Models and Motion Planning

We study the complexity of the motion planning problem for a bounded-reach robot in the situation where the n obstacles in its workspace satisfy two of the realistic models proposed in the literature, namely unclutteredness and small simple-cover complexity. We show that the maximum complexity of the free space of a robot with f degrees of freedom in the plane is (nf/2 + n) for uncluttered environments as well as environments with small simple-cover complexity. The maximum complexity of the free space of a robot moving in a three-dimensional uncluttered environment is (n2f/3 +n). All these bounds fit nicely between the (n) bound for the maximum free-space complexity for low-density environments and the (nf ) bound for unrestricted environments. Surprisingly--because contrary to the situation in the plane--the maximum free-space complexity is (nf ) for a three-dimensional environment with small simple-cover complexity.

• Type: Conference
• Year: 1998
• Where: SWAT
• Authors: Mark de Berg, Matthew J. Katz, Mark H. Overmars, A. Frank van der Stappen, Jules Vleugels
• Keywords: Algorithms, Maximum Complexity, Maximum Free-space Complexity, Small Simple-cover Complexity, SWAT 1998