Abstract

The parametric variations and external perturbations in the coupled subject-exoskeleton system delay and hinder effective gait tracking in clinical rehabilitation. This problem becomes more challenging in the case of the pediatric exoskeleton system. In this work, to address this benchmark challenge, a fast terminal sliding mode with a rapid reaching law (FTSM-RRL) control scheme is introduced for an uncertain lower-extremity exoskeleton aimed at assisting pediatric gait under different walking speeds. At first, the computer-aided design of the gait exoskeleton system is demonstrated with details of the desired gait trajectories of a male boy aged 12 years (weight: 40 kg, height: 132 cm). A fast terminal sliding mode controller is proposed with a varied exponential approaching rule to guarantee the rapid convergence of system states on the sliding manifold and then towards the origin in a finite period. After that, an upper limit criterion is involved within the reaching control law to compensate for the adverse effects of uncertainties and disturbances as a lumped parameter. Lyapunov’s theory is presented to ensure the expeditious convergence of the tracking error in the reaching and sliding phases. The proposed FTSM-RRL strategy is incorporated to obtain the desired trajectory tracking at slow, self-selected, and fast walking speeds. From numerical experiments, the proposed FTSM-RRL controller is found to be consistently effective ( \(> 71\%\) in X-direction and \(> 62\%\) in Y-direction) over the PID controller and ( \(> 7\%\) in X-direction and \(> 10\%\) in Y-direction) over the FTSM-ERL controller. In joint space, the proposed FTSM-RRL control consistently surpasses both PID and FTSM-ERL controls in tracking hip movement. While the proposed controller outperforms PID and FTSM-ERL for knee joint tracking, the extent of improvement diminishes at higher speeds. For ankle joint tracking, the proposed control exhibits substantial enhancement at slow speeds but comparatively poorer performance at self-selected and fast speeds when compared to PID control. However, FTSM-RRL consistently outperforms FTSM-ERL across all speeds for ankle joint tracking. Compared to FTSM-ERL control, the proposed FTSM-RRL control accelerates the hip and knee joint sliding surface convergence by 0.52s and 0.24s (slow walking), 0.55s and 0.33s (self-selected walking), and 0.61s and 0.09s (fast walking). The results obtained in this study ensure fast and efficient passive-assist gait training for the pediatric groups using exoskeleton technology.

中文翻译：

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具有快速趋近律的儿童步态外骨骼系统的快速终端滑模控制

摘要

耦合的受试者外骨骼系统中的参数变化和外部扰动延迟并阻碍了临床康复中的有效步态跟踪。对于儿科外骨骼系统来说，这个问题变得更具挑战性。在这项工作中，为了应对这一基准挑战，针对不确定的下肢外骨骼引入了一种具有快速到达律的快速终端滑动模式（FTSM-RRL）控制方案，旨在帮助不同步行速度下的儿童步态。首先，通过一个 12 岁男孩（体重：40 公斤，身高：132 厘米）所需步态轨迹的细节来演示步态外骨骼系统的计算机辅助设计。提出了一种快速终端滑模控制器，该控制器具有多种指数逼近规则，以保证系统状态在滑动流形上快速收敛，然后在有限时间内向原点收敛。之后，在到达控制律中加入上限准则，以作为集总参数来补偿不确定性和干扰的不利影响。李亚普诺夫理论的提出保证了到达阶段和滑动阶段跟踪误差的快速收敛。所提出的 FTSM-RRL 策略被纳入以在慢速、自选和快速步行速度下获得所需的轨迹跟踪。从数值实验中，发现所提出的 FTSM-RRL 控制器在 X 方向上始终有效（ \(> 71\%\) ，在 Y 方向上\(> 62\%\)）优于 PID 控制器，并且（\ (> 7\%\)在 X 方向和\(> 10\%\)在 Y 方向）通过 FTSM-ERL 控制器。在关节空间中，所提出的 FTSM-RRL 控制在跟踪髋部运动方面始终优于 PID 和 FTSM-ERL 控制。虽然所提出的控制器在膝关节跟踪方面优于 PID 和 FTSM-ERL，但改进程度在较高速度下会减弱。对于踝关节跟踪，与 PID 控制相比，所提出的控制在低速时表现出显着的增强，但在自选和快速时性能相对较差。然而，在踝关节跟踪的所有速度上，FTSM-RRL 始终优于 FTSM-ERL。与 FTSM-ERL 控制相比，所提出的 FTSM-RRL 控制将髋关节和膝关节滑动面收敛加速了 0.52s 和 0.24s（慢速行走）、0.55s 和 0.33s（自选行走）以及 0.61s 和 0.09 s（快走）。本研究获得的结果确保使用外骨骼技术为儿科群体提供快速有效的被动辅助步态训练。