Motion planning and control for a tethered, rimless wheel differential drive vehicle

This paper considers motion planning and control problems that are motivated by the design of tethered, extreme terrain robots. We abstract the mobility structure of these systems using a tethered differential drive robot with rimless wheels. We analyze several important issues related to this geometry. First it is shown that this vehicle cannot be modeled deterministically unless an additional degree of freedom relative to the standard differential drive vehicle is provided. The simplest kinematically consistent model is one that allows for slight prismatic motion of the axle, approximating the effects of wheel slip. We show that under mild assumptions, such a vehicle´s reachable set is dense in SE(2), implying local maneuverability. Next we study some of the constraints which the tether places on the vehicle´s motions and derive scaling laws relating wheel and vehicle speeds. Using these results, we provide simple planning and approximate path-following methods that allow tether management. In particular, we consider trajectories produced by solving an optimal control problem to minimize the integral of absolute tether-reeling rate.