In this paper we propose a calculation method for the optimal trajectory of a biped locomotion ma... more In this paper we propose a calculation method for the optimal trajectory of a biped locomotion machine which is based on inverse kinematics and inverse dynamics. First, the trajectory of the waist is expressed by a Fourier series, where the bases are selected appropriately so that the periodic boundary conditions are strictly satisfied. A biped locomotion machine establishes optimal walking by using kicking forces to the ground at the moment of switching legs. In order to include the effecs of the kicking forces, additional terms that indicate the impulsive forces at the moment of switching legs are included in the formulation. Then the angles of each joint are determined by inverse kinematics, and using inverse dynamics, the input torques of each joint are expressed in terms of Fourier coefficients. By defining the performance index as a quadratic form of the input torques, the motion planning problem is formulated as an optimization problem of the trajectory of the waist, whose paramaters are Fourier coefficients of the trajactory of the waist. Using the successive quadratic programming (SQP) method, the optimal trajectory of a biped locomotion machine is obtained.
This paper deals with the attitude control of a rigid spacecraft with two reaction wheels. First,... more This paper deals with the attitude control of a rigid spacecraft with two reaction wheels. First, we derive a discontinuous state feedback law based on Lyapunov control. When the angular momentum of the system is zero, the derived controller makes the desired point the only stable equilibrium point of the system. Next, we investigate the behavior of the controlled system when the angular momentum is not zero but small.
This paper deals with a design of a control system for a multipod robot based on CPG principle. O... more This paper deals with a design of a control system for a multipod robot based on CPG principle. Oscillators are assigned at each leg and drive the periodic motion of legs. The phase of CPG is controlled by the signal of touch sensor which is mounted at the tip of the leg. It is confirmed through numerical simulation that the robot changes its gait pattern adaptively to variances of the environment.
The authors have proposed a dynamic turning control system of a quadruped robot by using nonlinea... more The authors have proposed a dynamic turning control system of a quadruped robot by using nonlinear oscillators. It is composed of a spontaneous locomotion controller and voluntary motion controller. In this article, capability of dynamic turning motion of the proposed control system is verified through numerical simulations and hardware experiments: Various turning speed and orientation make the motion of the robot asymmetry in terms of duty ratio, stride and center of pressure. The proposed controller actively and adaptively controls redundant DOF to cancel the dynamic asymmetry and established stable turning motion at various locomotion speed and turning orientation.
We have proposed an optimization method for a combinatorial optimization problem using replicator... more We have proposed an optimization method for a combinatorial optimization problem using replicator equations. To improve the solution further, a deterministic annealing algorithm may be applied. During the annealing process, bifurcations of equilibrium solutions will occur and affect the performance of the deterministic annealing algorithm. In this paper, the bifurcation structure of the proposed model is analyzed in detail. It is shown that only pitchfork bifurcations occur in the annealing process, and the solution obtained by the annealing is the branch uniquely connected with the uniform solution. It is also shown experimentally that in many cases, this solution corresponds to a good approximate solution of the optimization problem. Based on the results, a deterministic annealing algorithm is proposed and applied to the quadratic assignment problem to verify its performance.
In this paper, first, stability of locomotion of the multilegged locomotion robot along a straigh... more In this paper, first, stability of locomotion of the multilegged locomotion robot along a straight line is analyzed, and then, based on the dynamic characteristics, a turning strategy is proposed. The effectiveness of the turning strategy is verified by the numerical simulations; the robot can turn with less slip to the ground by decreasing the stability of the straight walk of the robot.
This article deals with the design of a control system for a quadrupedal locomotion robot. The pr... more This article deals with the design of a control system for a quadrupedal locomotion robot. The proposed control system is composed of a leg motion controller and a gait pattern controller within a hierarchical architecture. The leg controller drives actuators at the joints of the legs using a high-gain local feedback control. It receives the command signal from the gait pattern controller. The gait pattern controller, on the other hand, involves nonlinear oscillators. These oscillators interact with each other through signals from the touch sensors located at the tips of the legs. Various gait patterns emerge through the mutual entrainment of these oscillators. As a result, the system walks stably in a wide velocity range by changing its gait patterns and limiting the increase in energy consumption of the actuators. The performance of the proposed control system is verified by numerical simulations.
