Stability analysis of quadruped bounding with asymmetrical body mass distribution

An analytical stability criterion for bounding of quadrupeds with asymmetrical mass distribution is developed in this work. Bounding is found to be passively stable when the dimensionless pitch moment of inertia of the body is less than 1 - β¹, where β is a dimensionless measure of the asymmetry. The criterion is derived under the assumptions of infinite leg stiffness and no energy loss. Simulation results show that the criterion is independent of the value of leg stiffness and a conservative estimate of the critical inertia value when energy losses are modeled with linear damping. Body symmetry appears to be more favorable to stable bounding than asymmetry, but only slightly so in practicality.