CN111168682B - Parallel robot and robust precise differentiator combined finite time convergence sliding mode control method - Google Patents

Parallel robot and robust precise differentiator combined finite time convergence sliding mode control method Download PDF

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CN111168682B
CN111168682B CN202010056924.9A CN202010056924A CN111168682B CN 111168682 B CN111168682 B CN 111168682B CN 202010056924 A CN202010056924 A CN 202010056924A CN 111168682 B CN111168682 B CN 111168682B
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高国琴
叶梦阳
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/003—Programme-controlled manipulators having parallel kinematics
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
    • B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1679—Programme controls characterised by the tasks executed

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Abstract

The invention discloses a finite time convergence sliding mode control method of a parallel robot for conveying combined with a robust accurate differentiator. Performing kinematic analysis on the parallel conveying robots and giving an expected motion track; a time delay estimation technology is adopted to obtain a dynamics model containing uncertain factors such as unknown dynamics, external interference and friction of the parallel robot for conveying on line in real time; aiming at a time delay estimation error generated by a time delay estimation technology, a finite time convergence robust accurate differentiator of a parallel robot system for conveying is designed for observation; further, a finite time convergence sliding mode controller is designed based on a feedforward compensation effect of a time delay estimation error observation value. And the limited time convergence sliding mode control of the parallel robot for conveying combined with the robust accurate differentiator feedforward compensation technology is realized through software programming. The method has obvious suppression effect on the sliding mode control buffeting, and the sliding mode variables and derivatives thereof are both limited in time and converged to the original point, so that the motion tracking precision is improved.

Description

并联机器人结合鲁棒精确微分器有限时间收敛滑模控制方法Finite-time convergent sliding mode control method for parallel robots combined with robust precise differentiators

技术领域technical field

本发明涉及一种输送用并联机器人，尤其涉及一种输送用并联机器人无模型结合鲁棒精确微分器有限时间收敛滑模控制方法。The invention relates to a parallel robot for conveying, in particular to a limited-time convergence sliding mode control method for a parallel robot for conveying which is model-free combined with a robust precise differentiator.

背景技术Background technique

为满足汽车涂装输送设备的工程应用需求，基于并联机构研制了一种输送用并联机器人，以克服现有采用悬臂梁串联结构的汽车电泳涂装输送设备承载能力不足、柔性化水平低的结构缺陷。该输送用并联机器人具有承载能力强、车型适用性广、定位精度高、末端构件运动惯量小、无累积误差且响应速度快等诸多优点。然而，输送用并联机器人的多支路闭链结构特点和各关节间的耦合关系也使其成为一种典型的多输入多输出、强耦合的复杂非线性系统。这类实际系统难以建立精确动力学模型，且实际运行时存在外界干扰、摩擦等不确定因素，使其运动控制问题成为控制研究领域的难点，而且直接关乎输送用并联机器人运行的稳定性和电泳涂装质量。In order to meet the engineering application requirements of automobile coating and conveying equipment, a parallel robot for conveying is developed based on the parallel mechanism to overcome the insufficient carrying capacity and low level of flexibility of the existing cantilever beam series structure of automobile electrophoretic coating conveying equipment. defect. The parallel robot for conveying has many advantages, such as strong carrying capacity, wide applicability of vehicle models, high positioning accuracy, small motion inertia of end components, no accumulated error and fast response speed. However, the multi-branch closed-chain structure and the coupling relationship between the joints of the parallel robot for conveying also make it a typical complex nonlinear system with multiple inputs and multiple outputs and strong coupling. This kind of actual system is difficult to establish an accurate dynamic model, and there are uncertain factors such as external interference and friction during actual operation, which makes the motion control problem a difficult point in the field of control research, and is directly related to the stability and electrophoresis of the parallel robot for transportation. paint quality.

