Version 1.0, August 31, 2001, Copyright, Hugh Jack 1993-2001
A different approach based on the calculus of variations has been developed by R.O.Buchal and D.B.Cherchas [1989]. The techniques use convex polygons to represent objects, and an iterative technique to find the best path which avoids these polygons. The path is subdivided into a number of smaller intervals, linking a set of pre specified via points. Convex hulls are used to represent the volume swept out by the motion of the moving object. The penetration depth, and penetration vector, are used to correct the path for each of the individual path segments.
Figure A.2 Path Segment Interference
The penalty function is formulated as to consider the limits on the joints and actuators. The optimization routine is used to correct the path segments, and this procedure takes about 1 minute on a VAX 11/750 for a 2D model, with manipulator considered, without manipulator collisions. The main objective of this routine is to minimize time. This method needs a set of path points specified for good solutions, and this is a potential area of research.