{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,17]],"date-time":"2026-08-17T15:00:49Z","timestamp":1786978849716,"version":"3.56.0"},"publisher-location":"Cham","reference-count":24,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783031417238","type":"print"},{"value":"9783031417245","type":"electronic"}],"license":[{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023]]},"DOI":"10.1007\/978-3-031-41724-5_21","type":"book-chapter","created":{"date-parts":[[2023,8,23]],"date-time":"2023-08-23T03:02:38Z","timestamp":1692759758000},"page":"393-419","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Inverse Kinematics and\u00a0Path Planning of\u00a0Manipulator Using Real Quantifier Elimination Based on\u00a0Comprehensive Gr\u00f6bner Systems"],"prefix":"10.1007","author":[{"given":"Mizuki","family":"Yoshizawa","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0846-3643","authenticated-orcid":false,"given":"Akira","family":"Terui","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2193-3198","authenticated-orcid":false,"given":"Masahiko","family":"Mikawa","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,8,24]]},"reference":[{"key":"21_CR1","doi-asserted-by":"publisher","unstructured":"Becker, E., W\u00f6ermann, T.: On the trace formula for quadratic forms. In: Recent Advances in Real Algebraic Geometry and Quadratic Forms (Berkeley, CA, 1990\/1991; San Francisco, CA, 1991), Contemporary Mathematics, vol. 155, pp. 271\u2013291. AMS, Providence (1994). https:\/\/doi.org\/10.1090\/conm\/155\/01385","DOI":"10.1090\/conm\/155\/01385"},{"key":"21_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1007\/978-3-642-23568-9_9","volume-title":"Computer Algebra in Scientific Computing","author":"C Chen","year":"2011","unstructured":"Chen, C., Maza, M.M.: Semi-algebraic description of the equilibria of dynamical systems. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds.) CASC 2011. LNCS, vol. 6885, pp. 101\u2013125. Springer, Heidelberg (2011). https:\/\/doi.org\/10.1007\/978-3-642-23568-9_9"},{"key":"21_CR3","doi-asserted-by":"publisher","DOI":"10.1007\/b138611","volume-title":"Using Algebraic Geometry","author":"DA Cox","year":"2005","unstructured":"Cox, D.A., Little, J., O\u2019Shea, D.: Using Algebraic Geometry, 2nd edn. Springer, Heidelberg (2005). https:\/\/doi.org\/10.1007\/b138611","edition":"2"},{"key":"21_CR4","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-16721-3","volume-title":"Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra","author":"DA Cox","year":"2015","unstructured":"Cox, D.A., Little, J., O\u2019Shea, D.: Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 4th edn. Springer, Heidelberg (2015). https:\/\/doi.org\/10.1007\/978-3-319-16721-3","edition":"4"},{"key":"21_CR5","unstructured":"Faug\u00e8re, J.C., Merlet, J.P., Rouillier, F.: On solving the direct kinematics problem for parallel robots. Research Report RR-5923, INRIA (2006). https:\/\/hal.inria.fr\/inria-00072366"},{"key":"21_CR6","doi-asserted-by":"publisher","unstructured":"Fukasaku, R., Iwane, H., Sato, Y.: Real quantifier elimination by computation of comprehensive Gr\u00f6bner systems. In: Proceedings of the 2015 ACM on International Symposium on Symbolic and Algebraic Computation, ISSAC 2015, pp. 173\u2013180. ACM, New York (2015). https:\/\/doi.org\/10.1145\/2755996.2756646","DOI":"10.1145\/2755996.2756646"},{"key":"21_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/978-3-030-52200-1_1","volume-title":"Mathematical Software \u2013 ICMS 2020","author":"N Horigome","year":"2020","unstructured":"Horigome, N., Terui, A., Mikawa, M.: A design and an implementation of an inverse kinematics computation in robotics using Gr\u00f6bner bases. In: Bigatti, A.M., Carette, J., Davenport, J.H., Joswig, M., de Wolff, T. (eds.) ICMS 2020. LNCS, vol. 12097, pp. 3\u201313. