic leg, which implements high-torque actuators with low-reduction transmissions. The transmission coupled with a high-torque and low-speed motor creates an actuator with low mechanical impedance and high backdrivability. This style of actuation presents several possible benefits over modern actuation styles in emerging robotic prosthetic legs, which include freeswinging knee motion, compliance with the ground, negligible unmodeled actuator dynamics, less acoustic noise, and power regeneration. Benchtop tests establish that both joints can be backdriven by small torques (~1-3 Nm) and confirm the small reflected inertia. Impedance control tests prove that the intrinsic impedance and unmodeled dynamics of the actuator are sufficiently small to control joint impedance without torque feedback or lengthy tuning trials. Walking experiments validate performance under the designed loading conditions with minimal tuning. Lastly, the regenerative abilities, low friction, and small reflected inertia of the presented actuators reduced power consumption and acoustic noise compared to state-of-art powered legs.
Extremum Seeking Control for Model-Free Auto-Tuning of Powered Prosthetic Legs. S. Kumar, A. Mohammadi, D. Quintero, S. Rezazadeh, N. Gans, and R. Gregg. IEEE Transactions on Control Systems Technology, 28(6): 2120-2135, 2020, DOI: 10.1109/TCST.2019.2928514. (Abstract, PDF, Videos)

Abstract: This paper proposes an extremum seeking controller (ESC) for simultaneously tuning the feedback control gains of a knee-ankle powered prosthetic leg using continuous-phase controllers. Previously, the proportional gains of the continuousphase controller for each joint were tuned manually by trialand- error, which required several iterations to achieve a balance between the prosthetic leg tracking error performance and the user's comfort. In this paper, a convex objective function is developed that incorporates these two goals. The developed cost function is then minimized by ESC in real-time to simultaneously tune the proportional gains of the knee and the ankle joints. The optimum of the objective function shifts at different walking speeds, and our algorithm is suitably fast to track these changes, providing real-time adaptation for different walking conditions. Benchtop and walking experiments verify the effectiveness of the proposed ESC across various walking speeds.
A Phase Variable Approach to Improved Rhythmic and Non-Rhythmic Control of Powered Knee-Ankle Prostheses. S. Rezazadeh, D. Quintero, N. Divekar, E. Reznick, L. Gray, and R. Gregg. IEEE Access, 7(1): 109840-109855, 2019, DOI: 10.1109/ACCESS.2019.2933614. (Abstract, PDF, Video)

Abstract: Although there has been recent progress in control of multi-joint prosthetic legs for rhythmic tasks such as walking, control of these systems for non-rhythmic motions and general real-world maneuvers is still an open problem. In this article, we develop a new controller that is capable of both rhythmic (constant-speed) walking, transitions between speeds and/or tasks, and some common volitional leg motions. We introduce a new piecewise holonomic phase variable, which, through a finite state machine, forms the basis of our controller. The phase variable is constructed by measuring the thigh angle, and the transitions in the finite state machine are formulated through sensing foot contact along with attributes of a nominal reference gait trajectory. The controller was implemented on a powered knee-ankle prosthesis and tested with a transfemoral amputee subject, who successfully performed a wide range of rhythmic and non-rhythmic tasks, including slow and fast walking, quick start and stop, backward walking, walking over obstacles, and kicking a soccer ball. Use of the powered leg resulted in clinically significant reductions in amputee compensations for rhythmic tasks (including vaulting and hip circumduction) when compared to use of the take-home passive leg. In addition, considerable improvements were also observed in the performance for non-rhythmic tasks. The proposed approach is expected to provide a better understanding of rhythmic and non-rhythmic motions in a unified framework, which in turn can lead to more reliable control of multi-joint prostheses for a wider range of real-world tasks.
Variable Impedance Control of Powered Knee Prostheses Using Human-Inspired Algebraic Curves. A. Mohammadi and R. Gregg. ASME Journal of Computational and Nonlinear Dynamics, 14(10): 101007, 2019, DOI: 10.1115/1.4043002. (Abstract, PDF)

Abstract: Achieving coordinated motion between transfemoral amputee patients and powered prosthetic joints is of paramount importance for powered prostheses control. In this article we propose employing an algebraic curve representation of nominal human walking data for powered knee prosthesis controller design. The proposed algebraic curve representation encodes the desired holonomic relationship between the human and the powered prosthetic joints with no dependence on joint velocities. For an impedance model of the knee joint motion driven by the hip angle signal, we create a continuum of equilibria along the gait cycle using a variable impedance scheme. Our variable impedance-based control law, which is designed using the parameter-dependent Lyapunov function framework, realizes the coordinated hip-knee motion with a family of spring and damper behaviors that continuously change along the human-inspired algebraic curve. In order to accommodate variability in the user's hip motion, we propose a computationally efficient radial projection-based algorithm onto the human-inspired algebraic curve in the hip-knee plane.
Intuitive Clinician Control Interface for a Powered Knee-Ankle Prosthesis: A Case Study. D. Quintero, E. Reznick, D. Lambert, S. Rezazadeh, L. Gray, and R. Gregg. IEEE Journal of Translational Engineering in Health and Medicine, 6(1): 1-9, 2018, DOI: 10.1109/JTEHM.2018.2880199. (Abstract, PDF, Video)

Abstract: This paper presents a potential solution to the challenge of configuring powered knee-ankle prostheses in a clinical setting. Typically, powered prostheses use impedance-based control schemes that contain several independent controllers which correspond to consecutive periods along the gait cycle. This control strategy has numerous control parameters and switching rules that are generally tuned by researchers or technicians and not by a certified prosthetist. We propose an intuitive clinician control interface in which clinicians tune a powered knee-ankle prosthesis based on a virtual constraint control scheme, which tracks desired periodic joint trajectories based on a continuous measurement of the phase (or progression) of gait. The interface derives virtual constraints from clinician-designed joint kinematic trajectories. An experiment was conducted in which a certified prosthetist used the control interface to configure a powered knee-ankle prosthesis for a transfemoral amputee subject during level-ground walking trials. While it usually takes engineers hours of tuning individual parameters by trial and error, the clinician control interface allowed the clinician to tune the powered prosthesis controller in under 10 minutes. This allowed the clinician to improve several amputee gait outcome metrics, such as gait symmetry. These results suggest that the clinician control interface can improve the clinical viability of emerging powered knee-ankle prostheses.
A Phase Variable Approach to Volitional Control of Powered Knee-Ankle Prostheses. S. Rezazadeh, D. Quintero, N. Divekar, and R. Gregg. In IEEE Int. Conf. Intelligent Robots & Systems, Spain, 2018. (Abstract, PDF, Video)

Abstract: Although there has been recent progress in control of multi-joint prosthetic legs for periodic tasks such as walking, volitional control of these systems for non-periodic maneuvers is still an open problem. In this paper, we develop a new controller that is capable of both periodic walking and common volitional leg motions based on a piecewise holonomic phase variable through a finite state machine. The phase variable is constructed by measuring the thigh angle, and the transitions in the finite state machine are formulated through sensing foot contact together with attributes of a nominal reference gait trajectory. The controller was implemented on a powered knee-ankle prosthesis and tested with a transfemoral amputee subject, who successfully performed a wide range of periodic and non-periodic tasks, including low- and high-speed walking, quick start and stop, backward walking, walking over obstacles, and kicking a soccer ball. The proposed approach is expected to provide better understanding of volitional motions and lead to more reliable control of multi-joint prostheses for a wider range of tasks.
Design and Benchtop Validation of a Powered Knee-Ankle Prosthesis with High-Torque, Low-Impedance Actuators. T. Elery, S. Rezazadeh, C. Nesler, J. Doan, H. Zhu, and R. Gregg. In IEEE Int. Conf. Robotics & Automation, Brisbane, Australia, 2018. (Abstract, PDF, Video)

Abstract: This paper describes the design of a powered knee-and-ankle transfemoral prosthetic leg, which implements high torque density actuators with low-reduction transmissions. The low reduction of the transmission coupled with a high-torque and low-speed motor creates an actuator with low mechanical impedance and high backdrivability. This style of actuation presents several possible benefits over modern actuation styles implemented in emerging robotic prosthetic legs. Such benefits include free-swinging knee motion, compliance with the ground, negligible unmodeled actuator dynamics, and greater potential for power regeneration. Benchtop validation experiments were conducted to verify some of these benefits. Backdrive and freeswinging knee tests confirm that both joints can be backdriven by small torques (~3 Nm). Bandwidth tests reveal that the actuator is capable of achieving frequencies required for walking and running. Lastly, open-loop impedance control tests prove that the intrinsic impedance and unmodeled dynamics of the actuator are sufficiently small to control joint impedance without torque feedback.
Continuous-Phase Control of a Powered Knee-Ankle Prosthesis: Amputee Experiments Across Speeds and Inclines. D. Quintero, D. Villarreal, D. Lambert, S. Kapp, and R. Gregg. IEEE Transactions on Robotics, 34(3): 686-701, 2018, DOI: 10.1109/TRO.2018.2794536. (Abstract, PDF, Video)

Abstract: Control systems for powered prosthetic legs typically divide the gait cycle into several periods with distinct controllers, resulting in dozens of control parameters that must be tuned across users and activities. To address this challenge, this paper presents a control approach that unifies the gait cycle of a powered knee-ankle prosthesis using a continuous, user-synchronized sense of phase. Virtual constraints characterize the desired periodic joint trajectories as functions of a phase variable across the entire stride. The phase variable is computed from residual thigh motion, giving the amputee control over the timing of the prosthetic joint patterns. This continuous sense of phase enabled three transfemoral amputee subjects to walk at speeds from 0.67 to 1.21 m/s and slopes from -2.5 to +9.0 deg. Virtual constraints based on task-specific kinematics facilitated normative adjustments in joint work across walking speeds. A fixed set of control gains generalized across these activities and users, which minimized the configuration time of the prosthesis.
Automatic Tuning of Virtual Constraint-Based Control Algorithms for Powered Knee-Ankle Prostheses. S. Kumar, A. Mohammadi, N. Gans, and R. Gregg. In IEEE Conference on Control Technology and Applications (Invited Session on Robotic Locomotion Control), Hawaii, 2017. Best Student Paper Award Finalist. (Abstract, PDF, Video)

Abstract: State-of-art powered prosthetic legs are often controlled using a collection of joint impedance controllers designed for different phases of a walking cycle. Consequently, finite state machines are used to control transitions between different phases. This approach requires a large number of impedance parameters and switching rules to be tuned. Since one set of control parameters cannot be used across different amputees, clinicians spend enormous time tuning these gains for each patient. This paper proposes a virtual constraint-based control scheme with a smaller set of control parameters, which are automatically tuned in real-time using an extremum seeking controller (ESC). ESC, being a model-free control method, assumes no prior knowledge of either the prosthesis or human. Using a singular perturbation analysis, we prove that the virtual constraint tracking errors are small and the PD gains remain bounded. Simulations demonstrate that our ESC-based method is capable of adapting the virtual-constraint based control parameters for amputees with different masses.
Piecewise and Unified Phase Variables in the Control of a Powered Prosthetic Leg. D. Villarreal, D. Quintero and R. Gregg. In IEEE International Conference on Rehabilitation Robotics, London, United Kingdom, 2017. (Abstract, PDF, Experiment Video)

Abstract: Many control methods have been proposed for powered prosthetic legs, ranging from finite state machines that switch between discrete phases of gait to unified controllers that have a continuous sense of phase. In particular, recent work has shown that a mechanical phase variable can parameterize the entire gait cycle for controlling a prosthetic leg during steady rhythmic locomotion. However, the unified approach does not provide voluntary control over non-rhythmic motions like stepping forward and back. In this paper we present a phasing algorithm that uses the amputee's hip angle to control both rhythmic and non-rhythmic motion through two modes: 1) a piecewise (PW) function that provides users voluntary control over stance and swing in a piecewise manner, and 2) a unified function that continuously synchronizes the motion of the prosthetic leg with the amputee user at different walking speeds. The two phase variable approaches are compared in experiments with a powered knee-ankle prosthesis used by an above-knee amputee subject.
Stable, Robust Hybrid Zero Dynamics Control of Powered Lower-Limb Prostheses. A. Martin and R. Gregg. IEEE Transactions on Automatic Control, 62(8): 3930-3942, 2017, DOI: 10.1109/TAC.2017.2648040. (Abstract, PDF)

Abstract: To improve the quality of life for lower-limb amputees, powered prostheses are being developed. Advanced control schemes from the field of bipedal robots, such as hybrid zero dynamics (HZD), may provide great performance. HZDbased control specifies the motion of the actuated joints using output functions to be zeroed, and the required torques are calculated using input-output linearization. For one-step periodic gaits, there is an analytic metric of stability. To apply HZD-based control on a powered prosthesis, several modifications must be made. Because the prosthesis and amputee are only connected via the socket, the prosthesis controller does not have access to the full state of the biped, which decentralizes the form of the input-output linearization. The differences between the amputated and contralateral sides result in a two-step periodic gait, which in turn requires the orbital stability metric to be extended. In addition, because human gait is variable, the prosthesis controller must be robust to continuous moderate perturbations. This robustness is proved using local input-to-state stability and demonstrated with simulations of an above-knee amputee model.
Toward Unified Control of a Powered Prosthetic Leg: A Simulation Study. D. Quintero, A. Martin, and R. Gregg. IEEE Transactions on Control Systems Technology, 26(1): 305-312, 2018, DOI: 10.1109/TCST.2016.2643566. (Abstract, PDF)

