A benchmark study on accuracy-controlled distance calculation between superellipsoid and superovoid contact geometries

• DOI: 10.1016/j.mechmachtheory.2017.04.008
• Publication Date: 2017-05-03T07:16:43Z
• Authors: Artur Alves Gonça...; Alexandre Bernardino; Joaquim Jorge; Daniel Simões Lopes
• Keywords: Parametric surface; iCub; Benchmark (surveying); Representation; Parametric equation; Volume mesh; Parametrization (atmospheric modeling)

Abstract Meshes are considered the gold standard regarding contact geometries of many mechanical models, even those represented with discrete surface contact elements. However, meshes may not be the best formulations when controlled precision and execution time become paramount. In this paper, we address parametric and implicit formulations for precise contact distance estimations between superovoidal shapes, which generalize superellipsoids. Parametric and implicit models provide more compact descriptions than meshes, while making it possible to approximate mechanical parts with great precision. Contrary to meshes, these geometric representations can then support fast calculation of distances with arbitrary precision without paying a storage or computation time penalty. We performed a benchmark study to compare different superellipsoidal and superovoidal contact geometry representations, including implicit surfaces, parametric surfaces and triangular meshes. We tested 10,000 contact pairs and also considered two application cases: robot fingers of an iCub and dental occlusion during bite. Our results show that the implicit model is the most efficient contact geometry representation, followed by parametric and mesh surfaces. In addition, results show that either implicit or parametric superovoids can provide more accurate distance estimations than meshes in practical settings where precise contact points, surface normals and clearance estimations are required.