文献《柔顺关节并联机器人动力学建模与控制研究》(天浩等，农业机械学报第45卷， 2014年5期，第278-283页)针对柔顺关节并联机器人采用拉格朗日法建立动力学模型，并设计了趋近律滑模控制器抑制系统不确定因素。该方法存在两个不足：(1)该控制方法要首先建立并联机器人的动力学模型，计算量大；(2)趋近律滑模控制的控制律存在不连续的符号函数，导致滑模控制抖振。The paper "Research on Dynamics Modeling and Control of Parallel Robot with Compliant Joints" (Tian Hao et al., Chinese Journal of Agricultural Machinery, Vol. 45, No. 5, 2014, pp. 278-283) uses Lagrangian method to establish power for compliant-joint parallel robots The learning model is used, and a reaching law sliding mode controller is designed to suppress the uncertain factors of the system. This method has two shortcomings: (1) the control method needs to establish the dynamic model of the parallel robot first, which requires a large amount of calculation; (2) the control law of the reaching law sliding mode control has a discontinuous sign function, which leads to the sliding mode control. chattering.

文献《混联式汽车电泳涂装输送机构的时延估计自适应滑模控制》(高国琴等，汽车工程第40卷，2018年12期，第1405-1412页)针对混联式汽车电泳涂装输送机构，设计了一种时延估计自适应滑模控制方法。该方法存在如下不足：(1)该控制方法直接采用滑模控制克服时延估计误差等不确定因素的影响，导致所需控制量大，且大的切换增益易加剧滑模控制抖振；(2)该控制方法引入自适应规则调整控制切换增益，但由于得到的滑模控制律仍然不连续，因此对滑模控制抖振的抑制能力有限，且自适应参数在实际应用时不易调整。(3)该控制方法属于一阶滑模控制，仅能保证滑模变量的收敛性。The document "Time Delay Estimation Adaptive Sliding Mode Control of Conveyor Mechanism for Hybrid Automobile Electrophoretic Coating" (Gao Guoqin et al., Automotive Engineering Vol. 40, No. 12, 2018, pp. 1405-1412) is aimed at hybrid automobile electrophoretic coating. Conveying mechanism, a time delay estimation adaptive sliding mode control method is designed. This method has the following shortcomings: (1) The control method directly adopts sliding mode control to overcome the influence of uncertain factors such as time delay estimation error, resulting in a large amount of required control, and a large switching gain is easy to aggravate the chattering of sliding mode control; ( 2) This control method introduces an adaptive rule to adjust the control switching gain, but because the obtained sliding-mode control law is still discontinuous, the ability to suppress chattering in sliding-mode control is limited, and the adaptive parameters are not easy to adjust in practical applications. (3) This control method belongs to the first-order sliding mode control, which can only guarantee the convergence of the sliding mode variables.

发明内容SUMMARY OF THE INVENTION

为克服现有技术的不足，本发明针对输送用并联机器人，建立时延估计动力学模型，提出一种结合鲁棒精确微分器前馈补偿技术的有限时间收敛滑模控制方法。该控制方法在无需系统动力学模型和不确定信息的前提下，首先设计输送用并联机器人系统的鲁棒精确微分器对时延估计误差进行有限时间精确观测并前馈补偿，然后设计输送用并联机器人系统的有限时间收敛光滑二阶滑模控制律，不仅能显著削弱滑模控制抖振，而且使得滑模变量及其导数均有限时间收敛至原点，有效提高输送用并联机器人控制系统的鲁棒性，利于实现其高精度轨迹跟踪控制。In order to overcome the deficiencies of the prior art, the present invention establishes a time delay estimation dynamic model for a parallel robot for conveying, and proposes a finite time convergence sliding mode control method combined with a robust accurate differentiator feedforward compensation technology. The control method does not require system dynamics model and uncertain information. First, a robust accurate differentiator of the parallel robot system for conveying is designed to accurately observe the delay estimation error in a limited time and feedforward compensation. The finite-time convergence smooth second-order sliding-mode control law of the robot system can not only significantly reduce the chattering of the sliding-mode control, but also make the sliding-mode variables and their derivatives converge to the origin in a finite time, effectively improving the robustness of the parallel robot control system for conveying. It is beneficial to realize its high-precision trajectory tracking control.

