Tracking Control of A Human Swing Leg as a Double-Pendulum Considering Self-Impact Joint Constraint by Feedback Linearization Method

Abstract

Walking is one of the main human gaits of leg locomotion. Despite the simplicity with which humans appear to walk, this gait is inherently complex with highly nonlinear dynamics. Walking is made up of two distinct phases: single support phase (SSP) and double support phase (DSP). Since single support phase accounts for a much larger share in a walking gait cycle; it has been the most interesting topic of studies in this field. In SSP, one leg appears as the swing (moving) leg and the other one will be stationary or stance leg; the swing leg is usually modelled as a double pendulum. The links of a double pendulum, in this case, will represent the thigh and shank of a human leg and its joints, hip and knee, will connect the upper body to thigh and then shank, respectively.

The main difference in this study, compared to the previous works, is the consideration of the joint self-impact constraint in double pendulum modeling at the knee joint. This constraint has an important role in realizing the practical characteristics of a swing leg; in other words, imposing this constraint necessitates that the shank link cannot assume the rotation angles which are greater than that of the thigh link. Therefore, prominent objective of this research is to propose a nonlinear model-based control method for a constrained (joint self-impact) double pendulum which models a more realistic swing leg. Due to complex nonlinear terms in dynamics equations of the joint self-impact swing leg, we propose to design the controller by taking advantage of the feedback linearization control method, which is a benchmark method for complex nonlinear systems.

To achieve this goal, the available data of normal human gait will be taken as the desired trajectories of the hip and knee joints. The simulation results of applying the proposed method to the constrained double pendulum demonstrate that the swing leg tracks the normal human gait with a negligible and acceptable error.