Stability analysis and robust control of a biped robot with four links and three actuators

In this paper, we propose motion control of a planar biped robot without ankle with its center of mass (COM) located at the hip using a novel model. Using the properties of this novel model, conditions of stability of periodic orbits are derived using inverted pendulum model and Poincare map method for nonlinear systems with impact. Using optimization of mechanical work and considering periodic and stability conditions with no slipping and no bouncing at heel, desired trajectories are obtained as functions of a time scale parameter. Upon designing a robust sliding mode controller, these trajectories are tracked. To compensate for underactuation, second derivative of the time-scale parameter is used as an input. Simulation results are finally presented to show stability of the motion.