Model-Based Control of Soft Pneumatic Robotic Joints with On/Off Valves

Soft pneumatic robotic joints driven by low-cost on/off solenoid valves are attractive for lightweight and compliant robotic systems, but precise control remains challenging because continuous actuation commands must be realized through discrete valve states subject to minimum pulse-width constraints. This paper presents a model-based constrained equivalent-control PWM (C-EC) framework for a dual-chamber bellows actuator driven by four on/off valves. An ideal duty ratio is derived so that the averaged differential pressure rate matches the desired value required to impose first-order inner-loop error dynamics. To make this law physically implementable, the ideal duty is projected onto the feasible duty set determined by the minimum reliable pulse width of the valves. The resulting duty projection error is explicitly incorporated into a Lyapunov-based analysis, yielding a uniform ultimate boundedness result for the closed-loop system under the proposed implementation and an analytical comparison with conventional discrete sliding-mode control (D-SMC). The valve flow model is parameterized through PWM step-test-based sonic conductance identification. The proposed framework is implemented on a custom 1-DOF rotary joint based on an aluminum-film spiral-duct bellows actuator. Experiments show that C-EC does not uniformly dominate D-SMC over all operating conditions, but it improves eRMS and RΔP in the medium-to-large positive-step regime and in long-hold regulation. In the representative 45∘–65∘–45∘ step-hold test, C-EC reduced the RMS tracking error by 39.3% and the differential pressure ripple by 34.5% relative to D-SMC. In the 65∘ long-hold test, the RMS tracking error and pressure ripple were further reduced by 35.4% and 37.9%, respectively. A loop-period comparison also showed that a 10 ms control period reduced duty projection and pressure ripple relative to 5 ms without degrading tracking accuracy.