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The robots environment is represented by a 3D geometric entity called Bump-Surface, which is embedded in a 4D Euclidean space. The multi-motion planning problem (MMPP) is resolved by simultaneously finding the paths for the set of robots represented by monoparametric smooth<jats:italic>C<\/jats:italic><jats:sup>2<\/jats:sup>curves onto the Bump-Surface, such that their inverse images onto the initial 2D workspace satisfy the optimization motion-planning criteria and constraints. The MMPP is expressed as an optimization problem, which is solved on the Bump-Surface using a genetic algorithm. The performance of the proposed approach is tested through a considerable number of simulated 2D dynamic environments with car-like robots.<\/jats:p>","DOI":"10.1017\/s0263574707003980","type":"journal-article","created":{"date-parts":[[2007,11,2]],"date-time":"2007-11-02T11:10:08Z","timestamp":1194001808000},"page":"525-536","source":"Crossref","is-referenced-by-count":10,"title":["Motion planning for multiple non-holonomic robots: a geometric approach"],"prefix":"10.1017","volume":"26","author":[{"given":"Elias K.","family":"Xidias","sequence":"first","affiliation":[]},{"given":"Nikos A.","family":"Aspragathos","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2008,7,1]]},"reference":[{"key":"S0263574707003980_ref34","first-page":"590","volume-title":"Proceedings of the 2006 I*PROMS NoE Virtual International Conference on Intelligent Production Machines and Systems","author":"Xidias"},{"key":"S0263574707003980_ref18","unstructured":"18. Hsu D. , Randomized Single-Query Motion Planning in Expansive Spaces Ph.D. Thesis (Stanford, CA: Computer Science Department, Stanford University, May 2000)."},{"key":"S0263574707003980_ref19","doi-asserted-by":"crossref","first-page":"2573","DOI":"10.1109\/ROBOT.1995.525645","volume-title":"Proceedings of The IEEE International Conference on Robotics and Automation","author":"Alami","year":"1995"},{"key":"S0263574707003980_ref16","first-page":"566","volume-title":"IEEE Trans. Robot Automat.","author":"Kavraki","year":"1996"},{"key":"S0263574707003980_ref14","first-page":"1012","volume-title":"IEEE Trans. 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