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Creators/Authors contains: "Vang, Bee"

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  1. ; (, IEEE American Control Conference)
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  2. ; (, IEEE Conference on Decision and Control)
    null (Ed.)
    In this paper, we present a simple geometric attitude controller that is globally, exponentially stable. To overcome the topological restriction, the controller is designed to follow a reference trajectory that in turn converges to the desired equilibrium (making it discontinuous in the initial conditions, but continuous in time). The system and reference dynamics are studied as a single augmented system that can be analyzed and tuned simultaneously. The controller's stability is proved using contraction analysis (on the manifold), and the bounds on the convergence rate can be found via a semi-definite program with linear matrix inequalities. Additionally, our approach allows the use of the Nelder-Mead algorithm to automatically select controller gains and reference trajectory parameters by optimizing the aforementioned bounds. The resulting controller is verified through simulations. 
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  3. ; (, IEEE Conference on Decision and Control (CDC))
    In this paper we propose a new analysis of a simple geometric attitude controller, showing that it is locally exponentially stable and almost globally asymptotically stable; the exponential convergence region is much larger than existing non-hybrid geometric controllers (and covers almost the entire rotation space). The controller's stability is proved using contraction analysis combined with optimization. The key in this combination is that the contraction metric is a linear matrix inequality with a special structure stemming from the configuration manifold SO(3). As an additional contribution, we propose a general framework to automatically select controller gains by optimizing bounds on the system's convergence rate; while this principle is quite general, its application is particularly straightforward with our contraction-based analysis. We demonstrate our results through simulations. 
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