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 3σ 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.