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Improved Extended Kalman Filter-Based Disturbance Observers for Exoskeletons

Shilei Li, Dawei Shi, Makoto Iwasaki, Yan Ning, Hongpeng Zhou, Ling Shi

TL;DR

This work tackles unknown disturbances in exoskeleton control and demonstrates a fundamental bias-variance trade-off in EKF-DOB when disturbance dynamics are not fully known. It introduces two novel observers, IMMEKF-DOB and MKCEKF-DOB, that adapt disturbance estimation via switching covariance and multi-kernel correntropy, respectively. Through simulations and real exoskeleton experiments, the proposed methods yield substantial improvements in hip and knee tracking under dynamic disturbances, reducing RMSE compared to EKF-DOB. The results highlight how adaptive disturbance covariance enhances robustness in human-robot interaction scenarios, with practical considerations for kernel bandwidth and model-switch design.

Abstract

The nominal performance of mechanical systems is often degraded by unknown disturbances. A two-degree-of-freedom control structure can decouple nominal performance from disturbance rejection. However, perfect disturbance rejection is unattainable when the disturbance dynamic is unknown. In this work, we reveal an inherent trade-off in disturbance estimation subject to tracking speed and tracking uncertainty. Then, we propose two novel methods to enhance disturbance estimation: an interacting multiple model extended Kalman filter-based disturbance observer and a multi-kernel correntropy extended Kalman filter-based disturbance observer. Experiments on an exoskeleton verify that the proposed two methods improve the tracking accuracy $36.3\%$ and $16.2\%$ in hip joint error, and $46.3\%$ and $24.4\%$ in knee joint error, respectively, compared to the extended Kalman filter-based disturbance observer, in a time-varying interaction force scenario, demonstrating the superiority of the proposed method.

Improved Extended Kalman Filter-Based Disturbance Observers for Exoskeletons

TL;DR

This work tackles unknown disturbances in exoskeleton control and demonstrates a fundamental bias-variance trade-off in EKF-DOB when disturbance dynamics are not fully known. It introduces two novel observers, IMMEKF-DOB and MKCEKF-DOB, that adapt disturbance estimation via switching covariance and multi-kernel correntropy, respectively. Through simulations and real exoskeleton experiments, the proposed methods yield substantial improvements in hip and knee tracking under dynamic disturbances, reducing RMSE compared to EKF-DOB. The results highlight how adaptive disturbance covariance enhances robustness in human-robot interaction scenarios, with practical considerations for kernel bandwidth and model-switch design.

Abstract

The nominal performance of mechanical systems is often degraded by unknown disturbances. A two-degree-of-freedom control structure can decouple nominal performance from disturbance rejection. However, perfect disturbance rejection is unattainable when the disturbance dynamic is unknown. In this work, we reveal an inherent trade-off in disturbance estimation subject to tracking speed and tracking uncertainty. Then, we propose two novel methods to enhance disturbance estimation: an interacting multiple model extended Kalman filter-based disturbance observer and a multi-kernel correntropy extended Kalman filter-based disturbance observer. Experiments on an exoskeleton verify that the proposed two methods improve the tracking accuracy and in hip joint error, and and in knee joint error, respectively, compared to the extended Kalman filter-based disturbance observer, in a time-varying interaction force scenario, demonstrating the superiority of the proposed method.
Paper Structure (22 sections, 1 theorem, 62 equations, 14 figures, 4 tables, 2 algorithms)

This paper contains 22 sections, 1 theorem, 62 equations, 14 figures, 4 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Problem Statement
  3. System Modeling
  4. Stability Analysis of the Augmented PD Controller
  5. Problem Statement
  6. Methodology
  7. Extended Kalman Filter-Based Disturbance Observer
  8. Interacting Multiple Model Extended Kalman Filter-Based Disturbance Observer
  9. Multi-Kernel Correntropy Extend Kalman Filter-based Disturbance Observer
  10. Simulations and Experiments
  11. Simulations
  12. Angle Tracking Experiments
  13. Dynamic Disturbance Experiments
  14. Conclusion
  15. Appendix I
  16. ...and 7 more sections

Key Result

Corollary 1

Given the bounded lumped disturbance error $\|l_e\| \leq \bar{l}_e$, the closed-loop system converges to the ellipsoidal invariant set: where the convergence radius $\kappa$ is defined as $\alpha_1$, $\alpha_2$, and $\epsilon$ are constants shown in equation expconv, and $\lambda_{\min}(\cdot)$ denotes the minimum eigenvalue of a positive definite matrix.

Figures (14)

  • Figure 1: The exoskeleton and the diagram of two-link robotic leg model. The symbol $m$ is the mass, $I$ is the inertia, $l$ is the link length, $r$ is the distance from joints to the center of mass along the direction of the link, $h$ is the distance from the center of mass to the link, and $\theta$ is the rotation angle. The subscript $1,2$ represents the corresponding values for link 1 and link 2.
  • Figure 2: The disturbance estimation and tracking errors in EKF-DOB, IMMEKF-DOB, and MKCEKF-DOB. (a) Results with $\eta=\exp(40)$. (b) Comparisons of EKF-DOB, IMMEKF-DOB, and MKCEKF-DOB
  • Figure 3: The visualization of bias-variance trade-off in EKF-DOB, IMMEKF-DOB, and MKCEKF-DOB. (a) Bias-variance effects of different algorithms in time series (95% confidence interval). (b) Bias-variance effects of EKF-DOB with different $\eta$ and corresponding results of IMMEKF-DOB and MKCEKF-DOB. Note that IMMEKF-DOB and MKCEKF-DOB are not a function of $\eta$ and hence are visualized as flat lines.
  • Figure 4: The experimental setup and commanded angle. (a) The experimental setup. (b) The commanded hip and knee angle with $f=0.1$ Hz.
  • Figure 5: Tracking errors and SNRs of different observers. (a) The hip and knee angle tracking errors. (b) The hip and knee SNRs.
  • ...and 9 more figures

Theorems & Definitions (3)

  • Corollary 1
  • proof
  • proof