Reaching a Goal with

We study two problems related to planar motion planning for robots with imperfect control, where, if the robot starts a linear movement in a certain commanded direction, we only know that its actual movement will be connned in a cone of angle centered around the speciied direction. First, we consider a single goal region, namely the \region at innnity", and a set of polygonal obstacles, modeled as a set S of n line segments. We are interested in the region R(S) from where we can reach innnity with a directional uncertainty of. We prove that the maximum complexity of R(S) is O(n== 5). Second, we consider a collection of k polygonal goal regions of total complexity m, but without any obstacles. Here we prove an O(k 3 m) bound on the complexity of the region from where we can reach a goal region with a directional uncertainty of. For both situations we also prove lower bounds on the maximum complexity, and we give eecient algorithms for computing the regions.