  Achieving collision avoidance between moving objects is an important
objective while determining robot trajectories. In performing collision
avoidance maneuvers, the relative shapes of the objects play an important role.
The literature largely models the shapes of the objects as spheres, and this
can make the avoidance maneuvers very conservative, especially when the objects
are of elongated shape and/or non-convex. In this paper, we model the shapes of
the objects using suitable combinations of ellipsoids and
one-sheeted/two-sheeted hyperboloids, and employ a collision cone approach to
achieve collision avoidance. We present a method to construct the 3-D collision
cone, and present simulation results demonstrating the working of the collision
avoidance laws.