Abstract: This brief presents a novel control strategy for a powered knee-ankle prosthesis that unifies the entire gait cycle, eliminating the need to switch between controllers during different periods of gait. A reduced-order Discrete Fourier Transformation (DFT) is used to define virtual constraints that continuously parameterize periodic joint patterns as functions of a mechanical phasing variable. In order to leverage the provable stability properties of Hybrid Zero Dynamics (HZD), hybrid-invariant Bezier polynomials are converted into unified DFT virtual constraints for various walking speeds. Simulations of an amputee biped model show that the unified prosthesis controller approximates the behavior of the original HZD design under ideal scenarios and has advantages over the HZD design when hybrid invariance is violated by mismatches with the human controller. Two implementations of the unified virtual constraints, a feedback linearizing controller and a more practical joint impedance controller, produce similar results in simulation.
Preliminary Experiments with a Unified Controller for a Powered Knee-Ankle Prosthetic Leg Across Walking Speeds. D. Quintero, D. Villarreal, and R. Gregg. In IEEE Int. Conf. Intelligent Robots & Systems, Daejeon, Korea, 2016. (Abstract, PDF, Experiment Video)

Abstract: This paper presents the experimental validation of a novel control strategy that unifies the entire gait cycle of a powered knee-ankle prosthetic leg without the need to switch between controllers for different periods of gait. Current control methods divide the gait cycle into several sequential periods each with independent controllers, resulting in many patient-specific control parameters and switching rules that must be tuned for a specific walking speed. The single controller presented is speed-invariant with a minimal number of control parameters to be tuned. A single, periodic virtual constraint is derived that exactly characterizes the desired actuated joint motion as a function of a mechanical phase variable across walking cycles. A single sensor was used to compute a phase variable related to the residual thigh angle's phase plane, which was recently shown to robustly represent the phase of nonsteady human gait. This phase variable allows the prosthesis to synchronize naturally with the human user for intuitive, biomimetic behavior. A custom powered knee-ankle prosthesis was designed and built to implement the control strategy and validate its performance. A human subject experiment was conducted across multiple walking speeds (1 to 3 miles per hour) in a continuous sequence with the single controller, demonstrating its adaptability to the user's intended speed.
A Haptic Feedback System for Phase-Based Sensory Restoration in Above-Knee Prosthetic Leg Users. A. Plauche, D. Villarreal, and R. Gregg. IEEE Transactions on Haptics, 9(3): 421-426, 2016, DOI: 10.1109/TOH.2016.2580507. (Abstract, PDF)

Abstract: Persons with amputations lack important senses from the amputated limb. With the absence of proprioception in the amputated leg, amputees have far more difficulty maintaining a natural gait with balance and stability. The biggest determinant of temporal limb behavior during locomotion is the phase in the gait cycle, which can be estimated using the center of pressure (COP) under the feet. We hypothesize that feedback from the COP of the prosthetic foot can help restore a more robust sense of phase in transfemoral (above-knee) amputees. This paper presents a device that provides vibrotactile feedback based on the COP from the prosthesis, providing proprioception and potentially an improved sense of phase to the user. Experiments showed that the haptic device significantly decreased variability of stride length, step width, and trunk sway in novice (able-bodied) users of a transfemoral prosthetic leg during treadmill locomotion (N=9), indicating improved gait stability.
Prosthetic Leg Control in the Nullspace of Human Interaction. R. Gregg and A. Martin. In Invited Session on Control Theory in Legged Locomotion, American Control Conf., Boston, MA, 2016. (Abstract, PDF)

Abstract: Recent work has extended the control method of virtual constraints, originally developed for autonomous walking robots, to powered prosthetic legs for lower-limb amputees. Virtual constraints define desired joint patterns as functions of a mechanical phasing variable, which are typically enforced by torque control laws that linearize the output dynamics associated with the virtual constraints. However, the output dynamics of a powered prosthetic leg generally depend on the human interaction forces, which must be measured and canceled by the feedback linearizing control law. This feedback requires expensive multi-axis load cells, and actively canceling the interaction forces may minimize the human's influence over the prosthesis. To address these limitations, this paper proposes a method for projecting virtual constraints into the nullspace of the human interaction terms in the output dynamics. The projected virtual constraints naturally render the output dynamics invariant with respect to the human interaction forces, which instead enter into the internal dynamics of the partially linearized prosthetic system. This method is illustrated with simulations of a transfemoral amputee model walking with a powered knee-ankle prosthesis that is controlled via virtual constraints with and without the proposed projection.
Evaluation of Transradial Body-Powered Prostheses Using a Robotic Simulator. R. Ayub, D. Villarreal, R. Gregg, and F. Gao. Prosthetics & Orthotics International, 41(2): 194-200, 2016, DOI: 10.1177/0309364616650077. (Abstract, Full Text)

Abstract: Background: Transradial body powered prostheses are extensively used by upper limb amputees. This prosthesis requires large muscle forces and great concentration by the patient, often leading to discomfort, muscle fatigue, and skin breakdown, limiting the capacity of the amputee to conduct daily activities. Since body-powered prostheses are commonplace, understanding their optimal operation to mitigate these drawbacks would be clinically meaningful. Objectives: Find the optimal operation of the prosthesis where the activation force is minimized and the grip force is maximized. Study Design/Methods: A computer-controlled robotic amputee simulator capable of rapidly testing multiple elbow, shoulder, and scapular combinations of the residual human arm was constructed. It was fitted with a transradial prosthesis and used to systematically test multiple configurations. Results: We found that increased shoulder flexion, scapular abduction, elbow extension, and the placement of the ring harness near the vertebra C7 correlates with higher gripper operation efficiency, defined as the relation between grip force and cable tension. Conclusions: We conclude that force transmission efficiency is closely related to body posture configuration. These results could help guide practitioners in clinical practice as well as motivate future studies in optimizing the operation of a body-powered prosthesis.
Unifying the Gait Cycle in the Control of a Powered Prosthetic Leg. D. Quintero, A. Martin, and R. Gregg. In IEEE Int. Conf. Rehabilitation Robotics, Singapore, 2015. (Abstract)

Abstract: This paper presents a novel control strategy for an above-knee powered prosthetic leg that unifies the entire gait cycle, eliminating the need to switch between controllers during different periods of gait. Current control methods divide the gait cycle into several sequential periods each with independent controllers, resulting in many patient-specific control parameters and switching rules that must be tuned by clinicians. Having a single controller could reduce the number of control parameters to be tuned for each patient, thereby reducing the clinical time and effort involved in fitting a powered prosthesis for a lowerlimb amputee. Using the Discrete Fourier Transformation, a single virtual constraint is derived that exactly characterizes the desired actuated joint motion over the entire gait cycle. Because the output of the virtual constraint is defined as a periodic function of a monotonically increasing phase variable, no switching or resetting is necessary within or across gait cycles. The output function is zeroed using feedback linearization to produce a single, unified controller. The method is illustrated with simulations of a powered knee-ankle prosthesis in an amputee biped model and examples of systematically generated output functions for different walking speeds.
Hybrid Invariance and Stability of a Feedback Linearizing Controller for Powered Prostheses. A. Martin and R. Gregg. In American Control Conference, Chicago, IL, 2015. (Abstract, PDF)

Abstract: The development of powered lower-limb prostheses has the potential to significantly improve amputees' quality of life. By applying advanced control schemes, such as hybrid zero dynamics (HZD), to prostheses, more intelligent prostheses could be designed. Originally developed to control bipedal robots, HZD-based control specifies the motion of the actuated degrees of freedom using output functions to be zeroed, and the required torques are calculated using feedback linearization. Previous work showed that an HZD-like prosthesis controller can successfully control the stance period of gait. This paper shows that an HZD-based prosthesis controller can be used for the entire gait cycle and that feedback linearization can be performed using only information measured with on-board sensors. An analytic metric for orbital stability of a twostep periodic gait is developed. The results are illustrated in simulation.
Virtual Constraint Control of a Powered Prosthetic Leg: From Simulation to Experiments with Transfemoral Amputees. R. Gregg, T. Lenzi, L. Hargrove, and J. Sensinger. IEEE Transactions on Robotics, 30(6): 1455-1471, 2014, DOI: 10.1109/TRO.2014.2361937.
(Abstract, PDF, Experiment Video)

Abstract: Recent powered (or robotic) prosthetic legs independently control different joints and time periods of the gait cycle, resulting in control parameters and switching rules that can be difficult to tune by clinicians. This challenge might be addressed by a unifying control model used by recent bipedal robots, in which virtual constraints define joint patterns as functions of a monotonic variable that continuously represents the gait cycle phase. In the first application of virtual constraints to amputee locomotion, this paper derives exact and approximate control laws for a partial feedback linearization to enforce virtual constraints on a prosthetic leg. We then encode a human-inspired invariance property called effective shape into virtual constraints for the stance period. After simulating the robustness of the partial feedback linearization to clinically meaningful conditions, we experimentally implement this control strategy on a powered transfemoral leg. We report the results of three amputee subjects walking overground and at variable cadences on a treadmill, demonstrating the clinical viability of this novel control approach.

Exoskeleton Design and Control

A Modular Framework for Task-Agnostic, Energy Shaping Control of Lower-Limb Exoskeletons. J. Lin, G. Thomas, N. Divekar, V. Peddinti, and R. Gregg. IEEE Trans. Control Systems Technology, 2024, conditionally accepted. (Abstract, Preprint, Video)

Abstract: Various backdrivable lower-limb exoskeletons have demonstrated the electromechanical capability to assist volitional motions of able-bodied users and people with mild to moderate gait disorders, but there does not exist a control framework that can be deployed on any joint(s) to assist any activity of daily life in a provably stable manner. This paper presents the modular, multi-task optimal energy shaping (M-TOES) framework, which uses a convex, data-driven optimization to train an analytical control model to instantaneously determine assistive joint torques across activities for any lower-limb exoskeleton joint configuration. The presented modular energy basis is sufficiently descriptive to fit normative human joint torques (given normative feedback from signals available to a given joint configuration) across sit-stand transitions, stair ascent/descent, ramp ascent/descent, and level walking at different speeds. We evaluated controllers for four joint configurations (unilateral/bilateral, hip/knee) of the modular M-BLUE exoskeleton on eight able-bodied users navigating a multi-activity circuit. The two unilateral conditions significantly lowered overall muscle activation across all tasks and subjects (p<0.001). In contrast, bilateral configurations had a minimal impact, possibly attributable to device weight and physical constraints.
Design and Validation of a Modular, Backdrivable Ankle Exoskeleton. S. Zhao, K. Walters, J. Montes Perez, and R. Gregg. To appear in IEEE Int. Conf. Biomedical Robotics and Biomechatronics, 2024. (Abstract, PDF, Video)

Abstract: Partial-assist ankle exoskeletons have been limited by inherent trade-offs between favorable characteristics including high torque capacity, high control bandwidth, backdrivability, compliance, and low mass. Emerging quasi-direct drive actuators have a rigid transmission with a low gear ratio, enabling inherent backdrivability and compliance with accurate torque and position control. Our existing modular, backdrivable exoskeleton system (M-BLUE) uses quasi-direct drive actuators at the hip and/or knee to deliver high assistive torques alongside low dynamic backdrive torques, enabling natural interaction with users with remnant voluntary motion. This paper extends our modular system with the design and validation of a backdrivable ankle exoskeleton module to assist both plantarflexion and dorsiflexion. The bi-directional torque capabilities enable the study of control methods and gait outcomes for able-bodied users and users with gait impairments. Benchtop tests of the actuator performance and control bandwidth indicate that the position, voltage, and current control modes can provide assistance to the ankle joint across activities of daily living (ADLs). We also implement an optimal task-agnostic energy shaping controller for an experiment with a single human subject to validate the ability of the ankle exoskeleton to provide biomimetic torque assistance across a circuit of ADLs.
Improving Task-Agnostic Energy Shaping Control of Powered Exoskeletons with Task/Gait Classification J. Lin, R. Gregg, and P. Shull. IEEE Robotics & Automation Letters, 2024. (Abstract, PDF)

Abstract: Emerging task-agnostic control methods offer a promising avenue for versatile assistance in powered exoskeletons without explicit task detection, but typically come with a performance trade-off for specific tasks and/or users. One such approach employs data-driven optimization of an energy shaping controller to provide naturalistic assistance across essential daily tasks with passivity/stability guarantees. This study introduces a novel control method that merges energy shaping with a machine learning-based classifier to deliver optimal support accommodating diverse individual tasks and users. The classifier detects transitions between multiple tasks and gait patterns in order to employ a more optimal, task-agnostic controller based on the weighted sum of multiple optimized energy-shaping controllers. To demonstrate the efficacy of this integrated control strategy, an in-silico assessment is conducted over a range of gait patterns and tasks, including incline walking, stairs ascent/descent, and stand-to-sit transitions. The proposed method surpasses benchmark approaches in 5-fold cross-validation (p<0.05), yielding 93.17 +/- 7.39% cosine similarity and 77.92 +/- 19.76% variance-accounted-for across tasks and users. These findings highlight the control approach's adaptability in aligning with human joint moments across various tasks.
An Energetic Approach to Task-Invariant Ankle Exoskeleton Control. K. Walters, G. Thomas, J. Lin, and R. Gregg. In IEEE Int. Conf. Intelligent Robots and Systems, 2023. (Abstract, PDF, Video)

Abstract: Robotic ankle exoskeletons have been shown to reduce human effort during walking. However, existing ankle exoskeleton control approaches are limited in their ability to apply biomimetic torque across diverse tasks outside of the controlled lab environment. Energy shaping control can provide task-invariant assistance without estimating the user's state, classifying task, or reproducing pre-defined torque trajectories. In previous work, we showed that an optimally task-invariant energy shaping controller implemented on a knee-ankle exoskeleton reduced the effort of certain muscles for a range of tasks. In this paper, we extend this approach to the sensor suite available at the ankle and present its implementation on a commercially-available, bilateral ankle exoskeleton. An experiment with three healthy subjects walking on a circuit and on a treadmill showed that the controller can approximate biomimetic profiles for varying terrains and task transitions without classifying tasks or switching control modes.
Optimal Energy Shaping Control for a Backdrivable Hip Exoskeleton. J. Zhang, J. Lin, V. Peddinti, and R. Gregg. In American Control Conference, 2023. (Abstract, Preprint, Video)