The author have proposed a dynamic turning control system of a quadruped robot by using nonlinear... more The author have proposed a dynamic turning control system of a quadruped robot by using nonlinear oscillators. It is composed of a motion controller and a motion planner. The motion controller drives the actuators of the legs by using local feedback control. The motion planner involves nonlinear oscillators with mutual interactions. In this paper, capability of dynamic turning motion of the proposed control system is verified through numerical simulations: In the slow speed turning, the robot has strong constraints geometrically. Whereas in the high speed turning, the robot has great influences of dynamic forces. These constraints conditions makes the motion of the robot asymmetry in terms of duty ratio, stride and center of force acting points. The proposed controller actively and adaptively controls the waist joint of the main body to satisfy the geometrical constraints during turning, and also controls the shoulder joints to incline the main body to cancel the centrifugal force in high speed turning by use of gravity force.
This article deals with the optimal gait pattern in terms of the proposed control system. The pha... more This article deals with the optimal gait pattern in terms of the proposed control system. The phase difference among the oscillators is selected as the optimization variable. The duty ratio is selected as the optimization parameter. The performance index is constructed as a quadratic form of the input torque vector at the joints. The simulated annealing (SA) method is used as the optimization algorithm and numerically derived the optimal gait patterns according to the various duty ratios.
Decentralized Autonomous Control of a Myriapod Locomotion Robot Ahmet Onat Sabanci University, Tu... more Decentralized Autonomous Control of a Myriapod Locomotion Robot Ahmet Onat Sabanci University, Turkey onat@sabanciuniv.edu Kazuo Tsuchiya Kyoto University, Japan tsuchiya@kuaero.kyoto-u.ac.jp Katsuyoshi Tsujita Kyoto University, Japan tsujita@kuaero.kyoto-...
In our previous work, we developed a locomotion control system of a biped robot which is composed... more In our previous work, we developed a locomotion control system of a biped robot which is composed of nonlinear oscillators and realized a stable straight walk of the biped robot against the changes of the environments. Then, we revealed that the adaptability to the changes of the environments is realized as the straight walk results in the change of the period of the motions of the legs. In this paper, we realize a turning walk of the biped robot by using the developed locomotion control system. First, we provide analysis of the turning behavior of the biped robot and reveal that, in this case, the turning behavior leads to the change of the duty ratios of the legs. Moreover, we realize the task that the robot pursues a target on the floor moving along a corner and it demonstrates that the robot can turn a corner successfully in the real world.
We discuss the motion control of a two-wheeled mobile robot. In the design of a controller for th... more We discuss the motion control of a two-wheeled mobile robot. In the design of a controller for the system, a kinematic model is usually used; the wheels do not skid at all and the mobile robot is regarded as a 3D 2-input nonholonomic system without drift. Many controllers based on the kinematic model have been proposed. However, in a real world, the wheels may skid on the ground or float away from the ground according to the rolling motion of the body. Therefore, we derive a dynamic model of a two-wheeled mobile robot which implies the translational motion with 3 degrees-of-freedom and the rotational motion with 3 degrees-of-freedom of the body and the rotational motion with one degree-of-freedom of each wheel, and then reduce the dynamic model to the kinematic model under certain assumptions. We design a controller based on the kinematic model by extending the Lyapunov control and analyze whether the designed controller works well in a real world by numerical simulations based on the dynamic model
This paper proposes the locomotion control system for a multi-legged locomotion robot. The propos... more This paper proposes the locomotion control system for a multi-legged locomotion robot. The proposed control system is composed of leg motion controllers and a gait pattern controller. The leg motion controllers drive the actuators of the legs by using local feedback control. The gait pattern controller is composed of non linear oscillators. The oscillators tune the phases through the mutual interactions and the feedback signals from the touch sensors at the tips of the legs. Various gait patterns emerge through the mutual entrainment of these oscillators. As a result, the robot with the controller walks stably by changing its gait patterns in a wide range of locomotion speed. Moreover, it continues to walk even if a part of leg controller breaks down. The performance of the proposed control system is verified by numerical simulations.
