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The Minkowski sum is used in a variety of applications such as robot motion planning and particle flow simulation requiring collision detection. Many of them are computed based on Minkowski sum, whose accuracy and processing time depend on how the mesh is created. We approximate Minkowski sum with a superellipsoid function. The superellipsoid has various shapes with the value of the exponents, and the computation of the parameters including the exponents is an algebraic computation with the time complexity <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\varvec{O}(1)$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mrow>\n                      <mml:mi>O<\/mml:mi>\n                    <\/mml:mrow>\n                    <mml:mo>(<\/mml:mo>\n                    <mml:mn>1<\/mml:mn>\n                    <mml:mo>)<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. As a result, approximation error is small and computation is fast in all combinations of rotational ellipsoids. In addition, collision is quickly detected by solving the inequality of superellipsoid.<\/jats:p>","DOI":"10.1007\/s00371-024-03445-9","type":"journal-article","created":{"date-parts":[[2024,6,17]],"date-time":"2024-06-17T10:01:53Z","timestamp":1718618513000},"page":"4609-4621","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Fast and precise approximation of Minkowski sum of two rotational ellipsoids with a superellipsoid"],"prefix":"10.1007","volume":"40","author":[{"given":"Ryunosuke","family":"Yamada","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1573-1928","authenticated-orcid":false,"given":"Tokuo","family":"Tsuji","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1053-583X","authenticated-orcid":false,"given":"Tatsuhiro","family":"Hiramitsu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1588-4825","authenticated-orcid":false,"given":"Hiroaki","family":"Seki","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2858-6368","authenticated-orcid":false,"given":"Toshihiro","family":"Nishimura","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6862-9719","authenticated-orcid":false,"given":"Yosuke","family":"Suzuki","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2549-1435","authenticated-orcid":false,"given":"Tetsuyou","family":"Watanabe","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,6,17]]},"reference":[{"key":"3445_CR1","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1109\/TIE.2003.809406","volume":"50","author":"K-S Hwang","year":"2003","unstructured":"Hwang, K.-S., Ju, M.-Y., Chen, Y.-J.: Speed alteration strategy for multi-joint robots in co-working environment. 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