Abstract: Task-dependent controllers widely used in exoskeletons track predefined trajectories, which overly constrain the volitional motion of individuals with remnant voluntary mobility. Energy shaping, on the other hand, provides task-invariant assistance by altering the human body's dynamic characteristics in the closed loop. While human-exoskeleton systems are often modeled using Euler-Lagrange equations, in our previous work we modeled the system as a port-controlled-Hamiltonian system, and a task-invariant controller was designed for a knee-ankle exoskeleton using interconnection-damping assignment passivity-based control. In this paper, we extend this framework to design a controller for a backdrivable hip exoskeleton to assist multiple tasks. A set of basis functions that contains information of kinematics is selected and corresponding coefficients are optimized, which allows the controller to provide torque that fits normative human torque for different activities of daily life. Human-subject experiments with two able-bodied subjects demonstrated the controller's capability to reduce muscle effort across different tasks.
Real-Time Gait Phase and Task Estimation for Controlling a Powered Ankle Exoskeleton on Extremely Uneven Terrain. R. Medrano, G. Thomas, C. Keais, E. Rouse, and R. Gregg. IEEE Transactions on Robotics, 2023, DOI: 10.1109/TRO.2023.3235584. (Abstract, Preprint, Video)

Abstract: Positive biomechanical outcomes have been reported with lower-limb exoskeletons in laboratory settings, but these devices have difficulty delivering appropriate assistance in synchrony with human gait as the task or rate of phase progression change in real-world environments. This paper presents a controller for an ankle exoskeleton that uses a data-driven kinematic model to continuously estimate the phase, phase rate, stride length, and ground incline states during locomotion. The controller enables the real-time adaptation of torque assistance based on the estimated phase and task variables to match human torques observed in a multi-activity database of 10 able-bodied subjects. We demonstrate in silico that the controller yields phase estimates that are more accurate than the state of the art, while also estimating task variables with comparable accuracy to recent machine learning approaches. The controller implemented in an ankle exoskeleton successfully adapts its assistance in response to changing phase and task variables, both during controlled treadmill trials (10 able-bodied subjects) and a real-world stress test with extremely uneven terrain.
Optimally Biomimetic Passivity-Based Control of a Lower-Limb Exoskeleton over the Primary Activities of Daily Life. J. Lin, N. Divekar, G. Thomas, and R. Gregg. IEEE Open Journal of Control Systems, 2022, DOI: 10.1109/OJCSYS.2022.3165733 (Abstract, Open Access, Supplemental Material, Video)

Abstract: Task-specific, trajectory-based control methods commonly used in exoskeletons may be appropriate for individuals with paraplegia, but they overly constrain the volitional motion of individuals with remnant voluntary ability (representing a far larger population). Human-exoskeleton systems can be represented in the form of the Euler-Lagrange equations or, equivalently, the port-controlled Hamiltonian equations to design control laws that provide \emph{task-invariant} assistance across a continuum of activities/environments by altering energetic properties of the human body. We previously introduced a port-controlled Hamiltonian framework that parameterizes the control law through basis functions related to gravitational and gyroscopic terms, which are optimized to fit normalized able-bodied joint torques across multiple walking gaits on different ground inclines. However, this approach did not have the flexibility to reproduce joint torques for a broader set of activities, including stair climbing and stand-to-sit, due to strict assumptions related to input-output passivity, which ensures the human remains in control of energy growth in the closed-loop dynamics. To provide biomimetic assistance across all primary activities of daily life, this paper generalizes this energy shaping framework by incorporating vertical ground reaction forces and global planar orientation into the basis set, while preserving passivity between the human joint torques and human joint velocities. We present an experimental implementation on a powered knee-ankle exoskeleton used by three able-bodied human subjects during walking on various inclines, ramp ascent/descent, and stand-to-sit, demonstrating the versatility of this control approach and its effect on muscular effort.
Enhancing Voluntary Motion with Modular, Backdrivable, Powered Hip and Knee Orthoses. C. Nesler, G. Thomas, N. Divekar, E. Rouse, and R. Gregg. IEEE Robotics & Automation Letters, 2022, DOI: 10.1109/LRA.2022.3145580. (Abstract, PDF, Assembly Video, Design Data)

Abstract: Mobility disabilities are prominent in society with wide-ranging deficits, motivating modular, partial-assist, lower-limb exoskeletons for this heterogeneous population. This paper introduces the Modular Backdrivable Lower-limb Unloading Exoskeleton (M-BLUE), which implements high torque, low mechanical impedance actuators on commercial orthoses with sheet metal modifications to produce a variety of hip- and/or knee-assisting configurations. Benchtop system identification verifies the desirable backdrive properties of the actuator, and allows for torque prediction within +/- 0.4 Nm. An able-bodied human subject experiment demonstrates that three unilateral configurations of M-BLUE (hip only, knee only, and hip-knee) with a simple gravity compensation controller can reduce muscle EMG readings in a lifting and lowering task relative to the bare condition. Reductions in mean muscular effort and peak muscle activation were seen across the primary squat musculature (excluding biceps femoris), demonstrating the potential to reduce fatigue leading to poor lifting posture. These promising results motivate applications of M-BLUE to additional populations, and the expansion of M-BLUE to bilateral and ankle configurations.
An Energy Shaping Exoskeleton Controller for Human Strength Amplification. G. Thomas and R. Gregg. In IEEE Conference on Decision and Control, 2021. (Abstract, PDF)

Abstract: In this work, we introduce a novel approach to assistive exoskeleton (or powered orthosis) control which avoids needing task and gait phase information. Our approach is based on directly designing the Hamiltonian dynamics of the target closed-loop behavior, shaping the energy of the human and the robot. Relative to previous energy shaping controllers for assistive exoskeletons, we introduce ground reaction force and torque information into the target behavior definition, reformulate the kinematics so as to avoid explicit matching conditions due to under-actuation, and avoid the need to switch between swing and stance energy shapes. Our controller introduces new states into the target Hamiltonian energy that represent a virtual second leg that is connected to the physical leg using virtual springs. The impulse the human imparts to the physical leg is amplified and applied to the virtual leg, but the ground reaction force acts only on the physical leg. A state transformation allows the proposed control to be available using only encoders, an IMU, and ground reaction force sensors. We prove that this controller is stable and passive when acted on by the ground reaction force and demonstrate the controller's strength amplifying behavior in a simulation. A linear analysis based on small signal assumptions allows us to explain the relationship between our tuning parameters and the frequency domain amplification bandwidth.
Design Principles for Compact, Backdrivable Actuation in Partial-Assist Powered Knee Orthoses. H. Zhu, C. Nesler, N. Divekar, Vamsi Peddinti, and R. Gregg. IEEE/ASME Trans. Mechatronics, 2021, DOI: 10.1109/TMECH.2021.3053226. (Abstract, PDF, Video)

Abstract: This paper presents the design and validation of a backdrivable powered knee orthosis for partial assistance of lower-limb musculature, which aims to facilitate daily activities in individuals with musculoskeletal disorders. The actuator design is guided by design principles that prioritize backdrivability, output torque, and compactness. First, we show that increasing the motor diameter while reducing the gear ratio for a fixed output torque ultimately reduces the reflected inertia (and thus backdrive torque). We also identify a tradeoff with actuator torque density that can be addressed by improving the motor's thermal environment, motivating our design of a custom Brushless DC motor with encapsulated windings. Finally, by designing a 7:1 planetary gearset directly into the stator, the actuator has a high package factor that reduces size and weight. Benchtop tests verify that the custom actuator can produce at least 23.9 Nm peak torque and 12.78 Nm continuous torque, yet has less than 2.68 Nm backdrive torque during walking conditions. Able-bodied human subjects experiments (N=3) demonstrate reduced quadriceps activation with bilateral orthosis assistance during lifting-lowering, sit-to-stand, and stair climbing. The minimal transmission also produces negligible acoustic noise.
Optimal Task-Invariant Energetic Control for a Knee-Ankle Exoskeleton. J. Lin, N. Divekar, G. Lv, and R. Gregg. IEEE Control Systems Letters, 5(5): 1711-1716, 2021, DOI: 10.1109/LCSYS.2020.3043838. (Abstract, PDF)

Abstract: Task-invariant control methods for powered exoskeletons provide flexibility in assisting humans across multiple activities and environments. Energy shaping control serves this purpose by altering the human body's dynamic characteristics in closed loop. Our previous work on potential energy shaping alters the gravitational vector to reduce the user's perceived gravity, but this method cannot provide velocity-dependent assistance. The interconnection and damping assignment passivity-based control (IDA-PBC) method provides more freedom to shape a dynamical system's energy through the interconnection structure of a port-controlled Hamiltonian system model. This paper derives a novel energetic control strategy based on IDA-PBC for a backdrivable knee-ankle exoskeleton. The control law provides torques that depend on various basis functions related to gravitational and gyroscopic terms. We optimize a set of constant weighting parameters for these basis functions to obtain a control law that produces able-bodied joint torques during walking on multiple ground slopes. We perform experiments with an able-bodied human subject wearing a knee-ankle exoskeleton to demonstrate reduced activation in certain lower-limb muscles.
Trajectory-Free Control of Lower-Limb Exoskeletons Through Underactuated Total Energy Shaping. G. Lv, J. Lin, and R. Gregg. IEEE Access, 2021, DOI: 10.1109/ACCESS.2021.3094979. (Abstract, PDF)

Abstract: Kinematic control approaches for exoskeletons replicate normative joint kinematics associated with one specific task and user at a time, which makes it difficult to adjust to continuously-varying activities during gait training. These approaches also overly constrain individuals who have partial or full volitional control of their limbs, preventing these individuals from choosing their own preferred gait patterns. To address these issues, we proposed a matching framework for underactuated total energy shaping (i.e., shaping both the potential and kinetic energies) with human and environmental interaction to provide task-invariant, energetic assistance. In our prior work, we designed assistive strategies to compensate for lower-limb inertia in the actuated part of the mass matrix while leaving mass related terms unshaped. While these strategies have demonstrated potentia l gait benefits, shaping mass related terms in addition to lower-limb inertia can produce greater benefits as they are more dominant in determining human dynamics during locomotion. Moreover, previous definitions of closed-loop mass matrix with reduced inertial parameters cannot guarantee its positive definiteness. Having a non-positive definite mass matrix in the closed loop can render chaotic behaviors such as unbounded exoskeleton torques that are dangerous to human users. In this paper, we generalize our prior work to shape all inertial terms in the actuated part of the mass matrix while ensuring its positive definiteness in the closed loop. In addition, given a positive-definite, closed-loop mass matrix, we prove passivity from human input to joint velocity and highlight two Lyapunov stability results based on common assumptions of human joint control policies. We then show beneficial effects of the proposed assistive strategies such as reduced metabolic cost in simulations of a human-like model. We also show that the corresponding assistive torques closely match the human torques of an able-bodied subject.
A Potential Energy Shaping Controller with Ground Reaction Force Feedback for a Multi-Activity Knee-Ankle Exoskeleton. N. Divekar, J. Lin, C. Nesler, and R. Gregg. In IEEE Int. Conf. Biomedical Robotics & Biomechatronics, 2020. (Abstract, PDF)

Abstract: This paper presents the design and implementation of a novel multi-activity control strategy for a backdrivable knee-ankle exoskeleton. Traditionally, exoskeletons have used trajectory-based control of highly geared exoskeletons for complete motion assistance. In contrast, we develop a potential energy shaping controller with ground reaction force (GRF) feedback that facilitates multi-activity assistance without prescribing pre-defined kinematics. This control strategy leverages the exoskeleton's backdrivable, torque-controlled actuators to enhance the user's voluntary motion. Although potential energy shaping was previously implemented in an exoskeleton to reduce the user's perceived gravity, this model-based approach assumes the stance leg is fully loaded with the weight of the user, resulting in excessive control torques as weight transfers to the contralateral leg during double support. The presented approach uses GRF feedback to taper the torque control output for any activity involving multiple supports, leading to a closer match with normative joint moments in simulations based on pre-recorded human data during level walking. To implement this strategy, we present a custom foot force sensor that provides GRF feedback to the previously designed exoskeleton. Comparison of our sensor with a force plate (taken as gold standard) shows high accuracy with a correlation coefficient of 0.99 and a mean square error of 0.03. Finally, results from an able-bodied human subject experiment demonstrate that the exoskeleton is able to reduce muscular activation of the primary muscles related to the knee and ankle joints during sit-to-stand, stand-to-sit, level walking, and stair climbing.
Extremum Seeking Control for Stiffness Auto-Tuning of a Quasi-Passive Ankle Exoskeleton. S. Kumar, M. Zwall, E. Bolivar, R. Gregg, and N. Gans. IEEE Robotics & Automation Letters, 5(3): 4604-4611, 2020, DOI: 10.1109/LRA.2020.3001541. (Abstract, PDF, Video)

