Collision Avoidance and Rendezvous of Quadric Surfaces Moving on Planar Environments

Achieving collision avoidance or rendezvous between moving objects are important objectives in robotic systems. In performing collision avoidance or rendezvous maneuvers, the relative shapes of the objects play an important role. The literature largely models the shapes of the objects as circles, and this can make the maneuvers very conservative, especially when the objects are of elongated shape. In this paper, we model the shapes of the objects using quadric surfaces. A collision/rendezvous cone concept is employed. A computationally efficient approach to compute the collision/rendezvous cone between finite-sized quadric surfaces (which are not necessarily of the same shape) is presented. Nonlinear analytical guidance laws that perform collision avoidance or rendezvous maneuvers, are subsequently developed. Simulation results demonstrating the working of the developed guidance laws are presented.