{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/18397"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/18397","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Geometric control and motion planning for three-dimensional bipedal locomotion","abstract":"\"This thesis presents a hierarchical geometric control approach for fast and energetically efficient bipedal dynamic walking in three-dimensional (3-D) space to enable motion planning applications that have previously been limited to inefficient quasi-static walkers. In order to produce exponentially stable hybrid limit cycles, we exploit system energetics, symmetry, and passivity through the energy-shaping method of controlled geometric reduction. This decouples a subsystem corresponding to a lower-dimensional robot through a passivity-based feedback transformation of the system Lagrangian into a special form of controlled Lagrangian with broken symmetry, which corresponds to an equivalent closed-loop Hamiltonian system with upper-triangular form. The first control term reduces to mechanically-realizable passive feedback that establishes a functional momentum conservation law that controls the \"\"divided\"\" cyclic variables to set-points or periodic orbits. We then prove extensive symmetries in the class of open kinematic chains to present the multistage application of controlled reduction. A reduction-based control law is derived to construct straight-ahead and turning gaits for a 4-DOF and 5-DOF hipped biped in 3-D space, based on the existence of stable hybrid limit cycles in the sagittal plane-of-motion. Given such a set of asymptotically stable gait primitives, a dynamic walker can be controlled as a discrete-time switched system that sequentially composes gait primitives from step to step. We derive \"\"funneling\"\" rules by which a walking path that is a sequence of these gaits may be stably followed by the robot. The primitive set generates a tree exploring the action space for feasible walking paths, where each primitive corresponds to walking along a nominal arc of constant curvature. Therefore, dynamically stable motion planning for dynamic walkers reduces to a discrete search problem, which we demonstrate for 3-D compass-gait bipeds. After reflecting on several connections to human biomechanics, we propose extensions of this energy-shaping control paradigm to robot-assisted locomotor rehabilitation. This work aims to offer a systematic design methodology for assistive control strategies that are amenable to sequential composition for novel progressive training therapies.\"","abstract_html":""This thesis presents a hierarchical geometric control approach for fast and energetically efficient bipedal dynamic walking in three-dimensional (3-D) space to enable motion planning applications that have previously been limited to inefficient quasi-static walkers. In order to produce exponentially stable hybrid limit cycles, we exploit system energetics, symmetry, and passivity through the energy-shaping method of controlled geometric reduction. This decouples a subsystem corresponding to a lower-dimensional robot through a passivity-based feedback transformation of the system Lagrangian into a special form of controlled Lagrangian with broken symmetry, which corresponds to an equivalent closed-loop Hamiltonian system with upper-triangular form. The first control term reduces to mechanically-realizable passive feedback that establishes a functional momentum conservation law that controls the ""divided"" cyclic variables to set-points or periodic orbits. We then prove extensive symmetries in the class of open kinematic chains to present the multistage application of controlled reduction. A reduction-based