Navigation in Landmark Networks

Abstract

Service robots for everyday use must maneuver accurately and repeatably throughout their work space. For large work spaces this, today still, requires some sort of devices like landmarks from which robot positions can be inferred. Here, trilateration is considered which means that robot positions are inferred from distances between landmarks and the robot. While robot localization calls for precision and, hence, for many landmarks, commercial issues call for few landmarks. The issue of their suitable placement prevails in both cases.

The predominant Gauss-Newton algorithm will be made robust against getting stuck in local minima by multi-start initialization. The approach is free of external parameters and, so, ideally suited for on-board robot use. Complementary, landmarks should be placed so that computed robot positions suffer least from measurement errors.

Dilution of precision (DOP) is adopted as a measure of quality for landmark positions. The dilution of precision can be shown to be proportional to the size of the error ellipses in two dimensions and increasing in the size of error ellipsoids in three dimensions. In both cases, the standard deviation of the position error is approximately proportional to the standard deviation of the measurements and the DOP. Though DOP minimization over the robot workspace is too complex for an automatic approach, it is well suited for simulation. Interactive planning support for the number and the positions of the landmarks becomes feasible.