Sliding Control without Reaching Phase and its Application to Bipedal Locomotion

A new variable structure control law based on the Lyapunov’s second method that can be used in trajectory planning problems of robotic systems 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 reaching phase, ii) it provides means to predict the entire motion and directly control the evolution of tracking errors, iii) it facilitates the trajectory planning process in the joint and/or cartesian spaces. A planar, five-link bipedal locomotion model has been developed. Five constraint relations that cast the motion of the biped in terms of four parameters are developed. The new control method is applied to regulate the locomotion of the system according to the five constraint relations. Numerical simulation is performed to verify the ability of the controller to achieve steady gait by applying the proposed control scheme. Bifurcation diagrams of the periodic motions of the biped are used to demonstrate the improvements in controller performance that arise from the application of the proposed method.