Mathematical Models for Physical Interactions of Robots in Planar Environments

This paper reports on the development of a collision capable omni-driven platform called Omnipuck with an accompanying reflection model capturing uncertainty present after collision events. Path planning and navigation strategies focus almost entirely on avoiding collisions, but this platform was designed to specifically benefit by colliding with obstacles in the environment. Collisions are modeled as partially reflected diffusions characterizing boundary interaction behaviors including uncertainty with experimentally validated parameters. Experiments highlighting convergence time demonstrate the potential benefits of using boundaries to partially recover impact energy in planning. The results herein lay the foundation for path planning and navigation strategies that exploit collisions.