Learning-based Delay Compensation for Enhanced Control of Assistive Soft Robots

TL;DR

The paper tackles the challenge of controlling soft robots under nonlinear dynamics and delays by introducing a learning-based approximation of the nonlinear Smith Predictor. It combines Legendre Delay Networks for compact input history representation with online Kernel Recursive Least Squares Tracker to learn the integral term driving delay compensation, integrated into a robust sliding-mode control framework. Experimental results on a two-module cable-driven soft robot arm show substantial tracking improvements, with up to a 64% reduction in XY tracking error at high gains, and faster learning for LDN-based variants. The approach is computationally efficient and adaptable online, offering safer and more accurate control for assistive care applications and paving the way for real-time human-robot interactions in unstructured environments.

Abstract

Soft robots are increasingly used in healthcare, especially for assistive care, due to their inherent safety and adaptability. Controlling soft robots is challenging due to their nonlinear dynamics and the presence of time delays, especially in applications like a soft robotic arm for patient care. This paper presents a learning-based approach to approximate the nonlinear state predictor (Smith Predictor), aiming to improve tracking performance in a two-module soft robot arm with a short inherent input delay. The method uses Kernel Recursive Least Squares Tracker (KRLST) for online learning of the system dynamics and a Legendre Delay Network (LDN) to compress past input history for efficient delay compensation. Experimental results demonstrate significant improvement in tracking performance compared to a baseline model-based non-linear controller. Statistical analysis confirms the significance of the improvements. The method is computationally efficient and adaptable online, making it suitable for real-world scenarios and highlighting its potential for enabling safer and more accurate control of soft robots in assistive care applications.

Figures (5)

• Figure 1: Soft robot arm with sensor and actuator setup. The cross-section shows the distribution of the three cables (C1, C2, C3) in one of the modules.
• Figure 2: Control architecture combining the model-based baseline control architecture (STSMC and inversion estimator) together with the proposed Learning Predictor to realize a Smith Predictor control architecture.
• Figure 3: Learning Predictor, showing the dependency on the variables $x(t), \dot{\hat{x}}(t)$ and either $m(t)$ for LDN or $u_{hist}(t)$ for raw history, and the Training and Inference phases.
• Figure 4: Comparison of XY tracking error (RMS) between baseline controller (red) and LDN-3 learning method (blue) across the gain conditions. Top plots show the trajectories in the x-y plane, with the spiral buildup faded-out; bottom plots show the x and y tracking errors that correspond to the top plots, with transient phase (first 22.3s) and stable phase (last 37.7s)
• Figure 5: Comparison of XY prediction error magnitude across gain settings and methods, averaged from all 20 experiments. Error shown for LDN-3 (blue), Hist-3 (green), Hist-7 (red) methods and the No-Pred case (black). Entire revolutions are indicated as Rev. "R", with "R" = {0,1,2,3}. Vertical axis shows a combination of a linear scale (0-5 mm) and log scale (5-15 mm)