Physics-Informed Residual Neural Dynamics for Data-Efficient Predictive Control in Legged Robots

Abstract

Model predictive control of floating-base legged systems requires dynamic formulations that balance real-time computational tractability with the capacity to capture unmodeled electro-mechanical and contact phenomena. While black-box neural dynamics can approximate nonlinear discrepancies, they de- mand extensive uniform state coverage, accumulate compounding drift over multi-step integration horizons, and frequently violate fundamental contact invariants. This paper presents Physics- Informed Neural Dynamics (PIND), a continuous-time residual framework tailored for data-efficient learning and predictive control of legged locomotion. PIND augments an analytical multi- body rigid-body model with two structured neural modules: an internal drivetrain residual strictly projected onto the actuated joint manifold, and a continuous contact compliance model. The network is trained using a composite physics-informed loss that regularizes generalized momentum balances, friction cone geometric admissibility, and unilateral contact complementarity. We prove an analytical trajectory error bound demonstrating that state forecasting error is explicitly bounded by the dynamic momentum residual scaled by the minimum eigenvalue of the generalized mass matrix. The learned continuous vector field is embedded into an interior-point Sequential Quadratic Programming (SQP) Nonlinear Model Predictive Control (NMPC) loop. Evaluated on the Unitree Go1 quadruped in MuJoCo subject to measurement noise, low training budgets (1%–100%), and parametric shifts in payload (+48%) and terrain friction (μ = 0.2), PIND achieves stable multi-step forecasting with 10% of the data required by black-box neural baselines and preserves dynamic feasibility for real-time 50 Hz execution.