{"id":"https://openalex.org/W4417508663","doi":"https://doi.org/10.1109/tie.2025.3637339","title":"Online Energy-Optimal Trajectory Planning for Servomotor Systems With Nonlinear Dynamics","display_name":"Online Energy-Optimal Trajectory Planning for Servomotor Systems With Nonlinear Dynamics","publication_year":2025,"publication_date":"2025-12-19","ids":{"openalex":"https://openalex.org/W4417508663","doi":"https://doi.org/10.1109/tie.2025.3637339"},"language":null,"primary_location":{"id":"doi:10.1109/tie.2025.3637339","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tie.2025.3637339","pdf_url":null,"source":{"id":"https://openalex.org/S58031724","display_name":"IEEE Transactions on Industrial Electronics","issn_l":"0278-0046","issn":["0278-0046","1557-9948"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Industrial Electronics","raw_type":"journal-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":null,"display_name":"Kuan Wang","orcid":"https://orcid.org/0009-0007-2653-1335"},"institutions":[{"id":"https://openalex.org/I36399199","display_name":"Nanjing University of Science and Technology","ror":"https://ror.org/00xp9wg62","country_code":"CN","type":"education","lineage":["https://openalex.org/I36399199"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kuan Wang","raw_affiliation_strings":["School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, China"],"raw_orcid":"https://orcid.org/0009-0007-2653-1335","affiliations":[{"raw_affiliation_string":"School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, China","institution_ids":["https://openalex.org/I36399199"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027366009","display_name":"Le Sun","orcid":"https://orcid.org/0000-0002-7594-9371"},"institutions":[{"id":"https://openalex.org/I36399199","display_name":"Nanjing University of Science and Technology","ror":"https://ror.org/00xp9wg62","country_code":"CN","type":"education","lineage":["https://openalex.org/I36399199"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Le Sun","raw_affiliation_strings":["School of Automation, Nanjing University of Science and Technology, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0002-7594-9371","affiliations":[{"raw_affiliation_string":"School of Automation, Nanjing University of Science and Technology, Nanjing, China","institution_ids":["https://openalex.org/I36399199"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103211202","display_name":"Longmiao Chen","orcid":"https://orcid.org/0000-0001-8437-1519"},"institutions":[{"id":"https://openalex.org/I36399199","display_name":"Nanjing University of Science and Technology","ror":"https://ror.org/00xp9wg62","country_code":"CN","type":"education","lineage":["https://openalex.org/I36399199"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Longmiao Chen","raw_affiliation_strings":["School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0001-8437-1519","affiliations":[{"raw_affiliation_string":"School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, China","institution_ids":["https://openalex.org/I36399199"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040987631","display_name":"Jingqi Dong","orcid":"https://orcid.org/0009-0008-8299-2707"},"institutions":[{"id":"https://openalex.org/I36399199","display_name":"Nanjing University of Science and Technology","ror":"https://ror.org/00xp9wg62","country_code":"CN","type":"education","lineage":["https://openalex.org/I36399199"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jingqi Dong","raw_affiliation_strings":["School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, China"],"raw_orcid":"https://orcid.org/0009-0008-8299-2707","affiliations":[{"raw_affiliation_string":"School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, China","institution_ids":["https://openalex.org/I36399199"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I36399199"],"apc_list":{"value":2645,"currency":"USD","value_usd":2645},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.31805206,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"73","issue":"4","first_page":"6346","last_page":"6357"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10571","display_name":"Robotic Mechanisms and Dynamics","score":0.4927000105381012,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T10571","display_name":"Robotic Mechanisms and Dynamics","score":0.4927000105381012,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T11749","display_name":"Iterative Learning Control Systems","score":0.20180000364780426,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T11372","display_name":"Hydraulic and Pneumatic Systems","score":0.052799999713897705,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/control-theory","display_name":"Control theory (sociology)","score":0.7677000164985657},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6263999938964844},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.5996999740600586},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5943999886512756},{"id":"https://openalex.org/keywords/servomotor","display_name":"Servomotor","score":0.579800009727478},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.5727999806404114},{"id":"https://openalex.org/keywords/torque","display_name":"Torque","score":0.5008999705314636},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.3856000006198883},{"id":"https://openalex.org/keywords/servo","display_name":"Servo","score":0.37310001254081726}],"concepts":[{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.7677000164985657},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6263999938964844},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6201000213623047},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.5996999740600586},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5943999886512756},{"id":"https://openalex.org/C109441226","wikidata":"https://www.wikidata.org/wiki/Q1137255","display_name":"Servomotor","level":2,"score":0.579800009727478},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.5727999806404114},{"id":"https://openalex.org/C144171764","wikidata":"https://www.wikidata.org/wiki/Q48103","display_name":"Torque","level":2,"score":0.5008999705314636},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.3856000006198883},{"id":"https://openalex.org/C107354338","wikidata":"https://www.wikidata.org/wiki/Q1937153","display_name":"Servo","level":2,"score":0.37310001254081726},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.33799999952316284},{"id":"https://openalex.org/C79487989","wikidata":"https://www.wikidata.org/wiki/Q934680","display_name":"Vehicle