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.     

Adaptive terminal sliding mode control for rigid robotic manipulators

In order to apply the terminal sliding mode control to robot manipulators, prior knowledge of the exact upper bound of parameter uncertainties, and external disturbances is necessary. However, this bound will not be easily determined because of the complexity and unpredictability of the structure of uncertainties in the dynamics of the robot. To resolve this problem in robot control, we propose a new robust adaptive terminal sliding mode control for tracking problems in robotic manipulators. By applying this adaptive controller, prior knowledge is not required because the controller is able to estimate the upper bound of uncertainties and disturbances. Also, the proposed controller can eliminate the chattering effect without losing the robustness property. The stability of the control algorithm can be easily verified by using Lyapunov theory. The proposed controller is tested in simulation on a two-degree-of-freedom robot to prove its effectiveness.     

Observer-Based Adaptive Controller Design of Flexible Manipulators Using Time-Delay Neuro-Fuzzy Networks

In this paper, a dynamical time-delay neuro-fuzzy controller is proposed for the adaptive control of a flexible manipulator. It is assumed that the robotic manipulator has only joint angle position measurements. A linear observer is used to estimate the robot joint angle velocity. For a perfect tracking control of the robot, the output redefinition approach is used in the adaptive controller design using time-delay neuro-fuzzy networks. The time-delay neuro-fuzzy networks with the rule representation of the TSK type fuzzy system have better learning ability for complex dynamics as compared with existing neural networks. The novel control structure and learning algorithm are given, and a simulation for the trajectory tracking of a flexible manipulator illustrates the control performance of the proposed control approach.     

A Robust Adaptive Terminal Sliding Mode Control for Rigid Robotic Manipulators

In this paper, a robust adaptive terminal sliding mode controller is developed for n-link rigid robotic manipulators with uncertain dynamics. An MIMO terminal sliding mode is defined for the error dynamics of a closed loop robot control system, and an adaptive mechanism is introduced to estimate the unknown parameters of the upper bounds of system uncertainties in the Lyapunov sense. The estimates are then used as controller parameters so that the effects of uncertain dynamics can be eliminated and a finite time error convergence in the terminal sliding mode can be guaranteed. Also, a useful bounded property of the derivative of the inertial matrix is explored, the convergence rate of the terminal sliding variable vector is investigated, and an experiment using a five bar robotic manipulator is carried out in support of the proposed control scheme.     

An adaptive fuzzy controller based on sliding mode for robotmanipulators

This paper considers adaptive fuzzy control of robotic manipulators based on sliding mode. It is first shown that an adaptive fuzzy system with the system representative point (RP, or as is often termed, a switching function in variable structure control (VSC) theory) and its derivative as inputs, can approximate the robot nonlinear dynamics in the neighborhood of the switching hyperplane. Then a new method for designing an adaptive fuzzy control system based on sliding mode is proposed for the trajectory tracking control of a robot with unknown nonlinear dynamics. The system stability and tracking error convergence are also proved by Lyapunov techniques.     

PHANTOM Omni机器人的自适应模糊滑模控制

针对PHANTOM Omni机器人的位置轨迹跟踪问题,采用了一种基于模糊逻辑的自适应模糊滑模控制方案。利用滑模控制中的切换函数作为输入,根据模糊系统的逼近能力设计控制器,并基于李雅谱诺夫方法设计自适应律对控制器所需参数进行实时调节。仿真中将其与传统的滑模控制进行了比较,仿真结果表明：自适应模糊滑模控制能使PHANTOM Omni机器人更好地实现期望的位置轨迹跟踪并有效地减轻抖振现象,从而证明了该方法在PHANTOM Omni机器人上实施的可行性。     

Neural network-based adaptive controller design of roboticmanipulators with an observer

A neural network (NN)-based adaptive controller with an observer is proposed for the trajectory tracking of robotic manipulators with unknown dynamics nonlinearities. It is assumed that the robotic manipulator has only joint angle position measurements. A linear observer is used to estimate the robot joint angle velocity, while NNs are employed to further improve the control performance of the controlled system through approximating the modified robot dynamics function. The adaptive controller for robots with an observer can guarantee the uniform ultimate bounds of the tracking errors and the observer errors as well as the bounds of the NN weights. For performance comparisons, the conventional adaptive algorithm with an observer using linearity in parameters of the robot dynamics is also developed in the same control framework as the NN approach for online approximating unknown nonlinearities of the robot dynamics. Main theoretical results for designing such an observer-based adaptive controller with the NN approach using multilayer NNs with sigmoidal activation functions, as well as with the conventional adaptive approach using linearity in parameters of the robot dynamics are given. The performance comparisons between the NN approach and the conventional adaptation approach with an observer is carried out to show the advantages of the proposed control approaches through simulation studies     

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.     

