Robot path planning using Voronoi classifiers

摘要

This paper details the development of a minimal set of locally distributed navigation beacons that can provide new waypoints in dense obstacle fields. The 'beacons' provide direction and magnitude inputs for the robot to use for its next waypoint. The beacons are placed in such a manner that all locations within a bounded playing field can reach a goal area in a desired number of steps. This guarantee of total coverage comes only with tuning the magnitudes and directions of each beacon (as well as their position in the field). Key to this approach is the underlying 'color map'. The color map assigns a color to regions of the playing field based on whether the region terminates at the goal ('green'); leaves the playing field and doesn't return ('red'); or doesn’t leave the playing field but does not terminate at the goal (within a fixed number of steps)-also know as 'stagnation' ('yellow'). Changes in the placement of the beacons and their associated parameters result in changes to the color map. A software tool has been developed to allow a user to see the instantaneous changes in the color map when changes are made to the beacons. This paper will also describe how the beacons are related to both Voronoi diagrams and nearest neighbor classifiers-thus generating the final name for the navigation beacons; Voronoi Classifiers. Future work is detailed including the development of color maps for other cost metrics (such as distance traveled, power consumed or terrain trafficabilty) and efforts in developing an algorithm to find the infimum solution (minimize the maximum steps, distance, etc.).