Trajectory Tracking in Robotic Systems using Variable Structure Control without a Reaching Phase

A new variable structure control law based on the Lyapunov´s seoond 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. Two applications representing a two-link manipulator and a five-link bipedal robot are considered. The manipulator example is used to demonstrate the improvements in controller performance that arises from the application of the proposed method. In the second application, five constraint relations that cast the motion of a planar, five-link 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.