This paper describes analytics and experiments on a novel 4-wheel vehicle. The vehicle has back wheel drive and steering in addition to wheels that can expand and change radius. The motivation for this design is to attain added navigation capability by expanding the wheels according to the requirements of the terrain. In this paper, we discuss the motion of the vehicle on a flat floor. The steering angle is kept at zero so that the vehicle has a planar motion. The contact point of the wheel with the ground is assumed to be directly underneath the center of the wheel and has no slip. The rolling constraints are nonholonomic, i.e., are non-integrable. The rate constraints are written in an input-affine drift-less control system. The structure of this drift-less control system allows to determine the differentially flat outputs of the system. Motion planning of the vehicle between two configurations is achieved through planning of these differentially flat outputs. These trajectories are then used to determine a feedback controller. A dynamic simulation is performed using MATLAB. The motions are currently being implemented on the physical hardware using a dSPACE control system.

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