Robust finite-time tracking control of nonholonomic mobile robots without velocity measurements

The problem of robust finite-time trajectory tracking of nonholonomic mobile robots with unmeasurable velocities is studied. The contributions of the paper are that: first, in the case that the angular velocity of the mobile robot is unmeasurable, a composite controller including the observer-based partial state feedback control and the disturbance feed-forward compensation is designed, which guarantees that the tracking errors converge to zero in finite time. Second, if the linear velocity as well as the angular velocity of mobile robot is unmeasurable, with a stronger constraint, the finite-time trajectory tracking control of nonholonomic mobile robot is also addressed. Finally, the effectiveness of the proposed control laws is demonstrated by simulation.     

非完整移动机器人的轨迹跟踪控制

讨论基于运动学模型的非完整移动机器人的轨迹跟踪控制问题。在一定的假设条件下实现了全局指数跟踪，该假设允许参考模型角速度和平移速度均趋于零，并将该方法推广到 动力学模型。仿真例子证明了该方法的有效性。     

An adaptive technique for trajectory tracking control of a wheeled mobile robots without velocity measurements

This paper addresses an adaptive method for designing a sensorless trajectory tracking control scheme for a wheeled mobile robot. In order to reduce the cost of the robot, a new Nonlinear Observer (NOB) is used to leave out velocity sensors in the robot. Also, an adaptive model reference technique is used for designing the dynamic controller. In order to ensure the implementability of proposed controller, dynamic controller and nonlinear observer are designed in the presence of uncertainties. In addition, the Observer-based Kinematic Controller (OKC) is designed in the presence of sliding velocity. In order to improve the performance of the kinematic controller, sliding velocity is estimated and used for modification of kinematic controller. Finally, the effectiveness of the proposed method is demonstrated by simulations.     

Neural adaptive PID formation control of car-like mobile robots without velocity measurements

A virtual leader–follower formation control of a group of car-like mobile robots is addressed in this paper. First, the kinematic and dynamic models of car-like robots are transformed into a second-order leader–follower formation model which inherits all structural properties of the robot dynamic model. Then, a new observer-based proportional–integral-derivative formation controller is proposed to force that all robots construct a desired formation with respect to a predefined virtual leader. To improve the formation tracking and observation performance, the integral action is incorporated into the design of the observer–controller scheme. Adaptive robust and neural network techniques are also employed to compensate uncertain parameters, unmodeled dynamics, and external disturbances. Lyapunov’s direct method is utilized to show that the formation tracking and observation errors are semi-globally uniformly ultimately bounded. Then, the proposed controller is extended to the leader–follower formation of a team of tractor–trailer systems. Finally, simulation results illustrate the efficiency of the proposed controller.     

Robust tracking control for a class of electrically driven flexible-joint robots without velocity measurements

This article addresses the motion tracking control for a class of flexible-joint robotic manipulators actuated by brushed direct current motors. This class of electrically driven flexible-joint robots is perturbed by time-varying parametric uncertainties and external disturbances. A novel observer-based robust dynamic feedback tracking controller without velocity measurements will be developed such that the resulting closed-loop system is locally stable, all the states and signals are bounded and the trajectory tracking errors can be made as small as possible. Only the measurements of link position and armature current are required for feedback and so the number of sensors in the practical implementation of the developed control scheme can be greatly reduced. The observer structure is of reduced order in the sense that the observer is constructed only to estimate the velocity signals and whose dimension is half of the dimension of flexible-joint robots. Especially, for the set-point regulation problem, the developed controller is simplified to a linear time-invariant controller. Consequently, the robust tracking control scheme developed in this study can be extended to handle a broader class of uncertain electrically driven flexible-joint robots and the developed robust control schemes possess the properties of computational simplicity and easy implementation. Finally, simulation results are presented to demonstrate the effectiveness of the proposed control algorithms.     

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。     

A new adaptive tracking control scheme of wheeled mobile robot without longitudinal velocity measurement

This paper proposes a new adaptive trajectory tracking control scheme of the wheeled mobile robot without longitudinal velocity measurement. First, based on a kinematic controller, we obtain a new tracking error equation, which is suitable to develop an adaptive controller. Then, we develop a new adaptive trajectory tracking controller, which does not need any accurate values of the wheeled mobile robot parameters, including the driving motor parameters. Moreover, as the longitudinal velocity measurement is still difficult, this controller is developed without longitudinal velocity measurement. In addition, this new adaptive controller introduces a method to improve the control performance. The stability of the closed‐loop system is presented using the direct Lyapunov method. Finally, numerous simulations verify the effectiveness of the new controller.     

