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The minimum-energy translational trajectory planning algorithm is proposed for battery-powered three-wheeled omni-directional mobile robots (TOMRs). We have chosen a practical cost function as the total energy drawn from the batteries, in order to lengthen the operational time of a mobile robot with given batteries. After establishing the dynamic equations of TOMRs, the optimal control theory is used to solve the minimum-energy trajectory, which gives the velocity profile in analytic form. Various simulations are performed and the consumed energy is compared to other velocity trajectories. Simulation results reveal that the energy saving is achieved of up to 2.4% compared with loss-minimization control, and up to 4.3% compared with conventional trapezoidal velocity profile.