Adaptive tracking control for uncertain dynamic nonholonomic mobile robots based on visual servoing

The trajectory tracking control problem of dynamic nonholonomic wheeled mobile robots is considered via visual servoing feedback. A kinematic controller is firstly presented for the kinematic model, and then, an adaptive sliding mode controller is designed for the uncertain dynamic model in the presence of parametric uncertainties associated with the camera system. The proposed controller is robust not only to structured uncertainties such as mass variation but also to unstructured one such as disturbances. The asymptotic convergence of tracking errors to equilibrium point is rigorously proved by the Lyapunov method. Simulation results are provided to illustrate the performance of the control law.     

Adaptive sliding mode control for trajectory tracking of nonholonomic mobile robot with uncertain kinematics and dynamics

ABSTRACT

This article designs a novel adaptive trajectory tracking controller for nonholonomic wheeled mobile robot under kinematic and dynamic uncertainties. A new velocity controller, in which kinematic parameter is estimated, produces velocity command of the robot. The designed adaptive sliding mode dynamic controller incorporates an estimator term to compensate for the external disturbances and dynamic uncertainties and a feedback term to improve the closed-loop stability and account for the estimation error of external disturbances. The system stability is analyzed using Lyapunov theory. Computer simulations affirm the robustness of the designed control scheme.     

Robust adaptive control for a nonholonomic mobile robot with unknown parameters

A robust adaptive controller for a nonholonomic mobile robot with unknown kinematic and dynamic parameters is proposed. A kinematic controller whose output is the input of the relevant dynamic controller is provided by using the concept of backstepping. An adaptive algorithm is developed in the kinematic controller to approximate the unknown kinematic parameters, and a simple single-layer neural network is used to express the highly nonlinear robot dynamics in terms of the known and unknown parameters. In order to attenuate the effects of the uncertainties and disturbances on tracking performance, a sliding mode control term is added to the dynamic controller. In the deterministic design of feedback controllers for the uncertain dynamic systems, upper bounds on the norm of the uncertainties are an important clue to guarantee the stability of the closed-loop system. However, sometimes these upper bounds may not be easily obtained because of the complexity of the structure of the uncertainties. Thereby, simple adaptation laws are proposed to approximate upper bounds on the norm of the uncertainties to address this problem. The stability of the proposed control system is shown through the Lyapunov method. Lastly, a design example for a mobile robot with two actuated wheels is provided and the feasibility of the controller is demonstrated by numerical simulations.     

基于视觉伺服反馈的不确定非完整动态移动机器人的自适应镇定

研究了带有固定在天花板上的摄像机系统的非完整动态移动机器人的镇定问题. 首先, 利用针孔摄像机模型引入了基于摄像机目标的视觉伺服运动学模型,并针对该运动学模型给出了一个运动学镇定控制器. 然后,在摄像机参数不确定的情形下设计了一个自适应滑模控制器实现了不确定动态移动机器人的镇定. 提出的控制器不仅对结构不确定性如质量变化, 而且对无结构不确定性如外部扰动都具有鲁棒性. 通过Lyapunov方法严格证明了提出的控制系统的稳定性和估计参数的有界性. 仿真结果证实了控制律的有效性.     

Intelligent tracking control of a dual‐arm wheeled mobile manipulator with dynamic uncertainties

This paper presents an intelligent control approach that incorporates sliding mode control (SMC) and fuzzy neural network (FNN) into the implementation of back‐stepping control for a path tracking problem of a dual‐arm wheeled mobile manipulator subject to dynamic uncertainties and nonholonomic constraints. By using the back‐stepping technique, the system equations are reformulated into two levels: the kinematic level and the dynamic level. A sliding manifold is constructed by considering the disturbance free kinematic level equations only. With all the system uncertainties concentrated in the dynamic level, an FNN controller associated with a switching type of control law is employed to enforce sliding mode on the prescribed manifold. All parameter adjustment rules for the proposed controller are derived from the Lyapunov theory such that uniform ultimate boundedness for both the tracking error and the FNN weighting updates is ensured. A simulation study, which compares different control design approaches, is included to illustrate the promise of the proposed SMC–FNN method. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

