Optimal walking trajectories for a biped

The objective of this study is to generate optimal gait cycles for the walking of a planar biped robot without an actuated ankle joint and four actuators. The evolution of four joint variables is assumed to be polynomial functions of the fourth order. The evolution of the other variable is deduced from the dynamic model of the biped. The coefficients of the polynomial functions are chosen to optimize the criteria and insure cyclic motion of the biped. The criteria chosen are maximal motion velocity, minimal torque, and minimal energy. These criteria are functions of some parameters, which define the configurations of the biped, its step length, and duration of the step. To minimize these functions means to find the optimal motion. Also, the optimal gait is defined with respect to given performances of actuators: the torques and velocities at the output of the gear are bounded. For this study, the physical parameters of a prototype are used