This paper proposes the locomotion control system for a biped locomotion robot. The propose contr... more This paper proposes the locomotion control system for a biped locomotion robot. The propose control system is composed of motion generator system and motion control system. Motion generator system is composed of nonlinear oscillators, which generate the commanded trajectories of the joints as functions of phases of oscillators. Motion control system is composed of motors with controllers installed at joints, which control motions of joints. The oscillators tune the phases through the mutual interactions and the feedback signals from the touch sensors at the tips of the legs. As a result, the robot with the controller walks stably by changing its period of locomotion in a changing environment. The performance of the proposed control system is verified by numerical simulations and experiments.
The development of an oscillator controller for a quadruped robot with antagonistic pairs of pneu... more The development of an oscillator controller for a quadruped robot with antagonistic pairs of pneumatic actuators is reported. Periodic motions of the legs switch between the swinging and supporting stages based on the phase of the oscillators. The oscillators receive touch sensor signals at the end of the legs as feedback when the leg touches the ground and compose a steady limit cycle of the total periodic dynamics of quadruped locomotion. And also muscle tone is adaptively controlled according to the dynamic state of the main body. This system can generate gait transition from one to another by changing locomotion speed and muscle tone. The effectiveness and performance of the proposed controller were evaluated with numerical simulations and experiments with the hardware.
The development of an oscillator controller for a quadruped robot with antagonistic pairs of pneu... more The development of an oscillator controller for a quadruped robot with antagonistic pairs of pneumatic actuators is reported. Periodic motions of the legs switch between the swinging and supporting stages based on the phase of the oscillators. The oscillators receive touch sensor signals at the end of the legs as feedback when the leg touches the ground and compose a steady limit cycle of the total periodic dynamics of quadruped locomotion. And also muscle tone is adaptively controlled according to the dynamic state of the main body. This system can generate gait transition from one to another by changing locomotion speed and muscle tone. The effectiveness and performance of the proposed controller were evaluated with numerical simulations and experiments with the hardware.
An oscillator-type gait controller for a quadruped robot with antagonistic pairs of pneumatic act... more An oscillator-type gait controller for a quadruped robot with antagonistic pairs of pneumatic actuators is proposed. By using the controller, a feasibility study on the stability of gait patterns with changeable body stiffness is reported. The periodic motions of the legs are generated and controlled by an oscillator network with state resetting. This type of controller has robustness in its gaits against variation in walking conditions or changes of environment. However, it sometimes loses robustness under conditions of actuation delay, decrease of actuator accuracy, etc. We investigated whether an oscillator-type controller with phase resetting is also effective under such conditions. The stability of locomotion also strongly depends on the mechanical properties of the body mechanism, especially the joint stiffness. In this report, the muscle tone of the robot on the pitching motion at the trunk is changeable by using the changeable elasticity of the pneumatic actuators. The stability of quadruped locomotion in walk and trot patterns with changeable body stiffness was evaluated with numerical simulations and hardware experiments.
The development of an oscillator controller for a bipedal robot with antagonistic pairs of pneuma... more The development of an oscillator controller for a bipedal robot with antagonistic pairs of pneumatic actuators is reported. Periodic motions of the legs switch between the swinging and supporting stages based on the phase of the oscillators. The oscillators receive touch sensor signals at the end of the legs as feedback when the leg touches the ground and compose a steady limit cycle of the total periodic dynamics of bipedal locomotion. The effectiveness and performance of the proposed controller were evaluated with numerical simulations and experiments with the hardware.
