Optimal Reference Motions for Walking of a Biped Robot

The objective of this study is to obtain optimal cyclic gaits for a biped without actuated ankle. For the walking, the gait is composed of successive single support phases and instantaneous double support phases that are modeled by passive impact equations. The legs swap their roles from one single support phase to the next one. During each phase the evolution of the joints variables is assumed to be polynomial functions of a scalar path parameter. The coefficients of the polynomial functions are chosen to optimise a torque criterion and to insure a cyclic motion for the biped. Furthermore, the optimal gait is defined with respect to given performances of actuators. The torques and velocities at the output of the gearbox are bounded. For this study, the physical parameters of a prototype are used. Initial starting motions that are composed of a double support and a transitional single support are also defined.