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This paper provides a new approach to the dynamic motion planning problems of mobile robots in uncertain dynamic environments based on the behavior dynamics from an optimal control point of view. The fundamental behavior of a mobile robot in motion planning is regarded as a dynamic process of the interaction between the robot and its local environment, and then it is modeled and controlled for the motion planning purpose. Based on the optimal control of the behavior dynamics, the dynamic motion-planning problem can be transformed into a conventional optimization problem in the robot's acceleration space, and the optimal motion behavior of the mobile robot can be obtained on line. No restrictions are assumed on the shape and trajectories of obstacles. Collision avoidance between multiple mobile robots can also be realized. Stability of the whole planning-and-control system can be guaranteed. Simulations illustrate our results.