Dynamic Effects in Statically Stable Walking Machines

Discontinuous gaits for walking machines present some advantages over wave gaits such as better stability margins and greater speed for small duty factors, for instance. The problem is that a machine using discontinuous gaits starts and stops its body motion several times per locomotion cycle. This means that high accelerations appear, therefore the theoretical static stability margin can be inadequate for measuring stability. This paper addresses how dynamic effects modify the measurement of the static stability of a discontinuous gait and determines the acceleration under which the criterion of using the static stability margin for measuring the stability is valid. For this study, a dynamic planar model of a four-legged walking machine was derived. Then, both the longitudinal and dynamic stability margins were computed and compared. Final results show that the static stability margin is an adequate measurement for studying stability in massless leg machines with the constraint that the acceleration of the body be smaller than the inversion acceleration. When the mass of the legs is significant, stability is determined by the dynamics of the legs and the distribution of the mass of the legs as well.