Gait orientation estimation and control of lower-limb exoskeletons for walking assistance

Abstract

Recently, lower-limb exoskeletons have demonstrated the ability to enhance human mobility and walking efficiency for both healthy subjects and patients. However, this technology is confined to the laboratory and its performance is unsatisfactory in a community environment due to: 1) as important components of the exoskeletons, the inertial measurement units (IMUs) are vulnerable to external acceleration and magnetic disturbance. 2) the control performance is significantly affected by external disturbance. 3) the user’s preference or the individualized walking coordination strategy is rarely considered in the assistance map construction. This thesis aims to cope with the aforementioned issues. Specifically, the first two issues can be regarded as performance degeneration of the state estimation with some channels containing non-Gaussian noises. In the conventional estimation framework, the mean squared error (MSE) has been widely used as a cost function due to its features of smoothness, convexity, and mathematical tractability. However, the optimality of the MSE is rooted in the Gaussian assumption, and its performance may be unsatisfactory with heavy-tailed noises. Actually, the correntropy is a better metric for non-Gaussian noises since it captures high-order error statistics. However, it is defined for random variables and is incapable of systems with partial non-Gaussian noises. In this thesis, we introduce a multi-kernel correntropy (MKC) which extends the definition of correntropy from random variables to random vectors. Some important properties of the MKC are given, and a multi-kernel correntropy Kalman filter (MKMCKF) is derived based on the MKC. The proposed estimator is robust against non-Gaussian noises and maintains good performance under Gaussian noises. Simulations verify the effectiveness of the proposed method. We further apply the MKMCKF to orientation estimation of IMUs and the disturbance estimation of an exoskeleton. Specifically, for six-axis IMUs, we derive a compact multi-kernel maximum correntropy Kalman filter (CMKMCKF) which has a minimal parameter number and has less computation penalty. For nine-axis IMUs, we tune the kernel bandwidths of the MKMCKF using Bayesian optimization. The proposed algorithms are compared with the benchmark methods. Simulations and experiments verify the effectiveness of the proposed algorithms, especially with external acceleration and magnetic disturbance. The MKC is further extended to a generalized multi-kernel correntropy (GMKC) under generalized Gaussian kernels. Comprehensive properties of the GMKC are given and the corresponding generalized multi-kernel correntropy loss (GMKCL) is introduced, which is proven to be more versatile than the traditional least mean p power (LMP) criterion. We reveal that the GMKCL is associated with a certain class of heavy-tailed distributions and is an optimal cost function based on the maximum a posteriori probability under some assumptions. Then, a new filter named the generalized multi-kernel maximum correntropy Kalman filter (GMKMCKF) is derived under the GMKCL, and it is utilized as a disturbance observer for a target tracking task using exoskeletons. Simulations show that the proposed disturbance observer outperforms the existing approaches. To involve the user’s preference in the control of the exoskeleton, a robust adaptive oscillator (RAO) is designed to estimate the gait phase and extract gait features. Meanwhile, the participant’s preferred assistance parameters and gait features are collected and stored. Then, the Gaussian process regression (GPR) is employed to construct the individualized assistance map based on the historical data. The effectiveness of the proposed method is validated by a hip exoskeleton at a speed of 5 km/h with 7 participants. Three muscles which include rectus femoris, tibialis anterior, and medial gastrocnemius are investigated in three conditions: user-preferred assistance (ASS), zero torque (ZT), and normal walking (NW). Results show that all muscles achieve an activity reduction in the ASS mode compared with the ZT or NW. Meanwhile, there is a statistically significant difference in medial gastrocnemius in the ASS mode with respect to the ZT and NW (−15.63±6.51% and −8.73±6.40%, respectively).

Date of Award	2022
Original language	English
Awarding Institution	The Hong Kong University of Science and Technology
Supervisor	Ling SHI (Supervisor)