Nonsingular Terminal Sliding Mode Control of Robot Manipulators Using Fuzzy Wavelet Networks

This paper presents an adaptive nonsingular terminal sliding mode (NTSM) tracking control design for robotic systems using fuzzy wavelet networks. Compared with linear hyperplane-based sliding control, terminal sliding mode controller can provide faster convergence and higher precision control. Therefore, a terminal sliding controller combined with the fuzzy wavelet network, which can accurately approximate unknown dynamics of robotic systems by using an adaptive learning algorithm, is an attractive control approach for robots. In addition, the proposed learning algorithm can on-line tune parameters of dilation and translation of fuzzy wavelet basis functions and hidden-to-output weights. Therefore, a robust control law is used to eliminate uncertainties including the inevitable approximation errors resulted from the finite number of fuzzy wavelet basis functions. The proposed controller requires no prior knowledge about the dynamics of the robot and no off-line learning phase. Moreover, both tracking performance and stability of the closed-loop robotic system can be guaranteed by Lyapunov theory. Finally, the effectiveness of the fuzzy wavelet network-based control approach is illustrated through comparative simulations on a six-link robot manipulator     

Robust fuzzy tracking control for robotic manipulators

In this paper, a stable adaptive fuzzy-based tracking control is developed for robot systems with parameter uncertainties and external disturbance. First, a fuzzy logic system is introduced to approximate the unknown robotic dynamics by using adaptive algorithm. Next, the effect of system uncertainties and external disturbance is removed by employing an integral sliding mode control algorithm. Consequently, a hybrid fuzzy adaptive robust controller is developed such that the resulting closed-loop robot system is stable and the trajectory tracking performance is guaranteed. The proposed controller is appropriate for the robust tracking of robotic systems with system uncertainties. The validity of the control scheme is shown by computer simulation of a two-link robotic manipulator.     

An optimal adaptive robust PID controller subject to fuzzy rules and sliding modes for MIMO uncertain chaotic systems

In this paper, an optimal adaptive robust PID controller based on fuzzy rules and sliding modes is introduced to present a general scheme to control MIMO uncertain chaotic nonlinear systems. In this control scheme, the gains of the PID controller are updated by using an adaptive mechanism, fuzzy rules, the gradient search method, and the chain rule of differentiation in order to minimize the sliding surfaces of sliding mode control. More precisely, sliding mode control is used as a supervisory controller to provide sufficient control inputs and guarantee the stability of the control approach. To ascertain the parameters of the proposed controller and avoid trial and error, the multi-objective genetic algorithm is employed to augment the performance of proposed controller. The chaotic system of a Duffing-Holmes oscillator and an industrial robotic manipulator are the case studies to evaluate the performance of the proposed control approach. The obtained results of this study regarding both systems are compared with the outcomes of two notable studies in the literature. The results and analysis prove the efficiency of the proposed controller with regard to MIMO uncertain systems having challenging external disturbances in terms of stability, minimum tracking error and optimal control inputs.     

An online GA-based output-feedback direct adaptive fuzzy-neural controller for uncertain nonlinear systems.

In this paper, we propose a novel design of a GA-based output-feedback direct adaptive fuzzy-neural controller (GODAF controller) for uncertain nonlinear dynamical systems. The weighting factors of the direct adaptive fuzzy-neural controller can successfully be tuned online via a GA approach. Because of the capability of genetic algorithms (GAs) in directed random search for global optimization, one is used to evolutionarily obtain the optimal weighting factors for the fuzzy-neural network. Specifically, we use a reduced-form genetic algorithm (RGA) to adjust the weightings of the fuzzy-neural network. In RGA, a sequential-search -based crossover point (SSCP) method determines a suitable crossover point before a single gene crossover actually takes place so that the speed of searching for an optimal weighting vector of the fuzzy-neural network can be improved. A new fitness function for online tuning the weighting vector of the fuzzy-neural controller is established by the Lyapunov design approach. A supervisory controller is incorporated into the GODAF controller to guarantee the stability of the closed-loop nonlinear system. Examples of nonlinear systems controlled by the GODAF controller are demonstrated to illustrate the effectiveness of the proposed method.     

基于RBF神经网络的多关节机器人固定时间滑模控制

针对具有典型非线性特性的多关节机器人轨迹跟踪控制问题,提出一种基于径向基函数(RBF)神经网络的固定时间滑模控制方法.首先,基于凯恩方法建立包括系统模型不确定性以及外部干扰在内的多关节机器人动力学模型;然后,根据机器人动力学模型设计一种固定时间收敛的滑模控制器,RBF神经网络用来逼近系统模型中的不确定性项,并利用Lyapunov理论证明该系统跟踪误差能在固定时间内收敛;最后,对特定型号的多关节机器人虚拟样机进行仿真分析,结果表明:与基于RBF神经网络的有限时间滑模控制器相比,所提出控制器具有良好的跟踪性能且能保证系统状态在固定时间内收敛.     