control law is derived to construct straight-ahead and turning gaits for a 4-DOF and 5-DOF hipped biped in 3-D space, based on the existence of stable hybrid limit cycles in the sagittal plane-of-motion. Given such a set of asymptotically stable gait primitives, a dynamic walker can be controlled as a discrete-time switched system that sequentially composes gait primitives from step to step. We derive ""funneling"" rules by which a walking path that is a sequence of these gaits may be stably followed by the robot. The primitive set generates a tree exploring the action space for feasible walking paths, where each primitive corresponds to walking along a nominal arc of constant curvature. Therefore, dynamically stable motion planning for dynamic walkers reduces to a discrete search problem, which we demonstrate for 3-D compass-gait bipeds. After reflecting on several connections to human biomechanics, we propose extensions of this energy-shaping control paradigm to robot-assisted locomotor rehabilitation. This work aims to offer a systematic design methodology for assistive control strategies that are amenable to sequential composition for novel progressive training therapies."","abstract_has_math":false,"creators":["Gregg, Robert D., IV"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Electrical & Computer Engr","degree_department":null,"school":null,"contributors":["Spong, Mark W.","Bretl, Timothy W.","Hutchinson, Seth A.","Mehta, Prashant G."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-01-14T22:49:05Z","date_published":"2011-01-14T22:49:05Z","updated_at":"2026-07-22T22:25:11Z","subjects":["Robots","Bipedal","Walking","Locomotion","Dynamic Walking","Geometric Control","Motion Planning","Three-Dimensional (3D)","Reduction-based Control","Controlled Reduction","Hybrid Limit Cycles"],"languages":["en"],"rights":["Copyright 2010 Robert D. Gregg IV Copyright 1999 SAGE Publications (Figures 1.4 and 7.1)"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/18397","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Spong, Mark W.","Bretl, Timothy W.","Hutchinson, Seth A.","Mehta, Prashant G."]},{"key":"dc:creator","label":"Author","values":["Gregg, Robert D., IV"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-01-14T22:49:05Z","2010-12"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Electrical & Computer Engr"]},{"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":["Robots","Bipedal","Walking","Locomotion","Dynamic Walking","Geometric Control","Motion Planning","Three-Dimensional (3D)","Reduction-based Control","Controlled Reduction","Hybrid Limit Cycles"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2010 Robert D. Gregg IV Copyright 1999 SAGE Publications (Figures 1.4 and 7.1)"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/18397"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["\"This thesis presents a hierarchical geometric control approach for fast and energetically efficient bipedal dynamic walking in three-dimensional (3-D) space to enable motion planning applications that have previously been limited to inefficient quasi-static walkers. In order to produce exponentially stable hybrid limit cycles, we exploit system energetics, symmetry, and passivity through the energy-shaping method of controlled geometric reduction. This decouples a subsystem corresponding to a lower-dimensional robot through a passivity-based feedback transformation of the system Lagrangian into a special form of controlled Lagrangian with broken symmetry, which corresponds to an equivalent closed-loop Hamiltonian system with upper-triangular form. The first control term reduces to mechanically-realizable passive feedback that establishes a