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-52200-1_1"},{"issue":"4","key":"21_CR8","doi-asserted-by":"publisher","first-page":"523","DOI":"10.1016\/0094-114X(93)90033-R","volume":"28","author":"CM Kalker-Kalkman","year":"1993","unstructured":"Kalker-Kalkman, C.M.: An implementation of Buchbergers\u2019 algorithm with applications to robotics. Mech. Mach. Theory 28(4), 523\u2013537 (1993). https:\/\/doi.org\/10.1016\/0094-114X(93)90033-R","journal-title":"Mech. Mach. Theory"},{"issue":"6","key":"21_CR9","doi-asserted-by":"publisher","first-page":"636","DOI":"10.1016\/j.jsc.2007.01.007","volume":"42","author":"D Lazard","year":"2007","unstructured":"Lazard, D., Rouillier, F.: Solving parametric polynomial systems. J. Symb. Comput. 42(6), 636\u2013667 (2007). https:\/\/doi.org\/10.1016\/j.jsc.2007.01.007","journal-title":"J. Symb. Comput."},{"key":"21_CR10","doi-asserted-by":"crossref","DOI":"10.1017\/9781316661239","volume-title":"Modern Robotics: Mechanics, Planning, and Control","author":"KM Lynch","year":"2017","unstructured":"Lynch, K.M., Park, F.C.: Modern Robotics: Mechanics, Planning, and Control. Cambridge University Press, Cambridge (2017)"},{"key":"21_CR11","doi-asserted-by":"publisher","unstructured":"Maekawa, M., Noro, M., Ohara, K., Takayama, N., Tamura, K.: The design and implementation of OpenXM-RFC 100 and 101. In: Shirayanagi, K., Yokoyama, K. (eds.) Computer Mathematics: Proceedings of the Fifth Asian Symposium on Computer Mathematics (ASCM 2001), pp. 102\u2013111. World Scientific (2001). https:\/\/doi.org\/10.1142\/9789812799661_0011","DOI":"10.1142\/9789812799661_0011"},{"key":"21_CR12","unstructured":"Nabeshima, K.: CGS: a program for computing comprehensive Gr\u00f6bner systems in a polynomial ring [computer software] (2018). https:\/\/www.rs.tus.ac.jp\/nabeshima\/softwares.html. Accessed 30 June 2023"},{"key":"21_CR13","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1007\/978-3-662-05148-1_8","volume-title":"Algebra, Geometry and Software Systems","author":"M Noro","year":"2003","unstructured":"Noro, M.: A computer algebra system: Risa\/Asir. In: Joswig, M., Takayama, N. (eds.) Algebra, Geometry and Software Systems, pp. 147\u2013162. Springer, Heidelberg (2003). https:\/\/doi.org\/10.1007\/978-3-662-05148-1_8"},{"key":"21_CR14","doi-asserted-by":"publisher","unstructured":"Otaki, S., Terui, A., Mikawa, M.: A design and an implementation of an inverse kinematics computation in robotics using real quantifier elimination based on comprehensive Gr\u00f6bner systems. Preprint (2021). https:\/\/doi.org\/10.48550\/arXiv.2111.00384, arXiv:2111.00384","DOI":"10.48550\/arXiv.2111.00384"},{"key":"21_CR15","doi-asserted-by":"publisher","unstructured":"Pedersen, P., Roy, M.F., Szpirglas, A.: Counting real zeros in the multivariate case. In: Computational Algebraic Geometry (Nice, 1992). Progress in Mathematics, vol. 109, pp. 203\u2013224. Birkh\u00e4user Boston, Boston (1993). https:\/\/doi.org\/10.1007\/978-1-4612-2752-6_15","DOI":"10.1007\/978-1-4612-2752-6_15"},{"key":"21_CR16","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-84628-642-1","volume-title":"Robotics: Modelling, Planning and Control","author":"B Siciliano","year":"2008","unstructured":"Siciliano, B., Sciavicco, L., Villani, L., Oriolo, G.: Robotics: Modelling, Planning and Control. Springer, Heidelberg (2008). https:\/\/doi.org\/10.1007\/978-1-84628-642-1"},{"key":"21_CR17","doi-asserted-by":"publisher","unstructured":"da Silva, S.R.X., Schnitman, L., Cesca Filho, V.: A solution of the inverse kinematics problem for a 7-degrees-of-freedom serial redundant manipulator using Gr\u00f6bner bases theory. Math. Probl. Eng. 2021, 6680687 (2021). https:\/\/doi.org\/10.1155\/2021\/6680687","DOI":"10.1155\/2021\/6680687"},{"key":"21_CR18","unstructured":"Terui, A., Yoshizawa, M., Mikawa, M.: ev3-cgs-qe-ik-2: an inverse kinematics solver based on the CGS-QE algorithm for an EV3 manipulator [computer software] (2023). https:\/\/github.com\/teamsnactsukuba\/ev3-cgs-qe-ik-2"},{"key":"21_CR19","unstructured":"The PARI Group, Univ. Bordeaux: PARI\/GP version 2.13.1 (2021). https:\/\/pari.math.u-bordeaux.fr\/"},{"key":"21_CR20","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1007\/s11044-010-9241-8","volume":"25","author":"T Uchida","year":"2011","unstructured":"Uchida, T., McPhee, J.: Triangularizing kinematic constraint equations using Gr\u00f6bner bases for real-time dynamic simulation. Multibody Syst. Dyn. 25, 335\u2013356 (2011). https:\/\/doi.org\/10.1007\/s11044-010-9241-8","journal-title":"Multibody Syst. Dyn."