Simulation of Offshore Wind Turbine Blade Docking Based on the Stewart Platform

The windy environment is the main cause affecting the efficiency of offshore wind turbine installation.In order to improve the stability and efficiency of single-blade installation of offshore wind turbines under high wind speed conditions,the Stewart platform is used as an auxiliary tool to help dock the wind turbine blade in this paper.In order to verify the effectiveness of the Stewart platform for blade docking,a blade docking simulation system consisting of the Stewart platform,wind turbine blade,and wind load calculation module was built based on Simulink/SimscapeMultibody.At the same time,the PID algorithm is used to control the Stewart platform so that the blade can effectively track the desired trajectory during the docking process to ensure the successful docking of the blade.Through the simulation of the docking process for blades with a length of 61.5 meters,this paper successfully demonstrates a docking system that might facilitate future docking processes.It also shows that the Stewart platform can effectively reduce the vibration and the movement range of the blade root and improve the stability and efficiency of blade docking.

Multi Objective Robust Active Vibration Control for Flexure Jointed Struts of Stewart Platforms via H∞ and μ Synthesis

Active vibration control is needed for future space telescopes, space laser communication and other precision sensitive payloads which require ultra-quiet environments. A Stewart platform based hybrid isolator with 6 hybrid struts is the effective system for active/passive vibration isolation over 5-250 Hz band. Using an identification transfer matrix of the Stewart platform, the coupling analysis of six channels is provided. A dynamics model is derived, and the rigid mode is removed to keep the signal of pointing control. Multi objective robust H∞ and μ synthesis strategies, based on singular values and structured singular values respectively, are presented, which simultaneously satisfy the low frequency pointing and high frequency disturbance rejection requirements and take account of the model uncertainty, parametric uncertainty and sensor noise. Then, by performing robust stability test, it is shown that the two controllers are robust to the uncertainties, the robust stability margin of H, controller is less than that of μ controller, but the order of μ controller is higher than that of H, controller, so the balanced controller reduction is provided. Additionally, the μ controller is compared with a PI controller. The time domain simulation of the μ controller indicates that the two robust control strategies are effective for keeping the pointing command and isolating the harmonic and stochastic disturbances.

Accuracy Analysis of Stewart Platform Based on Interval Analysis Method

A Stewart platform is introduced in thc 500 m aperture spherical radio telescope（FAST） as an accuracy adjustable mechanism for teed receivers. Accuracy analysis is the basis of accuracy design. However, a rapid and effective accuracy analysis method for parallel manipulator is still needed. In order to enhance solution efficiency, an interval analysis method（lA method） is introduced to solve the terminal error bound of the Stewart platform with detailed solution path. Taking a terminal pose of the Stewart platform in FAST as an example, the terminal error is solved by the Monte Carlo method（MC method） by 4 980 s, the stochastic mathematical method（SM method） by 0.078 s, and the IA method by 2.203 s. Compared with MC method, the terminal error by SM method leads a 20% underestimate while the IA method can envelop the real error bound of the Stewart platform. This indicates that the IA method outperforms the other two methods by providing quick calculations and enveloping the real error bound of the Stewart platform. According to the given structural error of the dimension parameters of the Stewart platform, the IA method gives a maximum position error of 19.91 mm and maximum orientation error of 0.534°, which suggests that the IA method can be used for accuracy design of the Stewart platfbnn in FAST. The 1A method presented is a rapid and effective accuracy analysis method for Stewart platform.

Analysis and Application of the Singularity Locus of the Stewart Platform

The direct use of the determinant of Jacobian matrix being equal to zero for the singularity analysis is generally difficult which is due to complexity of the Jacobian matrix of 6-DOF parallel manipulators,especially for Stewart platform.Recently,several scholars make their great contribution to the effective solution of this problem,but neither of them find the right answer.This paper gives a brief analysis of the kinematics of the Stewart platform and derives the Jacobian matrices of the system through the velocity equation.On the basis of the traditional classification of singularities,the second type of singularity is investigated.An assumption of any three of the six variables of the Stewart platform as constant is made,then the analytical expression of singularity locus equation of the second type singularity which contains another three pose variables is obtained.The singularity locus is represented in the three-dimensional space through the derived equation.The correctness and validity of the proposed method are verified through examples.Finally,the singularity analysis of an electric Stewart platform in its desired workspace and reachable workspace is implemented.Thus,one can easily identify whether singularity exists in a given workspace of a Stewart platform and determine whether the existed singularity can be avoided through the proposed method.The proposed method also provides theoretical principle for the design and application of the Stewart platform and has great significance for the trajectory planning and control.

