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This paper presents a new optimal motion planning aiming to minimize the energy consumption of a wheeled mobile robot in robot applications. A model that can be used to formulate the energy consumption for kinetic energy transformation and for overcoming traction resistance is developed first. This model will provide a base for minimizing the robot energy consumption through a proper motion planning. To design the robot path, the A* algorithm is employed to generate an energy-efficient path where a new energy-related criterion is utilized in the cost function. To achieve a smooth trajectory along the generated path, the appropriate arrival time and velocity at the defined waypoints are selected for minimum energy consumption. Simulations and experiments are performed to demonstrate the energy-saving efficiency of the proposed motion planning approach.