Systems In Chained Form Research Articles

Finite-Time Stabilization of Dynamic Nonholonomic Wheeled Mobile Robots with Parameter Uncertainties

The finite-time stabilization problem of dynamic nonholonomic wheeled mobile robots with parameter uncertainties is considered for the first time. By the equivalent coordinate transformation of states, an uncertain 5-order chained form system can be obtained, based on which a discontinuous switching controller is proposed such that all the states of the robots can be stabilized to the origin equilibrium point within any given settling time. The systematic strategy combines the theory of finite-time stability with a new switching control design method. Finally, the simulation result illustrates the effectiveness of the proposed controller.

A global steering method for nonholonomic systems

In this paper, we present an iterative steering algorithm for nonholonomic systems (also called driftless control-affine systems) and we prove its global convergence under the sole assumption that the Lie Algebraic Rank Condition (LARC) holds true everywhere. That algorithm is an extension of the one introduced in Jean et al. (2005) [21] for regular systems. The first novelty here consists in the explicit algebraic construction, starting from the original control system, of a lifted control system which is regular. The second contribution of the paper is an exact motion planning method for nilpotent systems, which makes use of sinusoidal control laws and which is a generalization of the algorithm described in Murray and Sastry (1993) [29] for chained-form systems.

State-feedback stabilisation for stochastic non-holonomic systems with time-varying delays

This study investigates the problem of state-feedback stabilisation for a class of stochastic non-holonomic systems in chained form with time-varying delays. By using input-state-scaling technique and backstepping recursive approach, and choosing an appropriate Lyapunov–Krasoviskii functional, a state-feedback controller is constructed. Based on switching strategy to eliminate the phenomenon of uncontrollability, the proposed controller could ensure that the closed-loop system is globally asymptotically regulated at origin in probability. A simulation example is provided to illustrate the effectiveness of the proposed method.

Finite‐Time Stabilization of Stochastic Nonholonomic Systems and Its Application to Mobile Robot

This paper investigates the problem of finite‐time stabilization for a class of stochastic nonholonomic systems in chained form. By using stochastic finite‐time stability theorem and the method of adding a power integrator, a recursive controller design procedure in the stochastic setting is developed. Based on switching strategy to overcome the uncontrollability problem associated with x0(0) = 0, global stochastic finite‐time regulation of the closed‐loop system states is achieved. The proposed scheme can be applied to the finite‐time control of nonholonomic mobile robot subject to stochastic disturbances. The simulation results demonstrate the validity of the presented algorithm.

Adaptive robust time-varying control of uncertain non-holonomic robotic systems

This study addresses the trajectory tracking control problem of dynamic non-holonomic robotic systems in chained form in presence of parametric and non-prarametric uncertainties. At first, a global adaptive tracking controller is designed by exploiting the full use of the backstepping technique. Then, the proposed controller is modified to preserve its robustness to non-parametric uncertainties. In contrast to most of the previously developed kinematic and dynamic tracking controllers, the proposed controller makes all tracking errors and parameter estimation errors be at least globally uniformly ultimately bounded (GUUB) and exponentially converge to a small ball containing the origin. A Lyapunov-based stability analysis is presented to guarantee the GUUB stability of the tracking errors. The controller is applied to a non-holonomic wheeled mobile robot and simulation results are presented to illustrate the effectiveness of the proposed control law.

Global 𝒦-exponential trackers for nonholonomic chained-form systems based on LMI

Global 𝒦-exponential controllers are constructed for the tracking control problem of nonholonomic systems in chained form. Compared to previously published papers, a difference is that the reference targets are allowed to converge to a point exponentially. By using a novel transformation and the cascade-design method, the tracking control problem is converted into a stabilisation problem composed of two simple subsystems. Then the LMI-design approach is developed for the stabilising one of the above two subsystems. Assumptions on the reference signal is much more relaxed than our previous papers. A peculiar character of the presented methodology is that global 𝒦-exponential tracking can be successfully obtained for nonholonomic chained-form systems without the popular condition of persistent excitation or not converging to zero. Simulation results on a unicycle mobile robot and an articulated vehicle are presented to show the validity of the proposed strategy.