Trajectory tracking control of flexible-joint robots

Inverse dynamics control of flexible-joint robots is addressed. It is shown that, in a flexible-joint robot, the acceleration level inverse dynamic equations are singular because the control torques do not have an instantaneous effect on the end-effector accelerations due to the elastic media. Implicit numerical integration methods that account for the higher order derivative information are utilized for solving the singular set of differential equations. The trajectory tracking control law presented linearizes and decouples the system and yields an asymptotically stable fourth order error dynamics for each end-effector degree of freedom. A 3R spatial robot with all joints flexible is simulated to illustrate the performance of the proposed algorithm.     

An adaptive link position tracking controller for rigid-linkflexible-joint robots without velocity measurements

This paper presents an adaptive partial state feedback controller for rigid-link flexible-joint (RLFJ) robots. The controller compensates for parametric uncertainty throughout the entire mechanical system while only requiring measurement of link position and actuator position. To eliminate the need for measuring link velocity and actuator velocity a set of filters is utilized as a surrogate for the unmeasurable quantities. Based on this set of filters, an adaptive integrator backstepping procedure is used to develop a torque input controller which guarantees semiglobal asymptotic link position tracking while also ensuring that all signals remain bounded during closed-loop operation. Simulation results for a two-link RLFJ robot are utilized to validate the performance of the proposed controller.     

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.     

Distributed formation control of nonholonomic mobile robots without global position measurements

This paper proposes a new class of distributed nonlinear controllers for leader-following formation control of unicycle robots without global position measurements. Nonlinear small-gain design methods are used to deal with the problem caused by the nonholonomic constraint of the unicycle robot and yield simple conditions for practical implementation. With the proposed distributed controllers, the formation control objective can be achieved without assuming any tree sensing structures. More interestingly, the distributed controller is robust to position measurement errors and the linear velocities of the robots can be restricted to specific bounded ranges.     

轮式移动机器人的位置量测输出反馈轨迹跟踪控制

针对机器人的姿态角难以精确测量的困难,本文研究基于位置测量的轮式移动机器人的轨迹跟踪问题.首先提出一种利用机器人的位置信息估计其姿态角的降维状态观测器,当机器人的线速度严格大于零时,可保证姿态角观测误差的指数收敛.然后给出一种新的状态反馈轨迹跟踪控制律,当参考轨迹满足一定的激励条件时,可以保证机器人的线速度严格大于零且跟踪误差全局渐近收敛.进一步结合姿态角观测器和状态反馈控制律,得到一种输出反馈轨迹跟踪控制算法.理论分析表明,当参考轨迹满足一定的激励条件时,所提出的输出反馈控制算法可以保证跟踪误差的全局渐近收敛.最后对所提出的姿态角观测器、状态反馈和输出反馈轨迹跟踪控制算法进行了仿真验证,证实了算法的有效性,并且当存在位置测量误差时,所提出的输出反馈轨迹跟踪控制算法仍可以保证机器人对参考轨迹的实际跟踪.     

基于行为动力学方法的移动机器人轨迹追踪

研究了基于行为动力学方法的移动机器人轨迹追踪。在总结行为动力学理论的基础上,根据轨迹追踪任务要求,确定航向角和速度作为行为变量,同时构建了接近吸引子动力学方程,并在考虑机器人与路径期望点之间距离这一间接耦合参数基础上,建立了速度动力学方程,并分析了该动力系统的收敛性。最后的仿真结果表明该方法正确、可行,且机器人能有效地完成追踪任务。     

Global trajectory tracking control of VTOL-UAVs without linear velocity measurements

This paper deals with the position control of Vertical Take-Off and Landing (VTOL) Unmanned Aerial Vehicles (UAVs) without linear velocity measurements. We propose a multistage constructive procedure, exploiting the cascade property of the translational and rotational dynamics. More precisely, we consider the force as a virtual control input for the translational dynamics, from which we extract the required (desired) system attitude and thrust achieving the tracking objective. Thereafter, the control torque is designed to drive the actual attitude to the desired one. A nonlinear observer, as well as some instrumental auxiliary variables are used to obviate the need for the linear velocity. Global asymptotic stability of the overall closed loop system is achieved. Simulation results are provided to show the effectiveness of the proposed control scheme.     

