PRIME: Physically-consistent Robotic Inertial and Motion Estimation for Legged and Humanoid Robots

2026-05-17

AI Summary

This work addresses the limitation of existing robot motion estimation methods, which typically recover only kinematic states and fail to satisfy rigid-body dynamics constraints—particularly in complex contact scenarios where accurate estimation of contact forces, contact timing, and inertial parameters remains challenging. To overcome this, the authors propose PRIME, a framework based on maximum a posteriori (MAP) estimation that fuses proprioceptive measurements and actuator commands. By incorporating differentiable contact dynamics, smooth complementarity constraints, and the Anitescu friction model, PRIME jointly optimizes dynamically consistent trajectories, contact forces, and physically plausible inertial parameters. This approach is the first to enable onboard-sensor-only simultaneous reconstruction of these quantities, demonstrating improved trajectory consistency and accurate inertial parameter identification on both quadrupedal and Unitree G1 humanoid robots, thereby providing high-quality labeled data for state estimation, feedback control, and foundational robot models.

Abstract

Humanoid and legged robots interact with the environment through intermittent contacts, making accurate motion estimation fundamentally dependent on reasoning about contact dynamics. However, standard sensing pipelines-whether based on onboard proprioception with Extended Kalman Filters (EKFs) or external motion capture systems-recover only kinematics, while contact forces, contact timing, and inertial parameters remain unobserved. As a result, purely kinematic reconstructions often violate rigid-body dynamics, particularly during contact-rich motions. To enable accurate motion estimation from onboard kinematics in real-world deployment, we propose PRIME (Physically-consistent Robotic Inertial and Motion Estimation), a Maximum A Posteriori (MAP) formulation that refines measured kinematics and actuator commands into a dynamically consistent trajectory while jointly estimating frictional contact forces and physically consistent inertial parameters. Our approach incorporates differentiable contact dynamics with smoothed complementarity constraints and an Anitescu-style friction model, yielding a smooth optimization problem that remains tractable across versatile contact transitions. We evaluate PRIME on contact-rich locomotion with quadrupedal robots and the Unitree G1 humanoid, demonstrating improved trajectory consistency and accurate inertial parameter identification. Beyond improving state estimation and feedback control with calibrated inertial parameters, PRIME produces force- and contact-annotated motion reconstructions from real robots in deployment, which can be used to provide high-quality data for downstream learning applications, including large-scale behavior modeling and robot foundation models.

Problem

• motion estimation
• contact dynamics
• inertial parameters
• legged robots
• humanoid robots

Innovation

• physically-consistent estimation
• contact dynamics
• inertial parameter identification
• differentiable optimization
• legged robotics