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Despite the different approaches and formulas, some important theoretical results, which drive toward distance-metrics definitions useful for design and application purposes, have been stated. This paper summarizes the two different approaches together with a critical review of the literature on the distance metrics they generated, and, then, it illustrates a technique, previously proposed by the author, for combining different metrics to obtain novel distance-metric definitions that are tailored to specific applications.<\/jats:p>","DOI":"10.1017\/s0263574723001388","type":"journal-article","created":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T11:05:19Z","timestamp":1698059119000},"page":"302-318","source":"Crossref","is-referenced-by-count":8,"title":["Metrics proposed for measuring the distance between two rigid-body poses: review, comparison, and combination"],"prefix":"10.1017","volume":"42","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3925-3016","authenticated-orcid":false,"given":"Raffaele","family":"Di Gregorio","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2023,10,23]]},"reference":[{"key":"S0263574723001388_ref12","unstructured":"[12] Larochelle, P. , \u201cOn the Geometry of Approximate Bi-invariant Projective Displacement Metrics,\u201d In: Procs. of the 10th World Congress on the Theory of Machines and Mechanisms, Oulu, Finland, vol. 2 (1999) pp. 548\u2013553."},{"key":"S0263574723001388_ref8","doi-asserted-by":"publisher","DOI":"10.1115\/1.2943301"},{"key":"S0263574723001388_ref16","doi-asserted-by":"publisher","DOI":"10.1115\/1.2735640"},{"key":"S0263574723001388_ref18","doi-asserted-by":"publisher","DOI":"10.1177\/027836499401300101"},{"key":"S0263574723001388_ref15","doi-asserted-by":"publisher","DOI":"10.1016\/j.mechmachtheory.2006.03.010"},{"key":"S0263574723001388_ref3","doi-asserted-by":"publisher","DOI":"10.1115\/1.2826115"},{"key":"S0263574723001388_ref22","unstructured":"[22] Zefran, M. , Continuous Methods for Motion Planning Ph.D. dissertation (Univ. 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