In this paper we propose a calculation method for the optimal trajectory of a biped locomotion ma... more In this paper we propose a calculation method for the optimal trajectory of a biped locomotion machine which is based on inverse kinematics and inverse dynamics. First, the trajectory of the waist is expressed by a Fourier series, where the bases are selected appropriately so that the periodic boundary conditions are strictly satisfied. A biped locomotion machine establishes optimal walking by using kicking forces to the ground at the moment of switching legs. In order to include the effecs of the kicking forces, additional terms that indicate the impulsive forces at the moment of switching legs are included in the formulation. Then the angles of each joint are determined by inverse kinematics, and using inverse dynamics, the input torques of each joint are expressed in terms of Fourier coefficients. By defining the performance index as a quadratic form of the input torques, the motion planning problem is formulated as an optimization problem of the trajectory of the waist, whose paramaters are Fourier coefficients of the trajactory of the waist. Using the successive quadratic programming (SQP) method, the optimal trajectory of a biped locomotion machine is obtained.
This paper deals with the attitude control of a rigid spacecraft with two reaction wheels. First,... more This paper deals with the attitude control of a rigid spacecraft with two reaction wheels. First, we derive a discontinuous state feedback law based on Lyapunov control. When the angular momentum of the system is zero, the derived controller makes the desired point the only stable equilibrium point of the system. Next, we investigate the behavior of the controlled system when the angular momentum is not zero but small.
This paper deals with a design of a control system for a multipod robot based on CPG principle. O... more This paper deals with a design of a control system for a multipod robot based on CPG principle. Oscillators are assigned at each leg and drive the periodic motion of legs. The phase of CPG is controlled by the signal of touch sensor which is mounted at the tip of the leg. It is confirmed through numerical simulation that the robot changes its gait pattern adaptively to variances of the environment.
The authors have proposed a dynamic turning control system of a quadruped robot by using nonlinea... more The authors have proposed a dynamic turning control system of a quadruped robot by using nonlinear oscillators. It is composed of a spontaneous locomotion controller and voluntary motion controller. In this article, capability of dynamic turning motion of the proposed control system is verified through numerical simulations and hardware experiments: Various turning speed and orientation make the motion of the robot asymmetry in terms of duty ratio, stride and center of pressure. The proposed controller actively and adaptively controls redundant DOF to cancel the dynamic asymmetry and established stable turning motion at various locomotion speed and turning orientation.
We have proposed an optimization method for a combinatorial optimization problem using replicator... more We have proposed an optimization method for a combinatorial optimization problem using replicator equations. To improve the solution further, a deterministic annealing algorithm may be applied. During the annealing process, bifurcations of equilibrium solutions will occur and affect the performance of the deterministic annealing algorithm. In this paper, the bifurcation structure of the proposed model is analyzed in detail. It is shown that only pitchfork bifurcations occur in the annealing process, and the solution obtained by the annealing is the branch uniquely connected with the uniform solution. It is also shown experimentally that in many cases, this solution corresponds to a good approximate solution of the optimization problem. Based on the results, a deterministic annealing algorithm is proposed and applied to the quadratic assignment problem to verify its performance.
In this paper, first, stability of locomotion of the multilegged locomotion robot along a straigh... more In this paper, first, stability of locomotion of the multilegged locomotion robot along a straight line is analyzed, and then, based on the dynamic characteristics, a turning strategy is proposed. The effectiveness of the turning strategy is verified by the numerical simulations; the robot can turn with less slip to the ground by decreasing the stability of the straight walk of the robot.
This article deals with the design of a control system for a quadrupedal locomotion robot. The pr... more This article deals with the design of a control system for a quadrupedal locomotion robot. The proposed control system is composed of a leg motion controller and a gait pattern controller within a hierarchical architecture. The leg controller drives actuators at the joints of the legs using a high-gain local feedback control. It receives the command signal from the gait pattern controller. The gait pattern controller, on the other hand, involves nonlinear oscillators. These oscillators interact with each other through signals from the touch sensors located at the tips of the legs. Various gait patterns emerge through the mutual entrainment of these oscillators. As a result, the system walks stably in a wide velocity range by changing its gait patterns and limiting the increase in energy consumption of the actuators. The performance of the proposed control system is verified by numerical simulations.
