Closed-Loop Kinematic and Indirect Force Control of a Cable-Driven Knee Exoskeleton: A Lyapunov-Based Switched Systems Approach

Abstract

Lower-limb exoskeletons can aid restoring mobility in people with movement disorders. Cable-driven exoskeletons can offload their actuators away from the human body to reduce the weight imposed on the user and enable precise control of joints. However, ensuring limb coordination through bidirectional motion control of joints using cables raise the technical challenge of preventing the occurrence of undesired cable slackness or counteracting forces between cables. Thus, motivation exists to develop a control design framework that integrates both a joint control loop to ensure suitable limb tracking and a cable control loop to maintain cable tension properly. In this article, a two-layer control structure consisting of high and low-level controllers are developed to ensure a knee-joint exoskeleton system follows the desired joint trajectories and adjusts the cable tension, respectively. A repetitive learning controller is designed for the high-level knee joint tracking objective motivated by the periodic nature of the desired leg swings (i.e., to achieve knee flexion and extension). Low-level robust controllers are developed for a pair of cables, each actuated by an electric motor, to track target motor trajectories composed of motor kinematics and offset angles to mitigate cable slackness. The offset angles are computed using admittance models that exploit measurements of the cable tensions as inputs. Each electric motor switches its role between tracking the knee joint trajectory (i.e., the motor acts as the leader motor to achieve flexion or extension) and implementing the low-level controller (i.e., the motor acts as the follower motor to reduce slackness). Hence, at any time, one motor is the leader and the other is the follower. A Lyapunov-based stability analysis is developed for the high-level joint controller to ensure global asymptotic tracking and the low-level follower controller to guarantee global exponential tracking. The designed controllers are implemented during leg swing experiments in six able-bodied individuals while wearing the knee joint cable-driven exoskeleton. A comparison of the results obtained in two trials with and without using the admittance model (i.e., exploiting cable tension measurements) is presented. The experimental results indicate improved knee joint tracking performance, smaller control input magnitudes, and reduced cable slackness in the trial that leveraged cable tension feedback compared to the trial that did not exploit tension feedback.

Keywords

• Human-in-the-loop
• lower-limb exoskeletons
• Lyapunov methods
• nonlinear control
• switched systems