Application of a new Lyapunov function to global adaptive attitude tracking
Copyright 1988 IEEE. Reprinted from Proceedings of the 27th IEEE Conference on Decision and Control, Volume 1, 1988, pages 63-68.
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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.
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.
Daniel E. Koditschek. "Application of a new Lyapunov function to global adaptive attitude tracking" Departmental Papers (ESE) (1988).
Available at: http://works.bepress.com/daniel_koditschek/22