{"id":"https://openalex.org/W4389666780","doi":"https://doi.org/10.1109/iros55552.2023.10342217","title":"A Unified Perspective on Multiple Shooting In Differential Dynamic Programming","display_name":"A Unified Perspective on Multiple Shooting In Differential Dynamic Programming","publication_year":2023,"publication_date":"2023-10-01","ids":{"openalex":"https://openalex.org/W4389666780","doi":"https://doi.org/10.1109/iros55552.2023.10342217"},"language":"en","primary_location":{"id":"doi:10.1109/iros55552.2023.10342217","is_oa":false,"landing_page_url":"https://doi.org/10.1109/iros55552.2023.10342217","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100661194","display_name":"He Li","orcid":"https://orcid.org/0000-0002-9826-2353"},"institutions":[{"id":"https://openalex.org/I107639228","display_name":"University of Notre Dame","ror":"https://ror.org/00mkhxb43","country_code":"US","type":"education","lineage":["https://openalex.org/I107639228"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"He Li","raw_affiliation_strings":["University of Notre Dame,IN,USA","University of Notre Dame, IN, USA"],"affiliations":[{"raw_affiliation_string":"University of Notre Dame,IN,USA","institution_ids":["https://openalex.org/I107639228"]},{"raw_affiliation_string":"University of Notre Dame, IN, USA","institution_ids":["https://openalex.org/I107639228"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101775413","display_name":"Wenhao Yu","orcid":"https://orcid.org/0000-0002-6052-0839"},"institutions":[{"id":"https://openalex.org/I1291425158","display_name":"Google (United States)","ror":"https://ror.org/00njsd438","country_code":"US","type":"company","lineage":["https://openalex.org/I1291425158","https://openalex.org/I4210128969"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Wenhao Yu","raw_affiliation_strings":["Robotics at Google,Mountain View,CA,USA","Robotics at Google, Mountain View, CA, USA"],"affiliations":[{"raw_affiliation_string":"Robotics at Google,Mountain View,CA,USA","institution_ids":["https://openalex.org/I1291425158"]},{"raw_affiliation_string":"Robotics at Google, Mountain View, CA, USA","institution_ids":["https://openalex.org/I1291425158"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086928709","display_name":"Tingnan Zhang","orcid":null},"institutions":[{"id":"https://openalex.org/I1291425158","display_name":"Google (United States)","ror":"https://ror.org/00njsd438","country_code":"US","type":"company","lineage":["https://openalex.org/I1291425158","https://openalex.org/I4210128969"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tingnan Zhang","raw_affiliation_strings":["Robotics at Google,Mountain View,CA,USA","Robotics at Google, Mountain View, CA, USA"],"affiliations":[{"raw_affiliation_string":"Robotics at Google,Mountain View,CA,USA","institution_ids":["https://openalex.org/I1291425158"]},{"raw_affiliation_string":"Robotics at Google, Mountain View, CA, USA","institution_ids":["https://openalex.org/I1291425158"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029126529","display_name":"Patrick M. Wensing","orcid":"https://orcid.org/0000-0002-9041-5175"},"institutions":[{"id":"https://openalex.org/I107639228","display_name":"University of Notre Dame","ror":"https://ror.org/00mkhxb43","country_code":"US","type":"education","lineage":["https://openalex.org/I107639228"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Patrick M. Wensing","raw_affiliation_strings":["University of Notre Dame,IN,USA","University of Notre Dame, IN, USA"],"affiliations":[{"raw_affiliation_string":"University of Notre Dame,IN,USA","institution_ids":["https://openalex.org/I107639228"]},{"raw_affiliation_string":"University of Notre Dame, IN, USA","institution_ids":["https://openalex.org/I107639228"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100661194"],"corresponding_institution_ids":["https://openalex.org/I107639228"],"apc_list":null,"apc_paid":null,"fwci":1.125,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.75928439,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"9978","last_page":"9985"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10879","display_name":"Robotic Locomotion and Control","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10879","display_name":"Robotic Locomotion and Control","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10462","display_name":"Reinforcement Learning in Robotics","score":0.9932000041007996,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11023","display_name":"Prosthetics and Rehabilitation Robotics","score":0.9793999791145325,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.7652479410171509},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6692871451377869},{"id":"https://openalex.org/keywords/differential-dynamic-programming","display_name":"Differential dynamic programming","score":0.6053600907325745},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5925620794296265},{"id":"https://openalex.org/keywords/shooting-method","display_name":"Shooting method","score":0.5875951051712036},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.565914511680603},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5401059985160828},{"id":"https://openalex.org/keywords/sequential-quadratic-programming","display_name":"Sequential quadratic programming","score":0.5381600856781006},{"id":"https://openalex.org/keywords/trajectory-optimization","display_name":"Trajectory optimization","score":0.5163382291793823},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5052443146705627},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.46490371227264404},{"id":"https://openalex.org/keywords/dynamic-programming","display_name":"Dynamic programming","score":0.4482800364494324},{"id":"https://openalex.org/keywords/penalty-method","display_name":"Penalty