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

2025-08-18

AI Summary

Soft continuum robots (SCRs) face dual challenges in dynamic control: high computational overhead and limited model adaptability. This paper proposes a domain-decoupled physics-informed neural network (DD-PINN), integrating Cosserat rod theory with variable bending stiffness characterization to construct a lightweight, high-fidelity dynamic surrogate model. Furthermore, we design a state estimation–control co-design framework that tightly couples DD-PINN with the unscented Kalman filter (UKF), enabling online system identification using only end-effector position feedback and supporting high-speed nonlinear model predictive control (NMPC). Implemented on GPU, the framework achieves real-time operation at 70 Hz. Simulation results show end-effector positioning error below 3 mm (2.3% of total length); experiments attain peak acceleration of 3.55 m/s². The approach significantly improves both control accuracy and dynamic response performance.

Technology Category

• Intelligent Robots: State Estimation
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

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 capture 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.

Problem

• Dynamic control of soft continuum robots is computationally demanding
• Existing data-driven methods lack adaptability and full shape capture
• Real-time nonlinear MPC for SCRs needs accurate, fast surrogate models

Innovation

• Adaptive MPC with physics-informed neural network
• Domain-decoupled PINN for real-time Cosserat rod model
• Unscented Kalman filter for state and compliance estimation