Physics-informed Neural Network Predictive Control for Quadruped Locomotion

TL;DR

This work addresses precise quadruped locomotion under unknown payloads by introducing OPI-PINNPC, a framework that unifies online payload identification, physics-informed neural networks, and nonlinear model predictive control. Payload estimates feed the PINN physics-informed loss, producing an accurate, real-time surrogate for the robot dynamics that replaces traditional numerical integration in NMPC. Hardware experiments on the Kirin quadruped (payloads 25–100 kg) show about 35% improvement in position and orientation tracking accuracy and faster convergence compared with a baseline adaptive controller, demonstrating robust performance across payload variations. The approach offers a scalable, computation-efficient method to maintain locomotion performance under changing load conditions.

Abstract

This study introduces a unified control framework that addresses the challenge of precise quadruped locomotion with unknown payloads, named as online payload identification-based physics-informed neural network predictive control (OPI-PINNPC). By integrating online payload identification with physics-informed neural networks (PINNs), our approach embeds identified mass parameters directly into the neural network's loss function, ensuring physical consistency while adapting to changing load conditions. The physics-constrained neural representation serves as an efficient surrogate model within our nonlinear model predictive controller, enabling real-time optimization despite the complex dynamics of legged locomotion. Experimental validation on our quadruped robot platform demonstrates 35% improvement in position and orientation tracking accuracy across diverse payload conditions (25-100 kg), with substantially faster convergence compared to previous adaptive control methods. Our framework provides a adaptive solution for maintaining locomotion performance under variable payload conditions without sacrificing computational efficiency.

Figures (5)

• Figure 1: The overall framework of OPI-PINNPC. (i) Training phase (switch $\bar{S}$ closed): OPI module estimates the unknown payload parameters via the input data. The identified parameters subsequently construct the physics-informed loss, which is combined with the data loss computed by labeled data to optimize the network weights through backpropagation. (ii) Prediction phase (switch $S$ closed): OPI synthesizes payload parameters using real-time robot states, followed by the PINNs state prediction fulfilling NMPC integration requirements, ultimately generating composite control inputs consisting of the optimal control via NMPC optimization and the feedback control.
• Figure 2: (a) shows the initial and terminal status of Kirin for payload identification. (b) represents the experiment scenario showing payloads of varying masses from 25 kg to 100 kg deployed on Kirin. (c) demonstrates the trotting test with 50kg payload.
• Figure 3: Position and orientation tracking error curves of trotting test under 50kg payload with OPI-PINNPC and ACQL. (a) demonstrates the position tracking errors along the x-, y-, and z-axes, respectively. (b) shows the orientation tracking errors in yaw, pitch, and roll angles, respectively.
• Figure 4: Position and orientation tracking error norm curves of trotting test under 50kg payload with OPI-PINNPC and ACQL. (a) presents the comparison position tracking error norm curves. (b) shows the comparison orientation tracking error norm curves.
• Figure 5: RMSE of position and orientation with OPI-PINNPC and ACQL across payload mass variations (25-100 kg). (a) demonstrates the comparison RMSE of position. (b) presents the comparison RMSE of orientation.