Almost-globally stable tracking for on compact Riemannian manifolds

Aradhana Nayak; Ravi Banavar

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arXiv · 1511.00796

Almost-globally stable tracking for on compact Riemannian manifolds

Aradhana Nayak·Ravi Banavar

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Abstract

In this article, we propose a control law for almost-global asymptotic tracking (AGAT) of a smooth reference trajectory for a fully actuated simple mechanical system (SMS) evolving on a Riemannian manifold which can be embedded in a Euclidean space. The existing results on tracking for an SMS are either local, or almost-global, only in the case the manifold is a Lie group. In the latter case, the notion of a configuration error is naturally defined by the group operation and facilitates a global analysis. However, such a notion is not intrinsic to a Riemannian manifold. In this paper, we define a configuration error followed by error dynamics on a Riemannian manifold, and then prove AGAT. The results are demonstrated for a spherical pendulum which is an SMS on $S^2$ and for a particle moving on a Lissajous curve in $\mathbb{R}^3$.

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Aradhana Nayak, Ravi Banavar. 2015-11-03. Almost-globally stable tracking for on compact Riemannian manifolds. https://arxiv.org/abs/1511.00796

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