An omnidirectional mobile robot is able, kinematically, to move in any direction regardless of current pose. To date, nearly all designs and analyses of omnidirectional mobile robots have considered the case of motion on flat, smooth terrain. In this paper, an investigation of the design and analysis of an omnidirectional mobile robot for use in rough terrain is presented. Kinematic and geometric properties of the active split offset caster drive mechanism are investigated along with system and subsystem design guidelines. An optimization method is implemented to explore the design space. Use of this method results in a robot that has higher mobility than a robot designed using engineering judgment. A point design generated by the optimization method is shown for a meter-scale mobile robot.