Invariant Filtering for Full-State Estimation of Ground Robots in Noninertial Environments

This article presents an invariant extended Kalman filter (InEKF) approach for estimating the relative pose and linear velocity of ground robots—either legged or wheeled—using an inertial measurement unit (IMU) attached to the robot, encoders, and an external IMU placed on the moving ground. The approach explicitly accounts for ground motion in noninertial environments, such as ships or airplanes, where the ground rotates or accelerates in the inertial frame. Unlike previous methods, it does not rely on known ground pose. This consideration introduces complexity due to the nonlinear dynamics and kinematics of the reference frame. Despite this complexity, the proposed filter, based on the InEKF methodology, includes a process model that partially satisfies the group affine condition. The leg odometry-based measurement model meets the right-invariant observation form for deterministic scenarios, though the wheel odometry model does not. Observability analysis demonstrates that all state variables are observable during a broad range of ground motions, overcoming the partial observability limitations of previous filters. Experiments on a Digit humanoid robot and a Jackal wheeled robot verify the filter’s effectiveness across various ground motions.