Dynamical Synthesis of a Walking Cyclic Gait for a Biped with Point Feet

Abstract

This paper deals with a methodology to design optimal reference trajectories for walking gaits. This methodology consists of two steps: (i) design a parameterized family of motions, and (ii) determine the optimal parameters giving the motion that minimizes a criterion and satisfies some constraints within this family. This approach is applied to a five link biped, the prototype Rabbit. It has point feet and four actuators which are located in each knee and haunch. Rabbit is underactuated in single support since it has no actuated feet and is overactuated in double support. To take into account this under-actuation, a characteristic of the family of motions considered is that the four actuated joints are prescribed as polynomials in function of the absolute orientation of the stance ankle. There is no impact. The chosen criterion is the integral of the square of torques. Different technological and physical constraints are taken into account to obtain a walking motion. Optimal process is solved considering an order of treatment of constraints, according to their importance on the feasibility of the walking gait. Numerical simulations of walking gaits are presented to illustrate this methodology.