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A Riemannian geometric approach to output tracking for nonholonomic systems

Simha, A and Raha, S (2019) A Riemannian geometric approach to output tracking for nonholonomic systems. In: 11th IFAC Symposium on Nonlinear Control Systems, NOLCOS 2019, 4-6 September 2019, Vienna; Austria, pp. 144-149.

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Official URL: http://dx.doi.org/10.1016/j.ifacol.2019.11.769


The problem of designing coordinate-invariant output tracking control laws for nonholonomic mechanical systems is addressed. The velocity constrained Euler-Lagrange equations of motion are expressed through a constrained affine connection which is compatible with the kinetic energy Riemannian metric. This formalism is used in designing an output tracking control law via backstepping, which is shown to guarantee exponential stability when the initial distance between the output and reference trajectory is within injectivity radius of the output manifold. In particular this enables almost-global tracking when the output manifold is a rank-1 symmetric space. The control law is intrinsic to the Riemannian structure, and is explicitly constructed. The control law is applied to the problem of tracking the reduced attitude of a rigid body with a nonholonomic velocity constraint. Numerical simulations illustrating the tracking performance are presented.

Item Type: Conference Paper
Publication: IFAC-PapersOnLine
Publisher: Elsevier B.V.
Additional Information: Copyright of this article belongs to Elsevier B.V.
Keywords: Backstepping; Equations of motion; Geometry; Kinetic energy; Kinetics; Navigation, Euler-Lagrange equations; Non-holonomic mechanical systems; Non-holonomic mechanics; Output tracking control; Reference trajectories; Riemannian geometry; Riemannian structure; Tracking controls, Control theory
Department/Centre: Division of Interdisciplinary Sciences > Computational and Data Sciences
Date Deposited: 28 Feb 2020 09:57
Last Modified: 28 Feb 2020 09:57
URI: http://eprints.iisc.ac.in/id/eprint/64378

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