Metrics proposed for measuring the distance between two rigid-body poses: review, comparison, and combination

The concept of distance between two rigid-body poses is important in path planning, positioning precision, mechanism synthesis, and in many other applications. In the definition of such a distance, two approaches mainly prevail, which lead to a number of formulas devised to match the needs of motion tasks. 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.