Motion Planning in Environments with Low Obstacle Density

We present a simple and e cient paradigm for computing the exact solution of the motionplanning problem in environments with a low obstacle density. Such environments frequently occur in practical instances of the motion planning problem. The complexity of the free space for such environments is known to be linear in the number of obstacles. Our paradigm is a new cell decomposition approach to motion planning and exploits properties that follow from the low density of the obstacles in the robot's workspace. These properties allowus to decompose the workspace, subject to some constraints, rather than to decompose the higher-dimensional free con guration space directly. A sequence of uniform steps transforms the workspace decomposition into a free space decomposition of asymptotically the same size. The approach leads to nearly-optimal Onlogn motion planning algorithms for free- ying robots with any xed number of degrees of freedom in workspaces with low obstacle density.

• Type: Journal
• Year: 1998
• Where: DCG
• Authors: A. Frank van der Stappen, Mark H. Overmars, Mark de Berg, Jules Vleugels
• Keywords: DCG 1998, Free Space, Low Obstacle Density, Workspaces