Application of a new Lyapunov function to global adaptive attitude tracking
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The introduction of "error coordinates" and a "tracking potential" on the rotations affords a global nonlinear version of inverse dynamics for attitude tracking. The resulting algorithm produces "almost global" asymptotically exact tracking: this convergence behavior is as strong as the topology of the phase space can allow. A new family of strict global Lyapunov functions for mechanical systems is applied to achieve an adaptive version of the inverse dynamics algorithm in the case that the inertial parameters of the rigid body are not known a priori. The resulting closed loop adaptive system is shown to be stable, and the rigid body phase errors are shown to converge to the limit trajectories of the non-adaptive algorithm.
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Copyright 1988 IEEE. Reprinted from Proceedings of the 27th IEEE Conference on Decision and Control, Volume 1, 1988, pages 63-68. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it. NOTE: At the time of publication, author Daniel Koditschek was affiliated with Yale University. Currently, he is a faculty member in the Department of Electrical and Systems Engineering at the University of Pennsylvania.