The author have proposed a dynamic turning control system of a quadruped robot by using nonlinear... more The author have proposed a dynamic turning control system of a quadruped robot by using nonlinear oscillators. It is composed of a motion controller and a motion planner. The motion controller drives the actuators of the legs by using local feedback control. The motion planner involves nonlinear oscillators with mutual interactions. In this paper, capability of dynamic turning motion of the proposed control system is verified through numerical simulations: In the slow speed turning, the robot has strong constraints geometrically. Whereas in the high speed turning, the robot has great influences of dynamic forces. These constraints conditions makes the motion of the robot asymmetry in terms of duty ratio, stride and center of force acting points. The proposed controller actively and adaptively controls the waist joint of the main body to satisfy the geometrical constraints during turning, and also controls the shoulder joints to incline the main body to cancel the centrifugal force in high speed turning by use of gravity force.
This article deals with the optimal gait pattern in terms of the proposed control system. The pha... more This article deals with the optimal gait pattern in terms of the proposed control system. The phase difference among the oscillators is selected as the optimization variable. The duty ratio is selected as the optimization parameter. The performance index is constructed as a quadratic form of the input torque vector at the joints. The simulated annealing (SA) method is used as the optimization algorithm and numerically derived the optimal gait patterns according to the various duty ratios.
Decentralized Autonomous Control of a Myriapod Locomotion Robot Ahmet Onat Sabanci University, Tu... more Decentralized Autonomous Control of a Myriapod Locomotion Robot Ahmet Onat Sabanci University, Turkey onat@sabanciuniv.edu Kazuo Tsuchiya Kyoto University, Japan tsuchiya@kuaero.kyoto-u.ac.jp Katsuyoshi Tsujita Kyoto University, Japan tsujita@kuaero.kyoto-...
In our previous work, we developed a locomotion control system of a biped robot which is composed... more In our previous work, we developed a locomotion control system of a biped robot which is composed of nonlinear oscillators and realized a stable straight walk of the biped robot against the changes of the environments. Then, we revealed that the adaptability to the changes of the environments is realized as the straight walk results in the change of the period of the motions of the legs. In this paper, we realize a turning walk of the biped robot by using the developed locomotion control system. First, we provide analysis of the turning behavior of the biped robot and reveal that, in this case, the turning behavior leads to the change of the duty ratios of the legs. Moreover, we realize the task that the robot pursues a target on the floor moving along a corner and it demonstrates that the robot can turn a corner successfully in the real world.
We discuss the motion control of a two-wheeled mobile robot. In the design of a controller for th... more We discuss the motion control of a two-wheeled mobile robot. In the design of a controller for the system, a kinematic model is usually used; the wheels do not skid at all and the mobile robot is regarded as a 3D 2-input nonholonomic system without drift. Many controllers based on the kinematic model have been proposed. However, in a real world, the wheels may skid on the ground or float away from the ground according to the rolling motion of the body. Therefore, we derive a dynamic model of a two-wheeled mobile robot which implies the translational motion with 3 degrees-of-freedom and the rotational motion with 3 degrees-of-freedom of the body and the rotational motion with one degree-of-freedom of each wheel, and then reduce the dynamic model to the kinematic model under certain assumptions. We design a controller based on the kinematic model by extending the Lyapunov control and analyze whether the designed controller works well in a real world by numerical simulations based on the dynamic model
This paper proposes the locomotion control system for a multi-legged locomotion robot. The propos... more This paper proposes the locomotion control system for a multi-legged locomotion robot. The proposed control system is composed of leg motion controllers and a gait pattern controller. The leg motion controllers drive the actuators of the legs by using local feedback control. The gait pattern controller is composed of non linear oscillators. The oscillators tune the phases through the mutual interactions and the feedback signals from the touch sensors at the tips of the legs. Various gait patterns emerge through the mutual entrainment of these oscillators. As a result, the robot with the controller walks stably by changing its gait patterns in a wide range of locomotion speed. Moreover, it continues to walk even if a part of leg controller breaks down. The performance of the proposed control system is verified by numerical simulations.
