Control Pneumatic Soft Bending Actuator with Feedforward Hysteresis Compensation by Pneumatic Physical Reservoir Computing

TL;DR

The paper tackles hysteresis-induced control challenges in soft pneumatic actuators by introducing a feedforward hysteresis compensation framework based on physical reservoir computing (PRC). It compares an ESN-based approach with a novel FPRC model that uses a dual-PAM physical reservoir processed by a Takagi-Sugeno fuzzy logic to generate the feedforward command $P_{\text{ff}}$, which is integrated with feedback control. Results show the FPRC achieves similar training performance to ESN but better generalization on unseen data and, crucially, a 97.6% reduction in test-time execution, indicating substantial real-time efficiency gains. The method demonstrates robust performance in open- and closed-loop bending tracking and resilience to environmental disturbances, advancing physical reservoir computing for nonlinear control of soft actuators and offering a practical tool for hysteresis compensation in pneumatic systems.

Abstract

The nonlinearities of soft robots bring control challenges like hysteresis but also provide them with computational capacities. This paper introduces a fuzzy pneumatic physical reservoir computing (FPRC) model for feedforward hysteresis compensation in motion tracking control of soft actuators. Our method utilizes a pneumatic bending actuator as a physical reservoir with nonlinear computing capacities to control another pneumatic bending actuator. The FPRC model employs a Takagi-Sugeno (T-S) fuzzy logic to process outputs from the physical reservoir. The proposed FPRC model shows equivalent training performance to an Echo State Network (ESN) model, whereas it exhibits better test accuracies with significantly reduced execution time. Experiments validate the FPRC model's effectiveness in controlling the bending motion of a pneumatic soft actuator with open-loop and closed-loop control system setups. The proposed FPRC model's robustness against environmental disturbances has also been experimentally verified. To the authors' knowledge, this is the first implementation of a physical system in the feedforward hysteresis compensation model for controlling soft actuators. This study is expected to advance physical reservoir computing in nonlinear control applications and extend the feedforward hysteresis compensation methods for controlling soft actuators.

Figures (17)

• Figure 1: Pneumatic soft bending actuator: (a) Structure; (b) Bending under pressurization; (c) Returning to initial straight shape upon depressurization.
• Figure 2: Dual-PAM actuator as a physical reservoir: (a) Structural design; (b) Atmospheric pressure in active PAM (PAM A) and pre-pressurized state in passive PAM (PAM B); (c) Actuation of PAM A and consequential pressure increase in compressed PAM B. (d) Schematic of the nonlinear mapping.
• Figure 3: Experimental apparatus. Blue and black lines in the right-located figure indicate the pneumatic and electronic circuits, respectively.
• Figure 4: Hysteresis experiments: (a) and (b) Sweep-frequency pressure input $P_\text{exp}$ and the corresponding hysteresis loops of the first experiment; (c) and (d) Complex pressure input $P_\text{exp}$ and hysteresis loops of the second experiment. The signal in (a) lasts 120 [s] and sweeps the frequencies from 0.1 Hz to 1 Hz. The signal in (c) is $35\sum_{i=1}^{5} \sin\left(2\pi f_i t - \pi/2\right)+175$ [kPa], where $t \in [0,80]$ is the time [s], $f_1 = 0.12$, $f_2 = 0.04$, $f_3 = 0.31$, $f_4 = 0.29$, and $f_5 = 0.25$.
• Figure 5: Hysteresis experiments: (a) Hysteresis between $P_o$ and the soft actuator's bending $\theta$ obtained from the first hysteresis experiment; (b) The corresponding hysteresis relationship obtained from the second experiment.