Abstract: Recently, it has been shown that light-weight, passive, ankle exoskeletons with spring-based energy captureand- return mechanisms can reduce the muscular effort of human walking. The stiffness of the spring in such a device must be properly tuned in order to minimize the muscular effort. However, this muscular effort changes for different locomotion conditions (e.g., walking speed), causing the optimal spring stiffness to vary as well. Existing passive exoskeletons have a fixed stiffness during operation, preventing it from responding to changes in walking conditions. Thus, there is a need of a device and auto-tuning algorithm that minimizes the muscular effort across different walking conditions, while preserving the advantages of passive exoskeletons. In this paper, we developed a pseudo-passive ankle exoskeleton with a variable stiffness mechanism capable of self-tuning. As the relationship between the muscular effort and the optimal spring stiffness across different walking speeds is not known a priori, a modelfree, discrete-time extremum seeking control (ESC) algorithm was implemented for real-time optimization of spring stiffness. Experiments with a healthy subject demonstrate that as the walking speed of the user changes, ESC automatically tunes the torsional stiffness about the ankle joint. In addition, the average RMS EMG readings of tibialis anterior and soleus muscles at slow walking speed decreased by 41.75% and 10.82%, respectively.
Design and Initial Validation of a Multiple Degree-of-Freedom Joint for an Ankle-Foot Orthosis. T. Elery, E. Reznick, S. Shearin, K. McCain, and R. Gregg. ASME J Medical Devices, 16(2): 021001, 2022, DOI: 10.1115/1.4053200 (Abstract)

Abstract: This paper presents the novel design of a multi-degree-of-freedom joint (M-DOF) for an ankle-foot orthosis (AFO) that aims to improve upon the commercially available double action joint (DAJ). The M-DOF is designed to maintain the functionality of the DAJ, while increasing dorsiflexion stiffness and introducing inversion/eversion. This increase in range of motion is designed to produce greater engagement from lower limb muscles during gait. The M-DOF was experimentally validated with one able-bodied and one stroke subject. Across walking speeds, the M-DOF AFO minimally affected the able-bodied subject's joint kinematics. The stroke subject's ankle dorsiflexion/plantarflexion and knee flexion were not heavily altered when wearing the M-DOF AFO, compared to the DAJ AFO. The new DOF allowed by the M-DOF AFO increased the inversion/eversion of the ankle by ~3 deg, without introducing any new compensations compared to their gait with the DAJ AFO.
Energy Shaping Control with Virtual Spring and Damper for Powered Exoskeletons. J. Lin, N. Divekar, G. Lv, and R. Gregg. In IEEE Conference on Decision and Control, 2019. (Abstract, PDF)

Abstract: Task-invariant feedback control laws for powered exoskeletons are preferred to assist human users across varying locomotor activities. This goal can be achieved with energy shaping methods, where certain nonlinear partial differential equations, i.e., matching conditions, must be satisfied to find the achievable dynamics. Based on the energy shaping methods, open-loop systems can be mapped to closed-loop systems with a desired analytical expression of energy. In this paper, the desired energy consists of modified potential energy that is welldefined and unified across different contact conditions along with the energy of virtual springs and dampers that improve energy recycling during walking. The human-exoskeleton system achieves the input-output passivity and Lyapunov stability during the whole walking period with the proposed method. The corresponding controller provides assistive torques that closely match the human torques of a simulated biped model and able-bodied human subjects' data.
Design and Validation of a Partial-Assist Knee Orthosis with Compact, Backdrivable Actuation. H. Zhu, C. Nesler, N. Divekar, M. Taha Ahmad, and R. Gregg. In IEEE Int. Conf. Rehab. Robotics, 2019. (Abstract, PDF, Video)

Abstract: This paper presents the mechatronic design and initial validation of a partial-assist knee orthosis for individuals with musculoskeletal disorders, e.g., knee osteoarthritis and lower back pain. This orthosis utilizes a quasi-direct drive actuator with a low-ratio transmission (7:1) to greatly reduce the reflected inertia for high backdrivability. To provide meaningful assistance, a custom Brushless DC (BLDC) motor is designed with encapsulated windings to improve the motor's thermal environment and thus its continuous torque output. The 2.69 kg orthosis is constructed from all custom-made components with a high package factor for lighter weight and a more compact size. The combination of compactness, backdrivability, and torque output enables the orthosis to provide partial assistance without obstructing the natural movement of the user. Several benchtop tests verify the actuator's capabilities, and a human subject experiment demonstrates reduced quadriceps muscle activation when assisted during a repetitive lifting and lowering task.
Contact-Invariant Total Energy Shaping for Powered Exoskeletons. J. Lin, G. Lv, and R. Gregg. In American Control Conference, 2019. (Abstract, PDF)

Abstract: Energy shaping methods can be used to design task-invariant feedback control laws for the powered exoskeletons (i.e., orthoses). In order to achieve a desired closed-loop energy, certain matching conditions must be satisfied, which are sets of nonlinear partial differential equations. In this paper, we solve the matching conditions and come up with a new solution for under-actuated systems by using Auckly's method.We find a unified feedback control law that is task-invariant with respect to human inputs and different contact conditions. We propose assistive and resistive shaping strategies to alter the mass/inertia matrix and simulate on a powered knee-ankle exoskeleton. The simulation results show the reduction and increment of the human model's metabolic cost of generating muscular forces in human walking. The interchange between the kinetic and potential energy and the changes in acceleration of the center of mass are also investigated in the simulation.
On the Design and Control of Highly Backdrivable Lower-Limb Exoskeletons. G. Lv, H. Zhu, and R. Gregg. IEEE Control Systems Magazine, 38(6): 88-113, 2018, DOI: 10.1109/MCS.2018.2866605. (Abstract, PDF)

Abstract: The majority of assistive exoskeletons are designed to rigidly track time-based kinematic patterns using highly geared actuators, which prevents users from moving their joints freely without help from the exoskeleton. Individuals with partial or full volitional control of their lower extremities require novel design and control methods for exoskeletons that are more compatible with human interaction. In order to assist or augment volitional human motion, exoskeleton joints must be backdrivable and the control strategy must be invariant to the user's joint kinematics. This paper presents the design philosophy behind two generations of highly backdrivable exoskeletons, which utilize torque-dense motors with low-ratio transmissions. Then we present a trajectory-free control framework based on energy shaping with environmental and human interaction. Simulations with a human-like biped demonstrate the assistive effect of shaping the human body's kinetic and potential energies, and experiments with a powered knee-ankle exoskeleton demonstrate the user-cooperative and task-invariant nature of the control approach.
Towards Total Energy Shaping Control of Lower-Limb Exoskeletons. G. Lv and R. Gregg. In American Control Conference, Seattle, WA, 2017. (Abstract, PDF)

Abstract: Current robotic exoskeletons use time-based kinematic control methodologies to enforce fixed reference joint patterns during gait rehabilitation. These control methods aim at replicating normal joint kinematics but do not facilitate learning. Trajectory-free control methods for exoskeletons are required to promote user control over joint kinematics. Our prior work on potential energy shaping provides virtual bodyweight support through a trajectory-free control law, but altering only the gravitational forces does not assist the subject in accelerating/decelerating the body forward. Kinetic energy is velocity dependent and thus shaping the kinetic energy in addition to potential energy can yield greater dynamical changes in closed loop. In this paper, we generalize our previous work to achieve underactuated total energy shaping of the human body through an exoskeleton. By shaping the fullyactuated part of the mass matrix, we satisfy the matching condition for three phases of the gait and obtain trajectoryfree control laws accordingly. Simulations of a human-like biped demonstrate speed regulation in addition to body-weight support, indicating the potential clinical value of this proposed control approach.
Design and Validation of a Torque Dense, Highly Backdrivable Powered Knee-Ankle Orthosis. H. Zhu, J. Doan, C. Stence, G. Lv, T. Elery, and R. Gregg. In IEEE Int. Conf. Robotics & Automation, Singapore, 2017. (Abstract, PDF, Experiment Video)

Abstract: This paper presents the mechatronic design and experimental validation of a novel powered knee-ankle orthosis for testing torque-driven rehabilitation control strategies. The modular actuator of the orthosis is designed with a torque dense motor and a custom low-ratio transmission (24:1) to provide mechanical transparency to the user, allowing them to actively contribute to their joint kinematics during gait training. The 4.88 kg orthosis utilizes frameless components and light materials, such as aluminum alloy and carbon fiber, to reduce its mass. A human subject experiment demonstrates accurate torque control with high output torque during stance and low backdrive torque during swing at fast walking speeds. This work shows that backdrivability, precise torque control, high torque output, and light weight can be achieved in a powered orthosis without the high cost and complexity of variable transmissions, clutches, and/or series elastic components.
Underactuated Potential Energy Shaping with Contact Constraints: Application to a Powered Knee-Ankle Orthosis. G. Lv and R. Gregg. IEEE Transactions on Control Systems Technology, 26(1): 181-193, 2018, DOI: 10.1109/TCST.2016.2646319. (Abstract, PDF)

Abstract: Body-weight support (i.e., gravity compensation) is an effective clinical tool for gait rehabilitation after neurological impairment. Body-weight supported training systems have been developed to help patients regain mobility and confidence during walking, but conventional systems constrain the patient's treatment in clinical environments. We propose that this challenge could be addressed by virtually providing patients with body-weight support through the actuators of a powered orthosis (or exoskeleton) utilizing potential energy shaping control. However, the changing contact conditions and degrees of underactuation encountered during human walking present significant challenges to consistently matching a desired potential energy for the human in closed loop. We therefore derive a generalized matching condition for shaping Lagrangian systems with holonomic contact constraints. By satisfying this matching condition for four phases of gait, we derive passivity-based control laws to achieve virtual body-weight support through a powered knee-ankle orthosis. We demonstrate beneficial effects of virtual body-weight support in simulations of a human-like biped model, indicating the potential clinical value of this proposed control approach.
Experimental Implementation of Underactuated Potential Energy Shaping on a Powered Ankle-Foot Orthosis. G. Lv, H. Zhu, T. Elery, L. Li, and R. Gregg. In IEEE Int. Conf. Robotics & Automation, Stockholm, Sweden, 2016. (Abstract, PDF, Experiment Video)

Abstract: Traditional control methodologies of rehabilitation orthoses/exoskeletons aim at replicating normal kinematics and thus fall into the category of kinematic control. This control paradigm depends on pre-defined reference trajectories, which can be difficult to adjust between different locomotor tasks and human subjects. An alternative control category, kinetic control, enforces kinetic goals (e.g., torques or energy) instead of kinematic trajectories, which could provide a flexible learning environment for the user while freeing up therapists to make corrections. We propose that the theory of underactuated potential energy shaping, which falls into the category of kinetic control, could be used to generate virtual body-weight support for stroke gait rehabilitation. After deriving the nonlinear control law and simulating it on a human-like biped model, we implemented this controller on a powered ankle-foot orthosis that was designed specifically for testing torque control strategies. Experimental results with an able-bodied human subject demonstrate the feasibility of the control approach for both positive and negative virtual body-weight augmentation.
Orthotic Body-Weight Support Through Underactuated Potential Energy Shaping with Contact Constraints. G. Lv and R. Gregg. In IEEE Conf. Decision & Control, Osaka, Japan, 2015. Best Student Paper Award. (Abstract, PDF)

Abstract: Body-weight support is an effective clinical tool for gait rehabilitation after neurological impairment. Body-weight supported training systems have been developed to help patients regain mobility and confidence during walking, but conventional systems constrain the patient's treatment in clinical environments. We propose that this challenge could be addressed by virtually providing patients with body-weight support through the actuators of a powered orthosis (or exoskeleton) utilizing potential energy shaping control. However, the changing contact conditions and degrees of underactuation encountered during human walking present significant challenges to consistently matching a desired potential energy for the human in closed loop. We therefore introduce a generalized matching condition for shaping Lagrangian systems with holonomic contact constraints. By satisfying this matching condition for four phases of gait, we derive control laws to achieve virtual bodyweight support through a powered knee-ankle orthosis. We demonstrate beneficial effects of virtual body-weight support in simulations of a human-like biped model, indicating the potential clinical value of this proposed control approach.

