A study on industrial robotic manipulator model using model based predictive controls

In this study, a single input single output (SISO) neural generalized predictive control (NGPC) was applied to a six joint robotic manipulator. The SISO generalized predictive control (GPC) was also used for comparison. Modeling of the dynamics of the robotic manipulator was made by using the Lagrange–Euler equations. The cubic trajectory principle is used for position reference and velocity reference trajectories. A simulation program was prepared by using Delphi 6.0. All computations for manipulator dynamics model, GPC-SISO, and NGPC-SISO were done on PC with 1.6 GHz Centrino CPUs by using this program. The parameter estimation algorithm used in the GPC-SISO is Recursive Least Squares. The minimization algorithm used in the NGPC-SISO is Newton–Raphson. According to the simulation results, the results of the NGPC-SISO algorithm were better than those of the GPC-SISO algorithm.     

基于干扰观测器的机械臂广义模型预测轨迹跟踪控制

为实现对多自由度机械臂关节运动精确轨迹跟踪,提出一种基于非线性干扰观测器的广义模型预测轨迹跟踪控制方法。针对机械臂轨迹跟踪运动学子系统,采用广义预测控制（Generalized Predictive Control,GPC）方法设计期望的虚拟关节角速度。对于机械臂轨迹跟踪动力学子系统,考虑机械臂的参数不确定性和未知外界扰动,利用GPC方法设计关节力矩控制输入,基于非线性干扰观测器方法实时估计和补偿系统模型中的不确定性。在李雅普诺夫稳定性理论框架下证明了机械臂关节角位置和角速度的跟踪误差最终收敛于零的小邻域。数值仿真验证了所提出控制方法的有效性和优越性。     

Design and performance of an intelligent predictive controller for a six-degree-of-freedom robot using the Elman network

The aim of this paper was to propose a recurrent neural network-based predictive controller for robotic manipulators. A neural network controller for a six-joint Stanford robotic manipulator was designed using the generalized predictive control (GPC) and the Elman network. The GPC algorithm, which is a class of digital control method, requires long computational time. This is a disadvantage in real-time robot control; therefore, the Elman network controller was designed to reduce processing time by avoiding the highly mathematical and computational complexity of the GPC. The main reason for choosing the Elman network, amongst several neural network algorithms, was that the presence of feedback loops have a profound impact on the learning capability of the network. The designed neural network controller was able to recover quickly because of its significant generalization capability, which allowed it to adapt very rapidly to changes in inputs. The performance of the controller was also shown graphically using simulation software, including the dynamics and kinematics of the robot model.     

基于不确定逼近的机械手自适应鲁棒预测控制

针对具有参数不确定性和未知外部干扰的机械手轨迹跟踪问题提出了一种多输入多输出自适应鲁棒预测控制方法. 首先根据机械手模型设计非线性鲁棒预测控制律, 并在控制律中引入监督控制项; 然后利用函数逼近的方法逼近控制律中因模型不确定性以及外部干扰引起的未知项. 理论证明了所设计的控制律能够使机械手无静差跟踪期望的关节角轨迹. 仿真验证了本文设计方法的有效性.     

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 Neural Net Predictive Control for Telerobots with Time Delay

This paper extends the Smith Predictor feedback control structure to unknown robotic systems in a rigorous fashion. A new recurrent neural net predictive control (RNNPC) strategy is proposed to deal with input and feedback time delays in telerobotic systems. The proposed control structure consists of a local linearized subsystem and a remote predictive controller. In the local linearized subsystem, a recurrent neural network (RNN) with on-line weight tuning algorithm is employed to approximate the dynamics of the time-delay-free nonlinear plant. The remote controller is a modified Smith predictor for the local linearized subsystem which provides prediction and maintains the desirable tracking performance. Stability analysis is given in the sense of Lyapunov. The result is an adaptive compensation scheme for unknown telerobotic systems with time delays, uncertainties, and external disturbances. A simulation of a two-link robotic manipulator is provided to illustrate the effectiveness of the proposed control strategy.     

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.     