机械手的模糊逆模型鲁棒控制

提出一种基于模糊聚类和滑动模控制的模糊逆模型控制方法,并将其应用于动力学 方程未知的机械手轨迹控制.首先,采用C均值聚类算法构造两关节机械手的高木-关野 (T-S)模糊模型,并由此构造模糊系统的逆模型.然后,在提出的模糊逆模型控制结构中, 离散时间滑动模控制和时延控制(TDC)用于补偿模糊建模误差和外扰动,保证系统的全局 稳定性并改进其动态和稳态性能.系统的稳定性和轨迹误差的收敛性可以通过稳定性定理来 证明.最后,以两关节机械手的轨迹跟随控制为例,揭示了该设计方法的控制性能.     

基于神经网络的机器人轨迹跟踪控制

针对机器人模型未知情况，讨论了用神经网络和反馈控制实现机械手的跟踪控制。提出一种基于参考误差的投影算法来训练网络权值，训练后网络输出能逼近期望的前馈力矩，并从理论上证明跟踪误差的收敛性。仿真结果表明方案具有较好的跟踪性能和较强的抗干扰能力。     

考虑关节柔性的绳驱动空中机械臂关节空间鲁棒控制

空中机械臂在外部环境交互作业方面表现出很强的研究和应用价值,但当前系统位姿控制性能较弱、负载能力不足以及续航时间短的问题严重制约其作业能力的提升.鉴于此,设计一种带有绳驱动机械臂的新型空中机械臂系统,并将引入绳驱动机制带来的柔性效应等价到关节处,建立考虑关节柔性的刚柔耦合动力学模型.首先,针对系统在集总干扰下的关节空间轨迹跟踪控制,采用线性扩张状态观测器对集总干扰进行估计和补偿,并采用超螺旋算子和分数阶非奇异终端滑模以保证系统在到达阶段和滑模阶段均有较好的控制性能;然后,在Lyapunov稳定性框架下验证所设计控制器的稳定性;最后,通过可视化仿真和地面实验对所设计控制器的有效性进行验证.实验结果表明,所设计的鲁棒控制器比其他两种现有的控制器具有更快的响应速度、更强的抗干扰能力以及更高的跟踪精度,能够满足绳驱动空中机械臂的控制需求.     

Design of an adaptive tracker for n-link rigid robotic manipulators based on super-twisting global nonlinear sliding mode control

This paper develops an adaptive super-twisting global nonlinear sliding mode control technique for n-link rigid robotic manipulators. A novel control law is designed to guarantee elimination of the reaching phase and existence of the sliding mode around the surface right from the initial time. Furthermore, the adaptive tuning law eliminates requirement of the knowledge about the upper bounds of external disturbances. By using the proposed method, a robust controller is designed so that the tracking error of rigid manipulator is convergent to the global nonlinear sliding surface in a finite time, and strong robustness with respect to large uncertainties and disturbances is guaranteed. Illustrative simulations on a two-link elbow robot manipulator and a three degree of freedom rigid manipulator are presented to show the robustness and effectiveness of the suggested design compared to other method. Moreover, a simulation as well as experimental study of a rotary inverted pendulum system demonstrates the applicability of the proposed method.     

Neural network-based sliding mode adaptive control for robot manipulators

This paper addresses the robust trajectory tracking problem for a robot manipulator in the presence of uncertainties and disturbances. First, a neural network-based sliding mode adaptive control (NNSMAC), which is a combination of sliding mode technique, neural network (NN) approximation and adaptive technique, is designed to ensure trajectory tracking by the robot manipulator. It is shown using the Lyapunov theory that the tracking error asymptotically converge to zero. However, the assumption on the availability of the robot manipulator dynamics is not always practical. So, an NN-based adaptive observer is designed to estimate the velocities of the links. Next, based on the observer, a neural network-based sliding mode adaptive output feedback control (NNSMAOFC) is designed. Then it is shown by the Lyapunov theory that the trajectory tracking errors, the observer estimation errors asymptotically converge to zero. The effectiveness of the designed NNSMAC, the NN-based adaptive observer and the NNSMAOFC is illustrated by simulations.     

