STRIDE: Structured Lagrangian and Stochastic Residual Dynamics via Flow Matching

TL;DR

STRIDE is proposed, a dynamics learning framework that explicitly separates conservative rigid-body mechanics from uncertain, effectively stochastic non-conservative interaction effects, and is evaluated on systems of increasing complexity, including a pendulum, the Unitree Go1 quadruped, and the Unitree G1 humanoid.

Abstract

Robotic systems operating in unstructured environments must operate under significant uncertainty arising from intermittent contacts, frictional variability, and unmodeled compliance. While recent model-free approaches have demonstrated impressive performance, many deployment settings still require predictive models that support planning, constraint handling, and online adaptation. Analytical rigid-body models provide strong physical structure but often fail to capture complex interaction effects, whereas purely data-driven models may violate physical consistency, exhibit data bias, and accumulate long-horizon drift. In this work, we propose STRIDE, a dynamics learning framework that explicitly separates conservative rigid-body mechanics from uncertain, effectively stochastic non-conservative interaction effects. The structured component is modeled using a Lagrangian Neural Network (LNN) to preserve energy-consistent inertial dynamics, while residual interaction forces are represented using Conditional Flow Matching (CFM) to capture multi-modal interaction phenomena. The two components are trained jointly end-to-end, enabling the model to retain physical structure while representing complex stochastic behavior. We evaluate STRIDE on systems of increasing complexity, including a pendulum, the Unitree Go1 quadruped, and the Unitree G1 humanoid. Results show 20% reduction in long-horizon prediction error and 30% reduction in contact force prediction error compared to deterministic residual baselines, supporting more reliable model-based control in uncertain robotic environments.

Figures (7)

• Figure 1: Conceptual overview of STRIDE. The proposed framework combines a structured Lagrangian prior with a stochastic residual to capture interaction uncertainty while preserving physical consistency.
• Figure 2: Long-horizon rollout error on complex legged systems (Unitree Go1 and Unitree G1). The ONN baseline exhibits rapid, near-exponential error growth, while the DeLaN reduces error growth to approximately linear. STRIDE further reduces long-horizon drift by capturing stochastic, contact-induced variability.
• Figure 3: Contact force prediction on the Unitree G1 humanoid during walking. Predicted vertical ground reaction forces are compared against ground truth for left and right legs. STRIDE closely tracks the timing and magnitude of stance–swing transitions, preserving sharp impact discontinuities and reducing force smoothing observed in deterministic baselines (DeLaN and LNN+Diff).
• Figure 4: Contact force prediction on the Unitree Go1 quadruped across multiple gaits (trot, pronk, bound, and pace). Vertical ground reaction forces are shown for all four legs (FL, FR, RL, RR).
• Figure 5: Inference-time comparison between diffusion sampling and CFM. Dotted curves show rollout error versus NFEs, and solid curves show inference frequency. CFM attains DeLaN-level rollout error with fewer evaluations while sustaining higher sampling frequency, highlighting its suitability for real-time deployment.