Design of Stabilizing Feedback Controllers for High-Order Nonholonomic Systems

This letter presents a novel stabilizing control design strategy for driftless control-affine systems with an arbitrary degree of nonholonomy. The proposed approach combines a time-varying control component that generates motion in the direction of prescribed Lie brackets with a state-dependent comp...

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Bibliographic Details
Published inIEEE control systems letters Vol. 8; pp. 988 - 993
Main Authors Grushkovskaya, Victoria, Zuyev, Alexander
Format Journal Article
LanguageEnglish
Published IEEE 2024
Subjects
Control design
Lie brackets
Lyapunov methods
Mathematics
Mobile robots
nonholonomic systems
oscillating control
stabilization
Time-varying systems
Trajectory
Vectors
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Summary:This letter presents a novel stabilizing control design strategy for driftless control-affine systems with an arbitrary degree of nonholonomy. The proposed approach combines a time-varying control component that generates motion in the direction of prescribed Lie brackets with a state-dependent component, ensuring the stability of the equilibrium. The coefficients of the state-dependent component are derived in such a way that the trajectories of the resulting closed-loop system approximate the gradient flow of a Lyapunov-like function. In the case of a quadratic Lyapunov function, this guarantees the exponential stability of the equilibrium. The usability of this approach is demonstrated on general two-input systems having the fourth degree of nonholonomy. The proposed stabilization scheme is illustrated with several examples.
ISSN:2475-1456
2475-1456
DOI:10.1109/LCSYS.2024.3406931