Finite time tracking of a fully actuated biped robot with pre-specified settling time: A second order sliding mode synthesis

A second order sliding mode controller is utilised to track reference trajectories for all the joints of a fully actuated biped robot. The existing tuning rules for the `twisting´ controller are used to guarantee a priori attainment of a prescribed settling time between two successive impacts. The joint torque is modeled as the control input. Smoothing of the discontinuous controller is carried out by introducing a high gain linear controller inside a boundary layer defined by an arbitrarily small region around the origin thereby avoiding numerical errors in the simulations. The overall accuracy of motion control is dictated by the size of this layer leading to practical stability of the closed-loop system. The main contribution of the paper is to provide straightforward and realizable engineering guidelines for the reference trajectory generation and for the tuning of a robust finite time controller for achieving stable gait of a biped in the presence of disturbances in both continuous and impact phases. Numerical simulations of a biped robot are shown to support the theoretical results.