[Paper Review] Learning-based Position and Stiffness Feedforward Control of Antagonistic Soft Pneumatic Actuators using Gaussian Processes

Tim-Lukas Habich, Sarah Kleinjohann+1 more|arXiv (Cornell University)|Mar 3, 2023

Prosthetics and Rehabilitation Robotics32 references1 citations

TL;DR

This paper presents a data-driven, learning-based feedforward control approach for antagonistic soft pneumatic actuators using Gaussian processes to simultaneously control joint position and stiffness without requiring a priori system models. By training on measured input-output data from a custom test bench, the method achieves average feedforward errors of 11.5% of the pressure range, enabling accurate and continuous adjustment of both position and stiffness across diverse configurations, validated experimentally on a modular soft robot prototype.

ABSTRACT

Variable stiffness actuator (VSA) designs are manifold. Conventional model-based control of these nonlinear systems is associated with high effort and design-dependent assumptions. In contrast, machine learning offers a promising alternative as models are trained on real measured data and nonlinearities are inherently taken into account. Our work presents a universal, learning-based approach for position and stiffness control of soft actuators. After introducing a soft pneumatic VSA, the model is learned with input-output data. For this purpose, a test bench was set up which enables automated measurement of the variable joint stiffness. During control, Gaussian processes are used to predict pressures for achieving desired position and stiffness. The feedforward error is on average 11.5% of the total pressure range and is compensated by feedback control. Experiments with the soft actuator show that the learning-based approach allows continuous adjustment of position and stiffness without model knowledge.© 2023 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

Motivation & Objective

• To develop a universal, model-free control approach for variable stiffness actuators (VSAs) in soft robotics.
• To enable continuous, simultaneous control of joint position and stiffness in antagonistic soft pneumatic actuators.
• To overcome the challenges of modeling complex nonlinearities in soft pneumatic systems using analytical methods.
• To validate the feasibility of a data-driven approach using real measured data from a custom test bench.
• To demonstrate the method's applicability across different actuator designs without design-specific assumptions.

Proposed method

• A modular soft pneumatic VSA with two antagonistic bellows was fabricated for experimental validation.
• An automated test bench was developed to collect input-output data for joint angle and stiffness under varying pressure inputs.
• Gaussian processes (GPs) were trained on measured data to learn the inverse mapping from desired position and stiffness to required pressure inputs.
• The GP model predicts feedforward pressure differences (ΔpFF) and average pressures (p̄FF) to achieve target joint angle and stiffness.
• Feedback control with tuned gains (KP = 0.025 bar/deg, KI = 0.05 bar·s/deg) compensates for GP prediction errors.
• Joint stiffness was measured using a motor-induced disturbance method during operation, enabling real-time feedback.

Experimental results

Research questions

• RQ1 Can a learning-based, model-free approach achieve simultaneous and continuous control of position and stiffness in soft pneumatic VSAs?
• RQ2 How accurately can Gaussian processes predict the required pressure inputs for desired joint states without prior system modeling?
• RQ3 To what extent does feedback control mitigate the inherent error in GP-based feedforward control?
• RQ4 Can the proposed method be applied universally across different VSA designs without design-specific assumptions?
• RQ5 How does feedback control affect the measured joint stiffness during operation, and can stiffness be accurately tracked?

Key findings

• The Gaussian process model achieved an average feedforward error of 11.5% of the total pressure range (0–0.4 bar), corresponding to a mean absolute error of 0.046 bar.
• Position tracking achieved a mean absolute error of 0.34°, which matches the encoder resolution of 0.35°, indicating high accuracy.
• The method successfully enabled continuous and simultaneous control of both joint angle and stiffness across seven different target angles with two stiffness levels each.
• In 10 out of 14 configurations, the desired stiffness was achieved with high accuracy, with only minor deviations observed at qd = −2° due to viscoelastic material effects.
• Feedback control effectively compensated for GP prediction errors, maintaining stable tracking without significantly degrading stiffness performance.
• The approach is design-agnostic and applicable to various VSA configurations, demonstrating broad potential for modular soft robotic systems.