Version 1.0, August 31, 2001, Copyright, Hugh Jack 1993-2001
Lozano-Perez and Wesley [1979] describe their work (see Cartesian Configuration Space) as being an improvement over the Optimization Technique of Spatial Planning. The basic concept they describe, is to explicitly compute the collision constraints on the position of a moving object relative to other obstacles. The trajectory picked is the shortest path which will satisfy all of the path constraints.
With objects modelled as convex polyhedra, vertices of the moving object may move between the obstacle surface planes and collide. This condition is easy to detect, because if a vertices is outside any plane of an obstacle, there is no collision. One possible simplification is to use a circle to represent the objects geometry, and just maintain a radial clearance from all objects. It should also be noted that the circular geometry is not sensitive to rotation. This was the path planning technique used in a mobile vehicular robot called SHAKEY by N.J.Nilsson [1969].
Figure B.2 Spatial Planning - Optimization
