Generation of Confi guration Space Obstacles I: The C ase of A Moving Sphere
Chanderjit Bajaj, Myungsoo Kim · Purdue e-Pubs (Purdue University System) · 1985
Using configuration space to plan collision free motion for a single rigid object amongst physical objectS, reduces the problem to planning motion for a mamematical point amongst "grown" configuration space obstacles, ( the poinrs in configuration space which correspond to me object overlapping one or more obstacles).The problem of collision free motion for a point is simple since a point can now be moved without restriction in any connected region of configuration space.The difficult pan of the recfmique comes in the construction of the configuration space obstacles.In the past object representations have been polyhedral approximations to the real object However it has progressively become easier for geometric modeling systems [Q deal with objecrs that are defined by quadric (degree 2) surfaces.It is in this sophisticated modeling environment that we characterize the surface boundary of me configuration space obstacles arising from the motion of a sphere amongst obstacles whose boundary is defined by patches of quadric surfaces.The problem of generating these configuration space obstacles is also shown to be closely related to the problem of blending quadric surfaces by spherical envelopes.