轮子纵向打滑条件下的移动机器人自适应跟踪控制

针对纵向滑动参数未知的轮式移动机器人的轨迹跟踪问题,提出一种自适应跟踪控制策略.利用两个未知参数来描述移动机器人左右轮的纵向打滑程度,建立了产生纵向滑动的差分驱动轮式移动机器人的运动学模型;设计了补偿纵向滑动的自适应非线性反馈控制律;应用 Lyapunov 稳定性理论与 Barbalat 定理证明了闭环系统的稳定性;同时,提出了一种由极点配置方法在线调整控制器增益的方法.仿真结果验证了所提出控制方法的有效性.     

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。     

On global tracking control of a VTOL aircraft without velocity measurements

This note develops a nonlinear output-feedback controller to force a nonminimum phase, underactuated vertical take-off and landing aircraft to globally asymptotically track a reference trajectory generated by a reference model. The control development is based on a global exponential observer, some global coordinate transformations, Lyapunov's direct method and an extension of the backstepping technique. Interestingly, the proposed methodology also yields new results for the previously studied problems of stabilization and output tracking or regulation. Numerical simulations illustrate the effectiveness of the proposed controller.     

Trajectory tracking control for robot manipulators using only position measurements

In the paper, the trajectory tracking control problem is investigated for robotic manipulators which are not equipped with the tachometers. Our contribution consists in establishing uniform asymptotic stability in closed-loop system by using the dynamic position-feedback controller with feedforward. Using Lyapunov vector function and comparison principle, we construct the non-linear controller with variable gain matrices and first-order linear dynamic compensator such that the origin of the closed-loop system is uniformly asymptotically stable. The controller is shown to be robust with respect to parameters incertainties. We illustrate the utility of our result by simulation tests with reference to a two-link planar elbow robot manipulator.     

Fuzzy target tracking control of autonomous mobile robots by using infrared sensors

The theme of this paper is to design a real-time fuzzy target tracking control scheme for autonomous mobile robots by using infrared sensors. At first two mobile robots are setup in the target tracking problem, where one is the target mobile robot with infrared transmitters and the other one is the tracker mobile robot with infrared receivers and reflective sensors. The former is designed to drive in a specific trajectory. The latter is designed to track the target mobile robot. Then we address the design of the fuzzy target tracking control unit, which consists of a behavior network and a gate network. The behavior network possesses the fuzzy wall following control (FWFC) mode, fuzzy target tracking control (FTTC) mode, and two fixed control modes to deal with different situations in real applications. Both the FWFC and FTTC are realized by the fuzzy sliding-mode control scheme. A gate network is used to address the fusion of measurements of two infrared sensors and is developed to recognize which situation is belonged to and which action should be executed. Moreover, the target tracking control with obstacle avoidance is also investigated in this paper. Both computer simulations and real-time implementation experiments of autonomous target tracking control demonstrate the effectiveness and feasibility of the proposed control schemes.     

Modeling and hierarchical tracking control of tri-wheeled mobile robots

After exploring the structure of the dynamics derived by using the Appell equation, we propose a hierarchical tracking controller for a tri-wheeled mobile robot in this paper. With appropriately chosen privileged variables, the reduced equations are decoupled from the kinematic equations associated with the underlying nonholonomic constraints. This special character of the system makes it possible to separate the design into three levels: motion planning, kinematic, and dynamic. In the proposed scheme, a fuzzy inference engine in the kinematic level is used to update the desired trajectory computed in the motion-planning level. An adaptive sliding-mode controller is then adopted to track the new reference values of privileged variables in the dynamic level, which subsequently drives the nonprivileged variables. Simulation results show the effectiveness of such a tracking-control scheme, which concurrently takes kinematics and dynamics into consideration. All system variables can be tracked asymptotically to their desired values, which are assured by the skew-symmetric property of the Appell equation.