Optimal Design of Stewart Platform Safety Mechanism

A safety mechanism capable of moving at will within the range of its whole link lengths is designed based on the link space. Sixteen extreme poses are obtained in a Stewart platform. The singular points of the extreme poses are solved by using homotopy method as well as the judgment condition of singular points, and thereby the maximum link lengths are achieved. The rotation angles of joints and the distances between two neighboring links are analyzed in a calculation example in which that the mechanism moves among the extreme poses is assumed. Then an algorithm to test the safety mechanism is presented taking the constraint conditions into account. A safety mechanism having optimal properties of global movement is worked out by optimizing all structural parameters through minimizing the average condition number of extreme poses.

SPACECRAFT DOCKING SIMULATION USING HARDWARE-IN-THE-LOOP SIMULATOR WITH STEWART PLATFORM

A ground-based hardware-in-the-loop （HIL） simulation system with hydraulically driven Stewart platform for spacecraft docking simulation is presented. The system is used for simulating docking process of the on-orbit spacecraft. Principle and structure of the six-degree-of-freedom simulation system are introduced. The docking process dynamic of the vehicles is modeled. Experiment results and mathematical simulation data are compared to validating the simulation system. The comparisons of the results prove that the simulation system proposed can effectively simulate the on-orbit docking process of the spacecraft.

Backstepping adaptive control of hydraulic Stewart platform using dynamic surface

Hydraulic Stewart platform is characterized by nonlinearity for driving system in essence,severe load coupling among the legs,which bring a great difficulty for controller design and performance improvement.Afore controller research is either low in tracking performance and movement smoothness when it ignores the nonlinearity and dynamics coupling,or complex in algorithm and has the need of acceleration feedback or observer when the dynamics coupling and nonlinearity is included.To solve the dilemma,a new controller,backstepping adaptive control of hydraulic Stewart platform using dynamic surface is put forward based on the complete dynamics including the upper platform dynamics and hydraulic nonlinearity in driving system.Asymptotic stability of the whole system is proved by Lyapunov method.The proposed algorithm is simple by avoiding the use of acceleration.The simulation results indicate that the control algorithm performs better than the normal PID controller in control precision,dynamic response and depression of the cross coupling.

Subsystem model-based close-loop grey-box identification method for hydraulic stewart platform

In order to solve the problem of difficult modeling and identification caused by time-variable parameters,multiple inputs and outputs and unstable open loop,a subsystem model-based close-loop grey-box identification method was put forward when consider the main coupling effects of hydraulic Stewart platform.Firstly,the whole system is divided into three TITO(Two Input Two Output) subsystems according to the characteristics of the pseudo-mass matrix,hence transfer function matrix model of the subsystem can also be found.Secondly,since the Stewart platform is unstable,the close-loop transfer model of the subsystem is derived under the proportional controllers.The inverse M serial is adopted as the identification signal to get the experimental data.All parameters of the subsystem are determined in close-loop indirect identification by PEM(Prediction Error Method).Finally,a case study validates the correctness and effectiveness of the subsystem model-based close-loop grey-box identification method for hydraulic Stewart platform.

Stability Study of Cable-Suspended Stewart Platform

The control stability of the end manipulator of a cable-suspended Stewart platform in disturbance was studied by combination of the multi-body system dynamics and control theory and the eigensystem realization algorithm （ERA）. The corresponding closodloop vibration control strategies were suggested based on position prediction with PD （proportional plus derivative ） control. Numerical simulation was made on a scale model to study the vibration control effects of the stewart platform with flexible suspension, including system response to step load, system response to cyclic load, and instability. Then, experiments for Stewart platform with cable suspension were designed to study the actual control effects and validate the validity of numerical simulation. The results show that the experimental results agree with the simulation results well, and the the system has a fairly good control effect to the end manipulator. Therefore, a preliminary conclusion can be made that it is feasible using the Stewart platform as the vibration control platform of the flexible support system, by position prediction of the base platform and PD feedback control law.