Modeling and Measuring Human Locomotion

Robustification of Bayesian-Inference-Based Gait Estimation for Lower-limb Wearable Robots. T.-W. Hsu, R. Gregg, and G. Thomas. IEEE Robotics & Automation Letters, 2024, DOI: 10.1109/LRA.2024.3354558. (Abstract, PDF)

Abstract: Lower-limb wearable robots designed to assist people in everyday activities must reliably recover from any momentary confusion about what the user is doing. Such confusion might arise from momentary sensor failure, collision with an obstacle, losing track of gait due to an out-of-distribution stride, etc. Systems that infer a user's walking condition from angle measurements using Bayesian filters (e.g., extended Kalman filters) have been shown to accurately track gait across a range of activities. However, due to the fundamental problem structure and assumptions of Bayesian filter implementations, such estimators risk becoming 'lost' with little hope of a quick recovery. In this paper, we 1) introduce a Monte Carlo-based metric to quantify the robustness of pattern-tracking gait estimators, 2) propose strategies for improving tracking robustness, and 3) systematically evaluate them against this new metric using a publicly available gait biomechanics dataset. Our results, aggregating 2,700 trials of simulated walking of 10 able-bodied subjects under random perturbations, suggest that drastic improvements in robustness (from 8.9% to 99%) are possible using relatively simple modifications to the estimation process without noticeably degrading estimator accuracy.
Effects of Personalization on Gait-State Tracking Performance Using Extended Kalman Filters. J. Montes-Perez, G. Thomas, and R. Gregg. In IEEE Int. Conf. Intelligent Robots and Systems, 2023. (Abstract, PDF)

Abstract: Emerging partial-assistance exoskeletons can enhance able-bodied performance and aid people with pathological gait or age-related immobility. However, every person walks differently, which makes it difficult to directly compute assistance torques from joint kinematics. Gait-state estimation-based controllers use phase (normalized stride time) and task variables (e.g., stride length and ground inclination) to parameterize the joint torques. Using kinematic models that depend on the gait-state, prior work has used an Extended Kalman filter (EKF) to estimate the gait-state online. However, this EKF suffered from kinematic errors since it used a subject-independent measurement model, and it is still unknown how personalization of this measurement model would reduce gait-state tracking error. This paper quantifies how much gait-state tracking improvement a personalized measurement model can have over a subject-independent measurement model when using an EKF-based gait-state estimator. Since the EKF performance depends on the measurement model covariance matrix, we tested on multiple different tuning parameters. Across reasonable values of tuning parameters that resulted in good performance, personalization improved estimation error on average by 8.5 +/- 13.8% for phase (mean +/- standard deviation), 27.2 +/- 8.1% for stride length, and 10.5 +/- 13.5% for ground inclination. These findings support the hypothesis that personalization of the measurement model significantly improves gait-state estimation performance in EKF based gait-state tracking (P << 0.05), which could ultimately enable reliable responses to faster human gait changes.
Predicting Individualized Joint Kinematics over Continuous Variations of Walking, Running, and Stair Climbing. E. Reznick, C. Gonzalez Welker, and R. Gregg. IEEE Open Journal of Engineering in Medicine and Biology, 2023, DOI: 10.1109/OJEMB.2023.3234431. (Abstract, Preprint)

Abstract: GOAL: Accounting for gait individuality is important to positive outcomes with wearable robots, but manually tuning multi-activity models is time-consuming and not viable in a clinic. Generalizations can possibly be made to predict gait individuality in unobserved conditions. METHODS: Kinematic individuality--how one person's joint angles differ from the group--is quantified for every subject, joint, ambulation mode (walking, running, stair ascent, and stair descent), and intramodal task (speed, incline) in an open-access dataset with 10 able-bodied subjects. Four N-way ANOVAs test how prediction methods affect the fit to experimental data between and within ambulation modes. We test whether walking individuality (measured at a single speed on level ground) carries across modes, or whether a mode-specific prediction (based on a single task for each mode) is significantly more effective. RESULTS: Kinematic individualization improves fit across joint and task if we consider each mode separately. Across all modes, tasks, and joints, modal individualization improved the fit in 81% of trials, improving the fit on average by 4.3 deg across the gait cycle. This was statistically significant at all joints for walking and running, and half the joints for stair ascent/descent. CONCLUSIONS: For walking and running, kinematic individuality can be easily generalized within mode, but the trends are mixed on stairs depending on joint.
Analysis of the Bayesian Gait-State Estimation Problem for Lower-Limb Wearable Robot Sensor Configurations. R. Medrano, G. Thomas, E. Rouse, and R. Gregg. IEEE Robotics & Automation Letters, 2022, DOI: 10.1109/LRA.2022.3183790 (Abstract, PDF)

Abstract: Many exoskeletons today are primarily tested in controlled, steady-state laboratory conditions that are unrealistic representations of their real-world usage in which walking conditions (e.g., speed, slope, and stride length) change constantly. One potential solution is to detect these changing walking conditions online using Bayesian state estimation to deliver assistance that continuously adapts to the wearer's gait. This paper investigates such an approach in silico, aiming to understand 1) which of the various Bayesian filter assumptions best match the problem, and 2) which gait parameters can be feasibly estimated with different combinations of sensors available to different exoskeleton configurations (pelvis, thigh, shank, and/or foot). Our results suggest that the assumptions of the Extended Kalman Filter are well suited to accurately estimate phase, stride frequency, stride length, and ramp inclination with a wide variety of sparse sensor configurations.
Modeling the Transitional Kinematics Between Variable-Incline Walking and Stair Climbing. S. Cheng, E. Bolivar, C. Gonzalez Welker, and R. Gregg. IEEE Transactions on Medical Robotics and Bionics, 2022, DOI: 10.1109/TMRB.2022.3185405. (Abstract, PDF)

Abstract: Although emerging powered prostheses can enable people with lower-limb amputation to walk and climb stairs over different task conditions (e.g., speeds and inclines), the control architecture typically uses a finite-state machine to switch between activity-specific controllers. Because these controllers focus on steady-state locomotion, powered prostheses abruptly switch between controllers during gait transitions rather than continuously adjusting leg biomechanics in synchrony with the users. This paper introduces a new framework for powered prosthesis control by modeling the lower-limb joint kinematics over a continuum of variable-incline walking and stair climbing, including steady-state and transitional gaits. Steady-state models for walking and stair climbing represent joint kinematics as continuous functions of gait phase, forward speed, and incline. Transition models interpolate kinematics as convex combinations of the two steady-state models, with an additional term to account for kinematics that fall outside their convex hull. The coefficients of this convex combination denote the similarity of the transitional kinematics to each steady-state mode, providing insight into how able-bodied individuals continuously transition between ambulation modes. Cross-validation demonstrates that the model predictions of untrained kinematics have errors within the range of physiological variability for all joints. Simulation results demonstrate the model's robustness to incline estimation and mode classification errors.
Lower-Limb Kinematics and Kinetics During Continuously Varying Human Locomotion. E. Reznick, K. Embry, R. Neuman, E. Bolivar, N. Fey, and R. Gregg. Scientific Data, 2021, DOI: 10.1038/s41597-021-01057-9. (Abstract, Open Access, Data)

Abstract: Human locomotion involves continuously variable activities including walking, running, and stair climbing over a range of speeds and inclinations as well as sit-stand, walk-run, and walk-stairs transitions. Understanding the kinematics and kinetics of the lower limbs during continuously varying locomotion is fundamental to developing robotic prostheses and exoskeletons that assist in community ambulation. However, available datasets on human locomotion neglect transitions between activities and/or continuous variations in speed and inclination during these activities. This data paper reports a new dataset that includes the lower-limb kinematics and kinetics of ten able-bodied subjects walking at multiple inclines (+/- 0, 5, and 10 deg) and speeds (0.8, 1, and 1.2 m/s), running at multiple speeds (1.8, 2, 2.2, and 2.4 m/s), walking and running with constant acceleration (+/- 0.2 and 0.5 m/s), and stair ascent/descent with multiple stair inclines (20, 25, 30, and 35 deg). This dataset also includes sit-stand transitions, walk-run transitions, and walk-stairs transitions. Data were recorded by a Vicon motion capture system and, for applicable tasks, a Bertec instrumented treadmill.
Real-Time Activity Recognition with Instantaneous Characteristic Features of Thigh Kinematics. S. Cheng, E. Bolivar, and R. Gregg. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 2021, DOI: 10.1109/TNSRE.2021.3107780. (Abstract, Open Access)

Abstract: Current supervised learning or deep learning-based activity recognition classifiers can achieve high accuracy in recognizing locomotion activities. Most available techniques use a high-dimensional space of features, e.g., combinations of EMG, kinematics and kinetics, and transformations over those signals. The associated classification rules are therefore complex; the machine tries to understand the human, but the human does not understand the machine. This paper presents an activity recognition system that uses signals from a thigh-mounted IMU and a force sensitive resistor to classify transitions between sitting, walking, stair ascending, and stair descending. The system uses the thigh's orientation and velocity with foot contact information at specific moments within a given activity as the features to classify transitions to other activities. We call these Instantaneous Characteristic Features (ICFs). Because these ICFs are biomechanically intuitive, they are easy for the user to understand and thus control the activity transitions of wearable robots. We assessed our classification algorithm offline using an existing dataset with 10 able-bodied subjects and online with another 10 able-bodied subjects wearing a real-time system. The offline study analyzed the effect of subject-dependency and ramp inclinations. The real-time classification accuracy was evaluated before and after training the subjects on the ICFs. The real-time system achieved overall pre-subject-training and post-subject-training error rates of 0.59% +/- 0.24% and 0.56% +/- 0.20%, respectively. We also evaluated the feasibility of our ICFs for amputee ambulation by analyzing a public dataset with the open-source bionic leg. The simplicity of these classification rules demonstrates a new paradigm for activity recognition where the human can understand the machine and vice-versa.
Parameterizing Human Locomotion Across Quasi-Random Treadmill Perturbations and Inclines. R. Macaluso, K. Embry, D. Villarreal, and R. Gregg. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 2021, DOI: 10.1109/TNSRE.2021.3057877. (Abstract, PDF, Data)

Abstract: Previous work has shown that it is possible to use a mechanical phase variable to accurately quantify the progression through a human gait cycle, even in the presence of disturbances. However, mechanical phase variables are highly dependent on the behavior of the body segment from which they are measured, which can change with the human's task or in response to different disturbances. In this study, we compare kinematic parameterization methods based on time, thigh phase angle, and tibia phase angle with motion capture data obtained from ten able-bodied subjects walking at three inclines while experiencing phase-shifting perturbations from a split-belt instrumented treadmill. The belt, direction, and timings of perturbations were quasi-randomly selected to prevent anticipatory action by the subjects and sample different types of perturbations. A statistical analysis revealed that both phase parameterization methods are superior to time parameterization, with thigh phase angle also being superior to tibia phase angle in most cases.
Analysis of Continuously Varying Kinematics for Prosthetic Leg Control Applications. K. Embry and R. Gregg. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 2020, DOI: 10.1109/TNSRE.2020.3045003. (Abstract, PDF)

Abstract: Powered prosthetic legs can improve quality of life for people with transfemoral amputations by providing net positive work at the knee and ankle, reducing the effort required from the wearer and making more tasks possible. However, the controllers for these devices use finite state machines that limit their use to a small set of pre-defined tasks that require many hours of tuning for each user. In previous work, we demonstrated that a continuous parameterization of joint kinematics over walking speeds and inclines provides more accurate predictions of reference kinematics for control than a finite state machine. However, our previous work did not account for measurement errors in gait phase, walking speed, and ground incline, nor subject-specific differences in reference kinematics, which occur in practice. In this work, we conduct a pilot experiment to characterize the accuracy of speed and incline measurements using sensors onboard our prototype prosthetic leg, and simulate phase measurements on ten able-bodied subjects using archived motion capture data. Our analysis shows that given demonstrated accuracy for speed, incline, and phase estimation, a continuous parameterization provides statistically significantly better predictions of knee and ankle kinematics than a comparable finite state machine, but both methods' primary source of predictive error is subject deviation from average kinematics.
Predicting Individualized Joint Kinematics over a Continuous Range of Slopes and Speeds. E. Reznick, K. Embry, and R. Gregg. In IEEE Int. Conf. Biomedical Robotics & Biomechatronics, 2020. (Abstract, PDF)

Abstract: Individuality in clinical gait analysis is often quantified by an individual's kinematic deviation from the norm, but it is unclear how these deviations generalize across different walking speeds and ground slopes. Understanding individuality across tasks has important implications in the tuning of prosthetic legs, where clinicians have limited time and resources to personalize the kinematic motion of the leg to therapeutically enhance the wearer's gait. This study seeks to determine an efficient way to predictively model an individual's kinematics over a continuous range of slopes and speeds given only one personalized task at level ground. We were able to predict the kinematics of able-bodied individuals at a wide variety of conditions that were not specifically tuned. The proposed method of individualization improves the modeling error with respect to each subject's true kinematic data by 27- 44% on average and decreases the max error seen at any point in the model by 15-21% depending on the joint. Our results indicate that knowing how an individual subject differs from the average subject at level ground alone is enough information to improve kinematic predictions across all tasks. This research offers a new method for personalizing robotic prosthetic legs over a variety of tasks without the need of an engineer, which could make these complex devices more clinically viable.
Modeling the Kinematics of Human Locomotion over Continuously Varying Speeds and Inclines. K. Embry, D. Villarreal, R. Macaluso, and R. Gregg. IEEE Trans. Neural Systems Rehabilitation Eng., 26(12): 2342-2350, 2018, DOI: 10.1109/TNSRE.2018.2879570 (Abstract, PDF, Data)

Abstract: Powered knee and ankle prostheses can perform a limited number of discrete ambulation tasks. This is due to their control architecture, which uses a finite-state machine to select among a set of task-specific controllers. A non-switching controller that supports many tasks is expected to facilitate smoother task transitions. This paper introduces a predictive model that represents gait kinematics as a continuous function of gait cycle percentage, speed, and incline. The basis model consists of two parts: basis functions that produce kinematic trajectories over the gait cycle, and task functions that smoothly alter the weight of basis functions in response to task. Kinematic data from ten able-bodied subjects walking at twenty-seven combinations of speed and incline generate training and validation data for this data-driven model. Convex optimization accurately fits the model to experimental data. Automated model order reduction improves predictive abilities by capturing only the most important kinematic changes due to walking tasks. Constraints on range of motion and jerk ensure the safety and comfort of the user. This model produces a smooth continuum of trajectories over task, an impossibility for finite-state control algorithms. Random subsampling validation indicates basis modeling predicts untrained kinematics more accurately than linear interpolation.
Human-Inspired Algebraic Curves for Wearable Robot Control. A. Mohammadi and R. Gregg. In ASME Dynamic Systems & Control Conference, 2018. (Abstract, PDF)

Abstract: Having unified representations of human walking gait data is of paramount importance for wearable robot control. In the rehabilitation robotics literature, control approaches that unify the gait cycle of wearable robots are more appealing than the conventional approaches that rely on dividing the gait cycle into several periods, each with their own distinct controllers. In this article we propose employing algebraic curves to represent human walking data for wearable robot controller design. In order to generate algebraic curves from human walking data, we employ the 3L fitting algorithm, a tool developed in the pattern recognition literature for fitting implicit polynomial curves to given datasets. For an impedance model of the knee joint motion driven by the hip angle signal, we provide conditions by which the generated algebraic curves satisfy a robust relative degree condition throughout the entire walking gait cycle. The robust relative degree property makes the algebraic curve representation of walking gaits amenable to various nonlinear output tracking controller design techniques.
Real-Time Continuous Gait Phase and Speed Estimation from a Single Sensor. D. Quintero, D. Lambert, D. Villarreal, and R. Gregg. In IEEE Conf. on Control Technology and Applications (Invited Session on Robotic Locomotion Control), Hawaii, 2017. (Abstract, PDF)

