Finite‐time tracking control of a nonholonomic mobile robot

In this paper, the finite‐time tracking problem is investigated for a nonholonomic wheeled mobile robot in a fifth‐order dynamic model. We consider the whole tracking error system as a cascaded system. Two continuous global finite‐time stabilizing controllers are designed for a second‐order subsystem and a third‐order subsystem respectively. Then finite‐time stability results for cascaded systems are employed to prove that the closed‐loop system satisfies the finite‐time stability. Thus the closed‐loop system can track the reference trajectory in finite‐time when the desired velocities satisfy some conditions. In particular, we discuss the control gains selection for the third‐order finite‐time controller and give sufficient conditions by using Lyapunov and backstepping techniques. Simulation results demonstrate the effectiveness of our method. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust tracking control for wheeled mobile robot based on extended state observer

This paper presents a new control scheme on trajectory tracking of wheeled mobile robot with nonholonomic constraints. Extended state observer is introduced to estimate unknown disturbances and velocity information. A robust tracking controller is designed to implement the accurate trajectory tracking and disturbance compensation. By theoretical, position and velocity tracking errors of wheeled mobile robot are proven uniformly ultimately asymptotically stable. Simulation results are given to illustrate the effectiveness of the developed technique.     

非完整移动机器人轨迹跟踪自适应控制器设计

针对轮式移动机器人的非完整运动学模型,将自适应反演控制技术和李亚普诺夫稳定性理论应用于机器人轨迹跟踪控制,设计了具有全局渐近稳定性的自适应轨迹跟踪控制器,并在Matlab环境下实现了移动机器人对直线和椭圆2种轨迹追踪的仿真实验.实验表明:该控制方法在轨迹跟踪控制中有较好的航向跟踪效果,对机器人非完整系统模型的非线性特性...     

基于反步法的移动机器人鲁棒跟踪控制

以四轮移动机器人为研究对象,建立了机器人完整的数学模型,包括运动学模型、动力学模型以及驱动电机模型。在机器人数学模型的基础上,采用反步法的思想设计具有全局收敛特性的鲁棒轨迹跟踪控制器,设计中考虑了驱动电机模型使控制器更符合实际控制要求,并将其分解为运动学控制器、动力学控制器以及电机控制器三部分,降低了控制器设计的难度。构造了系统的李雅普诺夫函数,证明了该类型移动机器人在所得控制器作用下,能实现对给定轨迹的全局渐近追踪。仿真实验结果表明基于反步法的控制器是有效的。     

基于后推设计的直接自适应模糊控制

针对一类严格反馈不确定非线性动态系统，提出一种直接鲁棒自适应模糊控制新方案．利用模糊系统的逼近能力、后推设计方法和积分型李亚普诺夫函数，依次确定各虚拟控制及模糊系统中可调参数的自适应律，并最终确定出控制律．为改善控制系统的性能，引入逼近误差的自适应补偿项．通过李亚普诺夫方法，证明了闭环系统是一致终结有界的．仿真结果表明了该方法的有效性。     

Robust finite‐time consensus formation control for multiple nonholonomic wheeled mobile robots via output feedback

The finite‐time formation control for multiple nonholonomic wheeled mobile robots with a leader‐following structure is studied. Different from the existing results, the considered mobile robot has the following features: (i) a higher‐order dynamic model, (ii) the robot's velocities cannot be measured, and (iii) there are external disturbances. To solve the problem, a finite‐time consensus formation control algorithm via output feedback is explicitly given. At the first step, some finite‐time convergent observers are skillfully constructed to estimate both the unknown velocity information and the disturbance in finite time by imposing certain assumptions on the disturbances. Then, on the basis of the integral sliding‐mode control method, a disturbance observer‐based finite‐time output feedback controller is developed. Rigorous proof shows that the finite‐time formation can be achieved in finite time. An example is finally given to verify the efficiency of the proposed method.     

含未校准摄像机参数的非完整移动机器人自适应动态反馈跟踪控制

研究基于视觉伺服的不确定非完整移动机器人的跟踪控制问题.基于视觉反馈和状态输入变换,提出一类非完整运动学系统的不确定模型,并运用两个新的变换,对3种不同情况分别设计自适应动态反馈控制器来跟踪不确定系统的期望轨迹.利用李雅普诺夫方法和推广的Barbalat引理,严格证明了误差系统的收敛性.仿真结果验证了所提方法的有效性.     

Cooperative adaptive consensus tracking for multiple nonholonomic mobile robots

This paper addresses the cooperative adaptive consensus tracking for a group of multiple nonholonomic mobile robots, where the nonholonomic robot model is assumed to be a canonical vehicle having two actuated wheels and one passive wheel. By integrating a kinematic controller and a torque controller for the nonholonomic robotic system, a cooperative adaptive consensus tracking strategy is developed for the uncertain dynamic models using Lyapunov-like analysis in combination with backstepping approach and sliding mode technique. A key feature of the developed adaptive consensus tracking algorithm is the introduction of a directed network topology into the control constraints based on algebraic graph theory to characterise the communication interaction among robots, which plays an important role in realising the cooperative consensus tracking with respect to a specific common reference trajectory. Furthermore, a novel framework is proposed for developing a unified methodology for the convergence analysis of the closed-loop control systems, which can fully ensure the desired adaptive consensus tracking for multiple nonholonomic mobile robots. Subsequently, illustrative examples and numerical simulations are provided to demonstrate and visualise the theoretical results.     

