On the algebraic geometry of contact formation cells for systems of polygons

The efficient planning of contact tasks for intelligent robotic systems requires a thorough understanding of the kinematic constraints imposed on the system by rolling and sliding contacts. In this paper, we derive closed-form analytic solutions for the position and orientation of a passive polygon moving in contact with two or three active polygons whose positions and orientations are independently controlled. This is done by applying elimination techniques to solve the systems of appropriate contact constraint equations. We prove that the systems of contact constraint equations are smooth submanifolds of configuration space