method","score":0.41748854517936707},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4143514335155487},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.287422776222229},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2576944828033447},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.2483217716217041},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.20882999897003174},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.17096883058547974}],"concepts":[{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.7652479410171509},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6692871451377869},{"id":"https://openalex.org/C92292787","wikidata":"https://www.wikidata.org/wiki/Q5275342","display_name":"Differential dynamic programming","level":3,"score":0.6053600907325745},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5925620794296265},{"id":"https://openalex.org/C4195266","wikidata":"https://www.wikidata.org/wiki/Q1749769","display_name":"Shooting method","level":3,"score":0.5875951051712036},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.565914511680603},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5401059985160828},{"id":"https://openalex.org/C198927703","wikidata":"https://www.wikidata.org/wiki/Q4373881","display_name":"Sequential quadratic programming","level":3,"score":0.5381600856781006},{"id":"https://openalex.org/C173246807","wikidata":"https://www.wikidata.org/wiki/Q7833062","display_name":"Trajectory optimization","level":3,"score":0.5163382291793823},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5052443146705627},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.46490371227264404},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.4482800364494324},{"id":"https://openalex.org/C6180225","wikidata":"https://www.wikidata.org/wiki/Q3411771","display_name":"Penalty method","level":2,"score":0.41748854517936707},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4143514335155487},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.287422776222229},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2576944828033447},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.2483217716217041},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.20882999897003174},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.17096883058547974},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/iros55552.2023.10342217","is_oa":false,"landing_page_url":"https://doi.org/10.1109/iros55552.2023.10342217","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W1562460111","https://openalex.org/W1566070776","https://openalex.org/W1582919213","https://openalex.org/W1945123189","https://openalex.org/W1970101292","https://openalex.org/W2087617385","https://openalex.org/W2158370675","https://openalex.org/W2198582666","https://openalex.org/W2529220408","https://openalex.org/W2909331752","https://openalex.org/W2963689432","https://openalex.org/W2963801017","https://openalex.org/W2968213087","https://openalex.org/W2970228732","https://openalex.org/W3000464739","https://openalex.org/W3004162504","https://openalex.org/W3041567964","https://openalex.org/W3081791272","https://openalex.org/W3093175803","https://openalex.org/W3093326211","https://openalex.org/W3105372678","https://openalex.org/W3123819824","https://openalex.org/W3132444912","https://openalex.org/W3184213034","https://openalex.org/W3200418126","https://openalex.org/W4221144238","https://openalex.org/W4225857316","https://openalex.org/W4281622689","https://openalex.org/W4286423847","https://openalex.org/W4301909677","https://openalex.org/W4365420601","https://openalex.org/W4378696928","https://openalex.org/W6633623183","https://openalex.org/W6843520547","https://openalex.org/W6845010705"],"related_works":["https://openalex.org/W1968991653","https://openalex.org/W2371283014","https://openalex.org/W2393133128","https://openalex.org/W4254090244","https://openalex.org/W2019540899","https://openalex.org/W298733438","https://openalex.org/W2997980259","https://openalex.org/W2036696762","https://openalex.org/W2557849661","https://openalex.org/W1573206772"],"abstract_inverted_index":{"Differential":[0],"Dynamic":[1],"Programming":[2],"(DDP)":[3],"is":[4,26,53,94,140],"an":[5,134],"efficient":[6],"computational":[7],"tool":[8],"for":[9,57,119,128,143,150],"solving":[10],"nonlinear":[11],"optimal":[12],"control":[13,98],"problems.":[14],"It":[15],"was":[16],"originally":[17],"designed":[18],"as":[19],"a":[20,112,132,137,154,161],"single":[21,162],"shooting":[22,42,61,163],"method":[23,93],"and":[24,82,111,136],"thus":[25],"sensitive":[27],"to":[28,40,47,86,96],"the":[29,36,58,64,84,99,104],"initial":[30,48],"guess":[31],"supplied.":[32],"This":[33],"work":[34],"considers":[35],"extension":[37],"of":[38,123],"DDP":[39,65],"multiple":[41,78],"(MS),":[43],"improving":[44,103],"its":[45,158],"robustness":[46],"guesses.":[49],"A":[50,91],"novel":[51],"derivation":[52,75],"proposed":[54],"that":[55],"accounts":[56],"defect":[59],"between":[60],"segments":[62],"during":[63],"backward":[66],"pass,":[67],"while":[68],"still":[69],"maintaining":[70],"quadratic":[71],"convergence":[72,105],"locally.":[73],"The":[74,121],"enables":[76],"unifying":[77],"previous":[79],"MS":[80],"algorithms,":[81],"opens":[83],"door":[85],"many":[87],"smaller":[88],"algorithmic":[89],"improvements.":[90],"penalty":[92],"introduced":[95],"strategically":[97],"step":[100],"size,":[101],"further":[102],"performance.":[106],"An":[107],"adaptive":[108],"merit":[109],"function":[110],"more":[113],"reliable":[114],"acceptance":[115],"condition":[116],"are":[117,126],"employed":[118],"globalization.":[120],"effects":[122],"these":[124],"improvements":[125],"benchmarked":[127],"trajectory":[129],"optimization":[130],"with":[131,153],"quadrotor,":[133],"acrobot,":[135],"manipulator.":[138],"MS-DDP":[139],"also":[141],"demonstrated":[142],"use":[144],"in":[145],"Model":[146],"Predictive":[147],"Control":[148],"(MPC)":[149],"dynamic":[151],"jumping":[152],"quadruped":[155],"robot,":[156],"showing":[157],"benefits":[159],"over":[160],"approach.":[164]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}