{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/113836"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/113836","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Robot motion planning via curve shortening flows","abstract":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-04-06 without embargo terms","abstract_html":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-04-06 without embargo terms","abstract_has_math":false,"creators":["Fan, Yinai"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mechanical Engineering","degree_department":null,"school":null,"contributors":["Belabbas, Mohamed-Ali","Mehta, Prashant","Dullerud, Geir Eirik","Liberzon, Daniel"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022-04-29T21:34:25Z","date_published":"2022-04-29T21:34:25Z","updated_at":"2026-07-22T22:24:53Z","subjects":["Mechanical science"],"languages":["en","eng"],"rights":["Copyright 2021 Yinai Fan"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/113836","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Belabbas, Mohamed-Ali","Mehta, Prashant","Dullerud, Geir Eirik","Liberzon, Daniel"]},{"key":"dc:creator","label":"Author","values":["Fan, Yinai"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2022-04-29T21:34:25Z","2021-12","2021-11-16"]},{"key":"dc:type","label":"Dc Type","values":["text","Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mechanical Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mechanical science"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2021 Yinai Fan"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/113836"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-04-06 without embargo terms","The student, Yinai Fan, accepted the attached license on 2021-11-12 at 02:45.","The student, Yinai Fan, submitted this Dissertation for approval on 2021-11-12 at 03:03.","This Dissertation was approved for publication on 2021-11-16 at 14:12.","DSpace SAF Submission Ingestion Package generated from Vireo submission #17201 on 2022-04-06 at 17:09:45","Made available in DSpace on 2022-04-29T21:34:25Z (GMT). No. of bitstreams: 3 FAN-DISSERTATION-2021.pdf: 1062032 bytes, checksum: a42e74a532cd34d1598258a03b24883d (MD5) LICENSE.txt: 4206 bytes, checksum: 47c830f8b3064a69f0bd1e110fbcad72 (MD5) PROQUEST_LICENSE.txt: 4552 bytes, checksum: 9eeec81047623dfed4f52c44a3b20184 (MD5) Previous issue date: 2021-11-16","This work will present a series of developments of geometric heat flow method in robot motion planning and estimation. The key of geometric heat flow is to formulate the motion planning problem into a curve shortening problem. By solving the geometric heat flow, an arbitrary initial curve can be deformed to a curve of minimal length, which corresponds to a feasible motion. Preliminary theories and algorithms for motion planning based on geometric heat flow have been developed for driftless control affine systems. The main contribution of this research is to extend the algorithm to robotic systems, which are dynamic systems with drifts and different types of constraint. Early stages of the research focus on adapting the algorithm to solve motion planning problems for systems with drift. To tackle systems with drift, actuated curve length and affine geometric heat flow is proposed. The method is then enriched to solve robot gymnastics motion planning, in which the effect of state constraints is encoded into curve length. Free boundary conditions are also studied to enforce the conservation of the robot's momentum. The second stage of the research focus on the construction of the geometric heat flow framework for robot locomotion planning, which involves hybrid dynamics due to contact. The activation and deactivation of phase-dependent constraints are controlled by activation functions. Lastly, to solve 3D problems in robotics, planning and estimation in SO(3) space is formulated using the geometric heat flow method."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Robot motion planning via curve shortening flows"]}]}],"canonical_facts":{"dc:contributor":["Belabbas, Mohamed-Ali","Mehta, Prashant","Dullerud, Geir Eirik","Liberzon, Daniel"],"dc:creator":["Fan, Yinai"],"dc:date":["2022-04-29T21:34:25Z","2021-12","2021-11-16"],"dc:description":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-04-06 without embargo terms","The student, Yinai Fan, accepted the attached license on 2021-11-12 at 02:45.","The student, Yinai Fan, submitted this Dissertation for approval on 2021-11-12 at 03:03.","This Dissertation was approved for publication on 2021-11-16 at 14:12.","DSpace SAF Submission Ingestion Package generated from Vireo submission #17201 on 2022-04-06 at 17:09:45","Made available in DSpace on 2022-04-29T21:34:25Z (GMT). No. of bitstreams: 3 FAN-DISSERTATION-2021.pdf: 1062032 bytes, checksum: a42e74a532cd34d1598258a03b24883d (MD5) LICENSE.txt: 4206 bytes, checksum: 47c830f8b3064a69f0bd1e110fbcad72 (MD5) PROQUEST_LICENSE.txt: 4552 bytes, checksum: 9eeec81047623dfed4f52c44a3b20184 (MD5) Previous issue date: 2021-11-16","This work will present a series of developments of geometric heat flow method in robot motion planning and estimation. The key of geometric heat flow is to formulate the motion planning problem into a curve shortening problem. By solving the geometric heat flow, an arbitrary initial curve can be deformed to a curve of minimal length, which corresponds to a feasible motion. Preliminary theories and algorithms for motion planning based on geometric heat flow have been developed for driftless control affine systems. The main contribution of this research is to extend the algorithm to robotic systems, which are dynamic systems with drifts and different types of constraint. Early stages of the research focus on adapting the algorithm to solve motion planning problems for systems with drift. To tackle systems with drift, actuated curve length and affine geometric heat flow is proposed. The method is then enriched to solve robot gymnastics motion planning, in which the effect of state constraints is encoded into curve length. Free boundary conditions are also studied to enforce the conservation of the robot's momentum. The second stage of the research focus on the construction of the geometric heat flow framework for robot locomotion planning, which involves hybrid dynamics due to contact. The activation and deactivation of phase-dependent constraints are controlled by activation functions. Lastly, to solve 3D problems in robotics, planning and estimation in SO(3) space is formulated using the geometric heat flow method."],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/2142/113836"],"dc:language":["en","eng"],"dc:rights":["Copyright 2021 Yinai Fan"],"dc:subject":["Mechanical science"],"dc:title":["Robot motion planning via curve shortening flows"],"dc:type":["text","Thesis"],"thesis:degree_discipline":["Mechanical Engineering"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:53Z"}