Collision Avoidance of Moving 3-D Objects in Dynamic Environments

In this paper, we consider the problem of reactive collision avoidance for objects that have elongated and/or non-convex shapes. The literature largely models objects using spheres, but this can either make the avoidance maneuvers over conservative (when a single large sphere is used to approximate each object) or lead to increased computational complexity (when multiple smaller spheres are used to approximate each object). We therefore model such objects using quadric surfaces that may include suitable combinations of ellipsoids, paraboloids and one-sheeted/two-sheeted hyperboloids. We present a method to construct the 3D collision cones for such object shapes using tools from projective geometry, as well as provide an analytical characterization of the $3\sigma $ bounds of the collision cone that account for noisy measurements. These are then used to devise suitable avoidance strategies. Computational analysis and simulation results are presented to demonstrate the efficacy of the methodology. Note to Practitioners—This paper is motivated by the problem of autonomous collision avoidance with moving obstacles having elongated or irregular shapes. Common approaches typically model obstacles as spheres. Using one large sphere for each object makes the avoidance too conservative, while using many smaller spheres makes it harder to calculate the avoidance commands quickly. Instead, we represent these objects with shapes that provide a tighter approximation to their actual forms. We outline a computationally efficient method to map out potential collision zones for these objects that account for their shapes, as well as velocities, and also adjust for sensor measurement errors. This approach is used to determine avoidance strategies.