Velocity bounds for motion planning in the presence of moving planar obstacles

This paper is concerned with motion planning for a mobile robot operating in a planar environment with multiple arbitrarily moving obstacles. The robot and obstacles are rigid bodies of arbitrary shapes. All rigid motion-rotation and translation-is considered for the obstacles; the robot can move only by translation. The robot has no advance information about the obstacles' shapes or motion, and obtains information about the surrounding environment from its sensors, in real time. Necessary and sufficient conditions are derived under which collision-free motion of the robot to its target position can be guaranteed. Namely, it is shown that if the maximum velocity of the robot is bounded below by a multiple of the maximum allowable velocity of the obstacles, then a provable motion planning algorithm can be devised. The constant multiple in this bound takes into account the nonconvexity of the obstacles and a bound on the (minimal) distance between any obstacle and the robot's target position.<>