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In this paper a design of four wheeled omni-directional vehicle is presented and its kinematic and dynamic model is developed. The motion equation of this system is non-linear and hard to deal with in applications where fast trajectory generation is needed with modest computation resource. Therefore a special design that the vehicle's motion equation can be simplified is proposed. With a set of constraints being satisfied, the system is greatly simplified and a near time-optimal bang-bang trajectory can be calculated with great computational efficiency.