Fuzzy-Basis-Function-Network-Based $H_infty$ Tracking Control for Robotic Manipulators Using Only Position Feedback

This paper presents an H _infin fuzzy output-feedback tracking-control scheme for robotic manipulators without measuring joint velocities. The developed controller and observer are based on a fuzzy basis function network (FBFN), which is employed to approximate nonlinear functions in the dynamics of controller and observer. The FBFN-based observer that estimates joint velocities can remove the needs of full-state measurements. According to the inevitable approximation errors and external disturbances, an H _infin auxiliary control signal is used to suppress the effects of the uncertainties. Moreover, all parameters of the fuzzy basis functions (FBFs) and FBF-to-output weights can be tuned online. The proposed controller requires no prior knowledge about the dynamics of the robot manipulator and no offline learning phase. Finally, comparative simulations on a three-link robot manipulator are provided to illustrate the tracking performance of the H _infin FBFN-based output-feedback control approach.     

Adaptive fuzzy terminal sliding mode controller for linear systems with mismatched time-varying uncertainties

A new design approach of an adaptive fuzzy terminal sliding mode controller for linear systems with mismatched time-varying uncertainties is presented in this paper. A fuzzy terminal sliding mode controller is designed to retain the advantages of the terminal sliding mode controller and to reduce the chattering occurred with the terminal sliding mode controller. The sufficient condition is provided for the uncertain system to be invariant on the sliding surface. The parameters of the output fuzzy sets in the fuzzy mechanism are adapted on-line to improve the performance of the fuzzy sliding mode control system. The bounds of the uncertainties are not required to be known in advance for the presented adaptive fuzzy sliding mode controller. The stability of the fuzzy control system is also guaranteed. Moreover, the chattering around the sliding surface in the sliding mode control can be reduced by the proposed design approach. Simulation results are included to illustrate the effectiveness of the proposed adaptive fuzzy terminal sliding mode controller.     

Robust adaptive fuzzy sliding mode trajectory tracking control for serial robotic manipulators

The ever increasingly stringent performance requirements of industrial robotic applications highlight significant importance of advanced robust control designs for serial robots that are generally subject to various uncertainties and external disturbances. Therefore, this paper proposes and investigates the design and implementation of a robust adaptive fuzzy sliding mode controller in the task space for uncertain serial robotic manipulators. The sliding mode control is well known for its robustness to system parameter variations and external disturbances, and is thus a highly desirable and cost-effective approach to achieve high precision control task for serial robots. The proposed controller is designed based on a fuzzy logic approximation to accomplish trajectory tracking with high accuracy and simultaneously attenuate effects from uncertainties. In the controller, the high-frequency uncertain term is approximated by using a fuzzy logic system while the low-frequency term is adaptively updated in real time based on a parametric adaption law. The control efficacy and effectiveness of the proposed control algorithm are comparatively verified against a recently proposed conventional controller. The test results demonstrate that the proposed controller has better trajectory tracking performances and is more robust against large disturbances than the conventional controller under the same operating conditions.     

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.     

基于自组织小波小脑模型关节控制器的不确定非线性系统鲁棒自适应终端滑模控制

针对一类不确定非线性系统的跟踪控制问题,在考虑建模误差、参数不确定和外部干扰情况下,以良好的跟踪性能及强鲁棒性为目标,提出基于自组织小脑模型(self-organizing wavelet cerebellar model articulation controller,SOWCMAC)的鲁棒自适应积分末端(terminal)滑模控制策略.首先,将小脑模型、自组织神经网络和小波函数各自优势相结合,给出一种SOWCMAC,以保证干扰估计方法具有快速学习能力和更好的泛化能力.其次,设计两种改进的terminal滑模面构造方法,并分别给出各自的收敛时间.然后,基于SOWCMAC和改进的积分terminal滑模面,给出不确定非线性系统鲁棒自适应非奇异terminal控制器的设计过程,其中通过构造自适应鲁棒项抑制干扰估计误差对系统跟踪性能的影响,并利用Lyapunov理论证明闭环系统的稳定性.最后,将该方法应用于近空间飞行器姿态的控制仿真实验,结果表明所提出方法有效性.     

