Motion planning for kinematically overconstrained vehicles using feedback primitives

In this paper we consider motion planning for kinematically overconstrained vehicles. Such vehicles are reasonably common in applications that require many axles for static stability. When a system is kinematically overconstrained, typically some contacts with the environment must slip, violating the constraint. This introduces nonsmooth behavior into the equations of motion, making classical motion planning strategies inapplicable. As an example, we consider a vehicle that has a simplified version of the kinematic structure of the rover from the first Mars mission. We introduce a provably complete motion planner for purposes of illustration. However, the primary purpose of this paper is to clearly identify some of the open problems in motion planning for these mechanisms and to propose a kinematic modeling framework that reveals the underlying complications due to slipping while maintaining the relative simplicity associated with kinematic systems over dynamic ones. The planner we describe has properties that we anticipate would be relevant to a general methodology for motion planning for both kinematically overconstrained systems as well as more general systems that have uncertain dynamics