Robust Stabilization of Nonholonomic Chained Form Systems with Uncertainties

摘要: 不确定非完整链式系统的镇定问题在过去十年中得到了许多有趣的结果, 涌现出了几类模型和相应的控制方法. 目前已经可以对这方面的发展做出总结. 本文给出了非完整链式系统的模型、镇定控制方法和一些结论, 特别是基于视觉传感器得到了一些新的有趣的不确定链式模型. 同时, 利用新的二步法、视觉反馈、状态缩放变换和切换等技术设计了新的不确定链式模型的鲁棒镇定控制器. 希望这项工作可以做到抛砖引玉, 也可以为这个领域的专家做一个较好的参考. 关键词: 非完整 / 运动学 / 移动机器人 / 不确定链式系统

Robust Stabilization of Nonholonomic Chained Form Systems with Uncertainties

A summary of recent developments concerning robust stabilization problems for the nonholonomic chained form systems with uncertainties is provided. Firstly, various models, main approaches, and results over past ten years for the uncertain chained form systems are presented. Then, several new exciting uncertain chained form models of special interest are proposed for the nonholonomic wheeled mobile robots. They are obtained by using the state and input transformations based on the visual servoing feedback. Finally, the novel robust regulation controllers are addressed for some new uncertain chained models by using two-steps technology, visual feedback, state-scaling and switching strategy. It is expected that this investigation will provide a good introduction about the development of robust stabilization for uncertain chained form systems.

Final Comments by the Authors

In this paper we deal with the state-feedback tracking control problem for a class of nonholonomic dynamic systems in chained form. By means of the recursive technique proposed in our recent work, we first show that the semiglobal exponential tracking can be easily obtained for systems in chained form. Then, we show that, whenever the control inputs are subject to saturation constraints, a semiglobal asymptotic tracking controller can be found on the basis of Lyapunov redesign and backstepping techniques.

Adaptive output feedback control for uncertain nonholonomic chained systems

An adaptive output feedback control was proposed to deal with a class of nonholonomic systems in chained form with strong nonlinear disturbances and drift terms. The objective was to design adaptive nonlinear output feedback laws such that the closed-loop systems were globally asymptotically stable, while the estimated parameters remained bounded. The proposed systematic strategy combined input-state-scaling with backstepping technique. The adaptive output feedback controller was designed for a general case of uncertain chained system. Furthermore, one special case was considered. Simulation results demonstrate the effectiveness of the proposed controllers.

非ホロノミック2次チェインドシステムの大域的指数安定化制御 : オブザーバと安定化補償器の設計(機械力学,計測,自動制御)

This paper considers the problem of controlling a class of nonholonomic systems in second-order chained form, which is described by a set of nonlinear differential equations. Our novel approach is based on coordinate transformations and sampled data control. First, the nonholonomic system is discretized by a zero order hold and a sampler. A time-varying discrete-time coordinate transformation is utilized to reduce the stabilization problem to a standard pole assignment problem for a linear time-invariant discrete-time system. Both a new state feedback controller and a new dynamic output feedback controller based on state-observer are presented for obtaining global exponential stabilization of the system. Moreover, the proposed design methods are simple and straightforward. Some simulations are performed to validate the effectiveness of the proposed controllers.

Robust adaptive control for nonholonomic systems with nonlinear parameterization

In this paper, an adaptive controller is designed for a class of nonholonomic systems in chained form with nonlinear parameterization. The robust adaptive control law is developed using parameter separation, state scaling and backstepping technique. Global asymptotic regulation of the closed-loop system states is achieved. The proposed control based switching strategy is proposed to overcome the uncontrollability problem associated with x 0 ( t 0 ) = 0 .

Stabilization of uncertain chained nonholonomic systems using adaptive output feedback

AbstractIn this paper, adaptive output feedback control is presented to solve the stabilization problem of nonholonomic systems in chained form with strong nonlinear drifts and uncertain parameters using output signals only. The objective is to design adaptive nonlinear output feedback laws which can steer the closed‐loop systems to globally converge to the origin, while the estimated parameters remain bounded. The proposed systematic strategy combines input‐state scaling with backstepping technique. Motivated from a special case, adaptive output feedback controllers are proposed for a class of uncertain chained systems. The simulation results demonstrate the effectiveness of the proposed controllers. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Adaptive stabilization of uncertain nonholonomic systems by output feedback

The adaptive output feedback control strategy is presented for a class of nonholonomic systems in chained form with nonlinearity uncertainties. A new observer and a filter are introduced for the states and parameter estimation. The proposed control strategies guarantee the convergence of the closed-loop system. The simulation example demonstrates the efficiency of the proposed method.

