Optimum Explorations in the Self-localization of Mobile Robots in Polygonal Environments

A straightforward method is presented for the determination of the optimal sensor explorations in a three degrees of freedom localization problem relative to a mobile robot moving within a known, polygonal environment. Optimality is intended in the sense of the a posteriori (i.e., after the explorations) covariance matrix of the robot position and orien ,tation parameters. The used sensor is an orientable laser range finder, mounted on the mobile robot. It is found that, under largely acceptable hypotheses, the optimum exploration points (i.e., the points of the environment towards which the range finder is aimed) are among the vertexes of the polygonal environment. The on-line processing time required to find the optimal vertexes is reasonable, since it is neglectable with respect to the time normally due to the sensor movement.