Variational solutions to simultaneous collisions between multiple rigid bodies

— We present a method of resolving simultaneous collisions between multiple rigid bodies based on the least action principle. By using the generalized directional derivative of the action, we use that the solution is related to the outcomes of nearby trajectories that experience consecutive single impacts. We present an algorithm based on this result, and prove its effectiveness by applying it to several low dimensionality examples based on billiard ball interactions, including a simplified version of Newton’s cradle.

• Type: Journal
• Year: 2010
• Where: ICRA
• Authors: Vlad Seghete, Todd D. Murphey
• Keywords: Consecutive Single Impacts, Generalized Directional Derivative, ICRA 2010, Multiple Rigid Bodies, Robotics