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Control Lyapunov Functions for Underactuated Soft Robots

Huy Pham, Zach J. Patterson

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.

Control Lyapunov Functions for Underactuated Soft Robots

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.
Paper Structure (22 sections, 26 equations, 5 figures, 2 tables)

This paper contains 22 sections, 26 equations, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Soft Robot Model Systems
  3. Robot Dynamics
  4. Robots
  5. Tendon-Driven Finger
  6. Trimmed Helicoid Soft Continuum
  7. Logarithmic Spiral Robot
  8. Control Methodology
  9. Input--Output Linearization
  10. CLF--QP Controller
  11. Soft ID--CLF--QP Controller
  12. Validation
  13. Baseline
  14. Impedance Control (IC)
  15. Underactuated Impedance Control (UIC)
  16. ...and 7 more sections

Figures (5)

  • Figure 1: Results of our proposed Soft ID-CLF-QP control approach operating on various soft robot architectures to solve the task-space control problem. The robot platforms are: (a) Finger (L = 0.24 m), (b) Helix (L = 0.45 m), and (c) SpiRob (L = 0.50 m).
  • Figure 2: Lyapunov functions over time for set points tracking experiment.
  • Figure 3: Lyapunov functions over time for trajectory tracking experiment.
  • Figure 4: Task-space convergence of the SpiRob during a set-point regulation experiment in the $x$--$z$ plane. The variables $x_d$ and $z_d$ denote the target point coordinates.
  • Figure 5: Task-space trajectory tracking performance during the second cycle across controllers for Finger (a) and Helix (b) for $\omega = 0.2\pi$ rad/s.