非完整移动机器人的神经网络鲁棒自适应控制

在非完整移动机器人轨迹跟踪问题中,针对机器人运动学与动力学模型的参数和非参数不确定性,提出了一种混合神经网络鲁棒自适应轨迹跟踪控制器,该控制器由运动学控制器和动力学控制器两部分组成;其中,采用了参数自适应的径向基神经网络对运动学模型的未知部分进行了建模,并采用权值在线调整的单层神经网络和自适应鲁棒控制项构成了动力学控制器;基于Lyapunov方法的设计过程保证了系统的稳定性和收敛性,仿真结果证明了算法的有效性。     

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.     

Adaptive feedback linearizing control of nonholonomic wheeled mobile robots in presence of parametric and nonparametric uncertainties

In this paper, the integrated kinematic and dynamic trajectory tracking control problem of wheeled mobile robots (WMRs) is addressed. An adaptive robust tracking controller for WMRs is proposed to cope with both parametric and nonparametric uncertainties in the robot model. At first, an adaptive nonlinear control law is designed based on input–output feedback linearization technique to get asymptotically exact cancellation of the parametric uncertainty in the WMR parameters. The designed adaptive feedback linearizing controller is modified by two methods to increase the robustness of the controller: (1) a leakage modification is applied to modify the integral action of the adaptation law and (2) the second modification is an adaptive robust controller, which is included to the linear control law in the outer loop of the adaptive feedback linearizing controller. The adaptive robust controller is designed such that it estimates the unknown constants of an upper bounding function of the uncertainty due to friction, disturbances and unmodeled dynamics. Finally, the proposed controller is developed for a type (2, 0) WMR and simulations are carried out to illustrate the robustness and tracking performance of the controller.     

Robust adaptive multi-task tracking control of redundant manipulators with dynamic and kinematic uncertainties and unknown disturbances

In this paper, a novel adaptive multi-priority controller for redundant manipulators is proposed to accomplish the multi-task tracking when kinematic/dynamic uncertainties and unknown disturbances exist. Prioritized redundancy resolution in kinematic level is incorporated into this passivity-based control framework. The kinematic and dynamic parameter adaptations are driven by both tracking error and prediction error. Moreover, the tracking information from both primary and subtasks are all utilized to accelerate the parameter estimation when the tasks are independent, whereas the inevitable tracking error of the subtasks due to algorithmic singularities is properly eliminated in the adaptation laws when the tasks are dependent. Potential ill-conditioned solution of the pseudoinverse is avoided using an improved singularity-robust inverse of the projected Jacobian. Along with the improvement of the multi-task tracking performance, smoothness of the commanded torques is still guaranteed for easy application. Measurements of the noisy joint acceleration and task velocity are avoided. The controller is mathematically derived based on Lyapunov stability analysis. Simulation results of the two cases are presented to verify the effectiveness and superiority of the proposed controller.     

Modeling and Control of Head Raising Snake Robots by Using Kinematic Redundancy

In this paper, we consider trajectory tracking control of a head raising snake robot on a flat plane by using kinematic redundancy. We discuss the motion control requirements to accomplish trajectory tracking and other tasks, such as singular configuration avoidance and obstacle avoidance, for the snake robot. The features of the internal motion caused by kinematic redundancy are considered, and a kinematic model and a dynamic model of the snake robot are derived by introducing two types of shape controllable point. The first is the head shape controllable point, and the other is the base shape controllable point. We analyzed the features of the two kinds of shape controllable point and proposed a controller to accomplish the trajectory tracking of the robot’s head as its main task along with several sub-tasks by using redundancy. The proposed method to accomplish several sub-tasks is useful for both the kinematic model and the dynamic model. Experimental results using a head raising snake robot which can control the angular velocity of its joints show the effectiveness of the proposed controller.     

