{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/151814"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/151814","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"A Koopman-Based Reduced-Order State Observer for Visual Localization of Robots","abstract":"A reduced-order observer using Koopman lifting linearization is developed for localization of a robot guided by a vision system. The Koopman operator is a powerful method for representing nonlinear robot dynamics as a linear model in a lifted space. Koopman faces two main challenges with robot localization. One is that the lifted linear system is not observable in general; standard Kalman filter and state observers cannot be applied to such non-observable systems. The other is that a large number of observables are required for accurate linearization. Here, we present 1) a new reduced-order state observer for a Koopman lifted linear model that satisfies the observability conditions, and 2) measurement of the multitude of Koopman observables by extracting many features from a camera image. These image features used as Koopman observables are directly measured in real-time and, thereby, make the observability matrix of the reduced-order state observer full rank. The method is developed for a robot crane system equipped with a vision system. We can estimate the endpoint of the robot using a reduced-order state observer of a lifted linear model where 20 observables are obtained from a visual image.","abstract_html":"A reduced-order observer using Koopman lifting linearization is developed for localization of a robot guided by a vision system. The Koopman operator is a powerful method for representing nonlinear robot dynamics as a linear model in a lifted space. Koopman faces two main challenges with robot localization. One is that the lifted linear system is not observable in general; standard Kalman filter and state observers cannot be applied to such non-observable systems. The other is that a large number of observables are required for accurate linearization. Here, we present 1) a new reduced-order state observer for a Koopman lifted linear model that satisfies the observability conditions, and 2) measurement of the multitude of Koopman observables by extracting many features from a camera image. These image features used as Koopman observables are directly measured in real-time and, thereby, make the observability matrix of the reduced-order state observer full rank. The method is developed for a robot crane system equipped with a vision system. We can estimate the endpoint of the robot using a reduced-order state observer of a lifted linear model where 20 observables are obtained from a visual image.","abstract_has_math":false,"creators":["Williams, Jadal"],"institution":"Massachusetts Institute of Technology","degree_name":"Master","degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Department of Mechanical Engineering","school":null,"contributors":[],"advisors":["Asada, H. Harry"],"committee_chairs":[],"committee_members":[],"year":2023,"date_issued":"2023-06","date_published":"2023-06","updated_at":"2026-07-22T22:20:55Z","subjects":[],"languages":[],"rights":["In Copyright - Educational Use Permitted","Copyright retained by author(s)"],"rights_urls":["https://rightsstatements.org/page/InC-EDU/1.0/"],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/1721.1/151814","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Asada, H. Harry"]},{"key":"dc:contributor.department","label":"Department","values":["Massachusetts Institute of Technology. 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The Koopman operator is a powerful method for representing nonlinear robot dynamics as a linear model in a lifted space. Koopman faces two main challenges with robot localization. One is that the lifted linear system is not observable in general; standard Kalman filter and state observers cannot be applied to such non-observable systems. The other is that a large number of observables are required for accurate linearization. Here, we present 1) a new reduced-order state observer for a Koopman lifted linear model that satisfies the observability conditions, and 2) measurement of the multitude of Koopman observables by extracting many features from a camera image. These image features used as Koopman observables are directly measured in real-time and, thereby, make the observability matrix of the reduced-order state observer full rank. The method is developed for a robot crane system equipped with a vision system. We can estimate the endpoint of the robot using a reduced-order state observer of a lifted linear model where 20 observables are obtained from a visual image."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["S.M."]},{"key":"dc:title","label":"Title","values":["A Koopman-Based Reduced-Order State Observer for Visual Localization of Robots"]}]}],"canonical_facts":{"dc:contributor.advisor":["Asada, H. Harry"],"dc:contributor.department":["Massachusetts Institute of Technology. Department of Mechanical Engineering"],"dc:creator":["Williams, Jadal"],"dc:date.accessioned":["2023-08-23T16:10:47Z"],"dc:date.available":["2023-08-23T16:10:47Z"],"dc:date.issued":["2023-06"],"dc:description.abstract":["A reduced-order observer using Koopman lifting linearization is developed for localization of a robot guided by a vision system. The Koopman operator is a powerful method for representing nonlinear robot dynamics as a linear model in a lifted space. Koopman faces two main challenges with robot localization. One is that the lifted linear system is not observable in general; standard Kalman filter and state observers cannot be applied to such non-observable systems. The other is that a large number of observables are required for accurate linearization. Here, we present 1) a new reduced-order state observer for a Koopman lifted linear model that satisfies the observability conditions, and 2) measurement of the multitude of Koopman observables by extracting many features from a camera image. These image features used as Koopman observables are directly measured in real-time and, thereby, make the observability matrix of the reduced-order state observer full rank. The method is developed for a robot crane system equipped with a vision system. We can estimate the endpoint of the robot using a reduced-order state observer of a lifted linear model where 20 observables are obtained from a visual image."],"dc:description.degree":["S.M."],"dc:identifier.uri":["https://hdl.handle.net/1721.1/151814"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["In Copyright - Educational Use Permitted","Copyright retained by author(s)"],"dc:rights.uri":["https://rightsstatements.org/page/InC-EDU/1.0/"],"dc:title":["A Koopman-Based Reduced-Order State Observer for Visual Localization of Robots"],"dc:type":["Thesis"],"thesis:degree_name":["Master","Master of Science in Mechanical Engineering"]},"updated_at":"2026-07-22T22:20:55Z"}