body dynamic and yields the input current vector of the servovalve, the dynamic gravity term including the gravity of platform, load and hydraulic cylinders is used to compensate the influence of gravity of parallel manipulator platform. 入电流矢量的伺服阀，动态重力项包括重力平台，负载和液压缸，用于补偿重力的影响，对并联机器人平台。
In analytical, the steady state errors converge asymptotically to zero, independent of load variation. 在分析，稳态误差渐近收敛于零，独立的负载变化。
The model-based controller, PD control with gravity compensation, is developed to reduce the effect of load variety of platform and eliminate steady state error of hydraulic driven parallel manipulator. 基于模型的控制器，控制重力补偿，以减少开发影响负载多种平台和消除稳态误差的液压驱动并联机器人。
MATHEMATICAL MODEL 数学模型The 6-DOF hydraulic driven parallel manipulator consist of a fixed base (down platform) and a moveable platform (upper platform) with six cylinders supporting it, all the cylinders are connected with movement platform and base with Hooke joints, as shown in Fig.1. 六自由度液压驱动并联机器人包括一个固定基地（下）和一个可移动的平台（平台）六缸支持它，所有气缸的运动平台和基地连接万向接头，如图1所示。
Figure 1. Hydraulic driven 6-DOF parallel manipulator 图1。
液压驱动六自由度并联机器人A. Kinematics ModelKinematics is the science of motion that treats the subject without regard to the forces that cause it [13], the kinematics of 6-DOF parallel manipulator include inverse kinematics and forward kinematics, forward kinematics is used to solve the generalized coordinates of A.运动学模型运动学是运动科学，对待这个问题没有考虑到的力量，因为它[ 13]，六自由度并联机器人的运动学逆运动学，包括运动学，运动学是用来解决广义坐标上平台与腿部的长度作为输入变量，正运动B. Dynamics ModelThe dynamics equations of the parallel manipulator are derived using Kane method, according to the theory, the active forces are equal to inertial forces, the dynamics state-space equation can be written byτ +G (Θ) =M (Θ) Θ+ V (Θ, Θ) Θ（3）B动力学模型并联机器人的动力学方程导出凯恩方法，根据理论，主动力等于惯性力，动态状态空间方程可以写的τ +G (Θ) =M (Θ) Θ+ V (Θ, Θ) Θ（3）The applied forces τ is transformed from mechanism actuator forces, which is given by τ=Jl T *Fa （4）应用部队τ转化机制的执行力，这是由τ=Jl T *Fa （4）where J l is a Jacobian 6×6 matrix of transformation between generalized velocity Θ of platform and protraction velocity l of hydraulic cylinders, and Fa is a 6×1 vector representing cylinder forces.The gravity term, G (Θ) , contains gravitational constantg and generalized coordinate Θ , it depends only on Θ , which can be described as G (Θ) =G p∑[(Juc,ai*Jai) T mu .g+(J dc,ai .J ai) T .m d .g)] （5）重力，G（Θ），包含引力常数G和广义坐标Θ，只取决于它Θ，可以描述为G (Θ) =G p ∑[(Juc,ai*Jai) Tmu .g+(J dc,ai .J ai) T .m d .g)] （5）where Gp is upper platform gravity item, G p =m p *(g,0) T , m p is the total mass of upper platform and load, and the 3×1 gravitational constant vector g =(0,0, g ) T , m u is the mass of piston, m d is the mass of hydraulic cylinder, J uc,ai is a Jacobian 3×3 matrix of velocity transformation between upper joints and the piston center of mass, J dc,ai is a Jacobian 3×3 matrix of velocity transformation between generalized velocity Θ and the hydraulic cylinder center of mass, and J ai, is is a Jacobian 3×6 matrix of velocity transformation between generalized velocity and upper joints G p是上平台重力项，G p=m p*(g,0) T,Mp是英国总质量上平台和负载，以及3×1重力常数r g =(0,0, g ) T，Mu 是质量是活塞，Md是液压缸的质量，J uc，ai是一个3×雅可比矩阵之间的转换3速度上和活塞质量中心，J dc，ai是一个3×3的雅可比矩阵之间的速度变换广义速度Θ和液压缸的质心，J ai，is是是一个3×雅可比矩阵之间的6速度变换广义速度和上接头CONTROL DESIGN 控制设计In 6-DOF hydraulic driven parallel manipulator, PID controller is applied to achieve tracking control of platform extensively, which is called Joint Space (JS) control scheme. 在六自由度液压驱动并联机器人，PID 控制可实现跟踪控制平台广泛，这是所谓的联合空间（JS）控制方案。
The JS uses mechanism inverse kinematics for computing desired cylinder length trajectories from desired Cartesian trajectories, see Fig. 2. JS利用机构逆运动学计算所需的气缸长度轨迹所需的笛卡尔轨迹，见图2。
Figure 2. Joint space control scheme for 6-DOF hydraulic Parallel manipulator platform图2。
关节空间控制方案的六自由度液压并联机器人平台The model-based controller considered the dynamic characteristic of parallel manipulator embedded the forward kinematics, dynamic gravity item and 基于模型的控制器是动态特性的并联机器人的运动学嵌入，动态重力项和反inverse of transfer of servovalve controlhydraulic cylinders and inverse of transpose of Jacobian matrix (J l T )−1 in inner control loop, see Fig. 3 转移的伺服阀控制液压缸和逆，转置雅可比矩阵(J l T )−1在内部控制回路中，见图3Figure 3. PD with gravity compensation control scheme for 6-DOF hydraulic driven parallel manipulator图3。
PD与具有重力补偿控制方案的六自由度液压驱动并联机器人The developed controller is extended to model-based control scheme allowing tracking of the reference inputs for platform 所设计的控制器扩展模型为基础的控制方案允许跟踪参考输入平台Desired position vector of hydraulic cylinders and actual position vector of hydraulic cylinders are used as input commands of the controller, and the controller provides the current sent to the servovale, the control law can be shown as u =(J l T ) -1*[( K p e K d e)--G (Θ) *V - ] (6) 理想的位置向量的液压缸，液压缸的实际位置向量是用来作为输入命令的控制器，与控制器提供当前发送到servovale，控制律可以证明u =(J l T ) -1*[( K p e K d e)--G (Θ) *V - ] (6)where u is the output 6×1 vector of the controller, Kp, Kd and Kd are control gain of system U是输出6×1矢量控制器，Kp，Kd和Kd是控制增益系统V is the transfer of the position of servovalve to the cylinder forces, e is the 6×1 cylinder length error of the upper platform, described as e =L d '−L' （7）V是转让的位置伺服阀的气缸，e是6×1缸长度误差的上平台，称为e =L d '−L' （7）where L d ' is the desired hydraulic cylinders position 6×1 vector, L' is the feedback hydraulic cylinder position 6×1 vector. L d '是理想的液压缸位置6×1矢量，L'是反馈的液压缸位置6×1矢量。