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This paper considers the problem of fast autonomous mobile robot navigation between obstacles while attempting to maximize velocity subject to safe braking constraints. The paper introduces position-velocity configuration space. Within this space, keeping a uniform braking distance from the obstacles can be modeled as forbidden regions called vc-obstacles. Using Morse Theory, the paper characterizes the critical position-velocity points where two vc-obstacles meet and locally disconnect the free position-velocity space. These points correspond to critical events where the robot's velocity becomes too large to support safe passage between neighboring obstacles. The velocity dependent critical points induce a cellular decomposition of the free position-velocity space into cells. Each cell is associated with a particular range of velocities that can be safely followed by the robot. The paper proposes a practical algorithm that searches the cells' adjacency graph for a maximum velocity path. The algorithm outputs a pseudo time optimal path which maintains safe braking distance from the obstacles throughout the robot motion. Simulations demonstrate the algorithm and highlight the usefulness of taking the path's velocity into account during the path planning process.

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