Sliding mode-based adaptive tube model predictive control for robotic manipulators with model uncertainty and state constraints

In this paper, the optimal tracking control for robotic manipulatorswith state constraints and uncertain dynamics is investigated, and a sliding mode-based adaptive tube model predictive control method is proposed. First, utilizing the high-order fully actuated system approach, the nominal model of the robotic manipulator is constructed as the predictive model. Based on the nominal model, a nominal model predictive controller with the sliding mode is designed, which relaxes the terminal constraints, and realizes the accurate and stable tracking of the desired trajectory by the nominal system. Then, an auxiliary controller based on the node-adaptive neural networks is constructed to dynamically compensate nonlinear uncertain dynamics of the robotic manipulator. Furthermore, the estimation deviation between the nominal and actual states is limited to the tube invariant sets. At the same time, the recursive feasibility of nominal model predictive control is verified, and the ultimately uniformly boundedness of all variables is proved according to the Lyapunov theorem. Finally, experiments show that the robotic manipulator can achieve fast and efficient trajectory tracking under the action 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.     

受约束空间机器人降阶自适应神经网络滑模控制

为了实现受约束空间机器人的高精度控制,提出了一种基于U-K(Udwadia-Kalaba)方程的降阶自适应神经网络滑模控制算法;基于U-K方程,同时考虑受约束空间机器人各个关节的理想约束力与非理想约束力,推导得到详细的动力学方程;考虑到非理想约束力具有不确定性且单独采用滑模控制会出现抖振现象,提出了自适应神经网络滑模控制算法,实现各关节角度、角速度以及非理想约束力的高精度跟踪;针对系统受约束模型,对动力学方程和滑模控制器进行了降阶求解,减少了变量并简化了计算过程;为了验证所提算法的正确性与合理性,以2自由度受约束空间机器人为例进行了仿真验证;仿真结果表明：受约束空间机器人的各关节角度、角速度以及非理想约束力的跟踪误差均低于10^-4量级。     

Output feedback tracking control of robot manipulators with model uncertainty via adaptive fuzzy logic

Many robot controllers require not only joint position measurements but also joint velocity measurements; however, most robotic systems are only equipped with joint position measurement devices. In this paper, a new output feedback tracking control approach is developed for the robot manipulators with model uncertainty. The approach suggested herein does not require velocity measurements and employs the adaptive fuzzy logic. The adaptive fuzzy logic allows us to approximate uncertain and nonlinear robot dynamics. Only one fuzzy system is used to implement the observer-controller structure of the output feedback robot system. It is shown in a rigorous manner that all the signals in a closed loop composed of a robot, an observer, and a controller are uniformly ultimately bounded. Finally, computer simulation results on three-link robot manipulators are presented to show the results which indicate good position tracking performance and robustness against payload uncertainty and external disturbances.     

机器人操作器的自适应模糊滑模控制器设计

针对机器人动力学系统提出了一种基于模糊逻辑的自适应模糊滑模控制方案.根据滑模控制原理并利用模糊系统的逼近能力设计控制器,基于李雅谱诺夫方法设计自适应律,证明了闭环模糊控制系统的稳定性和跟踪误差的收敛性.控制结构简单,不需要复杂的运算.该设计方案柔化了控制信号,减轻了一般滑模控制的抖振现象.仿真结果表明了所提控制策略的有效性.     

一种新的自适应模糊滑模控制器设计方法

对一类非线性系统提出一种新的自适应模糊滑模控制器设计方法。将自适应模糊控制与滑模控制有效地结合在一起,先用滑模控制使跟踪误差进入边界层内,然后启动自适应模糊控制器。该控制器可消除滑模控制器中出现的抖振,并可在存在模糊逻辑系统逼近误差情况下使系统跟踪误差小于预先给定的任意常数。仿真算例验证了所提出方法的有效性。     

On-line genetic algorithm-based fuzzy-neural sliding mode controller using improved adaptive bound reduced-form genetic algorithm

In this article, a novel on-line genetic algorithm-based fuzzy-neural sliding mode controller trained by an improved adaptive bound reduced-form genetic algorithm is developed to guarantee robust stability and good tracking performance for a robot manipulator with uncertainties and external disturbances. A general sliding manifold, which can be non-linear or time varying, is used to construct a sliding surface and reduce control law chattering. In this article, the sliding surface is used to derive a genetic algorithm-based fuzzy-neural sliding mode controller. To identify structured system dynamics, a B-spline membership function fuzzy-neural network, which is trained by the improved genetic algorithm, is used to approximate the regressor of the robot manipulator. The sliding mode control with a general sliding surface plays the role of a compensator when the fuzzy-neural network does not approximate the dynamics regressor of the robot manipulator well in the transient period. The adjustable parameters of the fuzzy-neural network are tuned by the improved genetic algorithm, which, with the use of the sequential-search-based crossover point method and the single gene crossover, converges quickly to near-optimal parameter values. Simulation results show that the proposed genetic algorithm-based fuzzy-neural sliding mode controller is effective and yields superior tracking performance for robot manipulators.