Stable Real-Time Feedback Control of a Pneumatic Soft Robot

TL;DR

This paper presents a real-time feedback control method for a soft pneumatic robot, translating an infinite-dimensional PDE-based controller into a finite-dimensional implementation that maintains stability and performance.

Contribution

It introduces a convex quadratic programming approach to tune PDE-based feedback gains for real-time control with limited actuators.

Findings

The finite-dimensional controller preserves the stability of the infinite-dimensional design.

Experimental results demonstrate effective planar motion control of the soft robot.

The method bridges the gap between PDE-based control theory and practical actuator implementation.

Abstract

Soft actuators offer compliant and safe interaction with an unstructured environment compared to their rigid counterparts. However, control of these systems is often challenging because they are inherently under-actuated, have infinite degrees of freedom (DoF), and their mechanical properties can change by unknown external loads. Existing works mainly relied on discretization and reduction, suffering from either low accuracy or high computational cost for real-time control purposes. Recently, we presented an infinite-dimensional feedback controller for soft manipulators modeled by partial differential equations (PDEs) based on the Cosserat rod theory. In this study, we examine how to implement this controller in real-time using only a limited number of actuators. To do so, we formulate a convex quadratic programming problem that tunes the feedback gains of the controller in real time such that it becomes realizable by the actuators. We evaluated the controller's performance through experiments on a physical soft robot capable of planar motions and show that the actual controller implemented by the finite-dimensional actuators still preserves the stabilizing property of the desired infinite-dimensional controller. This research fills the gap between the infinite-dimensional control design and finite-dimensional actuation in practice and suggests a promising direction for exploring PDE-based control design for soft robots.