STRIDE: Structured Lagrangian and Stochastic Residual Dynamics via Flow Matching

Accurate dynamics models are essential for model-based robotic control, yet nominal Euler--Lagrange models often become inaccurate in the presence of payload variation, unmodeled coupling, friction, aerodynamic effects, and changing operating conditions. Most learning-based correction methods improve prediction accuracy by introducing a single additive residual, but do not preserve the internal mechanical structure of Euler--Lagrange systems. This leads to models that do not preserve symmetry, positive-definiteness, or the coupling between inertia and velocity-dependent terms, which can result in physically inconsistent predictions and reduced reliability when embedded in model-based controllers. We propose a structure-preserving residual learning framework that decomposes model mismatch into an inertia correction, the corresponding induced Coriolis term, and a generalized-force residual. The mechanical component is learned under physical constraints, while the disturbance-sensitive component is represented through a sparse history-dependent latent interaction model and adapted online using Bayesian linear regression. This separation preserves key mechanical structure while restricting adaptation to the part of the dynamics most affected by changing conditions. Experiments across multiple robotic platforms, including mobile, aerial, and manipulator systems, show that the proposed method improves dynamics prediction and trajectory tracking under coupled and time-varying dynamics. These results highlight the value of combining structured residual modeling, compact latent interaction selection, and selective online adaptation for real-world model-based control.

Compared with analytical physics, learned dynamics models promise robot simulation that is faster, inherently differentiable, and easily adaptable to real data. Neural Robot Dynamics (NeRD) pursues this by keeping collision detection analytical and replacing a simulator's numerical dynamics for the robot with a learned model. Three limitations remain. NeRD offers little speedup over the simulator it learned from, accepts contact only at predefined points, and has no two-way coupling with objects it manipulates. FlashNeRD removes all three with a parallel streaming architecture that makes each prediction faster and more accurate, an encoder that accepts contacts wherever they occur, and two-way coupling with objects simulated by analytical solvers. Experiments across five robots show faster and more accurate dynamics, faster policy learning, and faster inference-time planning. Across three robots, FlashNeRD's dynamics model is up to $55\times$ faster than an optimized NeRD and more accurate over long rollouts. This speedup extends to policy learning, where PPO trains an ANYmal locomotion policy in 34 seconds, $3.8\times$ faster than the analytical simulator and $2.7\times$ faster than an optimized NeRD. With DIAL-MPC, a sampling-based MPC method, the robot climbs all six test platforms where fixed-contact NeRD manages one, at approximately half the analytical simulator's planning time. Cube-reorientation policies trained with FlashNeRD complete within 2% of the simulator-trained policy's target count.

State of the art quadrupedal locomotion approaches integrate Model Predictive Control (MPC) with Reinforcement Learning (RL), enabling complex motion capabilities with planning and terrain adaptive behaviors. However, they often face compounding errors over long horizons and have limited interpretability due to the absence of physical inductive biases. We address these issues by integrating Lagrangian Neural Networks (LNNs) into an RL MPC framework, enabling physically consistent dynamics learning. At deployment, our inverse dynamics infinite horizon MPC scheme avoids costly matrix inversions, improving computational efficiency by up to 4x with minimal loss of task performance. We validate our framework through multiple ablations of the proposed LNN and its variants. We show improved sample efficiency, reduced long-horizon error, and faster real time planning compared to unstructured neural dynamics. Lastly, we also test our framework on the Unitree Go1 robot to show real world viability.