Adaptive proxy-based sliding mode control for a class of second-order nonlinear systems and its application to pneumatic muscle actuators.

The human-centered robotic systems demand safe and robust controllers in many applications. This paper proposes an adaptive proxy-based sliding mode control approach for a class of typical second-order nonlinear systems. A new PID-type virtual coupling is designed between a virtual proxy and the physical object. Considering the unknown bound of lumped disturbances, an adaptation law is applied to online adjust the gain of a sign function which ensures the proxy to track the reference accurately. By using the Lyapunov theorem, the closed-loop system stability is proved. Both simulations and experiments are conducted to verify the proposed method based on a real-world pneumatic muscle actuator control platform. The results show that the proposed adaptive proxy-based sliding mode control approach presents better tracking accuracy, safety, and robustness than the conventional PID control and sliding mode control.