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.

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.

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。

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。

Theory and methodology for kinematic design of Gough-Stewart platforms

The kinematic design issue of Gough-Stewart platforms is investigated. Based upon a full understanding of the geometrical characteristics of workspace boundary, a spherically-shaped prescribed workspace having a given orientation capability is defined for the synthesis of a well behaved workspace. Two performance measures are presented, i.e. the local dexterity and workspace radius ratio. The dimensions of the platform are determined with a prior knowledge of how the design parameters affect the dexterity and workspace radius ratio, resulting in an optimal design in terms of these performance indices. An example of application to the kinematic design of a hexapod machine tool is given to illustrate the effectiveness of this approach.

Optimal design of Stewart platforms based on expanding the control bandwidth while considering the hydraulic system design

We proposed an optimal design method to expand the bandwidth for the control of large hydraulic Stewart platform.The method is based on generalized natural frequency and takes hydraulic oil into consideration.A Lagrangian formulation which considers the whole leg inertia is presented to obtain the accurate equivalent mass matrix.Using the model,the effect of leg inertia and the influence of design parameters on the generalized natural frequency are investigated.Finally,numerical examples are presented to validate and confirm the efficiency of the mathematical model.The results show that the leg inertia,especially the piston part plays an important role in the dynamics.The optimum diameter ratio of the base to the moving platform is between 2 and 3,and the optimum joint angle ratio of the base to the moving platform is about 1.The smaller joint angles and a longer leg stroke are favorable for raising system frequencies.The system oil should be preprocessed for large platforms with a requirement for good dynamic performance.

LQG Controller Design Applied to a Pneumatic Stewart-Gough Platform

This paper is concerned with the practical application control of a pneumatically actuated Stewart-Gough platform with 6-degrees of freedom （6-DOF）. The control approach for motion control of the platform is presented using a modern control technique, namely, linear quadratic Gaussinn （LQG） with reference tracking. The LQG controller is the combination of a Kalman filter, i.e., a linear-quadratic estimator （LQE） with a linear-quadratic regulator （LQR）. The robustness of the control scheme is accessed under various load conditions, and the experimental results are shown.

基于Jerk约束的Stewart平台在线轨迹规划

为解决高精度Stewart平台在点位控制下生成平滑轨迹和在线更新轨迹问题,提出了一种基于Jerk约束的在线轨迹规划方法。首先,提出单自由度轨迹决策算法确定各自由度时间最优轨迹曲线;同时,为获得非线性轨迹方程目标最优解,提出基于Quasi-Monte Carlo和Brent算法的数值分析方法;然后,根据多自由度时间同步轨迹规划方法确定平台运动轨迹;最后,通过仿真实验验证算法实时性与可靠性。实验表明:算法满足毫秒级实时性要求,平台能够根据外部命令实时更新轨迹参数序列,最终使平台稳定到达目标运动状态。