The Usage of Kinematic Singularities to Produce Periodic High-Powered Locomotion

Legged robots primarily energize their center of mass through external contact during stance phase. This links their range of possible motions to actuator power limits applied during usually short periods of time. Enabling limb actuators to pump energy into the system during non-contact phases can greatly extend the energetic profile of possible motions. However, funneling this extra energy into useful dynamics is a problem of its own. In this paper, we propose designing limb mechanisms that purposefully integrate kinematic singularities into their configuration space to enable airborne energization and enhance gait periodicity before sensors and feedback control are incorporated. The result produces a mechanical reflex that unloads spring energy stored during flight phase into a useful push-off motion as triggered by the onset of stance phase. The implementation generates an "S" shaped curve into a specific slice of the configuration space, motivating the name S-curve. We compare our proposed approach to more conventional strategies and survey the design parameters that can be used to shape an S-curve. Ranges of useful S-curves are determined through a simulation study and a linkage mechanism capable of producing an S-curve is displayed.