本发明的技术方案为：一种输送用并联机器人无模型结合鲁棒精确微分器前馈补偿技术的有限时间收敛滑模控制方法，包括如下步骤：The technical scheme of the present invention is: a finite-time convergence sliding mode control method of a parallel robot for conveying, which is model-free and combined with a robust accurate differentiator feedforward compensation technology, comprising the following steps:

1)以输送用并联机器人为被控对象，采用解析法对输送用并联机器人进行运动学逆解分析，进一步求得其运动学正解和雅克比矩阵；1) Taking the parallel robot for conveying as the controlled object, the inverse kinematics analysis of the parallel robot for conveying is carried out by analytical method, and the positive kinematic solution and Jacobian matrix are further obtained;

2)根据汽车电泳涂装工艺要求，设计输送用并联机器人连接杆中点的期望运动轨迹，并结合运动学逆解求得主动关节的期望运动轨迹；2) According to the requirements of the automotive electrophoretic coating process, the desired motion trajectory of the midpoint of the connecting rod of the parallel robot for conveying is designed, and the desired motion trajectory of the active joint is obtained by combining the inverse kinematics solution;

3)采用时延估计技术实时在线获取输送用并联机器人包含未知动力学、外界干扰和摩擦等不确定因素的动力学模型；3) Using the time delay estimation technology to obtain the dynamic model of the parallel robot for conveying in real time, including uncertain factors such as unknown dynamics, external interference and friction;

4)针对步骤3)中时延估计技术产生的时延估计误差，设计一种输送用并联机器人系统的鲁棒精确微分器在有限时间内对其进行观测；4) Aiming at the time delay estimation error generated by the time delay estimation technique in step 3), a robust and precise differentiator of the parallel robot system for conveying is designed to observe it in a limited time;

5)基于步骤3)和步骤4)，利用鲁棒精确微分器得到的观测值进行前馈补偿，设计一种输送用并联机器人无模型结合鲁棒精确微分器前馈补偿技术的有限时间收敛滑模控制器；5) Based on step 3) and step 4), use the observation value obtained by the robust precise differentiator to perform feedforward compensation, and design a model-free parallel robot for conveying combined with the robust precise differentiator feedforward compensation technology. model controller;

6)采用分布式结构构建输送用并联机器人无模型结合鲁棒精确微分器前馈补偿技术的有限时间收敛滑模控制系统；6) A distributed structure is used to construct a finite-time convergent sliding mode control system with a model-free parallel robot for conveying combined with a robust accurate differentiator feedforward compensation technology;

7)将计算所得的输送用并联机器人各主动关节控制量发送至各电机驱动器，使其按期望轨迹运动。7) Send the calculated control quantities of each active joint of the parallel robot for conveying to each motor driver to make it move according to the desired trajectory.

进一步，所述步骤1)中，对运动学逆解方程两端进行求导，即得：Further, in the described step 1), the two ends of the kinematics inverse solution equation are derived to obtain:

Figure GDA0003475610710000021
Figure GDA0003475610710000021

式中，J即为输送用并联机器人系统的雅克比矩阵；

Figure GDA0003475610710000022
是输送用并联机器人主动关节位姿矢量，其中x1，x2，x3，x4分别表示输送用并联机器人四个滑块的位移，
Figure GDA0003475610710000023
分别表示输送用并联机器人两个主动轮的旋转角度，
Figure GDA0003475610710000024
是主动关节速度矢量；
Figure GDA0003475610710000025
是连接杆中点速度矢量。In the formula, J is the Jacobian matrix of the parallel robot system for conveying;
Figure GDA0003475610710000022
is the active joint pose vector of the parallel robot for conveying, where x 1 , x 2 , x 3 , and x 4 represent the displacements of the four sliders of the parallel robot for conveying, respectively.
Figure GDA0003475610710000023
respectively represent the rotation angles of the two driving wheels of the conveying parallel robot,
Figure GDA0003475610710000024
is the active joint velocity vector;
Figure GDA0003475610710000025
is the velocity vector at the midpoint of the connecting rod.

