Characteristic equations and gravity effects on virtual passive bipedal walking

An in-depth understanding of passive bipedal walking is expected to contribute to the design of energy-efficient bipedal gaits and passivity-mimicking control laws. In this paper we investigate virtual passive bipedal walking in terms of generalized force and kinetic energy, and derive three characteristic equations which describe some essential mechanism of virtual passive bipedal walking and can be used to design a control law for completely passive bipedal walking on a level. We also show by simulation that the step length of passive bipedal walking is independent of the gravity, the step period is inversely proportional to the one-second power of the gravity, and the average speed of progression is proportional to the one-second power of the gravity.