考虑柔性关节的机械臂自适应运动控制策略研究

具有柔性关节的轻型机械臂因其自重轻、响应迅速、操作灵活等优点,取得了广泛应用;针对具有柔性关节的机械臂系统的关节空间轨迹跟踪控制系统动力学参数不精确的问题,提出一种结合滑模变结构设计的自适应控制器算法;通过自适应控制的思想对系统动力学参数进行在线辨识,并采用Lyapunov方法证明了闭环系统的稳定性;仿真结果表明,该控制策略保证了机械臂系统对期望轨迹的快速跟踪,具有良好的跟踪精度,系统具有稳定性。     

An Adaptive Fuzzy Control Model for Multi-Joint Manipulators

Multi-joint manipulator systems are subject to nonlinear influences such as frictional characteristics, random disturbances and load variations. To account for uncertain disturbances in the operation of manipulators, we propose an adaptive manipulator control method based on a multi-joint fuzzy system, in which the upper bound information of the fuzzy system is constant and the state variables of the manipulator control system are measurable. The control algorithm of the system is a MIMO (multi-input-multi-output) fuzzy system that can approximate system error by using a robust adaptive control law to eliminate the shadow caused by approximation error. It can ensure the stability of complex manipulator control systems and reduce the number of fuzzy rules required. Comparison of experimental and simulation data shows that the controller designed using this algorithm has highly-precise trajectory-tracking control and can control robotic systems with complex characteristics of non-linearity, coupling and uncertainty. Therefore, the proposed algorithm has good practical application prospects and promotes the development of complex control systems.     

A study of neural network based inverse kinematics solution for a three-joint robot

A neural network based inverse kinematics solution of a robotic manipulator is presented in this paper. Inverse kinematics problem is generally more complex for robotic manipulators. Many traditional solutions such as geometric, iterative and algebraic are inadequate if the joint structure of the manipulator is more complex. In this study, a three-joint robotic manipulator simulation software, developed in our previous studies, is used. Firstly, we have generated many initial and final points in the work volume of the robotic manipulator by using cubic trajectory planning. Then, all of the angles according to the real-world coordinates (x, y, z) are recorded in a file named as training set of neural network. Lastly, we have used a designed neural network to solve the inverse kinematics problem. The designed neural network has given the correct angles according to the given (x, y, z) cartesian coordinates. The online working feature of neural network makes it very successful and popular in this solution.     

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.     

Control of robotic manipulators—a neural network approach

A neural-network-based scheme is used for the control of a robotic manipulator. The main idea is that, by using a neural network to learn the characteristics of the robot system (or specifically its inverse dynamics), accurate trajectory following and good performance results are obtained. However, the traditional back-propagation algorithm commonly used for control and identification of nonlinear systems suffers from a slow rate of convergence. We investigate the effect of adusting the slope of the activation function (the node nonlinearity) on the performance of a back-propagation algorithm. It is shown that learning speed is increased significantly by making the slope of non-linearity adaptive. The results demonstrate that the proposed method gives better error minimization and faster convergence. The suggested method is applied to a two-link robotic manipulator. The resulting controller is sufficiently robust with respect to the changing conditions.     

Neural network-based robust finite-time control for robotic manipulators considering actuator dynamics

A novel neural network-based robust finite-time control strategy is proposed for the trajectory tracking of robotic manipulators with structured and unstructured uncertainties, in which the actuator dynamics is fully considered. The controller, which possesses finite-time convergence and strong robustness, consists of two parts, namely a neural network for approximating the nonlinear uncertainty function and a modified variable structure term for eliminating the approximate error and guaranteeing the finite-time convergence. According to the analysis based on the Lyapunov theory and the relative finite-time stability theory, the neural network is asymptotically convergent and the controlled robotic system is finite time stable. The proposed controller is then verified on a two-link robotic manipulator by simulations and experiments, with satisfactory control performance being obtained even in the presence of various uncertainties and external disturbances.     

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     

On the sliding mode control of MIMO nonlinear systems: An input‐output approach

We address the sliding mode control design problem for output reference trajectory tracking problems in the special class of MIMO flat systems known as static feedback linearizable systems. We assume unavailable system state components but rely on available inputs and measurable flat outputs. Each controller will largely ignore state and control input couplings by adopting a standard sliding mode controller scheme derived from the SISO case and used this as decoupled input‐to‐flat‐output model. The standard controller arises from a vastly simplified pure integration, additively perturbed, system. The simplified pure integration system controlled trajectories are shown to be time‐scale homotopically equivalent to those of the nonlinear flat system. The basic sliding surface coordinate function design is approached from the perspective of structural integral reconstructors requiring only the inputs and the flat outputs of the system. Integral structural reconstructors were introduced by Fliess et al for the control of linear SISO and MIMO systems, giving rise to the generalized proportional integral control method. Simulations are presented for SISO and MIMO systems and experimental results are reported for a two‐degree‐of‐freedom fully actuated robotic manipulator.     