进一步，步骤2)中，根据汽车白车身入槽、翻转、出槽的电泳涂装工艺要求，确定输送用并联机器人连接杆中点的期望运动轨迹为xd＝(zd，βd)T，其中，zd为连接杆中点在Z 方向的期望位移，βd为末端执行器绕Y轴逆时针旋转的期望角度，结合运动学逆解方程，进一步求得主动关节的期望运动轨迹

Figure GDA0003475610710000031
其中xd1，xd2，xd3，xd4分别表示输送用并联机器人四个滑块的期望位移，
Figure GDA0003475610710000032
分别表示输送用并联机器人两个主动轮的期望旋转角度。Further, in step 2), according to the electrophoretic coating process requirements of the car body-in-white entering the tank, turning over, and exiting the tank, determine the desired motion trajectory of the midpoint of the connecting rod of the parallel robot for conveying as x d =(z d , β d ) T , where z d is the expected displacement of the midpoint of the connecting rod in the Z direction, β d is the expected counterclockwise rotation angle of the end effector around the Y axis, and the desired motion trajectory of the active joint is further obtained by combining the kinematic inverse equations
Figure GDA0003475610710000031
where x d1 , x d2 , x d3 , x d4 respectively represent the expected displacement of the four sliders of the parallel robot for conveying,
Figure GDA0003475610710000032
respectively represent the expected rotation angles of the two driving wheels of the parallel robot for conveying.

进一步，所述步骤3)的具体过程为：Further, the concrete process of described step 3) is:

输送用并联机器人动力学模型的一般形式为：The general form of the dynamic model of the parallel robot for conveying is:

Figure GDA0003475610710000033
Figure GDA0003475610710000033

式中，M(q)为对称正定的惯性矩阵；

Figure GDA0003475610710000034
为哥氏力和离心力项；G(q)为重力项(单位 N.m)；
Figure GDA0003475610710000035
为摩擦力项(单位N.m)；τd为外界干扰项(单位N.m)；τ为控制力矩矢量(单位N.m)；where M(q) is a symmetric positive definite inertia matrix;
Figure GDA0003475610710000034
is the term of Coriolis force and centrifugal force; G(q) is the term of gravity (unit Nm);
Figure GDA0003475610710000035
is the friction term (unit Nm); τ d is the external disturbance term (unit Nm); τ is the control torque vector (unit Nm);

为应用时延估计技术，引入正定常数对角阵

Figure GDA0003475610710000036
将动力学模型(1)简写为：In order to apply the delay estimation technique, a positive definite constant diagonal matrix is introduced
Figure GDA0003475610710000036
The kinetic model (1) is abbreviated as:

Figure GDA0003475610710000037
Figure GDA0003475610710000037

式中，

Figure GDA0003475610710000038
表示包含输送用并联机器人非线性未知动力学、外界干扰和摩擦等不确定因素的动力学信息项；In the formula,
Figure GDA0003475610710000038
Represents the dynamic information item containing uncertain factors such as nonlinear unknown dynamics, external disturbance and friction of the parallel robot for conveying;

采用时延估计技术实时在线获取输送用并联机器人系统动力学信息为：The dynamic information of the parallel robot system for conveying is obtained online in real time by using the time delay estimation technology as follows:

Figure GDA0003475610710000039
Figure GDA0003475610710000039

式中，

Figure GDA00034756107100000310
是
Figure GDA00034756107100000311
的时延估计值；带下标t-η的上述变量表示此时刻变量的值，即变量的时滞值，其中η是延迟时间，η最小值可设置为采样周期。In the formula,
Figure GDA00034756107100000310
Yes
Figure GDA00034756107100000311
The above-mentioned variable with subscript t-η represents the value of the variable at this moment, that is, the time delay value of the variable, where η is the delay time, and the minimum value of η can be set as the sampling period.

