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.

The problem of collision prediction in dynamic environments appears in several diverse fields, which include robotics, air vehicles, underwater vehicles, and computer animation. In this paper, collision prediction of objects that move in 3-D environments is considered. Most work on collision prediction assumes objects to be modeled as spheres. However, there are many instances of object shapes where an ellipsoidal or a hyperboloid-like bounding box would be more appropriate. In this paper, a collision cone approach is used to determine collision between objects whose shapes can be modeled by general quadric surfaces. Exact collision conditions for such quadric surfaces are obtained in the form of analytical expressions in the relative velocity space. For objects of arbitrary shapes, exact representations of planar sections of the 3-D collision cone are obtained.

Recent news illustrates the frequent occurrence of pileup crashes on highways. A predominant reason for the occurrence of such crashes is that current vehicles (including those equipped with an automatic cruise control system) do not provide drivers with advance information of events occurring far ahead of them. The use of intervehicular communication to provide advance warnings to enhance automotive safety is therefore being actively discussed in the research community. In this paper, we investigate scenarios wherein only a subset of the vehicles in a multivehicle stream is equipped with such advance-warning capabilities. These vehicles (which are equipped with the capability to receive far-ahead information) are arbitrarily distributed among other unequipped vehicles that are capable of receiving only local near-neighbor information. It is seen that there are conditions wherein even a partial equipage of the system can be beneficial to both equipped and unequipped vehicles in a mixed-vehicle stream. We demonstrate this through both simulations and a theoretical analysis. We also developed a prototype of an advance-warning system and conducted road tests to test the concept. These road tests have demonstrated the system's performance to be satisfactory, subject to good communication links, for the class of scenarios tested.

A novel collision cone approach is proposed as an aid to collision detection and avoidance between irregularly shaped moving objects with unknown trajectories. It is shown that the collision cone can be effectively used to determine whether collision between a robot and an obstacle (both moving in a dynamic environment) is imminent. No restrictions are placed on the shapes of either the robot or the obstacle, i.e., they can both be of any arbitrary shape. The collision cone concept is developed in a phased manner starting from existing analytical results that enable prediction of collision between two moving point objects. These results are extended to predict collision between a point and a circular object, between a point and an irregularly shaped object, between two circular objects, and finally between two irregularly shaped objects. Using the collision cone approach, several strategies that the robot can follow in order to avoid collision, are presented. A discussion on how the shapes of the robot and obstacles can be approximated in order to reduce computational burden is also presented. A number of examples are given to illustrate both collision prediction and avoidance strategies of the robot.