{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/86908"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/86908","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Pareto Optimization in Robotics With Acceleration Constraints","abstract":"Earlier work demonstrated a finite number of Pareto-optimal classes of motion plans when the robots are subjected to velocity bounds but no acceleration bounds. We prove that, when velocity and acceleration are bounded, the finiteness result still holds for systems involving only two robots. In tins setting, we separate acceleration bounds into two opposite assumptions: initial bounded accelerations and terminal bounded accelerations. Initial bounded accelerations are the cases when certain instantaneous stops are allowed. In contrast, terminal bounded accelerations allow infinite accelerations toward moving directions. We shows that either assumption does not alter the finiteness result for Pareto optimal path classes. General bounded accelerations can be derived by combining the two assumptions. However, in the general case, the acceleration bounds can lead to continua of Pareto optima. We give a counter examples involving three robots and explain the result in terms of the geometry of phase space. We also shows that with certain bounds on obstacle distributions finiteness results can be recovered.","abstract_html":"Earlier work demonstrated a finite number of Pareto-optimal classes of motion plans when the robots are subjected to velocity bounds but no acceleration bounds. We prove that, when velocity and acceleration are bounded, the finiteness result still holds for systems involving only two robots. In tins setting, we separate acceleration bounds into two opposite assumptions: initial bounded accelerations and terminal bounded accelerations. Initial bounded accelerations are the cases when certain instantaneous stops are allowed. In contrast, terminal bounded accelerations allow infinite accelerations toward moving directions. We shows that either assumption does not alter the finiteness result for Pareto optimal path classes. General bounded accelerations can be derived by combining the two assumptions. However, in the general case, the acceleration bounds can lead to continua of Pareto optima. We give a counter examples involving three robots and explain the result in terms of the geometry of phase space. We also shows that with certain bounds on obstacle distributions finiteness results can be recovered.","abstract_has_math":false,"creators":["Jung, Jaebum"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Stephanie Alexander"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-28T15:20:07Z","date_published":"2015-09-28T15:20:07Z","updated_at":"2026-07-22T22:26:28Z","subjects":["Engineering, Robotics"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI3337815"],"render_values":[{"text":"(MiAaPQ)AAI3337815","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/86908","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Stephanie Alexander"]},{"key":"dc:creator","label":"Author","values":["Jung, Jaebum"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-28T15:20:07Z","10000-01-01","2008"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"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":["Engineering, Robotics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/86908","(MiAaPQ)AAI3337815"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Earlier work demonstrated a finite number of Pareto-optimal classes of motion plans when the robots are subjected to velocity bounds but no acceleration bounds. We prove that, when velocity and acceleration are bounded, the finiteness result still holds for systems involving only two robots. In tins setting, we separate acceleration bounds into two opposite assumptions: initial bounded accelerations and terminal bounded accelerations. Initial bounded accelerations are the cases when certain instantaneous stops are allowed. In contrast, terminal bounded accelerations allow infinite accelerations toward moving directions. We shows that either assumption does not alter the finiteness result for Pareto optimal path classes. General bounded accelerations can be derived by combining the two assumptions. However, in the general case, the acceleration bounds can lead to continua of Pareto optima. We give a counter examples involving three robots and explain the result in terms of the geometry of phase space. We also shows that with certain bounds on obstacle distributions finiteness results can be recovered.","Made available in DSpace on 2015-09-28T15:20:07Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3337815.pdf: 1551613 bytes, checksum: 18fc14cab72aabdec4eb02beccbf734c (MD5) Previous issue date: 2008","Embargo set by: Seth Robbins for item 88189 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","86 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2008."]},{"key":"dc:title","label":"Title","values":["Pareto Optimization in Robotics With Acceleration Constraints"]}]}],"canonical_facts":{"dc:contributor":["Stephanie Alexander"],"dc:creator":["Jung, Jaebum"],"dc:date":["2015-09-28T15:20:07Z","10000-01-01","2008"],"dc:description":["Earlier work demonstrated a finite number of Pareto-optimal classes of motion plans when the robots are subjected to velocity bounds but no acceleration bounds. We prove that, when velocity and acceleration are bounded, the finiteness result still holds for systems involving only two robots. In tins setting, we separate acceleration bounds into two opposite assumptions: initial bounded accelerations and terminal bounded accelerations. Initial bounded accelerations are the cases when certain instantaneous stops are allowed. In contrast, terminal bounded accelerations allow infinite accelerations toward moving directions. We shows that either assumption does not alter the finiteness result for Pareto optimal path classes. General bounded accelerations can be derived by combining the two assumptions. However, in the general case, the acceleration bounds can lead to continua of Pareto optima. We give a counter examples involving three robots and explain the result in terms of the geometry of phase space. We also shows that with certain bounds on obstacle distributions finiteness results can be recovered.","Made available in DSpace on 2015-09-28T15:20:07Z (GMT). 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