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When analyzing the solution process of the <jats:inline-formula>\n                     <c:math xmlns:c=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\">\n                        <c:mtext>S<\/c:mtext>\n                     <\/c:math>\n                  <\/jats:inline-formula>-shape acceleration and deceleration directly, using a traditional numerical solution method, the phenomenon of \u201csolving the interval jump\u201d arises, which is the main reason for low efficiency and poor stability of the solution. According to the <jats:inline-formula>\n                     <e:math xmlns:e=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\">\n                        <e:mtext>S<\/e:mtext>\n                     <\/e:math>\n                  <\/jats:inline-formula>-curve profile and solution, the concept of separating the curve profile recognition from the velocity solution was proposed, and a method of quickly identifying the interval of the solution location was introduced. Through the method mentioned above, the complete acceleration and deceleration curve parameters can be obtained through a one-time plan and a one-time solution, and the solution efficiency and stability are guaranteed; solving the Newton problem depends too much on the initial value of Newton velocity, which not only retains the speed advantage of the Newton method but also uses the downhill factor to ensure its convergence. Through the simulation comparison and analysis, the efficiency, stability, and universality of the method are verified.<\/jats:p>","DOI":"10.1155\/2020\/8884678","type":"journal-article","created":{"date-parts":[[2020,11,27]],"date-time":"2020-11-27T03:35:08Z","timestamp":1606448108000},"page":"1-14","source":"Crossref","is-referenced-by-count":3,"title":["Efficient Planning and Solving Algorithm of <a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\">\n                     <a:mi>S<\/a:mi>\n                  <\/a:math>-Shape Acceleration and Deceleration"],"prefix":"10.1155","volume":"2020","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3379-9579","authenticated-orcid":true,"given":"Zhijie","family":"Li","sequence":"first","affiliation":[{"name":"Institute of Advanced Manufacturing and Intelligent Technology, Beijing University of Technology, Beijing 100124, China"},{"name":"Beijing Key Laboratory of Advanced Manufacturing Technology, Beijing University of Technology, Beijing 100124, China"},{"name":"College of Mechanical and Electronics Engineering, North China Institute of Aerospace Engineering, Langfang 065600, China"},{"name":"Machinery Industry Key Laboratory of Heavy Machine Tool Digital Design and Testing Technology, Beijing 100124, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3510-3766","authenticated-orcid":true,"given":"Ligang","family":"Cai","sequence":"additional","affiliation":[{"name":"Beijing Key Laboratory of Advanced Manufacturing Technology, Beijing University of Technology, Beijing 100124, China"},{"name":"Machinery Industry Key Laboratory of Heavy Machine Tool Digital Design and Testing Technology, Beijing 100124, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6164-3283","authenticated-orcid":true,"given":"Zhifeng","family":"Liu","sequence":"additional","affiliation":[{"name":"Institute of Advanced Manufacturing and Intelligent Technology, Beijing University of Technology, Beijing 100124, China"},{"name":"Beijing Key Laboratory of Advanced Manufacturing Technology, Beijing University of Technology, Beijing 100124, China"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1109\/41.824135"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1007\/s00170-004-1884-2"},{"key":"3","first-page":"39","article-title":"Improved exponential acceleration and deceleration algorithm","volume":"1","author":"Y. 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