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

Venue: RSS 2026 (Sydney, Jul 13–17) · Session: Humanoids · paper #29 Authors: Jiarong Kang, Kunzhao Ren, Tao Pang, Xiaobin Xiong arXiv: 2605.17681 · program page

Summary compiled from the arXiv paper (v1); all numbers quoted from the paper. Trend context: RSS 2026 survey.

Pipeline from real-world Unitree G1 motion (left) through kinematics data + actuator sensing, robot dynamics + contact dynamics, to a physics-consistent motion-inertia-contact reconstruction (right); sensors feed a differential-dynamics-plus-optimization backend that annotates the trajectory with contact forces (yellow markers).

Problem

Standard estimation pipelines for legged/humanoid robots — EKF-based proprioceptive estimators or external motion capture — recover only kinematics; contact forces, contact timing, and inertial parameters stay unobserved, so reconstructed motions often violate rigid-body dynamics during contact-rich phases. That undermines planning/control and pollutes data intended for imitation learning, VLA, and robot foundation models.

Method

PRIME casts joint motion and parameter estimation as a Maximum A Posteriori / full-information estimation problem: it refines measured kinematics (IMU, joint sensors, mocap) and actuator commands into a dynamically consistent trajectory while jointly estimating frictional contact forces and inertial parameters. Contact is modeled with differentiable dynamics using smoothed complementarity constraints (log-barrier relaxation) and an Anitescu-style convex friction cone; inertial parameters use a physically consistent Cholesky parameterization (10 numbers per link). The resulting parameter-FIE problem is solved with a multiple-shooting, feasibility-driven DDP variant over 10-20 s horizons.

Results

On a Unitree Go2 with a 4.6 kg belly payload, PRIME recovers roughly +4.8 kg added mass and the downward torso-COM shift; in MuJoCo trials it identifies a +3 kg payload and a -0.1 m COM shift against ground truth (Table I). On the Unitree G1 (walking, running, dancing), it estimates approximately +3.4 kg of the unmodeled mass (measured 38.029 kg vs nominal 35.115 kg, difference 2.914 kg; barbell plates 2×2.3 kg) and improves force-plate-verified contact-force reconstruction (RMSE_F around 24.5 N with the refined inertial model, Table III), with smaller residuals than the unrefined model.

Significance

Positions physically consistent state/force/inertia reconstruction as a data engine: force- and contact-annotated real-robot trajectories are exactly what large-scale behavior modeling and robot foundation models lack — connective tissue to Review-Humanoid-VLA and low-level System-0 layers in Review-System-0-1-2.

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