Collision avoidance in cooperative missions: Bézier surfaces for circumnavigating uncertain speed profiles

This paper presents a collision-prediction and avoidance algorithm for multivehicle cooperative missions. Using Bézier surfaces, the algorithm avoids time discretization of trajectories and is capable of considering uncertainties in speed profiles. The algorithm runs independently onboard each vehicle and, upon detection of a possible collision, replans its trajectory. Under a few assumptions, the modified trajectory is guaranteed to avoid the predicted collision as well as satisfy mission specific constraints. The deviations in position, velocity, and acceleration caused by the avoidance maneuver are small and respect bounds that can be computed offline. These bounds can be used during the mission-planning phase to guarantee satisfaction of vehicle dynamic constraints and intervehicle safety distances even during collision-avoidance maneuvers.