An omnidirectional mobile robot is able, kinematically, to move in any planar direction regardless of current pose. To date, nearly all designs and analyses of omnidirectional robots have considered the case of motion on flat, smooth terrain. This paper presents design constraints and guidelines for designing an omnidirectional mobile robot propelled by active split offset casters to be driven in rough terrain. Geometric constraints on wheel and linkage sizes are presented. The effects of terrain roughness and loss of wheel contact are analyzed. The vehicle design is optimized for kinematic isotropy, ability to maintain ground contact, traversable obstacle height, and maximum traversable distance over four diverse terrain types. The results are contrasted with a baseline design. ©2008 IEEE.