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Modified Integral Control Globally Counters Symmetry-Breaking Biases

Zhifei Zhang 1, 2 Zhihao Ling 1 Alain Sarlette 3, 2
3 QUANTIC - QUANTum Information Circuits
ENS Paris - École normale supérieure - Paris, MINES ParisTech - École nationale supérieure des mines de Paris, SU - Sorbonne Université, Inria de Paris
Abstract : We propose a modified integral controller to treat actuation biases in nonholonomic systems. In such systems, although one cannot directly counter biases along all directions, one can still aim at restoring the symmetry of coordinated motion that the biases would break. Focusing on the example of steering controlled planar vehicles, we indeed show how to perfectly stabilize a circular trajectory coordinated with the leader, despite any unknown actuation bias. The proposed solution is a simple modified integral control term, and we prove via a detailed analysis of averaging theory that this control gadget globally stabilizes the perfect coordinated motion. The corresponding general observation is that stabilizing such symmetry-preserving situation can be viewed as rejecting a bias affecting the output measurement, instead of the input command. The symmetry-restoring control then becomes an output bias rejection, dual to the more standard input bias rejection with standard integral control.
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https://hal.inria.fr/hal-02394405
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Submitted on : Wednesday, December 4, 2019 - 5:24:39 PM
Last modification on : Monday, December 14, 2020 - 9:49:47 AM
Long-term archiving on: : Thursday, March 5, 2020 - 9:44:33 PM

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Zhifei Zhang, Zhihao Ling, Alain Sarlette. Modified Integral Control Globally Counters Symmetry-Breaking Biases. Symmetry, MDPI, 2019, ⟨10.3390/sym11050639⟩. ⟨hal-02394405⟩

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