进一步，所述步骤4)中，设计一种输送用并联机器人系统的鲁棒精确微分器在有限时间内观测时延估计误差：Further, in the step 4), a robust and precise differentiator of the parallel robot system for conveying is designed to observe the time delay estimation error in a limited time:

采用时延估计技术在线获取输送用并联机器人动力学模型时，由于使用上一时刻采样值近似输送用并联机器人系统非线性项和不确定项的当前值会产生时延估计误差，其表达式为：When using the time delay estimation technology to obtain the dynamic model of the parallel robot for transportation online, the time delay estimation error will occur due to the use of the sampling value at the previous moment to approximate the current values of the nonlinear and uncertain terms of the parallel robot system for transportation, and its expression is: :

Figure GDA0003475610710000041
Figure GDA0003475610710000041

其中，

Figure GDA0003475610710000042
为正定常数对角矩阵，N∈R6表示包含输送用并联机器人非线性未知动力学、外界干扰和摩擦等不确定因素的动力学信息项，
Figure GDA0003475610710000043
是N的时延估计值；in,
Figure GDA0003475610710000042
is a positive definite constant diagonal matrix, N ∈ R 6 represents the dynamic information item containing uncertain factors such as nonlinear unknown dynamics, external disturbance and friction of the parallel robot for conveying,
Figure GDA0003475610710000043
is the delay estimate of N;

设

Figure GDA0003475610710000044
和
Figure GDA0003475610710000045
分别为输送用并联机器人主动关节的实际运动轨迹和期望运动轨迹，定义输送用并联机器人主动关节轨迹跟踪误差为：Assume
Figure GDA0003475610710000044
and
Figure GDA0003475610710000045
are the actual motion trajectory and the expected motion trajectory of the active joint of the parallel robot for conveying, respectively, and define the trajectory tracking error of the active joint of the parallel robot for conveying as:

e(t)＝q(t)-qd(t)e(t)=q(t)-q d (t)

选取输送用并联机器人无模型结合鲁棒精确微分器有限时间收敛滑模控制的滑模变量为：The sliding mode variable for the finite-time convergence sliding mode control of the parallel robot for conveying is selected as follows:

Figure GDA0003475610710000046
Figure GDA0003475610710000046

式中，A是正定对角矩阵；where A is a positive definite diagonal matrix;

为得到输送用并联机器人非线性项和不确定项的时延估计误差ε的有限时间观测值，设计输送用并联机器人系统的鲁棒精确微分器为：In order to obtain the finite-time observation value of the delay estimation error ε of the nonlinear terms and uncertain terms of the parallel robot for transportation, the robust and accurate differentiator of the parallel robot system for transportation is designed as:

Figure GDA0003475610710000047
Figure GDA0003475610710000047

式中，u为虚拟控制律，z0，z1，z2∈R6，z1是ε的观测值，z1将在有限时间内收敛到ε；vj∈R6，j＝0，1，2；；λi＝diag(λi1，λi2，…，λi6)，(i＝0，1，2)；L＝diag(l1，l2，…，l6)是

Figure GDA0003475610710000048
的Lipshitz常数且li＞0，
Figure GDA0003475610710000049
设x＝(x1，…，xn)T，定义符号sign(x)＝(sign(x1)，…，sign(xn))T，|x|qsign(x)＝(|x1|qsign(x1)，…，|xn|qsign(xn))T。where u is the virtual control law, z 0 , z 1 , z 2 ∈ R 6 , z 1 is the observed value of ε, z 1 will converge to ε in a finite time; v j ∈ R 6 , j=0, 1, 2; λ i =diag(λ i1 ,λ i2 ,...,λ i6 ),(i=0,1,2); L=diag(l 1 ,l 2 ,...,l 6 ) is
Figure GDA0003475610710000048
The Lipshitz constant of and li > 0,
Figure GDA0003475610710000049
Let x=(x 1 ,..., x n ) T , define the sign sign(x) = (sign(x 1 ),..., sign(x n )) T , |x| 1 | q sign(x 1 ), …, |x n | q sign(x n )) T .

