The trajectory tracking of robots: Via a fuzzy linear pulse transfer function.. matrix based variable structure control

Due to the complexity of robot, its exact description is difficult. On the contrary, a linear model about a specific operating point for a nominal robot is easy. Then, a nominal robot can be approximated by the weighted combination of N subsystems described by the pulse transfer function matrices. The approximation error between the robot and the fuzzy linear pulse transfer function matrix system (FLPTFMS) includes two categories: the structural one caused by parameter variations and the unstructural one caused by measurement noise, and external disturbance. The approximation error is represented by the weighted combination of the output disturbance in every subsystem. In addition, the output response of the ith closed-loop subsystem is subjected to the uncertainties caused by the output disturbance and the interaction dynamics resulting from the other subsystems. Due to the existence of the (remaining) uncertainties, a disadvantageous response often occurs. Under the circumstances, a switching control in every subsystem is designed to reinforce the system performance. The experiments of two-joint robot in the horizontal plane with (or without) payload confirm the practicality of the proposed control.