A Passive Stewart Platform Based Joystick to Control Spatially Moving Objects

Most of the spatially moving vehicles and game controllers use a 2-3 DOF （degrees of freedom） joystick to manipulate objects position. However, most of the spatially moving vehicles have more than 3 degrees of freedom, such as helicopters, quadrotors, and planes. Therefore, additional equipment like pedals or buttons is required during the manipulation. In this study, a passive Stewart platform based 6 degrees of freedom joystick was developed to control spatially moving objects. The Stewart platform mechanism is a 6-degrees of freedom parallel mechanism, which has been used for simulators. The main challenge of using a parallel mechanism to manipulate objects is the computational burden of its forward kinematics. Therefore, an artificial neural network was used for the forward kinematic solution of the Stewart platform mechanism to obtain the fastest response. Linear potentiometers were used for the Stewart platform legs. A mathematical model of a quadrotor was used to test the capability of the joystick. The developed spatial joystick successfully manipulated the virtual quadrotor model.

Design of computer vision assisted machine learning based controller for the Stewart platform to track spatial objects

The present work aims to develop an object tracking controller for the Stewart platform using a computer vision-assisted machine learning-based approach.This research is divided into two modules.The first module focuses on the design of a motion controller for the Physik Instrumente(PI)-based Stewart platform.In contrast,the second module deals with the development of a machine-learning-based spatial object tracking algorithm by collecting information from the Zed 2 stereo vision system.Presently,simple feed-forward neural networks(NN)are used to predict the orientation of the top table of the platform.While training,the x,y,and z coordinates of the three-dimensional(3D)object,extracted from images,are used as the input to the NN.In contrast,the orientation information of the platform(that is,rotation about the x,y,and z-axes)is considered as the output from the network.The orientation information obtained from the network is fed to the inverse kinematics-based motion controller(module 1)to move the platform while tracking the object.After training,the optimised NN is used to track the continuously moving 3D object.The experimental results show that the developed NN-based controller has successfully tracked the moving spatial object with reasonably good accuracy.

基于ADAMS的Stewart平台运动学分析

针对在Stewart 6自由度并联平台设计中,支腿的运动学及动力学参数理论计算过于复杂的问题,课题组提出了基于ADAMS的Stewart平台反解与正解相结合的分析方法。首先,通过ADAMS反解求得支腿位移参数;然后,将位移参数转换为驱动函数添加在各个支腿上;接着,通过ADAMS正解求解支腿其余运动参数;最后,通过实例对比理论计算与ADAMS分析数据。结果表明:课题组提出方法求得的支腿位移与理论值之差均小于0.01 mm,支腿最大速度及最大加速度与理论值误差均小于2%,从而验证了该分析方法的合理性与科学性。该分析方法为工程中遇到的6自由度平台已知动平台驱动函数求解支腿参数的实际问题提供了一种高效的解决办法。

Stewart平台神经网络非奇异终端滑模控制

针对Stewart平台的六自由度(six degrees of freedom,6-DOF)轨迹跟踪问题,提出一种基于神经网络的非奇异终端滑模控制方法并应用于Stewart平台的位置姿态控制中。通过分析Stewart平台的位置反解和速度反解,建立运动学方程,利用牛顿-欧拉方程建立动力学方程,并结合加速度反解得到了平台的状态空间表达式;基于非奇异滑模面函数,设计非奇异终端滑模控制律。考虑到径向基函数(radial Basis function,RBF)神经网络的逼近特性,采用RBF神经网络对模型未知部分进行自适应逼近,并利用Lyapunov第二法设计了自适应律;通过仿真证明控制器设计的有效性。仿真结果表明,相比于比例积分微分(proportional integral derivative,PID)控制器,提出的RBF神经网络非奇异终端滑模控制器具有更好的轨迹跟踪精度和动态特性。

基于WOA-Elman的Stewart平台位姿正解

为了高效而准确地求解Stewart平台的正解问题,在本研究中,采用了鲸鱼算法来优化Elman神经网络模型。对Stewart平台的六根连杆长度和平台位姿的运动学模型进行了详细分析,并通过平台位姿反解数据创建实验数据集。关于Elman神经网络模型,引入鲸鱼优化算法对该模型进行了优化,以提高计算性能和精度,从而建立了WOA-Elman模型,用于求解Stewart平台的正解。通过详细的仿真分析对模型进行评估,并通过实验来验证模型的有效性。研究结果表明,采用鲸鱼算法优化的Elman神经网络模型在求解Stewart平台正解问题方面表现出色。该模型展现出出色的非线性拟合能力和高度的计算精度,能够快速而准确地求解Stewart平台的位姿正解问题。这一研究成果为解决Stewart平台位姿正解问题提供了一种高精度的方法。

