Hybrid Dynamical Model of a Gait Training Robot: : Using Maggiʼs Method for Constrained Motions

Abstract

Robotic gait therapy has become one of the most interesting topics in the robotics research field due to its effect on enhancing the efficiency of treatments in rehabilitation process of disabled individuals. According to this, in case of gait training, efforts have been made to propose walking assist mechanisms such as orthoses and exoskeletons, which have to provide a stable walking pattern for the individuals. We intend to develop a type of exoskeleton that is mounted on parallel bars to assist, control and improve the patients' walking pattern. Hence, in this paper, as the first step, this plan is modeled and its hybrid dynamics, including equations of motion during swing and stance phases, and impact map is derived. This plan is a simple planar 1-legged robot that composed of three links; an unactuated pelvis-link that slides unidirectionally on a supporting bar, and two rigid links connected to it. Since the prismatic joint connects the pelvis-link to the bar, the height of the robot remains constant during both stance and swing phases. Hence, there are constrained motions, and it is necessary to know the value of constraint forces to check the correct conditions of walking. We employ Maggi's equation to obtain the equations of motion as well as to evaluate the value of the constraint forces independently. A numerical simulation shows the validity of the proposed model, finally.