Proprioceptive Invariant State Estimation for Humanoid Robots on Non-Inertial Ground

2026-06-17

AI Summary

This work proposes a proprioception-based real-time state estimation method for humanoid robots operating without external sensors or prior knowledge of ground motion. By fusing foot-mounted IMU measurements with kinematic constraints, the authors formulate a right-invariant extended Kalman filter (InEKF) and, for the first time, introduce a right-invariant observation model to non-inertial ground scenarios, thereby ensuring system observability and enabling rapid convergence. Experimental validation on the Digit robot demonstrates a 96% improvement in convergence speed and an 80% reduction in position estimation error compared to existing approaches. Notably, even when walking on a rotating surface with an initial position error as large as one meter, the method maintains an average position estimation error below 9 centimeters.

Abstract

This paper presents an invariant extended Kalman filtering (InEKF) approach for real-time state estimation of humanoid robots operating on non-inertial ground using only onboard proprioceptive sensing. The proposed approach estimates the robot's base position and velocity relative to the moving ground frame without requiring direct measurements of ground motion or externally mounted sensors. By exploiting kinematic constraints at the stance foot through foot-mounted IMUs, the filter accounts for ground-induced nonlinearities in the process and measurement models while remaining fully proprioceptive. The estimator is formulated to admit a right-invariant measurement model, enabling favorable error dynamics under large initial uncertainties. Observability analysis establishes conditions under which the robot's relative base position and velocity are observable with respect to the non-inertial ground frame. Experiments with the Digit humanoid robot standing and squatting atop a swaying and pitching ground showcase a 96% speedup in convergence rate and an 80% reduction in position estimate errors over existing InEKFs. Walking experiments on a uni-axially rotating ground achieve an average estimation error of less than 9 cm for an initial error of up to 1 m.

Problem

• proprioceptive sensing
• state estimation
• humanoid robots
• non-inertial ground
• invariant filtering

Innovation

• Invariant Extended Kalman Filter
• Proprioceptive Sensing
• Non-Inertial Ground
• Humanoid Robot State Estimation
• Right-Invariant Observer