H2- and H∞-Optimal Model Predictive Controllers for Robust Legged Locomotion

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dc.contributor.authorPandala, Abhisheken
dc.contributor.authorAmes, Aaron D.en
dc.contributor.authorHamed, Kaveh Akbarien
dc.date.accessioned2025-02-18T13:27:18Zen
dc.date.available2025-02-18T13:27:18Zen
dc.date.issued2024-05-31en
dc.description.abstractThis paper formally develops robust optimal predictive control solutions that can accommodate disturbances and stabilize periodic legged locomotion. To this end, we build upon existing optimization-based control paradigms, particularly quadratic programming (QP)-based model predictive controllers (MPCs). We present conditions under which the closed-loop reduced-order systems (i.e., template models) with MPC have the continuous differentiability property on an open neighborhood of gaits. We then linearize the resulting discrete-time, closed-loop nonlinear template system around the gait to obtain a linear time-varying (LTV) system. This periodic LTV system is further transformed into a linear system with a constant state-transition matrix using discrete-time Floquet transform. The system is then analyzed to accommodate parametric uncertainties and to synthesize robust optimal H2 and H∞ feedback controllers via linear matrix inequalities (LMIs). The paper then extends the theoretical results to the single rigid body (SRB) template dynamics and numerically verifies them. The proposed robust optimal predictive controllers are used in a layered control structure, where the optimal reduced-order trajectories are provided to a full-order nonlinear whole-body controller (WBC) for tracking at the low level. The developed layered controllers are numerically and experimentally validated for the robust locomotion of the A1 quadrupedal robot subject to various disturbances and uneven terrains. Our numerical results suggest that the H2-and H∞-optimal MPC controllers significantly improve the robust stability of the gaits compared to the normal MPC.en
dc.description.versionPublished versionen
dc.format.extentPages 225-238en
dc.format.extent14 page(s)en
dc.format.mimetypeapplication/pdfen
dc.identifier.doihttps://doi.org/10.1109/OJCSYS.2024.3407999en
dc.identifier.eissn2694-085Xen
dc.identifier.issn2694-085Xen
dc.identifier.orcidAkbari Hamed, Kaveh [0000-0001-9597-1691]en
dc.identifier.urihttps://hdl.handle.net/10919/124641en
dc.identifier.volume3en
dc.language.isoenen
dc.publisherIEEEen
dc.rightsCreative Commons Attribution-NonCommercial-NoDerivatives 4.0 Internationalen
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/en
dc.subjectLegged locomotionen
dc.subjectRobotsen
dc.subjectQuadrupedal robotsen
dc.subjectUncertaintyen
dc.subjectControl systemsen
dc.subjectRobust controlen
dc.subjectReal-time systemsen
dc.subjectNonlinear systems and controlen
dc.subjectoptimal controlen
dc.subjectroboticsen
dc.subjectstability of nonlinear systemsen
dc.titleH<sub>2</sub>- and H<sub>∞</sub>-Optimal Model Predictive Controllers for Robust Legged Locomotionen
dc.title.serialIEEE Open Journal of Control Systemsen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten
dc.type.otherArticleen
dc.type.otherJournalen
pubs.organisational-groupVirginia Techen
pubs.organisational-groupVirginia Tech/Engineeringen
pubs.organisational-groupVirginia Tech/Engineering/Mechanical Engineeringen
pubs.organisational-groupVirginia Tech/All T&R Facultyen
pubs.organisational-groupVirginia Tech/Engineering/COE T&R Facultyen

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