Proceedings International Conference on Advanced Robotics, Spain, September 1995. 1 OPTIMUM EXPLORATIONS IN THE SELF-LOCALIZATION OF MOBILE ROBOTS IN POLYGONAL ENVIRONMENTS G. Borghi*+ and V. Caglioti* * PM-AI&R Project - Dipartimento di Elettronica e Informazione Politecnico di Milano P.za Leonardo da Vinci, 32 - 20133 Milano, Italy + Institute LADSEB of CNR (National Research Council of Italy) Corso Stati Uniti 4, 35020 Padova, Italy phone : +39 2 2399 3622; Fax : +39 2 2399 3411; E-mail: {borghi, caglioti}@elet.polimi.it Abstract - 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. 1. INTRODUCTION The accurate self-location of a mobile robot is often required, when, e.g., moving from a navigation phase to a manipulation phase, or while navigating in a cluttered environment (in order to avoid collisions). The use of simple sensors, such as, e.g., orientable range finders, is appealing because of their simplicity. However, due to the reduced amount of information they provide, often many sensor measurements are needed in order to accurately localize a mobile robot. In order to expedite the robot location, the number of the required sensor detections must be restricted: thus detections must be selected, that maximally reduce the residual (a posteriori) positional uncertainty [2]. This paper addresses the case in which the environment is known and polygonal. Many practical cases fall within such a situation. A straightforward method is illustrated to retrieve a sequence of sensor explorations, which minimizes a criterion based on the a posteriori uncertainty of the robot position. It is supposed that a current estimate of the robot position is given together with the covariance matrix of the position parameters. This current information can be derived from, e.g., odometry or from previous sensor observations. The main result presented in this paper is that, under widely acceptable hypotheses, the best exploration points are to be found among the endpoints of the segments constituting the polygonal environment. An uncertainty criterion is considered, given by the determinant the covariance matrix of the robot position parameters. The determination of optimal sensor explorations is not a new issue in the robotics literature ([1], [3], [4], [5]). In [3] the optimal exploration is determined for the characterization of an unknown object. In [1] the optimal viewpoint is determined that allows a best recognition of the observed object among a given, finite set of possible ones. In [5] the optimal placement of a hit-or-miss sensor is determined for the discrimination of a “context” among a finite set of given ones. Hit-or-miss sensors are used also in [4], where a variety of problems are considered, such as localization and recognition. Most of the above methods require the analysis of the whole set of the possible sensor explorations in order to determine the optimal one, because of the generality of the considered problems. The specificity of the problem addressed in this paper makes it possible to derive a straightforward method to determine the optimal sensor exploration: in particular, for each of the linear segments which constitute the environment boundary, only the two endpoints must be examined. In Sect. 2. the minimization problem is formulated. In Sect. 3 the main result of this paper is derived. Experimental results on a mobile robot are reported in Sect. 4. Section 5 contains some concluding remarks. 2. PROBLEM FORMULATION The environment, within which a mobile robot has to be localized, is represented by a line L, constituted by a set of straight segments. For instance, L may represent the internal contour of a room, within which the position of a mobile robot has to be determined. The robot position is represented by the Cartesian coordinates (x,y) of the origin O of a robot centered reference and by its orientation with respect to the environment L. We suppose that an a priori estimate of the position parameters is given, derived from, e.g., odometry, together with their covariance matrix Λ :