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Integral Control on Lie Groups

Zhifei Zhang 1, 2 Alain Sarlette 3 Zhihao Ling 2 
3 QUANTIC - QUANTum Information Circuits
ENS-PSL - École normale supérieure - Paris, Inria Paris-Rocquencourt, UPMC - Université Pierre et Marie Curie - Paris 6, Mines Paris - PSL (École nationale supérieure des mines de Paris), CNRS - Centre National de la Recherche Scientifique : UMR8551
Abstract : In this paper, we extend the popular integral control technique to systems evolving on Lie groups. More explicitly, we provide an alternative definition of ‘‘integral action’’ for proportional(–derivative)-controlled systems whose configuration evolves on a nonlinear space, where configuration errors cannot be simply added up to compute a definite integral. We then prove that the proposed integral control allows to cancel the drift induced by a constant bias in both first order (velocity) and second order (torque) control inputs for fully actuated systems evolving on abstract Lie groups. We illustrate the approach by 3-dimensional motion control applications.
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Submitted on : Monday, December 28, 2015 - 5:50:35 PM
Last modification on : Wednesday, October 26, 2022 - 2:08:50 PM


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  • HAL Id : hal-01093913, version 2
  • ARXIV : 1410.7614


Zhifei Zhang, Alain Sarlette, Zhihao Ling. Integral Control on Lie Groups. Systems and Control Letters, 2015, 80, pp.9-15. ⟨hal-01093913v2⟩



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