Abstract: Human gait involves a repetitive cycle of movements, and the phase of gait represents the location in this cycle. Gait phase is measured across many areas of study (e.g., for analyzing gait and controlling powered lower-limb prosthetic and orthotic devices). Current gait phase detection methods measure discrete gait events (e.g., heel strike, flat foot, toe off, etc.) by placing multiple sensors on the subject's lower-limbs. Using multiple sensors can create difficulty in experimental setup and real-time data processing. In addition, detecting only discrete events during the gait cycle limits the amount of information available during locomotion. In this paper we propose a real-time and continuous measurement of gait phase parameterized by a mechanical variable (i.e., phase variable) from a single sensor measuring the human thigh motion. Human subject experiments demonstrate the ability of the phase variable to accurately parameterize gait progression for different walking/running speeds (1 to 9 miles/hour). Our results show that this real-time method can also estimate gait speed from the same sensor.
A Robust Parameterization of Human Gait Patterns Across Phase-Shifting Perturbations. D. Villarreal, H. Poonawala, and R. Gregg. IEEE Trans. Neural Systems & Rehabilitation Engineering, 25(3): 265-278, 2017, DOI: 10.1109/TNSRE.2016.2569019. (Abstract, PDF, Video)

Abstract: The phase of human gait is difficult to quantify accurately in the presence of disturbances. In contrast, recent bipedal robots use time-independent controllers relying on a mechanical phase variable to synchronize joint patterns through the gait cycle. This concept has inspired studies to determine if human joint patterns can also be parameterized by a mechanical variable. Although many phase variable candidates have been proposed, it remains unclear which, if any, provide a robust representation of phase for human gait analysis or control. In this paper we analytically derive an ideal phase variable (the hip phase angle) that is provably monotonic and bounded throughout the gait cycle. To examine the robustness of this phase variable, ten able-bodied human subjects walked over a platform that randomly applied phase-shifting perturbations to the stance leg. A statistical analysis found the correlations between nominal and perturbed joint trajectories to be significantly greater when parameterized by the hip phase angle (0.95+) than by time or a different phase variable. The hip phase angle also best parameterized the transient errors about the nominal periodic orbit. Finally, interlimb phasing was best explained by local (ipsilateral) hip phase angles that are synchronized during the double-support period.
Unified Phase Variables of Relative Degree Two for Human Locomotion. D. Villarreal and R. Gregg. In IEEE Engineering in Medicine and Biology Conference, Orlando, FL, 2016. (Abstract, PDF)

Abstract: A starting point to achieve stable locomotion is synchronizing the leg joint kinematics during the gait cycle. Some biped robots parameterize a nonlinear controller (e.g., input-output feedback linearization) whose main objective is to track specific kinematic trajectories as a function of a single mechanical variable (i.e., a phase variable) in order to allow the robot to walk. A phase variable capable of parameterizing the entire gait cycle, the hip phase angle, has been used to control wearable robots and was recently shown to provide a robust representation of the phase of human gait. However, this unified phase variable relies on hip velocity, which is difficult to measure in real-time and prevents the use of derivative corrections in phase-based controllers for wearable robots. One derivative of this phase variable yields accelerations (i.e., the equations of motion), so the system is said to be relative degree-one. This means that there are states of the system that cannot be controlled. The goal of this paper is to offer relative degree-two alternatives to the hip phase angle and examine their robustness for parameterizing human gait.
A Unified Parameterization of Human Gait Across Ambulation Modes. K. Embry, D. Villarreal, and R. Gregg. In IEEE Engineering in Medicine and Biology Conference, Orlando, FL, 2016. (Abstract, PDF)

Abstract: This paper introduces a novel gait parameterization method that models gait kinematics as a continuous function of gait cycle phase, walking speed, and ground slope. Kinematic data was recorded from seven able-bodied subjects walking on a treadmill at twenty-seven combinations of walking speed and ground slope. Convex optimization was used to determine the parameters of a function of three variables that fits this experimental data. This function may be able to provide desired trajectories to a virtual constraint controller over a continuum of gait phases and ambulation modes. This could allow for a single, non-switching controller to control a prosthetic leg for a variety of tasks, avoiding many of the problems associated with the ubiquitous use of finite state machines in prosthesis control.
A Perturbation Mechanism for Investigations of Phase-Dependent Behavior in Human Locomotion. D. Villarreal, D. Quintero, and R. Gregg. IEEE Access, 4: 893-904, 2016, DOI: 10.1109/ACCESS.2016.2535661. (Abstract, Open Access, Data)

Abstract: Bipedal locomotion is a popular area of study across multiple fields (e.g., biomechanics, neuroscience and robotics). Different hypotheses and models have tried explaining how humans achieve stable locomotion. Perturbations that produce shifts in the nominal periodic orbit of the joint kinematics during locomotion could inform about the manner in which the human neuromechanics represent the phase of gait. Ideally, this type of perturbation would modify the progression of the human subject through the gait cycle without deviating from the nominal kinematic orbits of the leg joints. However, there is a lack of publicly available experimental data with this type of perturbation. This paper presents the design and validation of a perturbation mechanism and an experimental protocol capable of producing phase-shifting perturbations of the gait cycle. The effects of this type of perturbation on the gait cycle are statistically quantified and analyzed in order to show that a clean phase shift in the gait cycle was achieved. The data collected during these experiments will be publicly available for the scientific community to test different hypotheses and models of human locomotion.
Incorporating Human-like Walking Variability in an HZD-Based Bipedal Model. A. Martin and R. Gregg. IEEE Transactions on Robotics, 32(4): 943-948, 2016, DOI: 10.1109/TRO.2016.2572687. (Abstract, PDF)

Abstract: Predictive simulations of human walking could be used to investigate a wide range of scientific questions, such as the effect of exoskeletons and prostheses. Promising moderately complex models of human walking have been developed using the robotics control technique hybrid zero dynamics (HZD). Fall risk is of great interest to clinicians and can be quantified using gait variability. Unfortunately, existing simulations of human walking only consider the mean motion, so they cannot be used to investigate fall risk. This work determines how to incorporate human-like variability into an HZD-based healthy human model to generate a more realistic gait. To do so, the output function used for feedback linearization is augmented with a sinusoidal variability function and a polynomial correction function. The variability function captures the variation in joint angles and is based on recent work with experimental data. The correction function is used to prevent the variability function from growing uncontrollably. The necessity of the correction function and the improvements with a reduction of stance ankle variability are demonstrated with simulation results. The variability in the temporal parameters is also shown to be similar to the corresponding experimental values.
Characterizing and Modeling the Joint-level Variability in Human Walking. A. Martin, D. Villarreal, and R. Gregg. Journal of Biomechanics, 49(14): 3298-3305, 2016, DOI: 10.1016/j.jbiomech.2016.08.015. (Abstract, PDF)

Abstract: Although human gait is often assumed to be periodic, significant variability exists. This variability appears to provide different information than the underlying periodic signal, particularly about fall risk. Most studies on variability have either used step-to-step metrics such as stride duration or point-wise standard deviations, neither of which explicitly capture the joint-level variability as a function of time. This work demonstrates that a second-order Fourier series for stance joints and a first-order Fourier series for swing joints can accurately capture the variability in joint angles as a function of time on a per-step basis for overground walking at the self-selected speed. It further demonstrates that a total of seven normal distributions, four linear relationships, and twelve continuity constraints can be used to describe how the Fourier series vary between steps. The ability of the proposed method to create curves that match human joint-level variability was evaluated both qualitatively and quantitatively using randomly generated curves.
A Perturbation Mechanism for Investigations of Phase Variables in Human Locomotion. D. Villarreal, D. Quintero, and R. Gregg. In IEEE Int. Conf. Robotics & Biomimetics (ROBIO), Zhuhai, China, 2015. (Abstract, PDF, Experiment Video)

Abstract: The concept of a phase variable, a mechanical measurement of the body's progression through the gait cycle, has been used to parameterize the leg joint patterns of autonomous bipedal robots, producing human-like gaits with robustness to external perturbations. It was recently proposed that the kinematic response of humans to a perturbation could also be parameterized by a phase variable. In order to properly study this phase variable hypothesis with human subjects, a custom perturbation mechanism was built to cause phase shifts in the gait cycle. The main goals of this study are to introduce the design of a novel perturbation mechanism and experimentally demonstrate its ability to effect phase changes during the gait cycle.
A Survey of Phase Variable Candidates of Human Locomotion. D. Villarreal and R. Gregg. In IEEE Engineering in Medicine and Biology Conference, Chicago, IL, 2014. (PDF)

Control of Autonomous Legged Robots

Using Energy Shaping and Regulation for Limit Cycle Stabilization, Generation, and Transition in Simple Locomotive Systems. M. Yeatman and R. Gregg. ASME Journal of Computational and Nonlinear Dynamics, 2021. (Abstract, PDF)

Abstract: This paper explores new ways to use energy shaping and regulation methods in walking systems to generate new passive-like gaits and dynamically transition between them. We recapitulate a control framework for Lagrangian hybrid systems, and show that regulating a state varying energy function is equivalent to applying energy shaping and regulating the system to a constant energy value. We then consider a simple 1-dimensional hopping robot and show how energy shaping and regulation control can be used to generate and transition between nearly globally stable hopping limit cycles. The principles from this example are then applied on two canonical walking models, the spring loaded inverted pendulum (SLIP) and compass gait biped, to generate and transition between locomotive gaits. These examples show that piecewise jumps in control parameters can be used to achieve stable changes in desired gait characteristics dynamically/online.
Distributed Controllers for Human-Robot Locomotion: A Scalable Approach Based on Decomposition and Hybrid Zero Dynamics. V. Kamidi, J. Horn, R. Gregg, and K. Hamed. IEEE Control Systems Letters, 2020. (Abstract, PDF)

Abstract: This paper presents a formal foundation, based on decomposition, hybrid zero dynamics (HZD), and a scalable optimization, to develop distributed control algorithms for hybrid models of collaborative human-robot locomotion. The proposed approach considers a centralized controller and then decomposes the dynamics and feedback laws with a parameterization to synthesize local controllers. The Jacobian matrix of the Poincare map with local controllers is studied and compared to that with centralized ones. An optimization problem is then set up to tune the parameters of the local controllers for asymptotic stability. The proposed approach can significantly reduce the number of controller parameters to be optimized for the synthesis of distributed controllers. The analytical results are numerically evaluated with simulations of a multi-domain hybrid model with $19$ degrees of freedom for stable amputee locomotion with a powered knee-ankle prosthetic leg.
Nonholonomic Virtual Constraint Design for Variable-Incline Bipedal Robotic Walking. J. Horn, A. Mohammadi, K. Hamed, and R. Gregg. IEEE Robotics & Automation Letters, 5(2): 3691-3698, 2020, DOI: 10.1109/LRA.2020.2977263. (Abstract, PDF)

Abstract: This paper presents a method of designing relative degree two nonholonomic virtual constraints (NHVCs) that allow for stable bipedal robotic walking across variable terrain slopes. Relative degree two NHVCs are virtual constraints that encode velocity-dependent walking gaits via momenta conjugate to the unactuated degrees of freedom for the robot. We recently introduced a systematic method of designing NHVCs, based on the hybrid zero dynamics (HZD) control framework, to achieve hybrid invariant flat ground walking without the use of dynamic reset variables. This work addresses the problem of walking over variable-inclined terrain disturbances.We propose a methodology for designing NHVCs, via an optimization problem, in order to achieve stable walking across variable terrain slopes. The end result is a single controller capable of walking over variable-inclined surfaces, that is also robust to inclines not considered in the optimization design problem, and uncertainties in the inertial parameters of the model.
Observer-Based Feedback Controllers for Exponential Stabilization of Periodic Orbits for Hybrid Dynamical Systems: Application to Underactuated 3D Bipedal Walking. K. Hamed and R. Gregg. ASME Journal of Dynamic Systems, Measurement, and Control, 141(12): 121011, 2019, DOI: 10.1115/1.4044618. (Abstract, PDF)

Abstract: This paper presents an analytical framework to systematically design observer-based output feedback controllers that exponentially stabilize periodic orbits for hybrid dynamical models of bipedal walking. We present a class of parameterized and smooth dynamic output feedback controllers such that (1) a periodic orbit is induced for the closed-loop hybrid system, and (2) the orbit is invariant under the change of the controller parameters. The properties of the Poincar'e map are investigated to show that the Jacobian linearization of the Poincar'e map around the fixed point takes a triangular form. This demonstrates the nonlinear separation principle for hybrid periodic orbits. In particular, the exponential stabilization problem of periodic orbits under dynamic output feedback control can be achieved by solving separate eigenvalue placement problems for the state feedback and observer synthesis. We then employ an iterative algorithm based on a sequence of optimization problems involving bilinear matrix inequalities (BMIs) to tune the state feedback and observer parameters.Aset of sufficient conditions for the convergence of the BMI algorithm to stabilizing parameters at a finite number of iterations is presented. Full state stability and stability modulo yaw under dynamic output feedback control are addressed. The power of the analytical approach is ultimately demonstrated through designing a nonlinear observer-based output feedback controller for dynamic walking of an underactuated 3D humanoid robot with 18 state variables, 54 state feedback parameters, and 271 observer parameters. The robustness of the closed-loop hybrid system against external disturbances is illustrated through numerical simulations.
Decentralized Passivity-Based Control with a Generalized Energy Storage Function for Robust Biped Locomotion. M. Yeatman, G. Lv, and R. Gregg. ASME Journal of Dynamic Systems, Measurement, and Control, 141(10): 101007, 2019, DOI: 10.1115/1.4043801. (Abstract, PDF)

