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Stable Real-Time Feedback Control of a Pneumatic Soft Robot

Sean Even, Tongjia Zheng, Hai Lin, Yasemin Ozkan-Aydin

TL;DR

This work tackles stable real-time control of soft robots modeled by Cosserat rod PDEs by projecting an infinite-dimensional PD controller onto a finite actuator space using a convex quadratic program that jointly tunes actuator pressure and a spatially varying feedback gain. The approach is demonstrated on a planar two-chamber soft robot with fabric sPAM actuators, integrating gravity and detailed actuator modeling, and controlled via vision-based state estimation. Key contributions include a practical real-time realization framework for PDE-based controllers, a formal QP formulation with actuator constraints, and experimental validation showing preserved stabilization properties despite finite actuation. The results indicate a promising direction for PDE-based control in soft robotics, enabling accurate, real-time shaping and tracking with limited hardware while highlighting challenges in measurement and high-pressure behavior.

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.

Stable Real-Time Feedback Control of a Pneumatic Soft Robot

TL;DR

This work tackles stable real-time control of soft robots modeled by Cosserat rod PDEs by projecting an infinite-dimensional PD controller onto a finite actuator space using a convex quadratic program that jointly tunes actuator pressure and a spatially varying feedback gain. The approach is demonstrated on a planar two-chamber soft robot with fabric sPAM actuators, integrating gravity and detailed actuator modeling, and controlled via vision-based state estimation. Key contributions include a practical real-time realization framework for PDE-based controllers, a formal QP formulation with actuator constraints, and experimental validation showing preserved stabilization properties despite finite actuation. The results indicate a promising direction for PDE-based control in soft robotics, enabling accurate, real-time shaping and tracking with limited hardware while highlighting challenges in measurement and high-pressure behavior.

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.
Paper Structure (11 sections, 1 theorem, 18 equations, 7 figures, 1 table)

This paper contains 11 sections, 1 theorem, 18 equations, 7 figures, 1 table.

Table of Contents

  1. Introduction
  2. Modeling
  3. Cosserat Rod Model for Planar Case
  4. Actuator Modeling
  5. Modeling Gravity
  6. Controller Design
  7. Experimental set-up
  8. Estimating Contraction
  9. Experimental Results
  10. Conclusion
  11. Awknowledgements

Key Result

Theorem 1

tongjia Consider the soft robot system eq:complete system. If there exist positive functions $k_\theta(s),k_{w_x}(s,t)$ such that $l\equiv l_*$ for all $t$, then $(e_\theta(s,t),e_{w_x}(s,t))\to0$ for all $s$ exponentially.

Figures (7)

  • Figure 1: Reference frames used in Cosserat Rod Theory. The global frame $\{y\}$ and the local frame described by
  • Figure 2: Symbolic representation of soft manipulator and visualization of the braid angle $\alpha_0$ and initial radius $r_0$.
  • Figure 3: Closed-loop shape tracking block diagram
  • Figure 4: Unactuated and actuated states of the fabric sPAMs.A. Unactuated (left, P = 0 kPa) and actuated (right, P = 30 kPa) states of a single fabric sPAM. B. Unactuated (left) and actuated (right) states of a two-segmented arm.
  • Figure 5: Image processing example (Left) An example image of the arm with markers. (right) Automatic detection of markers (red circles) and markers' orientation (green lines inside red circles).
  • ...and 2 more figures

Theorems & Definitions (2)

  • Theorem 1
  • Remark 1