Domain-decoupled Physics-informed Neural Networks with Closed-form Gradients for Fast Model Learning of Dynamical Systems

Physics-informed neural networks (PINNs) are trained using physical equations and can also incorporate unmodeled effects by learning from data. PINNs for control (PINCs) of dynamical systems are gaining interest due to their prediction speed compared to classical numerical integration methods for nonlinear state-space models, making them suitable for real-time control applications. We introduce the domain-decoupled physics-informed neural network (DD-PINN) to address current limitations of PINC in handling large and complex nonlinear dynamic systems. The time domain is decoupled from the feed-forward neural network to construct an Ansatz function, allowing for calculation of gradients in closed form. This approach significantly reduces training times, especially for large dynamical systems, compared to PINC, which relies on graph-based automatic differentiation. Additionally, the DD-PINN inherently fulfills the initial condition and supports higher-order excitation inputs, simplifying the training process and enabling improved prediction accuracy. Validation on three systems - a nonlinear mass-spring-damper, a five-mass-chain, and a two-link robot - demonstrates that the DD-PINN achieves significantly shorter training times. In cases where the PINC's prediction diverges, the DD-PINN's prediction remains stable and accurate due to higher physics loss reduction or use of a higher-order excitation input. The DD-PINN allows for fast and accurate learning of large dynamical systems previously out of reach for the PINC.

Enhanced Model-Free Dynamic State Estimation for a Soft Robot Finger Using an Embedded Optical Waveguide Sensor

In this letter, an advanced stretchable optical waveguide sensor is implemented into a multidirectional PneuNet soft actuator to enhance dynamic state estimation through a NARX neural network. The stretchable waveguide featuring a semidivided core design from previous work is sensitive to multiple strain modes. It is integrated into a soft finger actuator with two pressure chambers that replicates human finger motions. The soft finger, designed for applications in soft robotic grippers or hands, is viewed in isolation under pneumatic actuation controlled by motorized linear stages. The research first characterizes the soft finger's workspace and sensor response. Subsequently, three dynamic state estimators are developed using NARX architecture, differing in the degree of incorporating the optical waveguide sensor response. Evaluation on a testing path reveals that the full sensor response significantly improves end effector position estimation, reducing mean error by 51\% from 5.70 mm to 2.80 mm, compared to only 21\% improvement to 4.53 mm using the estimator representing a single core waveguide design. The letter concludes by discussing the application of these estimators for (open-loop) model-predictive control and recommends future focus on advanced, structured soft (optical) sensors for model-free state estimation and control of soft robots.