Balancing and Trajectory Tracking of Two-Wheeled Mobile Robot Using Backstepping Sliding Mode Control: Design and Experiments

The key attributes of Two Wheeled Balancing Mobile Robots (TWBMRs) are nonholonomic constraints and inherent instability. This paper deals with the problem of balancing and trajectory tracking of TWBMR using backstepping Sliding Mode Controller (SMC). First, the mathematical representation of TWBMR is derived using Lagrangian method by incorporating the dynamics of DC motors. Then, a decoupling approach is applied for simplifying the dynamic equations. The backstepping SMC technique is finally adopted to achieve the balancing and trajectory tracking of the TWBMR, whereas both model uncertainties and exogenous disturbance are taken into account in the controller design methodology. In order to determine the velocity, the trajectory tracking is achieved by the kinematic control, which is a common backstepping controller. For the velocity convergence of TWBMR to the generated desired value, two SMCs are designed, in which the motors voltage are directly controlled as the control laws. Simplicity in practical implementation and control law, ability to overcome uncertainties and appropriate performance are the main advantages of the proposed controller. The effectiveness of the proposed controller is verified through simulation and experimental results.     

Adaptive Robust Control of an Omnidirectional Mobile Platform for Autonomous Service Robots in Polar Coordinates

This paper presents an adaptive robust control method for trajectory tracking and path following of an omni-directional wheeled mobile platform with actuators’ uncertainties. The polar-space kinematic model of the platform with three independent driving omnidirectional wheels equally spaced at 120 from one another is briefly introduced, and the dynamic models of the three uncertain servomotors mounted on the driving wheels are also described. With the platform’s kinematic model and the motors’ dynamic model associated two unknown parameters, the adaptive robust controller is synthesized via the integral backstepping approach. Computer simulations and experimental results are conducted to show the effectiveness and merits of the proposed control method in comparison with a conventional PI feedback control method.     

Robust Tracking Control For A Wheeled Mobile Manipulator With Dual Arms Using Hybrid Sliding‐Mode Neural Network

In this paper, a robust tracking controller is proposed for the trajectory tracking problem of a dual‐arm wheeled mobile manipulator subject to some modeling uncertainties and external disturbances. Based on backstepping techniques, the design procedure is divided into two levels. In the kinematic level, the auxiliary velocity commands for each subsystem are first presented. A sliding‐mode equivalent controller, composed of neural network control, robust scheme and proportional control, is constructed in the dynamic level to deal with the dynamic effect. To deal with inadequate modeling and parameter uncertainties, the neural network controller is used to mimic the sliding‐mode equivalent control law; the robust controller is designed to compensate for the approximation error and to incorporate the system dynamics into the sliding manifold. The proportional controller is added to improve the system's transient performance, which may be degraded by the neural network's random initialization. All the parameter adjustment rules for the proposed controller are derived from the Lyapunov stability theory and e‐modification such that uniform ultimate boundedness (UUB) can be assured. A comparative simulation study with different controllers is included to illustrate the effectiveness of the proposed method.     

Task-space fully distributed tracking control of networked uncertain robotic manipulators without velocity measurements

This paper investigates the task-space synchronised tracking problem of uncertain networked manipulators interconnected on directed graphs, where the dynamic leader is available to only a subset of followers and followers have only local interaction. A fully distributed tracking controller is proposed, which is composed of a distributed desired trajectory estimator, a joint-space velocity observer and an adaptive cooperative control algorithm. Specifically, the proposed controller allows each manipulator to track the dynamic leader solely using local task-space position measurements. Besides, in the presence of both dynamic and kinematic uncertainties, the adaptive cooperative control algorithm indeed improves the system's robustness. Furthermore, it is strictly proved that the proposed control scheme ensures that both task-space position and velocity tracking errors converge to zero as time tends to infinity. In the end, simulation results are provided to demonstrate the effectiveness of the proposed controller.     