An exponentially convergent adaptive sliding mode control of robot manipulators

A new robust adaptive algorithm for control of robot manipulators is proposed to account for a desired transient response with global exponential convergence of tracking errors without any persistent excitating assumption on the regressor. Its novelty lies in a new dynamic sliding surface that allows a systematic combination of adaptive control and variable structure control to yield a sliding mode inside an adaptive control loop. During sliding mode, parameter uncertainty appears in terms of known variables in such a manner that a new robust parameter estimator with enhanced stability properties is established. On the other hand, if the regressor meets the persistent exciting condition, the global uniform exponential stability of the equilibrium concerning the adaptive closed-loop error equation is easily established. The proposed controller from the VSS viewpoint relaxes the longstanding condition on a priori knowledge of the size of the parametric uncertainty to induce a sliding mode. On the other hand, from the adaptive control viewpoint it relaxes the standard assumption of the persistent excitation on the regressor to obtain the exponential convergence of tracking errors. Also, the stability against time-varying parameters is briefly discussed. Concluding remarks concerning its structural behaviour are given, and computer simulation data show a robust performance.     

基于自适应动态规划的移动装弹机械臂轨迹控制

针对移动装弹机械臂系统非线性、强耦合、受多种不确定因素影响的问题,本文基于自适应动态规划方法,提出了仅包含评价网络结构的轨迹跟踪控制方法,有效减小了系统跟踪误差.首先,考虑到系统非线性特性、变量间强耦合作用及重力因素的影响,通过拉格朗日方程建立了移动装弹机械臂的动力学模型.其次,针对系统存在不确定性上界未知的问题,建立单网络评价结构,通过策略迭代算法,求解哈密顿–雅可比–贝尔曼方程,基于李雅普诺夫稳定性理论,设计了自适应动态规划轨迹跟踪控制方法.最后,通过仿真实验将该控制方法与自适应滑模控制方法进行了对比,进一步检验了所设计控制方法的有效性.     

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.     

Evolutionary learning of BMF fuzzy-neural networks using a reduced-form genetic algorithm

In this paper, a novel approach to adjust both the control points of B-spline membership functions (BMFs) and the weightings of fuzzy-neural networks using a reduced-form genetic algorithm (RGA) is proposed. Fuzzy-neural networks are traditionally trained by using gradient-based methods, which may fall into local minimum during the learning process. To overcome the problems encountered by the conventional learning methods, genetic algorithms are adopted because of their capabilities of directed random search for global optimization. It is well known, however, that the searching speed of the conventional genetic algorithms is not desirable. Such conventional genetic algorithms are inherently incapable of dealing with a vast number (over 100) of adjustable parameters in the fuzzy-neural networks. In this paper, the RGA is proposed by using a sequential-search-based crossover point (SSCP) method in which a better crossover point is determined and only the gene at the specified crossover point is crossed, serving as a single gene crossover operation. Chromosomes consisting of both, the control points of BMFs and the weightings of the fuzzy-neural network are coded as an adjustable vector with real number components that are searched by the RGA. Simulation results have shown that faster convergence of the evolution process searching for an optimal fuzzy-neural network can be achieved. Examples of nonlinear functions approximated by using the fuzzy-neural network via the RGA are demonstrated to illustrate the effectiveness of the proposed method.     

Sliding mode force,motion control,and stabilization of elastic manipulator in the presence of uncertainties

This article considers the question of position and force control of three-link elastic robotic systems on a constraint surface in the presence of robot parameter and environmental constraint geometry uncertainties. The approach of this article is applicable to any multi-link elastic robot. A sliding mode control law is derived for the position and force trajectory control of manipulator. Unlike the rigid robots, sliding mode control of an end point gives rise to unstable zero dynamics. Instability of the zero dynamics is avoided by Controlling a point that lies in the neighborhood of the actual end point position. The sliding mode controller accomplishes tracking of the end-effector and force trajectories on the constrained surface; however, the maneuver of the arm causes elastic mode excitation. For point-to-point control on the constraint surface, a stabilizer is designed for the final capture of the terminal state and vibration suppression. Numerical results are presented to show that in the closed-loop system position and force control is accomplished in spite of payload and constraint surface geometry uncertainty. © 1995 John Wiley & Sons, Inc.     

