Modeling and Finite-Time Walking Control of a Biped Robot with Feet

摘要

This paper addresses the problem of modeling and controlling a planar biped robot with six degrees of freedom,which are generated by the interaction of seven links including feet. The biped is modeled as a hybrid dynamicalsystem with a fully actuated single-support phase and an instantaneous double-support phase. The mathematicalmodeling is detailed in the first part of the paper. In the second part, we present the synthesis of a controller based onvirtual constraints, which are codified in an output function that allows defining a local diffeomorphism to linearizethe robot dynamics. Finite-time convergence of the output to the origin ensures a collision between the swing footand the ground with an appropriate configuration for the robot to give a step forward. The components of the outputtrack adequate references that encode a walking pattern. Finite-time convergence of the tracking errors is enforcedby using second-order sliding mode control. The main contribution of the paper is an evaluation and comparison ofdiscontinuous and continuous sliding mode control in the presence of parametric uncertainty and external disturbances. The robot model and the synthesized controller are evaluated through numerical simulations.