Adaptive Model-Predictive Control of a Soft Continuum Robot Using a Physics-Informed Neural Network Based on Cosserat Rod Theory

TL;DR

This paper presents a real-time nonlinear model-predictive control framework for soft continuum robots using a physics-informed neural network based on Cosserat rod theory, enabling fast, accurate control and shape estimation.

Contribution

It introduces a domain-decoupled physics-informed neural network as a surrogate model for dynamic control of SCRs, achieving high speed and adaptability.

Findings

Speed-up factor of 44000 for the neural network surrogate

End-effector position errors below 3 mm in simulation

Achieves accelerations up to 3.55 m/s² in real experiments

Abstract

Dynamic control of soft continuum robots (SCRs) holds great potential for expanding their applications, but remains a challenging problem due to the high computational demands of accurate dynamic models. While data-driven approaches like Koopman-operator-based methods have been proposed, they typically lack adaptability and cannot reconstruct the full robot shape, limiting their applicability. This work introduces a real-time-capable nonlinear model-predictive control (MPC) framework for SCRs based on a domain-decoupled physics-informed neural network (DD-PINN) with adaptable bending stiffness. The DD-PINN serves as a surrogate for the dynamic Cosserat rod model with a speed-up factor of 44000. It is also used within an unscented Kalman filter for estimating the model states and bending compliance from end-effector position measurements. We implement a nonlinear evolutionary MPC running at 70 Hz on the GPU. In simulation, it demonstrates accurate tracking of dynamic trajectories and setpoint control with end-effector position errors below 3 mm (2.3% of the actuator's length). In real-world experiments, the controller achieves similar accuracy and accelerations up to 3.55 m/s2.