Graceful Gait Transitions for Hopping Robots on Deformable Terrain

This paper proposes an approach to find graceful transitions between periodic orbits of hybrid systems. Our method involves formulating an optimization problem that captures the notion of a graceful transition. Solution of the optimization problem will yield open loop trajectories that achieve graceful transitions between two distinct orbits. This is illustrated on two example nonlinear hybrid systems: A 1D hopper jumping in the vertical direction on granular media and a 2D planar jumper jumping in the vertical and horizontal direction on springy terrain.