Control Lyapunov Functions for Underactuated Soft Robots

TL;DR

This paper introduces a control framework for underactuated soft robots that guarantees stability and respects actuator limits, demonstrated through simulations on various robotic platforms with improved accuracy and convergence.

Contribution

It presents a novel convex optimization-based control method that enforces Lyapunov stability for underactuated soft robots under input constraints, a significant advancement over existing approaches.

Findings

Enhanced task-space accuracy in simulations

Stable Lyapunov convergence under input bounds

Superior tracking performance compared to baseline methods

Abstract

Soft and soft-rigid hybrid robots are inherently underactuated and operate under tight actuator limits, making task-space control with stability guarantees challenging. Common nonlinear strategies for soft robots (e.g., those based on PD control) often rely on the assumption of full actuation with no actuator limits. This paper presents a general control framework for task-space regulation and tracking of underactuated soft robots under bounded inputs. The method enforces a rapidly exponentially stabilizing control Lyapunov function as a convex inequality constraint while simultaneously satisfying underactuated full-body dynamics and actuator bounds. We validate the approach in simulation on several platforms spanning increasing underactuation: a simple two link tendon-driven "finger", a trimmed helicoid manipulator, and a highly underactuated spiral robot. We compare against a number of baseline methods from the literature. Results show improved task-space accuracy and consistent Lyapunov convergence under input limits, achieving superior set-point and trajectory-tracking performance.