A trajectory tracking of biped robots using fuzzy-model-based sliding-mode control

In this paper, a biped robot system with the unmodeled dynamics is approximated by the weighting combination of N fuzzy-based linear state-space subsystems those are achieved from the linearization of the biped,robot system about a desired trajectory. Then, the same fuzzy sets of the system rule are applied to establish the fuzzy reference models with desired amplitude and phase properties. The reason to introduce the reference model is not only to obtain a tracking error system but also to guide the suitable response for the dynamic walking of the biped robot. The system uncertainties contain the approximation error of the fuzzy-model, the unmodeled dynamics of the biped robot (e.g., only the dynamics in two dimension is considered; the concentrative mass of link is supposed; the friction torque is neglected), the discontinuity of velocity as contacted with ground, and the interaction dynamics resulting from the other subsystems. Under these circumstances, a robust controller with easy design is required. Based on the concept of parallel distribution compensation, a fuzzy-model-based sliding-mode control (FMBSMC) is designed. The proposed control includes a fuzzy equivalent control and a fuzzy switching control. The fuzzy equivalent control is to obtain the desired behavior; the fuzzy switching control is employed to cope with the uncertainties such that the robust performance is improved. The stability of the overall system is then verified by Lyapunov stability theory. In short, only the dominant dynamics of the biped robot is required for the proposed control to obtain a guaranteed performance. The illustrative example of three-link biped robot is given to explain the design procedure.