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Legged Robot State Estimation within Non-inertial Environments

Zijian He, Sangli Teng, Tzu-Yuan Lin, Maani Ghaffari, Yan Gu

TL;DR

Hardware experiments on a humanoid robot moving on a rotating and translating treadmill demonstrate the high convergence rate and accuracy of the proposed InEKF even under significant treadmill pitch sway, as well as large estimation errors.

Abstract

This paper investigates the robot state estimation problem within a non-inertial environment. The proposed state estimation approach relaxes the common assumption of static ground in the system modeling. The process and measurement models explicitly treat the movement of the non-inertial environments without requiring knowledge of its motion in the inertial frame or relying on GPS or sensing environmental landmarks. Further, the proposed state estimator is formulated as an invariant extended Kalman filter (InEKF) with the deterministic part of its process model obeying the group-affine property, leading to log-linear error dynamics. The observability analysis of the filter confirms that the robot's pose (i.e., position and orientation) and velocity relative to the non-inertial environment are observable. Hardware experiments on a humanoid robot moving on a rotating and translating treadmill demonstrate the high convergence rate and accuracy of the proposed InEKF even under significant treadmill pitch sway, as well as large estimation errors.

Legged Robot State Estimation within Non-inertial Environments

TL;DR

Hardware experiments on a humanoid robot moving on a rotating and translating treadmill demonstrate the high convergence rate and accuracy of the proposed InEKF even under significant treadmill pitch sway, as well as large estimation errors.

Abstract

This paper investigates the robot state estimation problem within a non-inertial environment. The proposed state estimation approach relaxes the common assumption of static ground in the system modeling. The process and measurement models explicitly treat the movement of the non-inertial environments without requiring knowledge of its motion in the inertial frame or relying on GPS or sensing environmental landmarks. Further, the proposed state estimator is formulated as an invariant extended Kalman filter (InEKF) with the deterministic part of its process model obeying the group-affine property, leading to log-linear error dynamics. The observability analysis of the filter confirms that the robot's pose (i.e., position and orientation) and velocity relative to the non-inertial environment are observable. Hardware experiments on a humanoid robot moving on a rotating and translating treadmill demonstrate the high convergence rate and accuracy of the proposed InEKF even under significant treadmill pitch sway, as well as large estimation errors.
Paper Structure (25 sections, 43 equations, 6 figures, 2 tables)

This paper contains 25 sections, 43 equations, 6 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Contributions
  3. Mathematical Preliminaries and Notations
  4. Problem Formulation
  5. Sensor Measurements
  6. IMU Motion Dynamics
  7. Leg Odometry
  8. Process and Measurement Models
  9. Process Model
  10. Process Model Discretization
  11. Measurement Model
  12. Filter Design
  13. Propagation Step
  14. Error Dynamics of Process Model
  15. State and Covariance Propagation
  16. ...and 10 more sections

Figures (6)

  • Figure 1: Illustration of the reference frames used in the filter derivation.
  • Figure 2: Experimental setup that includes a Digit robot, motion capture cameras, a pitch sway treadmill, and an IMU mounted on the dynamic ground.
  • Figure 3: Estimation results of the SRS filter during the transient period.
  • Figure 4: Estimation results of the proposed filter during the transient period.
  • Figure 5: Estimation results of the SRS filter near the steady state.
  • ...and 1 more figures