Modeling and optimal trajectory planning of a biped robot using Newton-Euler formulation

The development of an algorithm to achieve optimal cyclic gaits in space for a thirteen-link biped and 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 criterion considered is represented by the integral of the torque norm. The algorithm is tested for a biped robot whose numerical walking results are presented.