Sensor based planning and nonsmooth analysis

This paper describes some initial steps towards sensor based path planning in an unknown static environment. The method is a based on a sensor-based incremental construction of a one-dimensional retract of the free space. In this paper we introduce a retract termed the generalized Voronoi graph, and also analyze the roadmap of Canny and Lin's opportunistic path planner (1990, 1993). The bulk of this paper is devoted to the application of nonsmooth analysis to the Euclidean distance function. We show that the distance function is in fact nonsmooth at the points which are required to construct the plan. This analysis leads directly to the incorporation of simple and realistic sensor models into the planning scheme.