This paper addresses the issue of motion safety in dynamic environments using Velocity Obstacles. Specifically, we propose the minimum time horizon for the velocity obstacle to ensure that the boundary of the velocity obstacle approximates conservatively that boundary of the set of inevitable collision states. Thus, using the velocity obstacle to select potential avoidance maneuvers would ensure that only safe maneuvers are being selected. The computation of the minimum time horizon is formulated as a minimum time problem, which is solved numerically for each static or moving obstacle. The ``safe'' velocity obstacles are used in an on-line planner that generates near-time optimal trajectories to the goal. The planner is demonstrated for on-line motion planning in very crowded static and dynamic environments.
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