Generalizable and Fast Surrogates: Model Predictive Control of Articulated Soft Robots using Physics-Informed Neural Networks

TL;DR

This work tackles the challenge of achieving fast, accurate, and generalizable forward models for articulated soft robots to enable real-time model predictive control. It introduces domain-aware physics-informed neural networks (PINNs), specifically PINC and the domain-decoupled DD-PINN, to fuse first-principles dynamics with data-driven learning. By incorporating a domain input that captures changes such as payload and base orientation, the DD-PINN demonstrates strong generalization to unseen dynamics while delivering prediction speeds orders of magnitude faster than stiff FP integration, enabling nonlinear MPC at frequencies up to ~${47}$ Hz. The approach is validated on a 5-DoF pneumatic ASR, showing substantial speed gains (up to ~${467}$x) with minimal accuracy loss and successful NMPC-based position tracking across multiple dynamic scenarios, highlighting practical potential for robust, real-time soft-robot control with limited training data. The work also contributes open-source PINN implementations and datasets to support reproducibility and extension to broader soft-robotic systems.

Abstract

Soft robots can revolutionize several applications with high demands on dexterity and safety. When operating these systems, real-time estimation and control require fast and accurate models. However, prediction with first-principles (FP) models is slow, and learned black-box models have poor generalizability. Physics-informed machine learning offers excellent advantages here, but it is currently limited to simple, often simulated systems without considering changes after training. We propose physics-informed neural networks (PINNs) for articulated soft robots (ASRs) with a focus on data efficiency. The amount of expensive real-world training data is reduced to a minimum -- one dataset in one system domain. Two hours of data in different domains are used for a comparison against two gold-standard approaches: In contrast to a recurrent neural network, the PINN provides a high generalizability. The prediction speed of an accurate FP model is exceeded with the PINN by up to a factor of 467 at slightly reduced accuracy. This enables nonlinear model predictive control (MPC) of a pneumatic ASR. Accurate position tracking with the MPC running at 47 Hz is achieved in six dynamic experiments.

Figures (15)

• Figure 1: (a) The objective of this work is to solve the trade-off between model accuracy/generalizability and prediction speed in the field of soft robotics by using physics-informed machine learning (ML). (b) During training, data from one training domain is available. Trained surrogate models extrapolate for changed system dynamics in unseen test domains. We consider changing the payload and the orientation of the robot base as possible modifications during operation.
• Figure 2: Graphical overview of the article's main part (Sec. \ref{['main_pinn']}).
• Figure 3: (a) Kinematic chain of the articulated soft robot with $n{=}5$ rotational actuators of height $h{=}53.4mm$ and coordinate frames ${\mathscr{F}}_{i}$. In this work, dynamics are changed by attaching a variable mass $m_\mathrm{e}$ to the last segment with mass $m_5$ and by changing the base orientation $\beta_\mathrm{g}$ against gravity. (b) Real robot with joint angles $q_i$ and antagonistic actuation via pneumatic pressures $p_{i1}$ and $p_{i2}$.
• Figure 4: Validation of the actuation model: (a) Experimental setup with torque sensor attached to the first actuator. (b) The mapping from pressures to torque with factor $A_\mathrm{p}r_\mathrm{p}$ applies for the entire pressure range.
• Figure 5: PINN structures with inputs in orange, feedforward network in blue with output in green. Both networks are extended by an additional domain input $\boldsymbol{\delta}$: (a) The PINC directly predicts the state $\hat{\boldsymbol{x}}$. During training, the network requires computationally expensive automatic differentiation for each collocation point (in each training epoch) and contains an additional loss term $\mathcal{L}_\mathrm{0}$ for the initial condition. (b) The DD-PINN predicts the ansatz vector $\boldsymbol{\alpha}$ of an ansatz function $\boldsymbol{a}(\boldsymbol{\alpha},t)$. The latter can be differentiated in closed form. Also, $\boldsymbol{a}(\boldsymbol{\alpha},0){\equiv}\boldsymbol{0}$ applies so that no initial-condition loss is necessary. Both drastically speed up the training time.