Design of a walking cyclic gait with single support phases and impacts for the locomotor system of a thirteen-link 3D biped using the parametric optimization

An algorithm of parametric optimization to achieve optimal cyclic gaits in space for a thirteen-link 3D bipedal robot with twelve actuated joints is proposed. The cyclic walking gait is composed of successive single support phases and impulsive impacts with full contact between the sole of the feet and the ground. The evolution of the joints are chosen as spline functions. The parameters to define the spline functions are determined using an optimization under constraints on the dynamic balance, on the ground reactions, on the validity of impact, on the torques and on the joints velocities. The cost functional considered is represented by the integral of the torques norm. The torques and the constraints are computed at sampling times during one step to evaluate the cost functional for a feasible walking gait. To improve the convergence of the optimization algorithm the explicit analytical gradient of the cost functional with respect to the optimization parameters is calculated using the recursive computation of torques. The algorithm is tested for a bipedal robot whose numerical walking results are presented.