Connecting Gaits in Energetically Conservative Legged Systems

In this work, we present a nonlinear dynamics perspective on generating and connecting gaits for energetically conservative models of legged systems. particular, show that the set constitutes connected space locally defined 1D submanifolds in gait space. These manifolds are coordinate-free parameterized by energy level. We algorithms identifying such families through use numerical continuation methods, sets bifurcation points. To end, also introduce several details implementation. Most importantly, establish necessary condition Delassus' matrix to preserve across impacts. An important application our work is with simple locomotion often able capture complexity just few degrees freedom small number physical parameters. demonstrate efficacy framework one-legged hopper four freedom.