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To fulfill this requirement, we introduce in each cell a local counter keeping track of the distance run by the wave from its source. This allows maintaining the wave velocity constant in all possible directions even in the presence of nonconductive local areas (obstacles) with complex spatial geometry. Then, we illustrate the model on the problem of real-time building of cognitive maps used for navigation of a mobile robot. The isotropic property of the CA helps obtaining \u201csmooth\u201d trajectories and hence natural robot movement. The accuracy and flexibility of the approach are proved experimentally by driving the robot to a target avoiding collisions with obstacles. <\/jats:p>","DOI":"10.1142\/s0219525916500120","type":"journal-article","created":{"date-parts":[[2016,12,23]],"date-time":"2016-12-23T15:37:51Z","timestamp":1482507471000},"page":"1650012","source":"Crossref","is-referenced-by-count":10,"title":["WAVES IN ISOTROPIC TOTALISTIC CELLULAR AUTOMATA: APPLICATION TO REAL-TIME ROBOT NAVIGATION"],"prefix":"10.1142","volume":"19","author":[{"given":"C.","family":"CALVO","sequence":"first","affiliation":[{"name":"Instituto de Matematica Interdiciplinar, Universidad Complutense de Madrid, Avda. Complutense s\/n, Madrid, 28040, Spain"}]},{"given":"J. A.","family":"VILLACORTA-ATIENZA","sequence":"additional","affiliation":[{"name":"Instituto de Matematica Interdiciplinar, Universidad Complutense de Madrid, Avda. Complutense s\/n, Madrid, 28040, Spain"}]},{"given":"V. 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