{"title":"利用Campbell-Baker-Hausdorff-Dynkin公式生成Chen-Fliess-Sussmann方程","authors":"I. Dulęba, J. Jagodziński","doi":"10.1109/MMAR.2011.6031316","DOIUrl":null,"url":null,"abstract":"Generating and solving the Chen-Fliess-Sussmann (CFS) equation for a given representation of motion is a crucial step in deriving controls to steer nilpotent nonholonomic systems using the Lafferriere-Sussmann method. The equation can be quite complicated, and its derivation differs substantially from one representation to another. Therefore instead to derive CFS for a given hard-to-compute representation we propose to derive it for any easy-to-compute representation and then to transform it to the given representation. For this purpose the Campbell-Baker-Hausdorff-Dynkin formula is applied. This approach is illustrated on generating and solving CFS for forward, backward and canonical representations.","PeriodicalId":440376,"journal":{"name":"2011 16th International Conference on Methods & Models in Automation & Robotics","volume":"40 4 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2011-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Generating Chen-Fliess-Sussmann equation via Campbell-Baker-Hausdorff-Dynkin formula\",\"authors\":\"I. Dulęba, J. Jagodziński\",\"doi\":\"10.1109/MMAR.2011.6031316\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Generating and solving the Chen-Fliess-Sussmann (CFS) equation for a given representation of motion is a crucial step in deriving controls to steer nilpotent nonholonomic systems using the Lafferriere-Sussmann method. The equation can be quite complicated, and its derivation differs substantially from one representation to another. Therefore instead to derive CFS for a given hard-to-compute representation we propose to derive it for any easy-to-compute representation and then to transform it to the given representation. For this purpose the Campbell-Baker-Hausdorff-Dynkin formula is applied. This approach is illustrated on generating and solving CFS for forward, backward and canonical representations.\",\"PeriodicalId\":440376,\"journal\":{\"name\":\"2011 16th International Conference on Methods & Models in Automation & Robotics\",\"volume\":\"40 4 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2011-09-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2011 16th International Conference on Methods & Models in Automation & Robotics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/MMAR.2011.6031316\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2011 16th International Conference on Methods & Models in Automation & Robotics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/MMAR.2011.6031316","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Generating Chen-Fliess-Sussmann equation via Campbell-Baker-Hausdorff-Dynkin formula
Generating and solving the Chen-Fliess-Sussmann (CFS) equation for a given representation of motion is a crucial step in deriving controls to steer nilpotent nonholonomic systems using the Lafferriere-Sussmann method. The equation can be quite complicated, and its derivation differs substantially from one representation to another. Therefore instead to derive CFS for a given hard-to-compute representation we propose to derive it for any easy-to-compute representation and then to transform it to the given representation. For this purpose the Campbell-Baker-Hausdorff-Dynkin formula is applied. This approach is illustrated on generating and solving CFS for forward, backward and canonical representations.
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