},{"key":"21_CR21","doi-asserted-by":"publisher","first-page":"144","DOI":"10.1016\/j.mechmachtheory.2012.01.015","volume":"52","author":"T Uchida","year":"2012","unstructured":"Uchida, T., McPhee, J.: Using Gr\u00f6bner bases to generate efficient kinematic solutions for the dynamic simulation of multi-loop mechanisms. Mech. Mach. Theory 52, 144\u2013157 (2012). https:\/\/doi.org\/10.1016\/j.mechmachtheory.2012.01.015","journal-title":"Mech. Mach. Theory"},{"key":"21_CR22","series-title":"Texts and Monographs in Symbolic Computation","doi-asserted-by":"publisher","first-page":"376","DOI":"10.1007\/978-3-7091-9459-1_20","volume-title":"Quantifier Elimination and Cylindrical Algebraic Decomposition","author":"V Weispfenning","year":"1998","unstructured":"Weispfenning, V.: A new approach to quantifier elimination for real algebra. In: Caviness, B.F., Johnson, J.R. (eds.) Quantifier Elimination and Cylindrical Algebraic Decomposition. Texts and Monographs in Symbolic Computation, pp. 376\u2013392. Springer, Vienna (1998). https:\/\/doi.org\/10.1007\/978-3-7091-9459-1_20"},{"key":"21_CR23","unstructured":"Wolfram Research Inc: Mathematica, Version 13.1 [computer software] (2022). https:\/\/www.wolfram.com\/mathematica. Accessed 14 May 2023"},{"issue":"1","key":"21_CR24","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1007\/BF02713938","volume":"44","author":"L Yang","year":"2001","unstructured":"Yang, L., Hou, X., Xia, B.: A complete algorithm for automated discovering of a class of inequality-type theorems. Sci. China Ser. F Inf. Sci. 44(1), 33\u201349 (2001). https:\/\/doi.org\/10.1007\/BF02713938","journal-title":"Sci. China Ser. F Inf. Sci."}],"container-title":["Lecture Notes in Computer Science","Computer Algebra in Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-41724-5_21","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,26]],"date-time":"2024-10-26T12:38:51Z","timestamp":1729946331000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-41724-5_21"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023]]},"ISBN":["9783031417238","9783031417245"],"references-count":24,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-41724-5_21","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023]]},"assertion":[{"value":"24 August 2023","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"CASC","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Workshop on Computer Algebra in Scientific Computing","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Havana","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Cuba","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2023","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"28 August 2023","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"1 September 2023","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"25","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"casc2023","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/casc-conference.org\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"EasyChair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"29","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"22","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"0","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"76% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3.17","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"1.41","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}