An overview of recent progress in high-order nonholonomic chained system control and distributed coordination

Huang, Jie; Chen, Jie; Fang, Hao; Dou, Lihua

doi:10.1080/23307706.2015.1004803

Cited by 22 publications

(9 citation statements)

References 74 publications

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“…The USV system () is subject to [24]

\begin{matrix} m_{22} false(\overset{x}{true} \sin ψ - ÿ \cos ψ false) & + false(m_{22} - m_{11} false) \overset{ψ}{true} false(\overset{x}{true} \cos ψ + \overset{y}{true} \sin ψ false) \\ + d_{22} false(\overset{x}{true} \sin ψ - \overset{y}{true} \cos ψ false) = 0, \end{matrix}

which is a second‐order nonholonomic constraint because it is a nonintegrable relation involving both generalized coordinates/velocities and generalized accelerations. Readers can also refer to the literature [20,21,33] and references therein for recognizing the nonholonomic constraint on USV.…”

Section: Problem Formulationmentioning

confidence: 99%

Robust smooth control for global uniform asymptotic stabilization of underactuated surface vessels with unknown model parameters

Xie

Fernando

et al. 2021

Asian Journal of Control

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This paper investigates how to design controllers to stabilize the underactuated surface vessel to desired constant location and orientation with vanishing velocities. The first control law is designed as a smooth function of position and orientation errors without using model parameters, where a gain is made time‐varying to get over the nonholonomic constraint on model. Skew‐symmetric and damping terms in model are exploited to help construct two particular Lyapunov functions, and Barbalat's lemma are combined to verify the global uniform asymptotic convergence of errors and velocities. Then, the second and the third control laws are devised as the forms of the first controller plus velocity feedbacks and can achieve the same stability as the first one but have a weaker gain condition. All the three controllers are robust to model parameters due to their absence in controllers and only require three model parameters' upper/lower bounds, decreasing the identification workload greatly. Moreover, they are the first smooth ones capable of achieving global uniform asymptotic full‐state stabilization control of vessel with unknown model parameters. Effectiveness of the proposed controllers is demonstrated by numerical simulations.

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“…The USV system () is subject to [24]

\begin{matrix} m_{22} false(\overset{x}{true} \sin ψ - ÿ \cos ψ false) & + false(m_{22} - m_{11} false) \overset{ψ}{true} false(\overset{x}{true} \cos ψ + \overset{y}{true} \sin ψ false) \\ + d_{22} false(\overset{x}{true} \sin ψ - \overset{y}{true} \cos ψ false) = 0, \end{matrix}

Section: Problem Formulationmentioning

confidence: 99%

Robust smooth control for global uniform asymptotic stabilization of underactuated surface vessels with unknown model parameters

Xie

Fernando

et al. 2021

Asian Journal of Control

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“…In recent years, much effort has been put in for tracking and stabilizing control of chained form systems. [14][15][16][17][18][19][20][21] Detailed progress on higher order nonholonomic chained system control has been presented by Huang et al 18…”

Section: Nonholonomic Chained Form Systemsmentioning

confidence: 99%

Robust stabilizing control of nonholonomic systems with uncertainties via adaptive integral sliding mode

Sarfraz

Rehman

Shah

2017

International Journal of Advanced Robotic Systems

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This article presents a robust stabilizing control for nonholonomic underwater systems that are affected by uncertainties. The methodology is based on adaptive integral sliding mode control. Firstly, the original underwater system is transformed in a way that the new system has uncertainties in matched form. A change of coordinates is carried out for this purpose, and the nonholonomic system is transformed into chained form system with matched uncertainties. Secondly, the chained form system with uncertainties is transformed into a special structure containing nominal part and some unknown terms through input transformation. The unknown terms are computed adaptively. Afterward, the transformed system is stabilized using integral sliding mode control. The stabilizing controller for the transformed system is constructed which consists of the nominal control plus some compensator control. The compensator controller and the adaptive laws are derived in a way that the derivative of a suitable Lyapunov function becomes strictly negative. Two different cases of perturbation are considered including the bounded uncertainty present in any single control input and the uncertainties present in the overall system model of the underwater vehicle. Finally, simulation results show the validity and correctness of the proposed controllers for both cases of nonholonomic underwater system affected by uncertainties.

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“…Typical group control objectives of agents include consensus [2], formation [3], flocking [4], and rendezvous [5], which have been widely studied for many practical mechanical systems, for example, aircrafts, ships, robots, and vehicles. As one research topic of this subject, cooperative control of nonholonomic unicycle vehicles has caught many researcher's eyes due to theoretical challenges and wide applications [6].…”

Section: Introductionmentioning

confidence: 99%

Global formation control of nonholonomic unicycle vehicles with guaranteed rate of convergence

Zhao

Huang

Liu

et al. 2021

Asian Journal of Control

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This paper studies the full‐state formation control problem of multiple nonholonomic unicycle vehicles. Firstly, the formation error model is transformed into standard nonholonomic chained form, including orientation and position error subsystems. For orientation subsystem, an angular velocity control law is designed to be a cooperative term plus an exponential decay function of time, ensuring orientations reach an agreement on a common value. For position error subsystem, a time‐varying output‐like variable is carefully constructed to ensure a stable zero dynamics, that is, the consensus of these output variables guarantees position formation, overcoming the intrinsic underactuated control difficulty. Then, a linear velocity control law is derived to realize consensus of outputs. It is proved that the proposed distributed time‐varying controller is capable of steering the vehicles to globally exponentially make into desired geometric position shape with the same orientations and vanishing velocities, provided that the communication topology is directed and having a spanning tree. The calculated convergence rates are shown dependent on controller coefficients; thus, the controller is modified to additionally reach a prescribed rate of convergence by redesigning conditions of controller parameters. Finally, two numerical simulations are implemented for five unicycle vehicles, demonstrating the effectiveness of the proposed control scheme.

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An overview of recent progress in high-order nonholonomic chained system control and distributed coordination

Cited by 22 publications

References 74 publications

Robust smooth control for global uniform asymptotic stabilization of underactuated surface vessels with unknown model parameters

Robust smooth control for global uniform asymptotic stabilization of underactuated surface vessels with unknown model parameters

Robust stabilizing control of nonholonomic systems with uncertainties via adaptive integral sliding mode

Global formation control of nonholonomic unicycle vehicles with guaranteed rate of convergence

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