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This paper presents an optimal motion planning of a mobile robot with the objective of minimum energy consumption. The energy consumption is analyzed in both geometric path planning and smooth trajectory planning. A global path planner is developed by treating energy efficiency as the central element in the cost function. Utilizing waypoints of the generated optimal path, a smooth trajectory is planned based on Bézier curve in terms of parameters of arrival time and velocity at each waypoint. Energy consumption is further minimized by optimizing these parameters. Simulations and experiments are finally performed to demonstrate the efficiency of the proposal motion planning approach to energy minimization.