functional momentum conservation law that controls the \"\"divided\"\" cyclic variables to set-points or periodic orbits. We then prove extensive symmetries in the class of open kinematic chains to present the multistage application of controlled reduction. A reduction-based control law is derived to construct straight-ahead and turning gaits for a 4-DOF and 5-DOF hipped biped in 3-D space, based on the existence of stable hybrid limit cycles in the sagittal plane-of-motion. Given such a set of asymptotically stable gait primitives, a dynamic walker can be controlled as a discrete-time switched system that sequentially composes gait primitives from step to step. We derive \"\"funneling\"\" rules by which a walking path that is a sequence of these gaits may be stably followed by the robot. The primitive set generates a tree exploring the action space for feasible walking paths, where each primitive corresponds to walking along a nominal arc of constant curvature. Therefore, dynamically stable motion planning for dynamic walkers reduces to a discrete search problem, which we demonstrate for 3-D compass-gait bipeds. After reflecting on several connections to human biomechanics, we propose extensions of this energy-shaping control paradigm to robot-assisted locomotor rehabilitation. This work aims to offer a systematic design methodology for assistive control strategies that are amenable to sequential composition for novel progressive training therapies.\"","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2010-09-17T19:26:06Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 19 figures.zip: 2273225 bytes, checksum: c79b3abd87a049ffa5f5c5607d475c25 (MD5) uiucecethesis09.cls: 21157 bytes, checksum: 8a2975a9bd857ec4f015bf1dcefcdf94 (MD5) IEEE_ECE.bst: 61786 bytes, checksum: e34f041873deb4165fc8d76725c453c4 (MD5) Dissertation.sty: 9648 bytes, checksum: 23536680e54ee7c37c08beb8e357c2bc (MD5) DissertationBib.bib: 51231 bytes, checksum: 6fb18d95907556618aa7f6b65fafab87 (MD5) Appendix.tex: 32501 bytes, checksum: aadb8c8228e277f1251156ecb051d4bb (MD5) ack.tex: 4867 bytes, checksum: 2dfc8deb26c0b5d7c16a525e84046017 (MD5) BipedWalking.tex: 74369 bytes, checksum: 47509ea40c3386a92a6bcc592af7b230 (MD5) concl.tex: 9121 bytes, checksum: 585ce4da44fc5668a2528e90ae439c27 (MD5) Rehab.tex: 22761 bytes, checksum: eaca380efeeff7e23190ba79af1d9226 (MD5) GaitPrimitives.tex: 51684 bytes, checksum: ae4f243260e3b662ded7a21239e56f74 (MD5) RBControl.tex: 37736 bytes, checksum: c1f25a165a9bbc0f5a5795e1e5938883 (MD5) ControlledReduction.tex: 62144 bytes, checksum: f32538ad21a04ade3044af050e60848f (MD5) Mechanical.tex: 26962 bytes, checksum: 87e4081d2789810a02cc70cdfc19cf4c (MD5) abs.tex: 2394 bytes, checksum: 56cabf359f6612e97f9b30eeaa3a5613 (MD5) aubio.tex: 1539 bytes, checksum: 8361c48f1eb3abf1878bccd9d62e750b (MD5) intro.tex: 32933 bytes, checksum: 4545e8e256c46d7b6c068e78c30eea7f (MD5) Dissertation.tex: 9962 bytes, checksum: dfaeb7988b9ba30acfa39f62fe08fe5a (MD5) Gregg_Robert.pdf: 2695035 bytes, checksum: 47511aeea433f04b4cf44ab6d878ce21 (MD5)","Made available in DSpace on 2011-01-14T22:49:05Z (GMT). No. of bitstreams: 20 Gregg_Robert.pdf: 2695035 bytes, checksum: 47511aeea433f04b4cf44ab6d878ce21 (MD5) license.txt: 4060 bytes, checksum: ec76352010e357de0f8c258a3f76da01 (MD5) Dissertation.tex: 9962 bytes, checksum: dfaeb7988b9ba30acfa39f62fe08fe5a (MD5) intro.tex: 32933 bytes, checksum: 4545e8e256c46d7b6c068e78c30eea7f (MD5) aubio.tex: 1539 bytes, checksum: 8361c48f1eb3abf1878bccd9d62e750b (MD5) abs.tex: 2394 bytes, checksum: 56cabf359f6612e97f9b30eeaa3a5613 (MD5) Mechanical.tex: 26962 bytes, checksum: 87e4081d2789810a02cc70cdfc19cf4c (MD5) ControlledReduction.tex: 62144 bytes, checksum: f32538ad21a04ade3044af050e60848f (MD5) RBControl.tex: 37736 bytes, checksum: c1f25a165a9bbc0f5a5795e1e5938883 (MD5) GaitPrimitives.tex: 51684 bytes, checksum: ae4f243260e3b662ded7a21239e56f74 (MD5) Rehab.tex: 22761 bytes, checksum: eaca380efeeff7e23190ba79af1d9226 (MD5) concl.tex: 9121 bytes, checksum: 585ce4da44fc5668a2528e90ae439c27 (MD5) BipedWalking.tex: 74369 bytes, checksum: 47509ea40c3386a92a6bcc592af7b230 (MD5) ack.tex: 4867 bytes, checksum: 2dfc8deb26c0b5d7c16a525e84046017 (MD5) Appendix.tex: 32501 bytes, checksum: aadb8c8228e277f1251156ecb051d4bb (MD5) DissertationBib.bib: 51231 bytes, checksum: 6fb18d95907556618aa7f6b65fafab87 (MD5) Dissertation.sty: 9648 bytes, checksum: 23536680e54ee7c37c08beb8e357c2bc (MD5) IEEE_ECE.bst: 61786 bytes, checksum: e34f041873deb4165fc8d76725c453c4 (MD5) uiucecethesis09.cls: 21157 bytes, checksum: 8a2975a9bd857ec4f015bf1dcefcdf94 (MD5) figures.zip: 2273225 bytes, checksum: c79b3abd87a049ffa5f5c5607d475c25 (MD5)"]},{"key":"dc:title","label":"Title","values":["Geometric control and motion planning for three-dimensional bipedal locomotion"]}]}],"canonical_facts":{"dc:contributor":["Spong, Mark W.","Bretl, Timothy W.","Hutchinson, Seth A.","Mehta, Prashant G."],"dc:creator":["Gregg, Robert D., IV"],"dc:date":["2011-01-14T22:49:05Z","2010-12"],"dc:description":["\"This thesis presents a hierarchical geometric control approach for fast and energetically efficient bipedal dynamic walking in three-dimensional (3-D) space to enable motion planning applications that have previously been limited to inefficient quasi-static walkers. In order to produce exponentially stable hybrid limit cycles, we exploit system energetics, symmetry, and passivity through the energy-shaping method of controlled geometric reduction. This decouples a subsystem corresponding to a lower-dimensional robot through a passivity-based feedback transformation of the system Lagrangian into a special form of controlled Lagrangian with broken symmetry, which corresponds to an equivalent closed-loop Hamiltonian system with upper-triangular form. The first control term reduces to mechanically-realizable passive feedback that establishes a functional momentum conservation law that controls the \"\"divided\"\" cyclic variables to set-points or periodic orbits. We then prove extensive symmetries in the class of open kinematic chains to present the multistage application of controlled reduction. A reduction-based control law is derived to construct straight-ahead and turning gaits for a 4-DOF and 5-DOF hipped biped in 3-D space, based on the existence of stable hybrid limit cycles in the sagittal plane-of-motion. Given such a set of asymptotically stable gait primitives, a dynamic walker can be controlled as a discrete-time switched system that sequentially composes gait primitives from step to step. We derive \"\"funneling\"\" rules by which a walking path that is a sequence of these gaits may be stably followed by the robot. The primitive set generates a tree exploring the action space for feasible walking paths, where each primitive corresponds to walking along a nominal arc of constant curvature. Therefore, dynamically stable motion planning for dynamic walkers reduces to a discrete search problem, which we demonstrate for 3-D compass-gait bipeds. After reflecting on several connections to human biomechanics, we propose extensions of this energy-shaping control paradigm to robot-assisted locomotor rehabilitation. This work aims to offer a systematic design methodology for assistive control strategies that are amenable to sequential composition for novel progressive training therapies.