A 3D Reactive Collision Avoidance Algorithm for Underactuated Vehicles

Abstract

This paper presents a 3D reactive collision avoidance algorithm for vehicles with underactuated dynamics. The underactuated states cannot be directly controlled, but are controlled indirectly by steering the direction of the vehicle's velocity vector. This vector is made to point a constant avoidance angle away from the obstacle, thus ensuring collision avoidance, while the forward speed is kept constant to maintain maneuverability. We choose an optimal pair of desired heading and pitch angles during the maneuver, thus taking advantage of the flexibility provided by operating in 3D. The algorithm incorporates limits on both the allowed pitch angle and the control inputs, which are limits that often are present in practical scenarios. Finally, we provide a mathematical proof that the collision avoidance maneuver is safe, and support the analysis through several simulations.