进一步，所述步骤5)中，利用输送用并联机器人系统的鲁棒精确微分器得到的有限时间观测值z1进行前馈补偿，设计无模型有限时间收敛滑模控制的虚拟控制律u为：Further, in the step 5), the finite-time observation value z 1 obtained by the robust precise differentiator of the parallel robot system for conveying is used to perform feedforward compensation, and the virtual control law u of the model-free finite-time convergence sliding mode control is designed as:

Figure GDA00034756107100000410
Figure GDA00034756107100000410

式中，m≥1，α1＝diag(α11，α12，…，α16)，α2＝diag(α21，α22，…，α26)，w是设计虚拟控制律u 时引入的中间变量。In the formula, m≥1, α 1 =diag(α 11 ,α 12 ,...,α 16 ), α 2 =diag(α 21 ,α 22 ,...,α 26 ), and w is introduced when designing the virtual control law u intermediate variable.

进一步，还包括：Further, it also includes:

在无模型有限时间收敛滑模控制的虚拟控制律u和输送用并联机器人系统鲁棒精确微分器所得观测值z1对时延估计误差ε的前馈补偿作用下，滑模变量s的动态为：Under the feedforward compensation of the time delay estimation error ε by the virtual control law u of the model-free finite-time convergent sliding mode control and the observation value z 1 obtained by the robust precise differentiator of the conveying parallel robot system, the dynamic of the sliding mode variable s is :

Figure GDA0003475610710000051
Figure GDA0003475610710000051

由于上述无模型结合鲁棒精确微分器有限时间收敛滑模控制的滑模变量动态系统有限时间稳定，故其滑模变量及其导数均有限时间收敛至原点，而且由于

Figure GDA0003475610710000052
是连续的，故虚拟控制律u不仅连续，而且光滑。Since the above-mentioned sliding mode variable dynamic system with finite time convergence sliding mode control of the model-free and robust exact differentiator is stable in finite time, its sliding mode variables and their derivatives converge to the origin in finite time, and due to the finite time
Figure GDA0003475610710000052
is continuous, so the virtual control law u is not only continuous, but also smooth.

进一步，所述步骤5)中还包括，在无需输送用并联机器人动力学模型和系统不确定性信息的情形下，基于输送用并联机器人时延估计动力学模型，根据无模型有限时间收敛滑模控制的虚拟控制律u，设计一种无模型结合鲁棒精确微分器前馈补偿技术的有限时间收敛滑模控制律τ为：Further, the step 5) also includes, without the need for the dynamic model of the parallel robot for conveying and the system uncertainty information, based on the time delay of the parallel robot for conveying The dynamic model is estimated, and the sliding mode converges according to the model-free finite time. The virtual control law u of the control, a finite-time convergent sliding-mode control law τ with a model-free combination of the robust accurate differentiator feedforward compensation technique is designed as:

Figure GDA0003475610710000053
Figure GDA0003475610710000053

本发明首次提出一种输送用并联机器人无模型结合鲁棒精确微分器前馈补偿技术的有限时间收敛滑模控制方法，以实现输送用并联机器人的高精度轨迹跟踪控制。其特点和有益效果是：The present invention firstly proposes a finite-time convergence sliding mode control method of a model-free parallel robot for conveying combined with a robust accurate differentiator feedforward compensation technology, so as to realize the high-precision trajectory tracking control of the parallel robot for conveying. Its characteristics and beneficial effects are:

1)由于采用时延估计技术在线获取包含未知动力学、外界干扰和摩擦等不确定因素的系统动力学信息，因此无需建立输送用并联机器人动力学模型。1) Since the time-delay estimation technology is used to obtain system dynamics information including unknown dynamics, external disturbances, friction and other uncertain factors online, there is no need to establish a dynamic model of a parallel robot for conveying.

