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