Biped gait stabilization via foot placement.

It is shown that stable biped gaits can be achieved by discrete foot placement based on feedback of information available at the time of foot placement. The model, developed by Townsend (1981, J. Biomechanics 14, p. 727) to evaluate the coordinations of torso motions, subsumes most of the salient body members and motions. The modeling yielded a generalized inverted pendulum with a movable support point which physically defines lateral foot placement. The principal result is that stable gaits can be defined by foot placements which are a linear function of the system center of mass position and velocity at the time of foot placement (only). Gaits may be 'smooth' or may have impulsive corrections to adjust the character of the motions and foot placement. Several general algorithms and specific simulations are presented, and calculations for non-impulsive gaits and impulsive corrections are presented. The model predictions are compared with published data. The predictions are sufficiently close to the data such that the general algorithms appear to be validated. Of particular interest are the non-sinusoidal character of the motions and the relatively simple algorithms. Indeed, the simplicity of the algorithms suggests the practical possibility of legged mobile robots. Accordingly, further investigation seems warranted for determining the parametric variation and control of gait. Some attention is also given to continuous-feedback control such as would exist during double-leg support and in specialized tasks such as rope walking or skating. Subsequent investigation will consider superposition of single and double leg support, although clearly the discrete gaits pose the more restrictive stability problem.