On efficiency and optimality of asymmetric dynamic bipedal gait

Period-doubling bifurcation and chaotic behavior are interesting phenomena in limit cycle walking. Their mechanisms are very complicated and their roles in dynamic biped locomotion are still unclear. This paper then investigates how the gait efficiency changes with the asymmetrization through analysis of a simple rimless wheel model. We mathematically show that the symmetric configuration gives the optimal solution when the mean value of the inter-leg angles is constant in terms of kinetic energy. This is derived from two magnitude relations of the energy-loss coefficient and restored mechanical energy. We also show that the symmetric gait is not always optimal from another viewpoint.