dynamics","level":2,"score":0.3197999894618988},{"id":"https://openalex.org/C49503481","wikidata":"https://www.wikidata.org/wiki/Q640815","display_name":"Servomechanism","level":2,"score":0.3093999922275543},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.29190000891685486},{"id":"https://openalex.org/C91581856","wikidata":"https://www.wikidata.org/wiki/Q2707001","display_name":"Nonlinear control","level":3,"score":0.28600001335144043},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.2777999937534332},{"id":"https://openalex.org/C19966478","wikidata":"https://www.wikidata.org/wiki/Q4810574","display_name":"Mobile robot","level":3,"score":0.2741999924182892},{"id":"https://openalex.org/C60692881","wikidata":"https://www.wikidata.org/wiki/Q584529","display_name":"Humanoid robot","level":3,"score":0.27399998903274536},{"id":"https://openalex.org/C150415221","wikidata":"https://www.wikidata.org/wiki/Q40687","display_name":"Robotic arm","level":2,"score":0.27140000462532043},{"id":"https://openalex.org/C2780165032","wikidata":"https://www.wikidata.org/wiki/Q16869822","display_name":"Energy consumption","level":2,"score":0.27000001072883606},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.26980000734329224},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.26669999957084656},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.26409998536109924},{"id":"https://openalex.org/C77405623","wikidata":"https://www.wikidata.org/wiki/Q598451","display_name":"System dynamics","level":2,"score":0.25920000672340393}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tie.2025.3637339","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tie.2025.3637339","pdf_url":null,"source":{"id":"https://openalex.org/S58031724","display_name":"IEEE Transactions on Industrial Electronics","issn_l":"0278-0046","issn":["0278-0046","1557-9948"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Industrial Electronics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W1920358242","https://openalex.org/W1972394793","https://openalex.org/W1980218901","https://openalex.org/W1983317756","https://openalex.org/W2023977572","https://openalex.org/W2070661769","https://openalex.org/W2079978280","https://openalex.org/W2091231427","https://openalex.org/W2099454002","https://openalex.org/W2134298283","https://openalex.org/W2152246064","https://openalex.org/W2405331748","https://openalex.org/W2906158882","https://openalex.org/W2962700304","https://openalex.org/W2990839847","https://openalex.org/W3036721101","https://openalex.org/W3045714839","https://openalex.org/W3126731237","https://openalex.org/W3138455672","https://openalex.org/W3167333926","https://openalex.org/W3195970720","https://openalex.org/W3207707396","https://openalex.org/W4200130564","https://openalex.org/W4225983583","https://openalex.org/W4290632288","https://openalex.org/W4295832068","https://openalex.org/W4386065466","https://openalex.org/W4388430752","https://openalex.org/W4388718457","https://openalex.org/W4390421999","https://openalex.org/W4400970598","https://openalex.org/W4402302348","https://openalex.org/W4410487478"],"related_works":[],"abstract_inverted_index":{"Online":[0],"computation":[1,110,130],"of":[2,79,81,181],"energy-optimal":[3,60,168],"trajectories":[4,169,185],"is":[5,64,72,83,115],"critically":[6],"important":[7],"for":[8,21],"single-axis":[9],"servo":[10,42],"systems":[11,36,43],"performing":[12],"point-to-point":[13],"positioning":[14,120],"tasks.":[15,121],"Indirect":[16],"methods":[17,31],"are":[18,32],"widely":[19],"adopted":[20],"this":[22],"purpose":[23],"due":[24],"to":[25,35,66,85,117,135,145,158,179],"their":[26],"computational":[27],"efficiency.":[28],"However,":[29],"existing":[30],"generally":[33],"limited":[34],"with":[37,51],"linear":[38],"dynamics,":[39],"while":[40,174],"practical":[41],"often":[44],"exhibit":[45],"nonlinear":[46,68,90],"load":[47,52,69],"torques":[48,70],"that":[49,71,125,166,180],"vary":[50],"position.":[53],"To":[54,106],"address":[55],"this,":[56],"a":[57,139,149],"novel":[58],"online":[59,109],"trajectory":[61],"planning":[62],"method":[63,78,114,128],"proposed":[65,127],"handle":[67],"continuously":[73],"differentiable":[74],"and":[75,100,142,186],"bounded.":[76],"The":[77],"variation":[80],"extremals":[82],"introduced":[84],"efficiently":[86],"solve":[87],"the":[88,126,162,167],"resulting":[89],"two-point":[91],"boundary":[92],"value":[93],"problems.":[94],"Additionally,":[95],"constraints":[96],"on":[97,138,148],"jerk,":[98],"acceleration,":[99],"speed":[101,184],"can":[102],"also":[103],"be":[104],"considered.":[105],"verify":[107],"its":[108],"performance,":[111],"an":[112],"orthogonal":[113],"employed":[116],"design":[118],"various":[119],"Numerical":[122],"results":[123,164],"show":[124],"achieves":[129],"times":[131],"ranging":[132],"from":[133,143],"7.2":[134],"55":[136],"ms":[137,147],"Raspberry":[140],"Pi":[141],"0.8":[144],"7.1":[146],"personal":[150],"computer,":[151],"outperforming":[152],"MATLAB\u2019s":[153],"bvp4c":[154],"solver":[155],"by":[156],"11":[157],"29":[159],"times.":[160],"Finally,":[161],"experimental":[163],"confirm":[165],"significantly":[170],"reduce":[171],"energy":[172],"consumption":[173],"maintaining":[175],"comparable":[176],"tracking":[177],"performance":[178],"conventional":[182],"trapezoidal":[183],"S-curve":[187],"trajectories.":[188]},"counts_by_year":[],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-12-19T00:00:00"}