三轮驱动移动机器人轨迹跟踪控制

针对三轮驱动移动机器人在轨迹跟踪控制过程中运动不平滑的问题,建立了移动机器人在一定运动约束条件下的运动学模型。根据移动机器人位姿误差微分方程的描述,设计了基于后退时变状态反馈方法的移动机器人轨迹跟踪控制器。基于李雅普诺夫方法,对轨迹跟踪控制器的稳定性进行了分析,证明了该控制器能够保证闭环系统全局一致渐进稳定。仿真结果验证了运动学模型的正确性,以及轨迹跟踪控制器的有效性。     

Practical consensus tracking control of multiple nonholonomic wheeled mobile robots in polar coordinates

This paper proposes a sliding‐mode control (SMC) method to achieve practical cooperative consensus tracking for a network of multiple nonholonomic wheeled mobile robots (MNWMRs) with input disturbances. A novel SMC surface under the nonholonomic constraints is first formulated to characterize the network communication interactions among the networked robots under the framework of polar coordinates. A unified distributed consensus tracking strategy is then proposed by systematically combining a position controller and a direction controller. Furthermore, a simple yet general criterion is derived to achieve the desired practical consensus of trajectory tracking and posture stabilization for MNWMRs. In particular, for a specific common consensus trajectory, the complete asymptotic tracking in heading direction can be fully guaranteed when the perfect asymptotic position‐tracking errors are realized. Accordingly, the developed consensus tracking strategy for MNWMRs demonstrates some advantages of control performance including stability, robustness, and effectiveness over the existing control method proposed for their single‐robot counterparts. Some comparative simulation results are given to confirm the effectiveness of the proposed cooperative consensus control method.     

Finite‐time formation control of multiple nonholonomic mobile robots

This paper considers finite‐time formation control problem for a group of nonholonomic mobile robots. The desired formation trajectory is represented by a virtual dynamic leader whose states are available to only a subset of the followers and the followers have only local interaction. First of all, a continuous distributed finite‐time observer is proposed for each follower to estimate the leader's states in a finite time. Then, a continuous distributed cooperative finite‐time tracking control law is designed for each mobile robot. Rigorous proof shows that the group of mobile robots converge to the desired geometric formation pattern in finite time. At the same time, all the robots can track the desired formation trajectory in finite time. Simulation example illustrates the effectiveness of our method. Copyright © 2012 John Wiley & Sons, Ltd.     

非完整移动机器人道路跟踪控制器设计及应用

讨论一类非完整约束条件下的移动机器人道路跟踪控制问题，综合后推方法与模糊滑模控制方法设计非完整移动机器人的状态反馈控制系统，并根据Lyapunov稳定性定理后推设计时变光滑反馈控制律，当存在较大侧向误差时，模糊滑模控制器确保移动机器人沿稳定的工作区域减小误差；当误差比较小时，时变光滑状态反馈控制实现对移动机器人的平稳镇定，采用移动机器人Amigobot作为实验平台，验证了控制器设计的有效性。     

Event‐triggered adaptive backstepping control for parametric strict‐feedback nonlinear systems

This paper proposes a novel adaptive backstepping control method for parametric strict‐feedback nonlinear systems with event‐sampled state and input vectors via impulsive dynamical systems tools. In the design procedure, both the parameter estimator and the controller are aperiodically updated only at the event‐sampled instants. An adaptive event sampling condition is designed to determine the event sampling instants. A positive lower bound on the minimal intersample time is provided to avoid Zeno behavior. The closed‐loop stability of the adaptive event‐triggered control system is rigorously proved via Lyapunov analysis for both the continuous and jump dynamics. Compared with the periodic updates in the traditional adaptive backstepping design, the proposed method can reduce the computation and the transmission cost. The effectiveness of the proposed method is illustrated using 2 simulation examples.     

Adaptive motion control of wheeled mobile robot with unknown slippage

As a major representative nonholonomic system, wheeled mobile robot (WMR) is often used to travel across off-road environments that could be unstructured environments. Slippage often occurs when WMR moves in slopes or uneven terrain, and the slippage generates large accumulated position errors in the vehicle, compared with conventional wheeled mobile robots. An estimation of the wheel slip ratio is essential to improve the accuracy of locomotion control. In this paper, we propose an improved adaptive controller to allow WMR to track the desired trajectory under unknown longitudinal slip, where the stabilisation of the closed-loop tracking system is guaranteed by the Lyapunov theory. All system states use neural network online weight tuning algorithms, which ensure small tracking errors and no loss of stability in robot motion with bounded input signals. We demonstrate superior tracking results using the proposed control method in various Matlab simulations.     