This paper proposes the locomotion control system for a biped locomotion robot. The propose contr... more This paper proposes the locomotion control system for a biped locomotion robot. The propose control system is composed of motion generator system and motion control system. Motion generator system is composed of nonlinear oscillators, which generate the commanded trajectories of the joints as functions of phases of oscillators. Motion control system is composed of motors with controllers installed at joints, which control motions of joints. The oscillators tune the phases through the mutual interactions and the feedback signals from the touch sensors at the tips of the legs. As a result, the robot with the controller walks stably by changing its period of locomotion in a changing environment. The performance of the proposed control system is verified by numerical simulations and experiments.
The development of an oscillator controller for a quadruped robot with antagonistic pairs of pneu... more The development of an oscillator controller for a quadruped robot with antagonistic pairs of pneumatic actuators is reported. Periodic motions of the legs switch between the swinging and supporting stages based on the phase of the oscillators. The oscillators receive touch sensor signals at the end of the legs as feedback when the leg touches the ground and compose a steady limit cycle of the total periodic dynamics of quadruped locomotion. And also muscle tone is adaptively controlled according to the dynamic state of the main body. This system can generate gait transition from one to another by changing locomotion speed and muscle tone. The effectiveness and performance of the proposed controller were evaluated with numerical simulations and experiments with the hardware.
The development of an oscillator controller for a quadruped robot with antagonistic pairs of pneu... more The development of an oscillator controller for a quadruped robot with antagonistic pairs of pneumatic actuators is reported. Periodic motions of the legs switch between the swinging and supporting stages based on the phase of the oscillators. The oscillators receive touch sensor signals at the end of the legs as feedback when the leg touches the ground and compose a steady limit cycle of the total periodic dynamics of quadruped locomotion. And also muscle tone is adaptively controlled according to the dynamic state of the main body. This system can generate gait transition from one to another by changing locomotion speed and muscle tone. The effectiveness and performance of the proposed controller were evaluated with numerical simulations and experiments with the hardware.
An oscillator-type gait controller for a quadruped robot with antagonistic pairs of pneumatic act... more An oscillator-type gait controller for a quadruped robot with antagonistic pairs of pneumatic actuators is proposed. By using the controller, a feasibility study on the stability of gait patterns with changeable body stiffness is reported. The periodic motions of the legs are generated and controlled by an oscillator network with state resetting. This type of controller has robustness in its gaits against variation in walking conditions or changes of environment. However, it sometimes loses robustness under conditions of actuation delay, decrease of actuator accuracy, etc. We investigated whether an oscillator-type controller with phase resetting is also effective under such conditions. The stability of locomotion also strongly depends on the mechanical properties of the body mechanism, especially the joint stiffness. In this report, the muscle tone of the robot on the pitching motion at the trunk is changeable by using the changeable elasticity of the pneumatic actuators. The stability of quadruped locomotion in walk and trot patterns with changeable body stiffness was evaluated with numerical simulations and hardware experiments.
The development of an oscillator controller for a bipedal robot with antagonistic pairs of pneuma... more The development of an oscillator controller for a bipedal robot with antagonistic pairs of pneumatic actuators is reported. Periodic motions of the legs switch between the swinging and supporting stages based on the phase of the oscillators. The oscillators receive touch sensor signals at the end of the legs as feedback when the leg touches the ground and compose a steady limit cycle of the total periodic dynamics of bipedal locomotion. The effectiveness and performance of the proposed controller were evaluated with numerical simulations and experiments with the hardware.
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