Balancing of a Planar Bouncing Object

While most previous work in planning manipulation tasks relies on the assumption of quasi-static conditions, there can be situations where the quasi-static assumption may not hold, and the assumptions about the environment must be relaxed. This is true, for example, in a situation where objects are making and breaking contact at high enough velocities that contact dynamics play a significant effect in the motion of the colliding objects. There has been some work studying models of collision, in particular for the design and analysis of systems with intermittent constraints, and for the design of juggling robots. Our work extends previous studies in planar juggling to the case of a polygonal object, using the model of rigid body impulsive collision. Simulations verify the results of a linearized analysis.