Robust neural network–based tracking control and stabilization of a wheeled mobile robot with input saturation

This paper presents a robust neural network–based control scheme to deal with the problem of tracking and stabilization simultaneously for a wheeled mobile robot subject to parametric uncertainties, external disturbances, and input saturation. At first, a new error‐state transformation scheme is designed by introducing some auxiliary variables as an additional virtual control signals to reduce the adverse effect caused by the underactuation. These variables can change their structures for different desired trajectories to be tracked. Then, a robust control law is proposed combining with a kinematic controller and a dynamic controller, while a three‐layer neural network system is applied to approximate model uncertainties. Stability analysis via the Lyapunov theory shows that the proposed controller can make tracking errors converge to bounded neighborhoods of the origin. Finally, some simulation results are illustrated to verify the effectiveness of the proposed control strategy.     

Design of a PID optimized neural networks and PD fuzzy logic controllers for a two‐wheeled mobile robot

In this paper, two intelligent techniques for a two‐wheeled differential mobile robot are designed and presented: A smart PID optimized neural networks based controller (SNNPIDC) and a PD fuzzy logic controller (PDFLC). Basically, mobile robots are required to work and navigate under exigent circumstances where the environment is hostile, full of disturbances such as holes and stones. The robot navigation leads to an autonomous decision making to overcome an obstacle and/or to stop the engine to protect it. In fact, the actuators that drive the robot should in no way be damaged and should stop to change direction in case of insurmountable disturbances. In this context, two controllers are implemented and a comparative study is carried out to demonstrate the effectiveness of the proposed approaches. For the first one, neural networks are used to optimize the parameters of a PID controller and for the second a fuzzy inference system type Mamdani based controller is adopted. The goal is to implement control algorithms for safe robot navigation while avoiding damage to the motors. In these two control cases, the smart robot has to quickly perform tasks and adapt to changing environment conditions while ensuring stability and accuracy and must be autonomous with regards to decision making. Simulations results aren't done in real environments, but are obtained with the Matlab/Simulink environment in which holes and stones are modeled by different load torques and are applied as disturbances on the mobile robot environment. These simulation results and the robot performances are satisfactory and are compared to a PID controller in which parameters are tuned by the Ziegler–Nichols tuning method. The applied methods have proven to be highly robust.     

基于“非伪”理论的非完整移动机器人轨迹跟踪控制

"非伪"控制是一种基于数据驱动的无模型控制方法,它根据输入-输出数据进行在线学习,计算与当前系统状态相匹配的控制量并作用于系统,以获得系统所要求的动静态品质,并以此检验系统是否满足该性能指标.基于"非伪"控制理论,研究了移动机器人的轨迹跟踪控制问题.根据非完整移动机器人的动态方程,采用"非伪"控制,直接作用于移动机器人的控制输入,使移动机器人能快速、准确地跟踪期望轨迹.     

带有未知参数和有界干扰的移动机器人轨迹跟踪控

针对模型参数未知和存在有界干扰的非完整移动机器人的轨迹跟踪控制问题,本文提出了一种鲁棒自适应轨迹跟踪控制器方法.非完整移动机器人的控制难点在于它的运动学系统是欠驱动的.针对这一难点,本文利用横截函数的思想,引入新的辅助控制器,使得非完整移动机器人系统不再是一个欠驱动系统,缩减了控制器设计的难度,进而利用非线性自适应算法和参数映射方法构造李雅谱诺夫函数.通过李雅普诺夫方法设计控制器和参数自适应器,从而使得非完整移动机器人的跟随误差任意小,即可以任意小的误差来跟随任意给定的参考轨迹.仿真结果证明了方法的有效性.     

Robust tracking control of nonholonomic dynamic systems with application to the bi-steerable mobile robot

A tracking controller for nonholonomic dynamic systems is proposed which allows global tracking of arbitrary reference trajectories and renders the closed loop system robust with respect to bounded disturbances. The controller is based on [Chwa, D. (2004). Sliding-mode tracking control of nonholonomic wheeled mobile robots in polar coordinates. IEEE Transactions on Control Systems Technology, 12(4), 637-644] and shows several generalizations and improvements. The control law for tracking of general nonholonomic systems using inverse kinematic models (IKM) and sliding surfaces is stated. Conditions are proven under which robust tracking is achieved for a specific system. Tracking control is applied to the bi-steerable mobile robot, and simulation results are presented.     

Distributed finite-time trajectory tracking control for multiple nonholonomic mobile robots with uncertainties and external disturbances

This paper investigates the distributed finite-time trajectory tracking control for a group of nonholonomic mobile robots with time-varying unknown parameters and external disturbances. At first, the tracking error system is derived for each mobile robot with the aid of a global invertible transformation, which consists of two subsystems, one is a first-order subsystem and another is a second-order subsystem. Then, the two subsystems are studied respectively, and finite-time disturbance observers are proposed for each robot to estimate the external disturbances. Meanwhile, distributed finite-time tracking controllers are developed for each mobile robot such that all states of each robot can reach the desired value in finite time, where the desired reference value is assumed to be the trajectory of a virtual leader whose information is available to only a subset of the followers, and the followers are assumed to have only local interaction. The effectiveness of the theoretical results is finally illustrated by numerical simulations.