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Velocity-Form Data-Enabled Predictive Control of Soft Robots under Unknown External Payloads

Huanqing Wang, Kaixiang Zhang, Kyungjoon Lee, Yu Mei, Vaibhav Srivastava, Jun Sheng, Ziyou Song, Zhaojian Li

TL;DR

The paper addresses robust control of soft robots under unknown payloads by introducing a velocity-form DeePC framework that leverages incremental input-output data to achieve offset-free, disturbance-tolerant tracking without pre-collected loaded data or explicit disturbance estimators. The approach combines Willems' non-parametric representation, regularized DeePC, and a velocity-form formulation to suppress payload-induced offset and improve robustness, incorporating mosaic Hankel extensions and SVD-based dimension reduction for computational efficiency. Experimental validation on a planar soft actuator shows that VDeePC outperforms standard DeePC across setpoint tracking, payload variations, and long trajectories, achieving significantly lower RMSEs under unknown loads. The method offers practical advantages for real-time soft-robot control in uncertain environments and lays groundwork for extending to multi-segment soft robots and more complex manipulation tasks.

Abstract

Data-driven control methods such as data-enabled predictive control (DeePC) have shown strong potential in efficient control of soft robots without explicit parametric models. However, in object manipulation tasks, unknown external payloads and disturbances can significantly alter the system dynamics and behavior, leading to offset error and degraded control performance. In this paper, we present a novel velocity-form DeePC framework that achieves robust and optimal control of soft robots under unknown payloads. The proposed framework leverages input-output data in an incremental representation to mitigate performance degradation induced by unknown payloads, eliminating the need for weighted datasets or disturbance estimators. We validate the method experimentally on a planar soft robot and demonstrate its superior performance compared to standard DeePC in scenarios involving unknown payloads.

Velocity-Form Data-Enabled Predictive Control of Soft Robots under Unknown External Payloads

TL;DR

The paper addresses robust control of soft robots under unknown payloads by introducing a velocity-form DeePC framework that leverages incremental input-output data to achieve offset-free, disturbance-tolerant tracking without pre-collected loaded data or explicit disturbance estimators. The approach combines Willems' non-parametric representation, regularized DeePC, and a velocity-form formulation to suppress payload-induced offset and improve robustness, incorporating mosaic Hankel extensions and SVD-based dimension reduction for computational efficiency. Experimental validation on a planar soft actuator shows that VDeePC outperforms standard DeePC across setpoint tracking, payload variations, and long trajectories, achieving significantly lower RMSEs under unknown loads. The method offers practical advantages for real-time soft-robot control in uncertain environments and lays groundwork for extending to multi-segment soft robots and more complex manipulation tasks.

Abstract

Data-driven control methods such as data-enabled predictive control (DeePC) have shown strong potential in efficient control of soft robots without explicit parametric models. However, in object manipulation tasks, unknown external payloads and disturbances can significantly alter the system dynamics and behavior, leading to offset error and degraded control performance. In this paper, we present a novel velocity-form DeePC framework that achieves robust and optimal control of soft robots under unknown payloads. The proposed framework leverages input-output data in an incremental representation to mitigate performance degradation induced by unknown payloads, eliminating the need for weighted datasets or disturbance estimators. We validate the method experimentally on a planar soft robot and demonstrate its superior performance compared to standard DeePC in scenarios involving unknown payloads.

Paper Structure

This paper contains 16 sections, 1 theorem, 23 equations, 7 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. System Description and Preliminaries
  3. System Description
  4. Non-Parametric Representation
  5. Control Methods
  6. Data-Enabled Predictive Control
  7. Regularized DeePC for Nonlinear Systems
  8. Velocity-Form DeePC
  9. Mosaic Hankel Matrix and Dimension Reduction
  10. Experiments
  11. Experimental Setup
  12. Data Collection
  13. Setpoint Control Evaluation
  14. Tracking Performance Under Varying Weights
  15. Long Trajectory Tracking with Multiple Reference Changes
  16. ...and 1 more sections

Key Result

Lemma 1

Consider a controllable LTI system with an input sequence $u_{[0,T-1]}^{\mathrm{d}}$ that is persistently exciting of order $n + L$ (see Definition def:pe). Any length $L$ sequence $(u_{[0,L-1]}, y_{[0,L-1]})$ is a valid input-output trajectory of the system if and only if for some vector $g \in \mathbb{R}^{(T - L + 1)}$.

Figures (7)

  • Figure 1: Illustration diagram of the soft robot, which consists of two chambers (left and right). Actuating one chamber with air produces a bending motion. The geometric centerline is shown in red.
  • Figure 2: The experimental setup of the soft robot control system. The soft robot is surrounded by a Qualisys motion capture system equipped with eight cameras.
  • Figure 3: The setpoint tracking results for the DeePC vs VDeePC without load.
  • Figure 4: The setpoint tracking results for the DeePC vs VDeePC with load.
  • Figure 5: Boxplot results of tracking errors under no-load and load conditions with six apples of different weights, comparing DeePC and VDeePC.
  • ...and 2 more figures

Theorems & Definitions (3)

  • Definition 1
  • Lemma 1: Fundamental Lemma WILLEMS2005325
  • Definition 2: Waarde2020