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The potential field method is widely used for autonomous mobile robot path planning due to its elegant mathematical analysis and simplicity. However, most researches have been focused on solving the motion planning problem in a stationary environment where both targets and obstacles are stationary. This paper proposes a new potential field method for motion planning of mobile robots in a dynamic environment where the target and the obstacles are moving. Firstly, the new potential function and the corresponding virtual force are defined. Then, the problem of local minima is discussed. Finally, extensive computer simulations and hardware experiments are carried out to demonstrate the effectiveness of the dynamic motion planning schemes based on the new potential field method.