P Arameterisedcontrol for an Underactuated Biped Robot

This paper presents a control la w for the tracking of an optimal reference trajectory by an underactuated biped robot. The degree of under-actuation is one during the single support phase. The control law is de ned in the following way. Only the geometric evolution of the robot is controlled, not its temporal evolution. To achiev e this objective, we consider a set of reference trajectories parameterised by a virtual time. The robot is under-actuated so its evolution is constrained and the evolution of the virtual time can be analysed. A analytical simple condition to assure convergence tow ard the optimal reference trajectory is deduced. For the biped and the studied optimal motion, this condition is naturally satis ed.