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Almost Global Consensus on the n-Sphere
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DOI：10.1109/TAC.2017.2752799.png)
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Abstract
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This paper establishes novel results regarding the global convergence properties of a large class of consensus protocols for multiagent systems that evolve in continuous time on the n-dimensional unit sphere or n-sphere. For any connected, undirected graph and all n is an element of N\{1}, each protocol in said class is shown to yield almost global consensus. The feedback laws are negative gradients of Lyapunov functions and one instance generates the canonical intrinsic gradient descent protocol. This convergence result sheds new light on the general problem of consensus on Riemannian manifolds; the n-sphere for n is an element of N\{1} differs from the circle and SO(3), where the corresponding protocols fail to generate almost global consensus. Moreover, we derive a novel consensus protocol on SO(3) by combining two almost globally convergent protocols on the n-sphere for n is an element of{1, 2}. Theoretical and simulation results suggest that the combined protocol yields almost global consensus on SO(3).
Keywords:
Aerospace
agents and autonomous systems
consensus
cooperative control
nonlinear systems
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