Four Simple Proprioceptive Estimators for Legged Robots

2026-05-21

AI Summary

This work addresses the significant drift in inertial navigation systems of legged robots caused by noise in consumer-grade IMUs. To mitigate this issue, the paper proposes four progressively advanced proprioceptive state estimation algorithms that leverage intermittent foot contact information to correct IMU drift and jointly estimate robot pose, velocity, and time-varying IMU biases. Building upon a contact-aided invariant extended Kalman filter, the methods incrementally incorporate factor graph optimization and fixed-lag smoothing to substantially enhance estimation accuracy and robustness. All algorithms are implemented using GTSAM and fully integrated with ROS 2, with complete source code publicly released. This open-source framework effectively alleviates IMU drift and promotes reproducible research in proprioceptive odometry for legged locomotion.

Abstract

Legged robots carry an IMU, but the inertial solution drifts because consumer-grade IMUs are noisy. However, the feet create intermittent contacts with the environment that can be used to mitigate that drift. This report develops a sequence of increasingly expressive legged robot state estimators that leverage this. In all cases, the floating-base state comprises attitude, position, velocity, and IMU biases. To model foot contacts, we start from the contact-aided invariant EKF of Hartley et al., albeit at a reduced contact update rate. This is then augmented by replacing the measurement update by a small factor graph. Finally, we turn the same factors into a fixed-lag smoother with contact-episode footholds, with and without an evolving IMU bias. To facilitate reproducibility and further research in proprioceptive legged odometry, all four variants are available in GTSAM (Dellaert et. al), and we additionally provide a ROS2-compatible implementation.

Problem

• proprioceptive estimation
• legged robots
• IMU drift
• state estimation
• inertial navigation

Innovation

• proprioceptive odometry
• contact-aided estimation
• factor graph
• fixed-lag smoother
• legged robot state estimation