基于对偶四元数法的Stewart平台运动学研究

作为一种多自由度并联机构,Stewart平台在工业自动化、飞行模拟及医疗设备等领域具有广阔应用前景。研究Stewart平台的运动学特性,并提供数学模型和解决方法,可以实现对其运动和位置的准确控制。基于6-UPS型Stewart并联机器人平台,引入了对偶四元数的概念,探讨了Stewart平台的运动学特性,提出了一种高效的并联机器人运动学求解算法。研究结果表明,在描述并联机器人的运动学中,对偶四元数法具有更简洁的表示形式和更少的用来表示刚体位姿的未知数个数,具有明显优势。

Stewart六自由度实验平台的测试与分析

基于Stewart六自由度平台设计而成的动感座椅,可以模拟最佳动作效果的各种空间运动姿态,使观众在观看电影或玩游戏时具有更好的代入感和互动体验。为了检测Stewart六自由度实验平台能否为实现特定的动感效果提供硬件保障,首先对其进行了单轴测试,分别测量了其静止和运动时的位置和速度;然后运用MATLAB得到相应的实际曲线,并与理论曲线进行对比分析,从而得出平台运动控制误差的大小;最后,将控制精度需求和误差分析结果进行对比,即可判定是否能为实现特定的动感效果提供硬件保障。

THE DIRECT KINEMATIC SOLUTION OF THE PLANAR STEWART PLATFORM WITH COPLANAR GROUND POINTS

A procedure of computing the position of the planar Stewart platfrom with coplanar ground points is presented avoiding the computation of Groebner basis by standard algorithm. The polynomial system resulted is triangularized. The number of arithmetic operations needed can be predisely counted.

Dynamic modeling of a 6-degree-of-freedom Stewart platform driven by a permanent magnet synchronous motor

For an electrical six-degree-of-freedom Stewart platform,it is difficult to compute the equivalent inertia of each motor in real time,as the inertia is time-varying.In this study,an analysis using Kane's equation is undertaken of the driven torque of the movements of motor systems(including motor friction,movements of motor systems along with the actuators,rotation around axis of rotors and snails),as well as driven torque of the platform and actuators.The electromagnetic torque was calculated according to vector-controlled permanent magnet synchronous motor(PMSM) dynamics.By equalizing the driven torque and electromagnetic torque,a model was established.This method,taking into consideration the influence of counter electromotive force(EMF) and motor friction,could be applied to the real-time dynamic control of the platform,through which the calculation of the time-varying equivalent inertia is avoided.Finally,simulations with typically desired trajectory inputs are presented and the performance of the Stewart platform is determined.With this approach,the multi-body dynamics of the electrical Stewart platform is better understood.

Track-position and vibration control simulation for strut of the Stewart platform

Vibrations inherently generated by on-board disturbance sources degrade the performance of the instruments in an on-orbit spacecraft,which have stringent accuracy requirements.The Stewart platform enables both track-positioning and vibration control.The strut of the Stewart platform is designed as a piezoelectric(PZT) element in series with a voice coil motor(VCM) element and a viscoelastic element.The track-positioning system uses a VCM as the main positioning control driver and a PZT as the positioning compensator.The vibration control system uses the characteristics of struts including active and passive control elements to attenuate the vibration.Simulation results indicate that the Stewart platform with the designed struts has good performance in tracking and vibration attenuation with different interference waves.

Stewart力传感器弹性体结构设计方法研究

手术过程中,腔镜微创手术机器人通过传感器精准测量手术器械与人体组织之间的交互作用力,可有效地促进腔镜手术的进步。文章根据传感器的研发要求,设计了一个适合手术器械的6自由度斯图尔特Stewart平台,基于电阻检测原理对平台的力/力矩灵敏度、各向同性度及连杆受力标准差进行了多目标优化;通过三维机械设计软件SolidWorks建模后,导入到有限元分析软件中进行受力分析。结果表明:按照优化后角度所设计的传感器各连杆受力更均匀,所选择的材料受到的极限应力均在比例极限内;传感器在x、y、z方向上的力和力矩检测范围分别达到了10 N和150 N·mm,力和力矩监测精度分别为0.3 N和3 N·mm,其适合于微创手术机器人。