作业型飞行机器人抓取后重心偏移的轨迹跟踪控制

作业型飞行机器人是指能够对环境施加主动影响的飞行机器人, 它通常由旋翼飞行器与机械臂组合而成. 本文针对作业型飞行机器人在动态飞行抓取后, 重心位置变化产生的系统控制难题, 设计了有效的跟踪控制策略. 首先, 在系统建模时引入重心偏移系统参数和重心偏移控制参数, 并考虑惯性张量不为常数, 提高了系统建模的精度. 然后, 在姿态解算时, 考虑重心偏移对系统性能的影响, 构建包含重心偏移系统参数的解算方法, 得到更高精度的期望翻滚角和期望俯仰角. 接着, 设计了基于滑模控制的重心偏移补偿位置控制器, 实现了有效的位置跟踪控制. 同时, 在姿态反演控制器的基础上, 加入自适应律估计重心偏移控制参数和变化的惯性张量, 再通过小脑神经网络逼近惯性张量的真实值, 提高姿态控制器的精度. 最后, 给出了所设计控制器的稳定性证明, 并在仿真环境下验证了所提出的方法的有效性和优越性.     

基于量子遗传算法的模糊滑模控制

针对一类具有不确定性的非线性系统,提出了一种新的基于量子遗传算法的模糊滑模控制器的设计方法.将模糊控制与滑模控制相结合,利用滑模控制使系统跟踪误差进入边界层内;启用模糊控制替代切换控制,并在边界层上通过监督函数平滑控制作用.在滑动模态产生条件下,通过量子遗传算法优化模糊控制器的控制规则,有效地解决了模糊滑模控制中模糊控制规则的确定问题,从而削弱了系统的抖振,改善了控制器的控制性能.仿真结果表明了该方法的有效性.     

基于RBF神经网络的作业型AUV自适应终端滑模控制方法及实验研究

研究了作业型AUV （自主水下机器人）的轨迹跟踪控制问题.实际作业中,水下机械手展开作业过程将引起AUV动力学性能变化,进而影响AUV轨迹跟踪控制;并且水流环境干扰亦将影响AUV轨迹跟踪控制.针对上述AUV轨迹跟踪控制问题,提出一种基于RBF （径向基函数）神经网络的AUV自适应终端滑模运动控制方法.该方法在李亚普诺夫稳定性理论框架下,采用RBF网络对机械手展开引起的AUV动力学性能变化和水流环境干扰进行在线逼近,并结合自适应终端滑模控制器对神经网络权值和AUV控制参数进行自适应在线调节.通过李亚普诺夫稳定性理论,证明AUV系统轨迹跟踪误差一致稳定有界.针对滑模控制项引起的控制量抖振问题,提出一种变滑模增益的饱和连续函数滑模抖振降低方法,以降低滑模控制量抖振.通过AUV实验样机的艏向和垂向的轨迹跟踪实验,验证了本文AUV系统控制方法和滑模降抖振方法的有效性.     

具有H_∞跟踪性能的机器人自适应PID控制

针对非线性不确定机器人系统的轨迹跟踪控制问题,提出一种鲁棒自适应PID控制算法.该控制器由主控制器和监督控制器组成.主控制器以常规PID控制为基础,基于滑模控制思想设计PID参数的自适应律,根据误差实时修正PID参数.基于Lyapunov函数设计的监督控制器补偿自适应PID控制器与理想控制器之间的差异,使系统具有设定的H_∞的跟踪性能.最后,两关节机器人的仿真实验结果表明了算法的有效性.

Abstract：

A robust adaptive PID control algorithm is proposed for trajectory tracking of robot manipulators with nonlinear uncertainties.The controller is composed of a main controller and a supervisory controller.The main controller is designed based on the traditional PID controller.The parameters of the PID controller are updated online according to the system running errors with the adaptation law based on the sliding mode control.The supervisory controller is proposed to compensate the error between the adaptive PID controller and the ideal controller in the sense of the Lyapunov function with the specified H_∞ tracking performance.Finally, the simulation results based on a two-joint robot manipulator show the effectiveness of the presented controller.     

Sliding Mode Neuro Adaptive Control in Trajectory Tracking for Mobile Robots

In this work a neural indirect sliding mode control method for mobile robots is proposed. Due to the nonholonomic property and restricted mobility, the trajectory tracking of this system has been one of the research topics for the last ten years. The proposed control structure combines a feedback linearization model, based on a kinematics nominal model, and a practical design that combines an indirect neural adaptation technique with sliding mode control to compensate the dynamics of the robot. Using an online adaptation scheme, a neural sliding mode controller is used to approximate the equivalent control in the neighbourhood of the sliding manifold. A sliding control is appended to ensure that the neural sliding mode control can achieve a stable closed-loop system for the trajectory-tracking control of a mobile robot with unknown nonlinear dynamics. The proposed design simultaneously guarantees the stability of the adaptation of the neural nets and obtains suitable equivalent control when the parameters of the robot model are unknown in advance. The robust adaptive scheme is applied to a mobile robot and shown to be able to guarantee that the output tracking error will converge to zero.