Proprioceptive Touch of a Soft Actuator Containing an Embedded Intrinsically Soft Sensor using Kinesthetic Feedback

Abstract

This paper presents an approach to a kinesthetic sense of touch for a finger-like soft robotic actuator innervated with a soft fluidic resistive sensor which is sensitive to bending. The approach is based on the sensor resistance reference tracking feedback controller and uses the reference tracking error as a measure of stress resulting from the contact between the actuator and an object. With the proposed approach, we accomplish tasks of detecting a touch between the actuator and an object, keeping the actuator in the compliant touch with the object and creating a map that visualizes objects in the operating space without any visual information. Our results demonstrate that the tracking error signal contains robust information regarding the contact interaction between the actuator and its environment.

Appendices

Appendix A: Soft Finger Design

The soft finger-like actuator (see Fig. 11) is a pneumatic-based actuator containing embedded ionically conductive fluidic sensors. Its design, which is based on our previously reported work [42], includes a curvature sensor for proprioceptive sensing along the dorsal side, a force sensor for tactile perception along the ventral side and inflation chambers for motivating the actuator, as shown in Fig. 11A. The actuator contains five layers constructed from both Ecoflex-0030 and Dragon Skin 10 (Fig. 11B) in order to increase grip strength without sacrificing sensor responsivity. The inflation chambers and force sensor are created using Dragon Skin 10, while the curvature sensor is created using Ecoflex-0030, so that the actuator maintains a curving motion when inflated.

Fig. 11

Soft robotic finger-like actuator with the embedded soft sensor model. ( A) The schematic of the complete finger. Shown in green are Curvature Sensor (which we use for state information and contact sensing) and Force Sensor (not used in our method, allowing it to be used for other haptic tasks). Shown in blue are Inflation chambers. Layers of silicone matrix are indicated in unshaded wireframe. (B) The complete soft robotic actuator contained within the mount. The overall mass of the actuator is 49.6 grams, length of the actuator is 110mm (without the interface 87mm), width 15mm and height 18mm (including sensors)

The actuator is integrated into a mount system that holds it securely to provide strain relief on the connecting wires (Fig. 11B). To increase the robustness and longevity of the actuator, the sensor fluid reservoirs are located under the actuator mount. This prevents the wires, which pierce the reservoirs, from breaking due to repeated bending stress as the actuator is inflated. Both sensor channels are filled with the ionic fluid 1-ethyl-3-methylimidazolium ethyl sulfate (1E3MES). A description of the electrical and air subsystems used in this work are described in the appendix since they are necessary for the correct functioning of the actuator along with the control design.

The block diagram of the overall system for the control of the actuator is shown in Fig. 12. An Arduino Nano is used to both run the feedback loop that controls the motion of the finger, and collect and relay data to the computer. The feedback loop combined with an off-board digital-to-analog converter (DAC) computes the desired pressure input to the digital pressure regulator actuator. The pressure range is 0-52 kPa, which is limited by the DAC, and is sufficient for the flexion range of the actuator. A relaxation oscillator converts the variable sensor impedance into a readable square wave signal. Other methods of measuring the impedance of the sensors using DC currents would result in the electrolysis of the ionic fluid 1E3MES and damage the sensors [47]. A relaxation oscillator was shown to work previously with 1E3MES [22], and works well with the ability of precise timing measurement of a microcontroller. The frequency output is measured by the Arduino using an interrupt and timer to get the period of the signal. To determine the impedance R_s from the period of the square wave signal T_s, we use

$$ R_{s} = \frac{1}{2C\ln{\frac{1+a}{1-a}}} T_{s}, $$

(1)

Fig. 12

The system setup needed to collect data and control the finger-like actuator. The central component of the system is the Arduino Nano which is used for both controlling the actuator and taking data in from the sensors. This data is then sent via serial port to the computer. A relaxation oscillator circuit is used to measure the impedance of the sensor fluid. The relaxation oscillator uses the resistor capacitor charge time constant to output a period square wave based on the sensor resistance. The red lines indicate analog data while the blue lines are digital

where a = R₁/(R₁ + R₂), R₁ = 680 Ω,R₂ = 9.9 kΩ,andC = 10 nF. The above expression takes values from the schematic shown in Fig. 12.

1.1 A.1: Static Pressure - Resistance Characteristics

To validate the sensor, we applied multiple inflation pressure (p) values in the 0 to 50kPa range to a freely moving finger. After a constant pressure was applied, we waited for the finger to stop and recorded the sensor resistance change ΔR(p). From the pressure - resistance data fit, we obtained the following polynomial [48]

$$ \begin{array}{@{}rcl@{}} {\Delta} R_{cf}(p) &=& 4.964 \cdot 10^{-5}p^{4} - 0.002687p^{3}\\ &&+ 0.05297p^{2} + 0.7648p + 0.1988. \end{array} $$

(2)

In the 0 to 50kPa range, the polynomial is monotonously increasing.

1.2 A.2: Force Load

To evaluate the force that can be achieved by the finger, we positioned it horizontally in the proximity of the horizontal plate. Then we applied multiple inflation pressure (p) values in the 0 to 50kPa range and used a scale to measure the force load from the finger’s tip to the plate. The data are provided in the table below.

Pressure (p) [kPa]	0	10	20	30	40	50
Force [N]	0	0.0108	0.0217	0.0391	0.0743	0.1163

The table above represents well the range of the load force in the interaction of the finger with objects in the environment. Naturally, the load force also depends on relative positions between the finger and the loaded object. The study of finger mechanical design validation is not strictly in the scope of this paper and for further details we point to data presented in [42] and [48].

Appendix B: Compliant Touch Pseudocode

We provide here a pseudocode for the implementation of the supervisory control for the firm and light touches depicted in Fig. 8. We show the implementation of the form of the “Compliant Touch” function. The function has one input variable that can be either “Ligh touch” or “Firm touch”. In this implementation, after the function call, State 0 is used for variable initialization and the collection of initial data necessary to start the feedback control loop. After the switch to State 1, the function implements the feedback controller from expression (15) in Section 5. The same controller is also used in State 2 and State 3. In State 1, the reference is defined by expression (18) in Section 6. After the error reaches the threshold T_t, the state changes to State 2 or State 3 as defined by the value of the “Compliant Touch” function input variable. In the case of “Light touch”, when the threshold is reached, the sensor resistance R_c is recorded as R_ckT and the state switches to State 2. In that state, the recorded value is used to compute the reference from expression (20) in Section 6. In the case of “Firm touch”, after the threshold is reached, there is a switch to State 3. In that state, the reference is constant and set to its last value in State 1.

The loop of the “Compliant Touch” function is coded to run indefinitely with a sample time h. The exit from the loop can be achieved if a (global) variable “exitFlag” is set externally to a value different than 0.