{"id":"https://openalex.org/W7151993658","doi":"https://doi.org/10.48550/arxiv.2604.05108","title":"Differentiable Invariant Sets for Hybrid Limit Cycles with Application to Legged Robots","display_name":"Differentiable Invariant Sets for Hybrid Limit Cycles with Application to Legged Robots","publication_year":2026,"publication_date":"2026-04-06","ids":{"openalex":"https://openalex.org/W7151993658","doi":"https://doi.org/10.48550/arxiv.2604.05108"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.05108","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.05108","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.05108","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5133192362","display_name":"Varun Madabushi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Madabushi, Varun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009482488","display_name":"Akash Harapanahalli","orcid":"https://orcid.org/0000-0001-8968-4565"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Harapanahalli, Akash","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010552433","display_name":"Samuel Coogan","orcid":"https://orcid.org/0000-0003-0495-1535"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Coogan, Samuel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5054944952","display_name":"Maegan Tucker","orcid":"https://orcid.org/0000-0001-7363-6809"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tucker, Maegan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10879","display_name":"Robotic Locomotion and Control","score":0.45660001039505005,"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":0.45660001039505005,"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/T10586","display_name":"Robotic Path Planning Algorithms","score":0.19050000607967377,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11615","display_name":"Control and Dynamics of Mobile Robots","score":0.08630000054836273,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.597599983215332},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5855000019073486},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.5450000166893005},{"id":"https://openalex.org/keywords/hybrid-system","display_name":"Hybrid system","score":0.5317999720573425},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.4991999864578247},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4950999915599823},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.46720001101493835},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.400299996137619},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.38929998874664307}],"concepts":[{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.597599983215332},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5855000019073486},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.5450000166893005},{"id":"https://openalex.org/C50897621","wikidata":"https://www.wikidata.org/wiki/Q2665508","display_name":"Hybrid system","level":2,"score":0.5317999720573425},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5090000033378601},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.4991999864578247},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4950999915599823},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.46720001101493835},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.400299996137619},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.38929998874664307},{"id":"https://openalex.org/C31531917","wikidata":"https://www.wikidata.org/wiki/Q915157","display_name":"Robust control","level":3,"score":0.38359999656677246},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37369999289512634},{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.34209999442100525},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.33390000462532043},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32899999618530273},{"id":"https://openalex.org/C141141315","wikidata":"https://www.wikidata.org/wiki/Q2379942","display_name":"Guard (computer science)","level":2,"score":0.31839999556541443},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3181999921798706},{"id":"https://openalex.org/C2984157986","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Periodic orbits","level":2,"score":0.31610000133514404},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.3100999891757965},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.30979999899864197},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.3068000078201294},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.30570000410079956},{"id":"https://openalex.org/C17500928","wikidata":"https://www.wikidata.org/wiki/Q959968","display_name":"Control system","level":2,"score":0.2962999939918518},{"id":"https://openalex.org/C87698059","wikidata":"https://www.wikidata.org/wiki/Q1808960","display_name":"LTI system theory","level":3,"score":0.29490000009536743},{"id":"https://openalex.org/C197115733","wikidata":"https://www.wikidata.org/wiki/Q1003136","display_name":"Forcing (mathematics)","level":2,"score":0.27959999442100525},{"id":"https://openalex.org/C63548660","wikidata":"https://www.wikidata.org/wiki/Q858223","display_name":"Limit point","level":2,"score":0.2761000096797943},{"id":"https://openalex.org/C2987469083","wikidata":"https://www.wikidata.org/wiki/Q166314","display_name":"Chaotic systems","level":3,"score":0.26840001344680786},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.26589998602867126},{"id":"https://openalex.org/C70834904","wikidata":"https://www.wikidata.org/wiki/Q1054638","display_name":"Differential inclusion","level":2,"score":0.25920000672340393},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.25369998812675476},{"id":"https://openalex.org/C177067428","wikidata":"https://www.wikidata.org/wiki/Q17013331","display_name":"Feasible region","level":2,"score":0.25060001015663147}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.05108","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.05108","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.05108","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.05108","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"For":[0],"hybrid":[1,134],"systems":[2,40,58],"exhibiting":[3],"periodic":[4,135],"behavior,":[5],"analyzing":[6],"the":[7,11,20,23,68,89,97,106,110,122,142,172,175],"invariant":[8,130,176],"set":[9,66,87,113,131,155],"containing":[10],"limit":[12],"cycle":[13],"is":[14,117],"a":[15,64,72,76,118,128,149,161,167],"natural":[16],"way":[17],"to":[18,37,62,165],"study":[19],"robustness":[21],"of":[22,56,71,75,121,174],"closed-loop":[24],"system.":[25],"However,":[26],"computing":[27],"these":[28,103],"sets":[29,55],"can":[30],"be":[31],"computationally":[32],"expensive,":[33],"especially":[34],"when":[35],"applied":[36],"contact-rich":[38],"cyber-physical":[39],"such":[41],"as":[42],"legged":[43],"robots.":[44],"In":[45],"this":[46,133,139],"work,":[47],"we":[48,125],"extend":[49],"existing":[50],"methods":[51],"for":[52,132,152],"overapproximating":[53,85],"reachable":[54,86,112,154],"continuous":[57,91],"using":[59,147],"parametric":[60,153],"embeddings":[61],"compute":[63],"forward-invariant":[65],"around":[67,88],"nominal":[69,90],"trajectory":[70],"simplified":[73],"model":[74,145],"bipedal":[77,143],"robot.":[78],"Our":[79],"three-step":[80],"approach":[81],"(i)":[82],"computes":[83],"an":[84],"flow,":[92],"(ii)":[93],"catalogs":[94],"intersections":[95,104],"with":[96],"guard":[98],"surface,":[99],"and":[100,157],"(iii)":[101],"passes":[102],"through":[105],"reset":[107],"map.":[108],"If":[109],"overapproximated":[111],"after":[114],"one":[115],"step":[116],"strict":[119],"subset":[120],"initial":[123],"set,":[124],"formally":[126],"verify":[127,138],"forward":[129],"orbit.":[136],"We":[137],"condition":[140],"on":[141],"walker":[144],"numerically":[146],"immrax,":[148],"JAX-based":[150],"library":[151],"computation,":[156],"use":[158],"it":[159],"within":[160],"bi-level":[162],"optimization":[163],"framework":[164],"design":[166],"tracking":[168],"controller":[169],"that":[170],"maximizes":[171],"size":[173],"set.":[177]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-04-09T00:00:00"}
