High-speed navigation of a uniformly braking mobile robot using position-velocity configuration space

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.