Simplest mechanical model of stable hopping with inelastic ground-foot impact

摘要

The dynamic analysis of legged locomotion is challenging because of many reasons, such as the possibly high degrees of freedom of the model, the alternating topology in certain phases of walking or running, the presence of under-actuation and over-actuation, the geometric nonlinearities and ground-foot impact induced non-smoothness. Control issues makes models even more complex, although having models which includes the control strategy of the brain is very helpful in biomechanics. Such models helps to understand how the brain keeps the body in balance, how the energy level is maintained and how the motion patterns are generated.Before developing a fully extended, very complex model of walking or running, we focus on the dynamic analysis of a piecewise smooth model of hopping, which possesses some fundamental characteristics of locomotion systems: 1) different topology in ground and flight-phase; 2) energy absorption due to partially/fully inelastic ground-foot collision; 3) active control strategy for maintaining a certain energy level; 4) different control strategies in ground and flight-phases.We prove that our two degrees of freedom model provides stable periodic motion, i.e. vertical hopping in wide range of parameters. We present the application of stability analysis methods that can be adapted for more complex models of legged locomotion.