SLIDING CONTROL WITHOUT REACHING PHASE AND ITS APPLICATION TO BIPEDALLOCOMOTION

A new variable structure control law based on the Lyapunov's second me thod that can be used in trajectory planning problems of robotic syste ms is developed. A modified approach to the formulation of the sliding domain equations in terms of tracking errors has been presented. This approach possesses three distinct advantages: (i) it eliminates the r eaching phase, (ii) it provides means to predict the entire motion and directly control the evolution of tracking errors, (iii) it facilitat es the trajectory planning process in the joint and/or cartesian space s. A planar, five-link bipedal locomotion model has been developed. Fi ve constraint relations that cast the motion of the biped in terms of four parameters are developed. The new control method is applied to re gulate the locomotion of the system according to the five constraint r elations. Numerical simulation performed to verify the ability of the controller to achieve steady gait by applying the proposed control sch eme. Bifurcation diagrams of the periodic motions of the biped are use d to demonstrate the improvements in controller performance that arise from the application of the proposed method.