Mutual Synchronization of Multiple Robot Manipulators with Unknown Dynamics

In this paper, we investigate the mutual synchronization control problem of multiple robot manipulators in the case that the desired trajectory is only available to a portion of the team members, and the dynamics and the external disturbances of the manipulators are unknown. Treating the weighted average of the outputs of the neighbors as the reference trajectory, an adaptive neural network (NN) tracking control is designed for each manipulator. Based on the Lyapunov analysis, rigid mathematical proof is provided for the proposed algorithm for both state feedback and output feedback cases. It is shown that, under the proposed adaptive NN control, the tracking error of each manipulator converges to an adjustable neighborhood of the origin. Simulations are provided to demonstrate the effectiveness of the proposed approach.     

基于RBF-BP算法的机械臂多自由度分拣控制系统设计

为提升机械臂设备的准确分拣能力,设计基于RBF-BP算法的机械臂多自由度分拣控制系统。利用RBF-BP前馈神经网络,规划机械臂设备的运动轨迹路线,实现基于RBF-BP算法的机械臂运动轨迹建模。确定工业相机在总功能框架中所处连接位置,根据机械臂选型情况,确定可编程逻辑控制器、变频控制器对于所选机械臂元件的调节能力,完成对系统功能模块的开发。借助传输信道,将Sorting分拣指令、ToolControl控制指令反馈回核心控制主机,建立完整的指令执行回路,再联合相关硬件设备结构,实现基于RBF-BP算法的机械臂多自由度分拣控制系统设计。实验结果表明,在抓取能力相同的情况下,应用RBF-BP算法控制系统机械臂成功分拣的工件数量为19件,机械臂抓取成功率为95%,说明所设计系统满足提升机械臂准确分拣能力的设计初衷。     

Event-Triggered Sliding Mode Control for Trajectory Tracking of Nonlinear Systems

In this paper, an event-triggered sliding mode control approach for trajectory tracking problem of nonlinear input affine system with disturbance has been proposed. A second order robotic manipulator system has been modeled into a general nonlinear input affine system. Initially, the global asymptotic stability is ensured with conventional periodic sampling approach for reference trajectory tracking. Then the proposed approach of event-triggered sliding mode control is discussed which guarantees semi-global uniform ultimate boundedness. The proposed control approach guarantees non-accumulation of control updates ensuring lower bounds on inter-event triggering instants avoiding Zeno behavior in presence of the disturbance. The system shows better performance in terms of reduced control updates, ensures system stability which further guarantees optimization of resource usage and cost. The simulation results are provided for validation of proposed methodology for tracking problem by a robotic manipulator. The number of aperiodic control updates is found to be approximately 44% and 61% in the presence of constant and time-varying disturbances respectively.     

Online constrained optimization based adaptive robust control of a class of MIMO nonlinear systems with matched uncertainties and input/state constraints

A performance oriented two-loop control approach is proposed for a class of multiple-input–multiple-output (MIMO) systems with input saturation, state constraints, matched parametric uncertainties and input disturbances. In the inner loop, a constrained adaptive robust control (ARC) law is synthesized to achieve the required robust tracking performances with respect to on-line replanned trajectory in the presence of input saturation and various types of matched uncertainties. In the outer loop, a replanned trajectory is generated by solving a constrained optimization algorithm online to minimize the converging time of the overall system response to the desired trajectory while not violating various constraints. Interaction of the two loops is explicitly characterized by a set of inequalities that the design variables of each loop have to satisfy. It is theoretically shown that the resulting closed-loop system can track feasible desired trajectories with a guaranteed converging time and steady-state tracking accuracy without violating the state constraints. Since the system in study is most appropriate to describe the dynamics of the robotic systems, the control of a two-axis planar robotic manipulator is used as an application example. Comparative simulation results demonstrate the advantage of the proposed approach over the traditional approaches in practical applications.     

面向未知环境基于智能预测的模糊控制器研究

提出了一种新的面向未知环境的智能预测算法，并将此算法应用于机器人力跟踪控制中．该方法利用机械手末端与未知受限环境产生的接触轨迹，通过模糊推理智能地预测阻抗控制模型中的参考轨迹，并根据力误差变化用参考比例因子对其进行调节，以适应未知环境刚度的变化．通过对阻抗模型参数进行模糊调节减少受限运动中的力误差，提高了全局的力控制效果．仿真结果证明了此算法的有效性．