Abstract: This paper details a decentralized passivity-based control to improve the robustness of biped locomotion in the presence of gait-generating external torques and parametric errors in the biped model. Previous work demonstrated a passive output for biped systems based on a generalized energy that, when directly used as a feedback control, increases the basin of attraction and convergence rate of the biped to a stable limit cycle. This paper extends the concept with a theoretical framework to address both uncertainty in the biped model and a lack of sensing hardware, by allowing the designer to neglect arbitrary states and parameters in the system. This framework also allows the control to be implemented on wearable devices, such as a lower-limb exoskeleton or powered prosthesis. Simulations on a 6-link biped model demonstrate that the proposed control scheme increases the convergence rate of the biped to a walking gait and improves the robustness to perturbations and to changes in ground slope.
Hybrid Zero Dynamics of Bipedal Robots Under Nonholonomic Virtual Constraints. J. Horn, A. Mohammadi, K. Hamed, and R. Gregg. IEEE Control Systems Letters, 3(2): 386-391, 2019, DOI: 10.1109/LCSYS.2018.2888571. (Abstract, PDF)

Abstract: This letter investigates the hybrid zero dynamics for planar bipedal robots with one degree of underactuation subject to nonholonomic virtual constraints (NHVC). We first derive the closed form expression of the bipedal robot zero dynamics under NHVCs. We next present conditions that make the NHVCs invariant with respect to rigid impacts with the ground. Lastly, a reduced dimensionality test, which is independent of the number of degrees of freedom of the bipedal robot, is proposed for checking existence and exponential stability of hybrid periodic orbits under NHVCs. Simulation results using the RABBIT biped robot demonstrate the robustness of the proposed NHVCs against a randomized horizontal push disturbance. A statistical significant difference between the mean number of steps until failure is shown between the NHVC and VHC control schemes.
Decentralized Event-Based Controllers for Robust Stabilization of Hybrid Periodic Orbits: Application to Underactuated 3D Bipedal Walking. K. Hamed and R. Gregg. IEEE Transactions on Automatic Control, 64(6): 2266-2281, 2019, DOI: 10.1109/TAC.2018.2863184. (Abstract, PDF)

Abstract: Models of bipedal walking are hybrid, with continuous-time dynamics representing the swing phases and discrete-time dynamics representing the impact events. The feedback controllers for these systems can be two-level, including both continuous- and discrete-time (event-based) actions. This paper presents a systematic framework to design decentralized event-based controllers for robust stabilization of hybrid periodic orbits against possible disturbances in discrete-time phases. The properties of the Poincar'e return map are investigated to study the orbital input-to-state stability for the closed-loop system with respect to disturbance inputs. An optimization problem involving bilinear matrix inequalities is then presented to design H2- and Hinf-optimal decentralized event-based controllers. The power of the proposed framework is finally demonstrated through designing a set of decentralized two-level controllers for underactuated walking of a 3D autonomous bipedal robot with nine degrees of freedom and a decentralization scheme motivated by amputee locomotion with a transpelvic prosthetic leg.
Hybrid Nonlinear Disturbance Observer Design for Underactuated Bipedal Robots. A. Mohammadi, S. Fakoorian, J. Horn, D. Simon, and R. Gregg. In IEEE Decision & Control Conference, 2018. (Abstract, PDF)

Abstract: Existence of disturbances in unknown environments is a pervasive challenge in robotic locomotion control. Disturbance observers are a class of unknown input observers that have been extensively used for disturbance rejection in numerous robotics applications. In this paper, we extend a class of widely used nonlinear disturbance observers to underactuated bipedal robots, which are controlled using hybrid zero dynamics-based control schemes. The proposed hybrid nonlinear disturbance observer provides the autonomous biped robot control system with disturbance rejection capabilities, while the underlying hybrid zero-dynamics based control law remains intact.
Passivity-Based Control with a Generalized Energy Storage Function for Robust Bipedal Walking. M. Yeatman, G. Lv, and R. Gregg. In American Control Conference, Milwaukee, WI, 2018. (Abstract, PDF)

Abstract: This paper offers a novel generalization of a passivity-based, energy tracking controller for robust bipedal walking. Past work has shown that a biped limit cycle with a known, constant mechanical energy can be made robust to uneven terrains and disturbances by actively driving energy to that reference. However, the assumption of a known, constant mechanical energy has limited application of this passivitybased method to simple toy models (often passive walkers). The method presented in this paper allows the passivity-based controller to be used in combination with an arbitrary innerloop control that creates a limit cycle with a constant generalized system energy. We also show that the proposed control method accommodates arbitrary degrees of underactuation. Simulations on a 7-link biped model demonstrate that the proposed control scheme enlarges the basin of attraction, increases the convergence rate to the limit cycle, and improves robustness to ground slopes.
Observer-Based Feedback Controllers for Exponential Stabilization of Hybrid Periodic Orbits: Application to Underactuated Bipedal Walking. K. Hamed, A. Ames, and R. Gregg. In American Control Conference, Milwaukee, WI, 2018. (Abstract, PDF)

Abstract: This paper presents a systematic approach to design observer-based output feedback controllers for hybrid dynamical systems arising from bipedal walking. We consider a class of parameterized observer-based output feedback controllers for exponential stabilization of hybrid periodic orbits. The properties of the Poincare map are investigated to show that the Jacobian linearization of the Poincare map takes a triangular form. This demonstrates the nonlinear separation principle for periodic orbits. In particular, the exponential stabilization of hybrid periodic orbits under dynamic output feedback control can be achieved by solving separate eigenvalue placement problems for the nonlinear state feedback and the observer. The paper then solves the state feedback and observer design problems by employing an iterative algorithm based on a sequence of optimization problems involving bilinear and linear matrix inequalities. The theoretical results are confirmed by designing a nonlinear observer-based output feedback controller for underactuated walking of a 3D humanoid model with 18 state variables, 54 state feedback parameters, and 271 observer parameters.
Exponentially Stabilizing Controllers for Multi-Contact 3D Bipedal Locomotion. K. Hamed, R. Gregg, and A. Ames. In American Control Conference, Milwaukee, WI, 2018. (Abstract, PDF)

Abstract: Models of bipedal walking are hybrid with continuous-time phases representing the Lagrangian stance dynamics and discrete-time transitions representing the impact of the swing leg with the walking surface. The design of continuous-time feedback controllers that exponentially stabilize periodic gaits for hybrid models of underactuated 3D bipedal walking is a significant challenge. We recently introduced a method based on an iterative sequence of optimization problems involving bilinear matrix inequalities (BMIs) to systematically design stabilizing continuous-time controllers for single domain hybrid models of underactuated bipedal robots with point feet. This paper addresses the exponential stabilization problem for multi-contact walking gaits with nontrivial feet. A family of parameterized continuous-time controllers is proposed for different phases of the walking cycle. The BMI algorithm is extended to the multi-domain hybrid models of anthropomorphic 3D walking locomotion to look for stabilizing controller parameters. The Poincare map is addressed and a new set of sufficient conditions is presented that guarantees the convergence of the BMI algorithm to a stabilizing set of controller parameters at a finite number of iterations. The power of the algorithm is ultimately demonstrated through the design of stabilizing virtual constraint controllers for dynamic walking of a 3D humanoid model with 28 state variables and 275 controller parameters.
Removing Phase Variables from Biped Robot Parametric Gaits. A. Mohammadi, J. Horn, and R. Gregg. In IEEE Conference on Control Technology and Applications (Invited Session on Robotic Locomotion Control), Hawaii, 2017. (Abstract, PDF)

Abstract: Hybrid zero dynamics-based control is a promising framework for controlling underactuated biped robots and powered prosthetic legs. In this control paradigm, stable walking gaits are implicitly encoded in polynomial output functions of the robot configuration variables, which are to be stabilized via feedback. The biped polynomial output functions are parameterized by a suitable mechanical phasing variable whose evolution determines the biped gait progression during each step. Determining a proper phase variable, however, might not always be a trivial task. In this paper, we present an elimination method for generating output functions from given parametric walking gaits without any explicit knowledge of the phase variable. Our elimination method is based on computing the resultant of polynomials, a fundamental tool in computer algebra.
Decentralized Feedback Controllers for Robust Stabilization of Periodic Orbits of Hybrid Systems: Application to Bipedal Walking. K. A. Hamed and R. Gregg. IEEE Transactions on Control Systems Technology, 25(4): 1153-1167, 2017, DOI: 10.1109/TCST.2016.2597741. (Abstract, PDF)

Abstract: This paper presents a systematic algorithm to design time-invariant decentralized feedback controllers to exponentially and robustly stabilize periodic orbits for hybrid dynamical systems against possible uncertainties in discrete-time phases. The algorithm assumes a family of parameterized and decentralized nonlinear controllers to coordinate interconnected hybrid subsystems based on a common phasing variable. The exponential and H_2 robust stabilization problems of periodic orbits are translated into an iterative sequence of optimization problems involving bilinear and linear matrix inequalities. By investigating the properties of the Poincare map, some sufficient conditions for the convergence of the iterative algorithm are presented. The power of the algorithm is finally demonstrated through designing a set of robust stabilizing local nonlinear controllers for walking of an underactuated 3D autonomous bipedal robot with 9 degrees of freedom, impact model uncertainties, and a decentralization scheme motivated by amputee locomotion with a transpelvic prosthetic leg.
A Control Framework for Anthropomorphic Biped Walking Based on Stabilizing Feedforward Trajectories. S. Rezazadeh and R. Gregg. In ASME Dynamic Systems & Control Conference, Minneapolis, MN, 2016. (Abstract, PDF)

Abstract: Although dynamic walking methods have had notable successes in control of bipedal robots in the recent years, still most of the humanoid robots rely on quasi-static Zero Moment Point controllers. This work is an attempt to design a highly stable controller for dynamic walking of a human-like model which can be used both for control of humanoid robots and prosthetic legs. The method is based on using time-based trajectories that can induce a highly stable limit cycle to the bipedal robot. The time-based nature of the controller motivates its use to entrain a model of an amputee walking, which can potentially lead to a better coordination of the interaction between the prosthesis and the human. The simulations demonstrate the stability of the controller and its robustness against external perturbations.
Decentralized Feedback Controllers for Exponential Stabilization of Hybrid Periodic Orbits: Application to Robotic Walking. K. Hamed and R. Gregg. In Invited Session on Control Theory in Legged Locomotion, American Control Conf., Boston, MA, 2016. (Abstract, PDF)

Abstract: This paper presents a systematic algorithm to design time-invariant decentralized feedback controllers to exponentially stabilize periodic orbits for a class of hybrid dynamical systems arising from bipedal walking. The algorithm assumes a class of parameterized and nonlinear decentralized feedback controllers which coordinate lower-dimensional hybrid subsystems based on a common phasing variable. The exponential stabilization problem is translated into an iterative sequence of optimization problems involving bilinear and linear matrix inequalities, which can be easily solved with available software packages. A set of sufficient conditions for the convergence of the iterative algorithm to a stabilizing decentralized feedback control solution is presented. The power of the algorithm is demonstrated by designing a set of local nonlinear controllers that cooperatively produce stable walking for a 3D autonomous biped with 9 degrees of freedom, 3 degrees of underactuation, and a decentralization scheme motivated by amputee locomotion.

Actuator Design, Optimization, and Control

A Control Framework for Accurate Mechanical Impedance Rendering with Series-Elastic Joints in Prosthetic Applications. I. Harris, E. Rouse, R. Gregg, and G. Thomas. IEEE Robotics & Automation Letters, 2024. (Abstract)

Abstract: In addition to lifting up the body during gait, human legs provide stabilizing torques that can be modeled as a spring-damper mechanical impedance. While powered prosthetic leg actuators can also imitate spring-damper behaviors, the rendered impedance can be quite different from the desired impedance, stemming from unmodeled torques in the transmission (e.g., sliding friction, bearing damping, gear inefficiency, etc.). Moreover, for powered prostheses to mimic human joint impedance, they will need actuators that accurately render a wide range of mechanical impedances in a variety of ground contact conditions, including nearly free-swinging behavior in swing phase and stiff spring-like behavior in stance phase. For series-elastic prosthetic leg actuators, as in Open-Source Leg (OSL), these sudden output inertia changes present a challenge for traditional cascaded impedance control. In this paper we propose a solution based on disturbance observers and full state feedback (FSF) impedance control. With transmission disturbances attenuated, the FSF controller can use pole-zero placement to specify the actuator impedance that couples to the uncertain joint inertia. We validate our control framework on an OSL-like two-actuator dynamometry testbed.
Convex Optimization for Spring Design of Parallel Elastic Actuators. S. Guo, R. Gregg, and E. Bolivar. In American Control Conference, 2022. (Abstract, PDF)

Abstract: Elastic actuation can improve human-robot interaction and energy efficiency for wearable robots. Previous work showed that the energy consumption of series elastic actuators can be a convex function of the series spring compliance. This function is useful to optimally select the series spring compliance that reduces the motor energy consumption. However, series springs have limited influence on the motor torque, which is a major source of the energy losses due to the associated Joule heating. Springs in parallel to the motor can significantly modify the motor torque and therefore reduce Joule heating, but it is unknown how to design springs that globally minimize energy consumption for a given motion of the load. In this work, we introduce the stiffness design of linear and nonlinear parallel elastic actuators via convex optimization. We show that the energy consumption of parallel elastic actuators is a convex function of the spring stiffness and compare the energy savings with that of optimal series elastic actuators. We analyze robustness of the solution in simulation by adding uncertainty of 20% of the RMS load kinematics and kinetics for the ankle, knee, and hip movements for level-ground human walking. When the winding Joule heating losses are dominant with respect to the viscous losses, our optimal PEA designs outperform SEA designs by further reducing the motor energy consumption up to 63%. Comparing to the linear PEA designs, our nonlinear PEA designs further reduced the motor energy consumption up to 31%. From our convex formulation, our global optimal nonlinear parallel elastic actuator designs give two different elongation-torque curves for positive and negative elongation, suggesting a clutching mechanism for the final implementation. In addition, the different torque-elongation profiles for positive and negative elongation for nonlinear parallel elastic actuators can cause sensitivity of the energy consumption to changes in the nominal load trajectory.
Convex Optimization for Spring Design in Series Elastic Actuators: From Theory to Practice. E. Bolivar, G. Thomas, E. Rouse, and R. Gregg. In IEEE Int. Conf. Intelligent Robots & Systems, 2021. (Abstract, PDF)