Kinematic path‐tracking of mobile robot using iterative learning control

This paper develops a kinematic path‐tracking algorithm for a nonholonomic mobile robot using an iterative learning control (ILC) technique. The proposed algorithm produces a robot velocity command, which is to be executed by the proper dynamic controller of the robot. The difference between the velocity command and the actual velocity acts as state disturbances in the kinematic model of the mobile robot. Given the kinematic model with state disturbances, we present an ILC‐based path‐tracking algorithm. An iterative learning rule with both predictive and current learning terms is used to overcome uncertainties and the disturbances in the system. It shows that the system states, outputs, and control inputs are guaranteed to converge to the desired trajectories with or without state disturbances, output disturbances, or initial state errors. Simulations and experiments using an actual mobile robot verify the feasibility and validity of the proposed learning algorithm. © 2005 Wiley Periodicals, Inc.     

具有未知参数的机器人-摄像机系统的自适应动态反馈跟踪控制

研究了不确定非完整移动机器人系统的跟踪问题.首先,基于视觉反馈和状态输入变换,展示了一种非完整移动机器人运动学系统的不确定链式模型.基于反步法思想和跟踪误差系统结构,给出了两个重要的新变换.然后运用李雅普诺夫直接方法和扩展巴巴拉引理设计了自适应控制律和动态反馈鲁棒控制器,以实现理想轨迹的跟踪控制.严格证明了闭环误差系统的渐近收敛性.最后,仿真结果证实了提出的控制策略有效.     

Adaptive inverse dynamics control of robots with uncertain kinematics and dynamics

It has been about two decades since the first globally convergent adaptive tracking controller was derived for robots with dynamic uncertainties. However, not until recently has the problem of concurrent adaptation to both the kinematic and dynamic uncertainties found its solution. This adaptive controller belongs to passivity-based control. Though passivity-based controllers have many attractive properties, in general, they are not able to guarantee the uniform performance of the robot over the entire workspace. Even in the ideal case of perfect knowledge of the manipulator parameters, the closed-loop system remains nonlinear and coupled. Thus the closed-loop tracking performance is difficult to quantify, while the inverse dynamics controllers can overcome these deficiencies. Therefore, in this work, we will develop a new adaptive Jacobian tracking controller based on the inverse manipulator dynamics. Using the Lyapunov approach, we have proved that the end-effector motion tracking errors converge asymptotically to zero. Simulation results are presented to show the performance of the proposed controller.     

非完整移动机器人的反步跟踪控制方法

移动机器人是典型的非完整系统,对其进行运动控制是一个热点且是一项具有挑战性的工作.目前的大部分研究都是基于运动学模型的,而在实际应用中,动力学特性不可忽视.针对轨迹跟踪这一典型控制任务,文中对一种轮式移动机器人进行了动力学建模.利用反步技术,提出了一种控制结构,综合了速度控制器和力矩控制器.该控制律不但能够得到稳定跟踪所需要的速度,而且同时能够计算出驱动移动机器人行进的电机力矩.仿真结果表明,该控制律可以良好地工作.控制结构的通用性保证了其他控制方法拓展的可能性.     

Global exponential tracking control of a mobile robot system via aPE condition

This paper presents the design of a differentiable, kinematic control law that achieves global asymptotic tracking. In addition, we also illustrate how the proposed kinematic controller provides global exponential tracking provided the reference trajectory satisfies a mild persistency of excitation (PE) condition. We also illustrate how the proposed kinematic controller can be slightly modified to provide for global asymptotic regulation of both the position and orientation of the mobile robot. Finally, we embed the differentiable kinematic controller inside of an adaptive controller that fosters global asymptotic tracking despite parametric uncertainty associated with the dynamic model. Experimental results are also provided to illustrate the performance of the proposed adaptive tracking controller.