Omni-directional mobile robots have been popularly employed in several application areas. However, the kinematics for these systems have not been clearly identified, specially for redundantly actuated case which is common in omni-directional mobile robot such as the Nomadic model. For such mobile robot systems, exploitation of redundant actuation as well as singularity analysis has not been extensively addressed. In light of this fact, this paper introduces two different kinematic approaches for omni-directional mobile robots. Then, a singular-free load distribution scheme for redundantly actuated three-wheeled omni-directional mobile robot is proposed. Through simulation, several advantages of redundantly actuated mobile robot in aspect of singularity avoidance, minimization of torque norm, and exploiting several subtasks are presented.