Conditions for uniqueness in simultaneous impact with application to mechanical design

We present a collision resolution method based on momentum maps and show how it extends to handling multiple simultaneous collisions. Simultaneous collisions, which are common in robots that walk or climb, do not necessarily have unique outcomes, but we show that for special configurations - e.g. when the surfaces of contact are orthogonal in the appropriate sense - simultaneous impacts have unique outcomes, making them considerably easier to understand and simulate. This uniqueness helps us develop a measure of the unpredictability of the impact outcome based on the state at impact and is used for gait and mechanism design, such that a mechanism's actions are more predictable and hence controllable. As a preliminary example, we explore the configuration space at impact for a model of the RHex running robot and find optimal configurations at which the unpredictability of the impact outcome is minimized.