Abstract: Natural dynamics, nonlinear optimization, and, more recently, convex optimization are available methods for stiffness design of energy-efficient series elastic actuators. Natural dynamics and general nonlinear optimization only work for a limited set of load kinetics and kinematics, cannot guarantee convergence to a global optimum, or depend on initial conditions to the numerical solver. Convex programs alleviate these limitations and allow a global solution in polynomial time, which is useful when the space of optimization variables grows (e.g., when designing optimal nonlinear springs or co-designing spring, controller, and reference trajectories). Our previous work introduced the stiffness design of series elastic actuators via convex optimization when the transmission dynamics are negligible, which is an assumption that applies mostly in theory or when the actuator uses a direct or quasi-direct drive. In this work, we extend our analysis to include the dynamics of the transmission. Coulomb friction at the transmission results in a non-convex expression for the energy dissipated as heat, but we illustrate a convex approximation for stiffness design. We experimentally validated our framework using a series elastic actuator with specifications similar to the knee joint of the Open Source Leg, an open-source robotic knee-ankle prosthesis.
A Convex Optimization Framework for Robust-Feasible Series Elastic Actuators. E. Bolivar, T. Summers, R. Gregg, and S. Rezazadeh. Mechatronics, 2021. (Abstract, PDF)

Abstract: Kinematic and kinetic requirements for robotic actuators are subject to uncertainty in the motion of the load. Safety factors account for uncertainty in the design stage, but defining factors that translate to reliable systems without over-designing is a challenge. Bulky or heavy actuators resulting from overdesign are undesirable in wearable or mobile robots, which are prone to uncertainty in the load due to human-robot or robot-environment interaction. In this paper, we use robust optimization to account for uncertainty in the design of series elastic actuators. We formulate a robust-feasible convex optimization program to select the optimal compliance-elongation profile of the series spring that minimizes one or multiple of the following objectives: spring elongation, motor energy consumption, motor torque, or motor velocity. To preserve convexity when minimizing energy consumption, we lump the energy losses in the transmission as viscous friction losses, which is a viable approximation for series elastic actuators powered by direct or quasi-direct drives. Our formulation guarantees that the motor torque, winding temperature, and speed are feasible despite uncertainty in the load kinematics, kinetics, or manufacturing of the spring. The globally optimal spring could be linear or nonlinear. As simulation case studies, we design the optimal compliance-elongation profiles for multiple series springs for a robotic prosthetic ankle. The simulation case studies illustrate examples of our methodology, evaluate the performance of robust feasible designs against optimal solutions that neglect uncertainty, and provide insight into the selection of different objective functions. With this framework the designer specifies uncertainty directly in the optimization and over the specific kinematics, kinetics, or manufacturing parameters, aiming for reliable robots that reduce overdesign.
Towards an Ankle-Foot Orthosis Powered by a Dielectric Elastomer Actuator. D. Allen, R. Little, J. Laube, J. Warren, W. Voit, and R. Gregg. Mechatronics, 76, 2021, DOI: 10.1016/j.mechatronics.2021.102551. (Abstract, PDF)

Abstract: Foot drop is the inability to dorsiflex the ankle (raise the toes) due to neuromuscular impairment, and this common condition can cause trips and falls. Current treatments for chronic foot drop provide dorsiflexion support, but they either impede ankle push off or are not suitable for all patients. Powered AFOs can counteract foot drop without these drawbacks, but they are heavy and bulky and have short battery life. To counteract foot drop without the drawbacks of current treatments or powered AFOs, we designed and built an AFO powered by DEAs, a type of artificial muscle technology. This paper presents our design and the results of benchtop testing. We found that the DEA AFO can provide 49% of the dorsiflexion support necessary to raise the foot, which would be helpful to a patient with partial dorsiflexor function. Further, charging the DEAs reduced the effort that would be required for plantarflexion compared to that with passive DEA behavior, and this operation could be powered for 6000 steps or more. DEAs are a promising approach for building an AFO that counteracts foot drop without impeding plantarflexion, and they may prove useful for other powered prosthesis and orthosis designs.
Robust Optimal Design of Series Elastic Actuators: Application to a Powered Prosthetic Ankle. E. Bolivar, S. Rezazadeh, T. Summers, and R. Gregg. In IEEE Int. Conf. Rehab. Robotics, 2019. (Abstract, PDF)

Abstract: Design of rehabilitation and physical assistance robots that work safely and efficiently despite uncertain operational conditions remains an important challenge. Current methods for the design of energy efficient series elastic actuators use an optimization formulation that typically assumes known operational requirements. This approach could lead to actuators that cannot satisfy elongation, speed, or torque requirements when the operation deviates from nominal conditions. Addressing this gap, we propose a convex optimization formulation to design the stiffness of series elastic actuators to minimize energy consumption and satisfy actuator constraints despite uncertainty due to manufacturing of the spring, unmodeled dynamics, efficiency of the transmission, and the kinematics and kinetics of the load. To achieve convexity, we write energy consumption as a scalar convex-quadratic function of compliance. As actuator constraints, we consider peak motor torque, peak motor velocity, limitations due to the speed-torque relationship of DC motors, and peak elongation of the spring. We apply our formulation to the robust design of a series elastic actuator for a powered prosthetic ankle. Our simulation results indicate that a small trade-off between energy efficiency and robustness is justified to design actuators that can operate with uncertainty.
Mechanical Simplification of Variable Stiffness Actuators Using Dielectric Elastomer Transducers. D. Allen, E. Bolivar, S. Farmer, W. Voit, and R. Gregg. Actuators, 8(2): 1-19, 2019, DOI: 10.3390/act8020044. (Abstract, PDF)

Abstract: Legged and gait-assistance robots can walk more efficiently if their actuators are compliant. The adjustable compliance of variable stiffness actuators (VSAs) can further enhance this benefit. However, the addition of mechanical components for adjusting the stiffness of a VSA makes VSAs impractical for some uses due to increased weight, volume, and cost. VSAs would be more practical if they could modulate the stiffness of their springs without additional components, which usually include moving parts and an additional motor. Therefore, we designed a VSA that uses dielectric elastomer transducers (DETs) for springs. It does not need mechanical stiffness adjusting components because DETs soften due to electrostatic forces. This paper presents details of our design and reports the performance of our DET VSA. Our DET VSA demonstrated independent modulation of its equilibrium position and stiffness without the need for mechanical stiffness adjusting components. Our design approach could make it practical to obtain the benefits of variable stiffness actuation without the weight, volume, and cost that normally accompany them, once weaknesses of DET technology are addressed.
Minimizing Energy Consumption and Peak Power of Series Elastic Actuators: a Convex Optimization Framework for Elastic Element Design. E. Bolivar, S. Rezazadeh, and R. Gregg. IEEE/ASME Transactions on Mechatronics, 24(3):1334-1345, 2019, DOI: 10.1109/TMECH.2019.2906887. (Abstract, PDF)

Abstract: Compared to rigid actuators, Series Elastic Actuators (SEAs) offer a potential reduction of motor energy consumption and peak power, though these benefits are highly dependent on the design of the torque-elongation profile of the elastic element. In the case of linear springs, natural dynamics is a traditional method for this design, but it has two major limitations: arbitrary load trajectories are difficult or impossible to analyze and it does not consider actuator constraints. Parametric optimization is also a popular design method that addresses these limitations, but solutions are only optimal within the space of the parameters. To overcome these limitations, we propose a non-parametric convex optimization program for the design of the nonlinear elastic element that minimizes energy consumption and peak power for an arbitrary periodic reference trajectory. To obtain convexity, we introduce a convex approximation to the expression of peak power; energy consumption is shown to be convex without approximation. The combination of peak power and energy consumption in the cost function leads to a multiobjective convex optimization framework that comprises the main contribution of this paper. As a case study, we recover the elongation-torque profile of a cubic spring, given its natural oscillation as the reference load. We then design nonlinear SEAs for an ankle prosthesis that minimize energy consumption and peak power for different trajectories and extend the range of achievable tasks when subject to actuator constraints.
Stretchable Conductive Fabric Simplifies Manufacturing of Low-Resistance Dielectric-Elastomer-System Electrodes. D. Allen, S. Farmer, R. Gregg, and W. Voit. In SPIE Electroactive Polymer Actuators and Devices, 2018. (Abstract, PDF)

Abstract: We made low-resistance electrodes for a dielectric elastomer system (DES) without the use of thin film deposition or wet lab processes by utilizing a stretchable conductive fabric, Less EMF Stretch Conductive Fabric (SCF), for electrode material. Carbon-based DES electrodes are easy to make, but they have high resistances (kilo ohms) that hamper dynamic operation and reduce energy efficiency. Metal and hydrogel DES electrodes have much lower resistances (tens to hundreds of ohms), but they require complex manufacturing processes, such as thin film deposition or wet lab synthesis. Conductive fabrics can have low resistance and they can be made into DES electrodes with merely a laser cutter and a dry lab environment, but their stiffness may hinder DES performance. This work reports electrical and mechanical properties of SCF and a more compliant, though less conductive fabric, MedTex P70+B, and describes the assembly and perfor-mance of DES variable stiffness modules using them. SCF had low sheet resistance, less than 3.0 ohm/square even during 125 % biaxial stretch, and both fabrics stretched beyond 200 % uniaxial elongation before mechanical failure. The assembly of modules with conductive fabric electrodes was comparable in terms of difficulty to that with carbon powder electrodes, and produced functional mod-ules. However, the stiffness of the fabrics diminished DES stiffness-reduction perfor-mance to merely 12.8 % and 13.4 % compared to the 24.5 % stiffness reduction a DES module with carbon powder electrodes achieved. Future work should investigate or de-velop more compliant conductive fabrics that would yield greater DES performance.
A General Framework for Minimizing Energy Consumption of Series Elastic Actuators with Regeneration. E. Bolivar, S. Rezazadeh, and R. Gregg. In ASME Dynamic Systems & Control Conference, Virginia, 2017. Best Student Robotics Paper. (Abstract, PDF)

Abstract: The use of actuators with inherent compliance, such as series elastic actuators (SEAs), has become traditional for robotic systems working in close contact with humans. SEAs can reduce the energy consumption for a given task compared to rigid actuators, but this reduction is highly dependent on the design of the SEA's elastic element. This design is often based on natural dynamics or a parameterized optimization, but both approaches have limitations. The natural dynamics approach cannot consider actuator constraints or arbitrary reference trajectories, and a parameterized elastic element can only be optimized within the given parameter space. In this work, we propose a solution to these limitations by formulating the design of the SEA's elastic element as a non-parametric convex optimization problem, which yields a globally optimal conservative elastic element while respecting actuator constraints. Convexity is proven for the case of an arbitrary periodic reference trajectory with a SEA capable of energy regeneration. We discuss the optimization results for the tasks defined by the human ankle motion during level-ground walking and the natural motion of a single mass-spring system with a nonlinear spring. For all these tasks, the designed SEA reduces energy consumption and satisfies the actuator's constraints.
Towards a Series Elastic Actuator with Electrically Modulated Stiffness for Powered Ankle-Foot Orthoses. E. Bolivar, D. Allen, G. Ellson, J. Cossio, W. Voit, and R. Gregg. In IEEE Conf Automation Science & Engineering, Fort Worth, TX, 2016. (Abstract, PDF)

Abstract: Series elastic actuators offer several benefits for powered ankle foot orthoses. One major benefit they offer for this application is the reduction of motor power requirements, which enables the reduction of motor weight. However, series elastic actuators commonly have a fixed stiffness value, which only yields optimal power reduction for one set of gait parameters such as gait type, user weight, and gait speed. These parameters vary during the normal use of orthotic devices. This paper presents a new variable stiffness series elastic actuator that can compensate for these variations. Our actuator uses a dielectric elastomer as the series elastic element so that the stiffness of the actuator can be electrically modulated, unlike current variable stiffness actuators that modulate their stiffness with a second motor. Experimental results indicate the viability of this approach for modulating stiffness and verify that the actuator generates forces meaningful for gait assistance.

Unreviewed Magazine Articles

Challenges for Control Research: Control of Powered Prosthetic Legs. R. Gregg, L. Hargrove, and J. Sensinger. The Impact of Control Technology, 2nd ed., T. Samad and A.M. Annaswamy (eds.), IEEE Control Systems Society, 2014, available at www.ieeecss.org. (PDF)

Visit the PI's Google Scholar page for past publications.

Locomotor
Control
Systems
Laboratory

Publications

Prosthesis Design and Control

Exoskeleton Design and Control

Modeling and Measuring Human Locomotion

Control of Autonomous Legged Robots

Actuator Design, Optimization, and Control

Other Control Topics

Prosthesis Design and Control

Exoskeleton Design and Control

Modeling and Measuring Human Locomotion

Control of Autonomous Legged Robots

Actuator Design, Optimization, and Control

Other Control Topics

Unreviewed Magazine Articles

LocoLab