Szukana fraza: [Abstract = "This paper presents a direct method for computing the time\-optimal trajectory for a robot among stationary and moving obstacles, subject to the robot's dynamics and actuator constraints. The motion planning problem is first formulated as an optimization problem, and then solved numerically using a gradient descent. The initial guess for the optimization is generated using a method based on the concept of Velocity Obstacles. The method is demonstrated for a 2\-DOF planar manipulator moving in static and dynamic environments."]

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