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Underactuated Control of Multiple Soft Pneumatic Actuators via Stable Inversion

Wu-Te Yang, Burak Kurkcu, Masayoshi Tomizuka

TL;DR

The paper tackles the challenge of underactuated coordination in a two-finger soft gripper driven by a single syringe pump. It develops a SIMO plant model Y(s) = P(s)U(s) and leverages stable inversion with a feedforward P†(s) and a corrective H(s) to achieve coordinated motion, while a feedback loop mitigates model perturbations. Hardware design uses optimized soft actuators and a compact syringe-pump module, with system dynamics captured through a cascaded actuator-pump model and multiplicative uncertainty sets. Simulations and experiments show rapid settling (≈0.6–0.7 s) and sub-degree tracking accuracy, even under disturbances, demonstrating effective reduction in required pumps and robust coordination across fingers. The framework offers practical pathways for scalable soft-gripper control in real-world manipulation tasks, while outlining limitations and avenues for extending beyond the image-space of the plant model.

Abstract

Soft grippers, with their inherent compliance and adaptability, show advantages for delicate and versatile manipulation tasks in robotics. This paper presents a novel approach to underactuated control of multiple soft actuators, explicitly focusing on the coordination of soft fingers within a soft gripper. Utilizing a single syringe pump as the actuation mechanism, we address the challenge of coordinating multiple degrees of freedom of a compliant system. The theoretical framework applies concepts from stable inversion theory, adapting them to the unique dynamics of the underactuated soft gripper. Through meticulous mechatronic system design and controller synthesis, we demonstrate the efficacy and applicability of our approach in achieving precise and coordinated manipulation tasks in simulation and experimentation. Our findings not only contribute to the advancement of soft robot control but also offer practical insights into the design and control of underactuated systems for real-world applications.

Underactuated Control of Multiple Soft Pneumatic Actuators via Stable Inversion

TL;DR

The paper tackles the challenge of underactuated coordination in a two-finger soft gripper driven by a single syringe pump. It develops a SIMO plant model Y(s) = P(s)U(s) and leverages stable inversion with a feedforward P†(s) and a corrective H(s) to achieve coordinated motion, while a feedback loop mitigates model perturbations. Hardware design uses optimized soft actuators and a compact syringe-pump module, with system dynamics captured through a cascaded actuator-pump model and multiplicative uncertainty sets. Simulations and experiments show rapid settling (≈0.6–0.7 s) and sub-degree tracking accuracy, even under disturbances, demonstrating effective reduction in required pumps and robust coordination across fingers. The framework offers practical pathways for scalable soft-gripper control in real-world manipulation tasks, while outlining limitations and avenues for extending beyond the image-space of the plant model.

Abstract

Soft grippers, with their inherent compliance and adaptability, show advantages for delicate and versatile manipulation tasks in robotics. This paper presents a novel approach to underactuated control of multiple soft actuators, explicitly focusing on the coordination of soft fingers within a soft gripper. Utilizing a single syringe pump as the actuation mechanism, we address the challenge of coordinating multiple degrees of freedom of a compliant system. The theoretical framework applies concepts from stable inversion theory, adapting them to the unique dynamics of the underactuated soft gripper. Through meticulous mechatronic system design and controller synthesis, we demonstrate the efficacy and applicability of our approach in achieving precise and coordinated manipulation tasks in simulation and experimentation. Our findings not only contribute to the advancement of soft robot control but also offer practical insights into the design and control of underactuated systems for real-world applications.
Paper Structure (26 sections, 3 theorems, 33 equations, 7 figures)

This paper contains 26 sections, 3 theorems, 33 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Mathematics Preliminaries
  4. Problem Statement
  5. Methodology
  6. Mechatronic Design
  7. Soft Actuator Design
  8. Syringe Pump Design
  9. Multi-finger Soft Gripper
  10. System Modeling
  11. Modeling Soft Actuators
  12. Modeling Syringe Pump
  13. Controller Design and Analysis
  14. Experimental Evaluation
  15. Preliminary Evaluations
  16. ...and 11 more sections

Key Result

Theorem 1

(Rouche-Capelli Theorem) Consider $P \in \Bbb{R}(s)^{n_y \times n_u}$ with $\textnormal{rank}_{\Bbb{R}(s)}(P)=r$ and $Y \in \Bbb{R}(s)^{n_y \times 1}$. The solution(s) $U$ for the equation $PU=Y$ is exist if and only if

Figures (7)

  • Figure 1: The soft gripper has two fingers and is driven by a single syringe pump to achieve underactuated control via model inversion. The control commands are generated in MATLAB®/Simulink and are converted to PWM for the stepper motor in the syringe pump. The bending angles of both fingers are measured by the flex sensor embedded in each soft gripper.
  • Figure 2: The design of the mechatronic system can be seen in (a), (b), and (c), while the system modeling is observed in (d), (e), and (f). (a) visualizes how the optimal dimensional parameters are searched in a non-convex space. (b) illustrates the fabrication process of the soft pneumatic actuator and the flex sensor is embedded during the fabrication process. (c) shows the appearance of the syringe pump, and it is made of a commercial linear actuator and a commercial syringe. The (d) and (e) visualize how the structure of the soft actuator is approximated by a cantilever beam and how the bending angle is measured. The modeling schematic of the syringe pump is displayed in (f).
  • Figure 3: The block diagram of the proposed controller including the feedforward control and feedback loop.
  • Figure 4: Several open-loop responses of both soft pneumatic actuators (soft fingers) are demonstrated in (a). The robustness weight selection of both soft fingers based on the modeling errors can be seen in (b).
  • Figure 5: The step responses of different speeds of SPA1 (left finger in Fig. \ref{['fig_1']}) are shown in (a). The robustness weight selection of SPA1 with high and slow speeds based on the modeling errors can be seen in (b).
  • ...and 2 more figures

Theorems & Definitions (7)

  • Theorem 1
  • Remark 1
  • Theorem 2
  • Definition 1
  • Remark 2
  • Remark 3
  • Theorem 3