Development of a complete dynamic model of a planar five-link biped and sliding mode control of its locomotion during the double support phase

This paper presents a complete dynamic model of a planar five-link biped walking on level ground. The single support phase (SSP), double support phase (DSP) and double impact occurring at the heel strike are included in the model. By modifying the conventional definition of certain physical parameters of the biped system, it is shown that the procedure of the derivation of the dynamic equations and their final forms are significantly simplified. For motion regulation during the DSP, our dynamic model is formulated as the motion of biped system under holonomic constraints, and the hip position and the trunk orientation are selected as the independent generalized coordinates to describe the constraint system and to eliminate the constraint forces from the equations of motion. Based on the presented dynamic formulation, we develop a sliding mode controller for motion regulation during the DSP where the biped is treated as a redundant manipulator. The stability and the robustness of the controller are investigated, and its effectiveness is demonstrated by computer simulations. To the best of our knowledge, it is the first time that a sliding mode controller is developed for biped walking during the DSP. This work makes it possible to provide robust sliding mode control to a full range of biped walking and to yield dexterity and versatility for performing specific gait patterns.