Velocity Profile Optimization for Multiple UAVs Collision-Free Mission Planning

Collision avoidance is a critical aspect of operating multiple Unmanned Aerial Vehicles (UAVs) or aircraft simultaneously. Traditional collision avoidance methods typically involve re-planning the flight paths to circumvent potential collisions, often resulting in significant deviations from the original trajectories. In this paper, we propose an innovative method that ensures collision avoidance without altering the predefined flight paths. Our approach guarantees that aircraft will traverse their intersection points with sufficient temporal separation to prevent collisions. We formulate an optimization problem that aims to determine the minimum time velocity profile for each aircraft, ensuring compliance with both speed constraints and collision avoidance requirements. To tackle the non-convex nature of this optimization problem, we employ a first-order optimization algorithm, which is well suited for efficiently handling such complex constraints. We validate the effectiveness of our proposed method through extensive simulations. These simulations include both simple intersection scenarios and more congested airspace situations, demonstrating the robustness and applicability of our algorithm across various operational environments. Our results show that the proposed method can effectively maintain the predefined paths while ensuring safe and collision-free operations of multiple UAVs or aircraft.