\"","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2010-09-17T19:26:06Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 19 figures.zip: 2273225 bytes, checksum: c79b3abd87a049ffa5f5c5607d475c25 (MD5) uiucecethesis09.cls: 21157 bytes, checksum: 8a2975a9bd857ec4f015bf1dcefcdf94 (MD5) IEEE_ECE.bst: 61786 bytes, checksum: e34f041873deb4165fc8d76725c453c4 (MD5) Dissertation.sty: 9648 bytes, checksum: 23536680e54ee7c37c08beb8e357c2bc (MD5) DissertationBib.bib: 51231 bytes, checksum: 6fb18d95907556618aa7f6b65fafab87 (MD5) Appendix.tex: 32501 bytes, checksum: aadb8c8228e277f1251156ecb051d4bb (MD5) ack.tex: 4867 bytes, checksum: 2dfc8deb26c0b5d7c16a525e84046017 (MD5) BipedWalking.tex: 74369 bytes, checksum: 47509ea40c3386a92a6bcc592af7b230 (MD5) concl.tex: 9121 bytes, checksum: 585ce4da44fc5668a2528e90ae439c27 (MD5) Rehab.tex: 22761 bytes, checksum: eaca380efeeff7e23190ba79af1d9226 (MD5) GaitPrimitives.tex: 51684 bytes, checksum: ae4f243260e3b662ded7a21239e56f74 (MD5) RBControl.tex: 37736 bytes, checksum: c1f25a165a9bbc0f5a5795e1e5938883 (MD5) ControlledReduction.tex: 62144 bytes, checksum: f32538ad21a04ade3044af050e60848f (MD5) Mechanical.tex: 26962 bytes, checksum: 87e4081d2789810a02cc70cdfc19cf4c (MD5) abs.tex: 2394 bytes, checksum: 56cabf359f6612e97f9b30eeaa3a5613 (MD5) aubio.tex: 1539 bytes, checksum: 8361c48f1eb3abf1878bccd9d62e750b (MD5) intro.tex: 32933 bytes, checksum: 4545e8e256c46d7b6c068e78c30eea7f (MD5) Dissertation.tex: 9962 bytes, checksum: dfaeb7988b9ba30acfa39f62fe08fe5a (MD5) Gregg_Robert.pdf: 2695035 bytes, checksum: 47511aeea433f04b4cf44ab6d878ce21 (MD5)","Made available in DSpace on 2011-01-14T22:49:05Z (GMT). No. of bitstreams: 20 Gregg_Robert.pdf: 2695035 bytes, checksum: 47511aeea433f04b4cf44ab6d878ce21 (MD5) license.txt: 4060 bytes, checksum: ec76352010e357de0f8c258a3f76da01 (MD5) Dissertation.tex: 9962 bytes, checksum: dfaeb7988b9ba30acfa39f62fe08fe5a (MD5) intro.tex: 32933 bytes, checksum: 4545e8e256c46d7b6c068e78c30eea7f (MD5) aubio.tex: 1539 bytes, checksum: 8361c48f1eb3abf1878bccd9d62e750b (MD5) abs.tex: 2394 bytes, checksum: 56cabf359f6612e97f9b30eeaa3a5613 (MD5) Mechanical.tex: 26962 bytes, checksum: 87e4081d2789810a02cc70cdfc19cf4c (MD5) ControlledReduction.tex: 62144 bytes, checksum: f32538ad21a04ade3044af050e60848f (MD5) RBControl.tex: 37736 bytes, checksum: c1f25a165a9bbc0f5a5795e1e5938883 (MD5) GaitPrimitives.tex: 51684 bytes, checksum: ae4f243260e3b662ded7a21239e56f74 (MD5) Rehab.tex: 22761 bytes, checksum: eaca380efeeff7e23190ba79af1d9226 (MD5) concl.tex: 9121 bytes, checksum: 585ce4da44fc5668a2528e90ae439c27 (MD5) BipedWalking.tex: 74369 bytes, checksum: 47509ea40c3386a92a6bcc592af7b230 (MD5) ack.tex: 4867 bytes, checksum: 2dfc8deb26c0b5d7c16a525e84046017 (MD5) Appendix.tex: 32501 bytes, checksum: aadb8c8228e277f1251156ecb051d4bb (MD5) DissertationBib.bib: 51231 bytes, checksum: 6fb18d95907556618aa7f6b65fafab87 (MD5) Dissertation.sty: 9648 bytes, checksum: 23536680e54ee7c37c08beb8e357c2bc (MD5) IEEE_ECE.bst: 61786 bytes, checksum: e34f041873deb4165fc8d76725c453c4 (MD5) uiucecethesis09.cls: 21157 bytes, checksum: 8a2975a9bd857ec4f015bf1dcefcdf94 (MD5) figures.zip: 2273225 bytes, checksum: c79b3abd87a049ffa5f5c5607d475c25 (MD5)"],"dc:identifier":["http://hdl.handle.net/2142/18397"],"dc:language":["en"],"dc:rights":["Copyright 2010 Robert D. Gregg IV Copyright 1999 SAGE Publications (Figures 1.4 and 7.1)"],"dc:subject":["Robots","Bipedal","Walking","Locomotion","Dynamic Walking","Geometric Control","Motion Planning","Three-Dimensional (3D)","Reduction-based Control","Controlled Reduction","Hybrid Limit Cycles"],"dc:title":["Geometric control and motion planning for three-dimensional bipedal locomotion"],"thesis:degree_discipline":["Electrical & Computer Engr"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:11Z"}