A new approach to certain motion-planning problems in robotics is introduced. This approach is based on the use of a generalized Voronoi diagram, and reduces the search for a collision-free continuous motion to a search for a connected path along the edges of such a diagram. This approach yields an O(n log n) algorithm for planning an obstacle-avoiding motion of a single circular disc amid polygonal obstacles. Later papers will show that extensions of the approach can solve other motion-planning problems, including those of moving a straight line segment or several coordinated discs in the plane amid polygonal obstacles.
ASJC Scopus subject areas
- Control and Optimization
- Computational Mathematics
- Computational Theory and Mathematics