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Kinematic Base State Estimation for Humanoid using Invariant Extended Kalman Filter

Amirhosein Vedadi, Aghil Yousefi-Koma, Masoud Shariat-Panahi, Mahdi Nozari

TL;DR

The results of the analysis demonstrate that the RIEKF exhibits reduced drift in localization and achieves estimation convergence in a shorter time compared to the QEKF, highlighting the effectiveness of the proposed RIEKF for accurate state estimation of the kinematic base in humanoid robotics.

Abstract

This paper presents the design and implementation of a Right Invariant Extended Kalman Filter (RIEKF) for estimating the states of the kinematic base of the Surena V humanoid robot. The state representation of the robot is defined on the Lie group $SE_4(3)$, encompassing the position, velocity, and orientation of the base, as well as the position of the left and right feet. In addition, we incorporated IMU biases as concatenated states within the filter. The prediction step of the RIEKF utilizes IMU equations, while the update step incorporates forward kinematics. To evaluate the performance of the RIEKF, we conducted experiments using the Choreonoid dynamic simulation framework and compared it against a Quaternion-based Extended Kalman Filter (QEKF). The results of the analysis demonstrate that the RIEKF exhibits reduced drift in localization and achieves estimation convergence in a shorter time compared to the QEKF. These findings highlight the effectiveness of the proposed RIEKF for accurate state estimation of the kinematic base in humanoid robotics.

Kinematic Base State Estimation for Humanoid using Invariant Extended Kalman Filter

TL;DR

The results of the analysis demonstrate that the RIEKF exhibits reduced drift in localization and achieves estimation convergence in a shorter time compared to the QEKF, highlighting the effectiveness of the proposed RIEKF for accurate state estimation of the kinematic base in humanoid robotics.

Abstract

This paper presents the design and implementation of a Right Invariant Extended Kalman Filter (RIEKF) for estimating the states of the kinematic base of the Surena V humanoid robot. The state representation of the robot is defined on the Lie group , encompassing the position, velocity, and orientation of the base, as well as the position of the left and right feet. In addition, we incorporated IMU biases as concatenated states within the filter. The prediction step of the RIEKF utilizes IMU equations, while the update step incorporates forward kinematics. To evaluate the performance of the RIEKF, we conducted experiments using the Choreonoid dynamic simulation framework and compared it against a Quaternion-based Extended Kalman Filter (QEKF). The results of the analysis demonstrate that the RIEKF exhibits reduced drift in localization and achieves estimation convergence in a shorter time compared to the QEKF. These findings highlight the effectiveness of the proposed RIEKF for accurate state estimation of the kinematic base in humanoid robotics.
Paper Structure (12 sections, 27 equations, 4 figures, 3 tables)

This paper contains 12 sections, 27 equations, 4 figures, 3 tables.

Table of Contents

  1. INTRODUCTION
  2. Material AND Methods
  3. Overview of Lie Group and Lie Algebra
  4. Invariant Extended Kalman Filter
  5. State Variables
  6. Prediction Equations
  7. Update Equations
  8. Simulations and Results
  9. System Overview
  10. Evaluation of Localization
  11. Evaluation of Convergence
  12. Conclusion

Figures (4)

  • Figure 1: Lower limb model of the Surena V robot in the Choreonoid simulator. Also, it illustrates the coordinate system for the kinematic base and feet.
  • Figure 2: Comparison of the output from both filters with the ground truth
  • Figure 3: Comparison of convergence for QEKF and RIEKF filters in the presence of noisy initial conditions of the states
  • Figure 4: Distribution of mean squared error (MSE) for different observable states