Neural network solution for suboptimal control of non-holonomic chained form system

In this paper, we develop fixed-final time nearly optimal control laws for a class of non-holonomic chained form systems by using neural networks to approximately solve a Hamilton—Jacobi—Bellman equation. A certain time-folding method is applied to recover uniform complete controllability for the chained form system. This method requires an innovative design of a certain dynamic control component. Using this time-folding method, the chained form system is mapped into a controllable linear system for which controllers can systematically be designed to ensure exponential or asymptotic stability as well as nearly optimal performance. The result is a neural network feedback controller that has time-varying coefficients found by a priori offline tuning. The results of this paper are demonstrated in an example.

Design and analysis of a spherical mobile robot

A spherical mobile robot, rolling on a plane with the help of two internal rotors and working on the principle of conservation of angular momentum has recently been fabricated in our group. The robot is a classic nonholonomic system. Path planning algorithms exist in the literature for certain classes of nonholonomic systems like chained form systems, nilpotent systems and differentially flat systems. The model of this spherical mobile robot however, does not fall into any of these classes and hence these existing algorithms are rendered inapplicable to this system. The final objective is to make this robot as a testbed for feasible path planning and feedback control algorithms.

Global κ-exponential Tracking Control of Nonholonomic Systems in Chained-form by Output Feedback

The output tracking control problem of nonholonomic chained form systems is studied in this paper and global κ-exponential output trackers are presented without persistent excitation or not-converging to zero on reference trajectories. First, a time-varying coordinate transformation is introduced to avoid manipulating exponentially converging signals. Then, with the help of theory of cascaded systems and linear perturbed systems, global κ-exponential output trackers are successfully obtained. A new feature of the proposed controller is that the output tracking control problem of nonholonomic chained form systems is also resolvable without the popular condition of persistent excitation or not converging to zero on reference signals in the previous works. The proposed method is demonstrated and discussed by means of nonholonomic mobile robots and cars with one trailer.

Predictive variable structure control of nonholonomic chained systems

A novel variable structure control strategy for a class of second-order nonlinear systems is presented based on the phase-plane analysis and computing prediction. In this strategy control is switched by online prediction of the trajectory behaviour of the closed-loop system; control switching does not occur continuously, so the chattering that occurs in conventional variable structure control methods can be avoided completely. It is proved that the states of the closed-loop system can be stabilized to the origin exponentially and the trajectory of the closed-loop system does not overshoot in general. As an application, the proposed predictive variable structure control strategy is used to stabilize nonholonomic systems in chained form. An example of a wheeled mobile robot is studied and associated simulation results demonstrate the effectiveness of the proposed control strategy.

Robust Adaptive Control of Nonholonomic Systems with Nonlinear Parameterization

A global-adaptive state feedback control strategy is presented for a class of nonholonomic systems in chained form with strong nonlinear drifts and unknown nonlinear parameters. A parameter separation technique is introduced to transform the nonlinear parameterization nonholonomic system into a linear-like parameterized nonholonomic system. Then, the feedback domination design is applied to design a global adaptive stabilization controller and a switching strategy is developed to eliminate the phenomenon of uncontrollability. The proposed controller can guarantee that all the system states globally converge to the origin, while other signals remain bounded. Simulation example demonstrates the effectiveness and the robust features of the proposed controller.

Time‐varying linear controllers for exponential tracking of non‐holonomic systems in chained form

AbstractIn this paper, the authors address the tracking problem for non‐holonomic systems in chained form with target signals that may exponentially decay to zero. By introducing a time‐varying co‐ordinate transformation and using the cascade‐design approach, smooth time‐varying controllers are constructed, which render the tracking‐error dynamics globally 𝒦‐exponentially stable. The result shows that the popular condition of persistent excitation or not converging to zero for the reference signals is not necessary even for the globally 𝒦‐exponential tracking of the chained‐form system. The effectiveness of the proposed controller is validated by simulation of two benchmark mechanical systems under non‐holonomic constraints. Copyright © 2006 John Wiley & Sons, Ltd.