Physics-Embedded Neural ODEs for Learning Antagonistic Pneumatic Artificial Muscle Dynamics

TL;DR

This paper introduces a physics-embedded neural ODE framework for modeling and controlling antagonistic pneumatic artificial muscles, achieving accurate predictions and reliable stiffness control in soft robotics applications.

Contribution

It presents a hybrid neural ODE model that integrates physical structure with learned dynamics for PAMs, enabling improved prediction and control of complex muscle behavior.

Findings

Achieved mean R² of 0.88 in predicting joint and pressure dynamics.

Demonstrated reliable stiffness control across a range of forces.

Outperformed static models in velocity-dependent impedance behavior.

Abstract

Pneumatic artificial muscles (PAMs) enable compliant actuation for soft wearable, assistive, and interactive robots. When arranged antagonistically, PAMs can provide variable impedance through co-contraction but exhibit coupled, nonlinear, and hysteretic dynamics that challenge modeling and control. This paper presents a hybrid neural ordinary differential equation (Neural ODE) framework that embeds physical structure into a learned model of antagonistic PAM dynamics. The formulation combines parametric joint mechanics and pneumatic state dynamics with a neural network force component that captures antagonistic coupling and rate-dependent hysteresis. The forward model predicts joint motion and chamber pressures with a mean R$^2$ of 0.88 across 225 co-contraction conditions. An inverse formulation, derived from the learned dynamics, computes pressure commands offline for desired motion and stiffness profiles, tracked in closed loop during execution. Experimental validation demonstrates reliable stiffness control across 126-176 N/mm and consistent impedance behavior across operating velocities, in contrast to a static model, which shows degraded stiffness consistency at higher velocities.