2)由于设计输送用并联机器人系统的鲁棒精确微分器进行前馈补偿，可以在有限时间内得到时延估计误差的精确观测值，以抑制输送用并联机器人非线性和不确定性的时延估计误差对控制性能的影响，从而提高系统鲁棒性；2) Due to the design of the robust and precise differentiator of the conveying parallel robot system for feedforward compensation, the accurate observation value of the delay estimation error can be obtained in a limited time, so as to suppress the nonlinear and uncertain delay of the conveying parallel robot. Estimate the effect of error on control performance, thereby improving system robustness;

3)设计一种输送用并联机器人系统的有限时间收敛光滑二阶滑模控制律，提高系统鲁棒性同时削弱滑模控制抖振，而且二阶滑模算法使得滑模变量及其导数均有限时间收敛到原点。因此，该方法在实际应用时能有效提高输送用并联机器人的运动跟踪控制性能。3) Design a finite-time convergent smooth second-order sliding-mode control law for a parallel robot system for conveying, which improves the robustness of the system and weakens the chattering of the sliding-mode control. Moreover, the second-order sliding-mode algorithm makes the sliding-mode variables and their derivatives limited. Time converges to the origin. Therefore, the method can effectively improve the motion tracking control performance of the parallel robot for conveying in practical application.

附图说明Description of drawings

以下结合附图和具体实施方式对本发明作进一步详细说明。The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

图1是输送用并联机器人结构简图。Figure 1 is a schematic structural diagram of a parallel robot for conveying.

图2是结合鲁棒精确微分器前馈补偿技术的有限时间收敛滑模控制系统原理图。Figure 2 is a schematic diagram of a finite-time convergent sliding-mode control system combined with a robust accurate differentiator feedforward compensation technique.

图3是升降翻转输送机构结构简图。Figure 3 is a schematic structural diagram of the lifting and turning conveying mechanism.

图4是输送用并联机器人样机系统及控制系统硬件平台。Figure 4 shows the parallel robot prototype system and control system hardware platform for conveying.

图5是各主动关节轨迹跟踪曲线。其中，图5中的(a)是第一滑块轨迹跟踪曲线，图5中的(b) 是第二滑块轨迹跟踪曲线，图5中的(c)是第一主动轮轨迹跟踪曲线。Fig. 5 is the trajectory tracking curve of each active joint. 5(a) is the first slider track tracking curve, FIG. 5(b) is the second slider track tracking curve, and FIG. 5(c) is the first capstan track tracking curve.

图6是各主动关节轨迹跟踪误差曲线。其中，图6中的(a)是第一滑块轨迹跟踪误差曲线，图6中的(b)是第二滑块轨迹跟踪误差曲线，图6中的(c)是第一主动轮轨迹跟踪误差曲线。FIG. 6 is the tracking error curve of each active joint trajectory. Among them, (a) in FIG. 6 is the tracking error curve of the first slider track, (b) in FIG. 6 is the tracking error curve of the second slider track, and (c) in FIG. 6 is the track tracking of the first driving wheel error curve.

图7是各主动关节对应电机驱动力矩。其中，图7中的(a)是第一滑块对应电机驱动力矩，图7中的(b)是第二滑块对应电机驱动力矩，图7中的(c)是第一主动轮对应电机驱动力矩。FIG. 7 is the motor driving torque corresponding to each active joint. Among them, (a) in FIG. 7 is the driving torque of the first slider corresponding to the motor, (b) in FIG. 7 is the driving torque corresponding to the motor of the second sliding block, and (c) in FIG. 7 is the motor corresponding to the first driving wheel driving torque.

图8是时延估计误差观测曲线。其中，图8中的(a)是时延估计误差第一分量的观测曲线，图8中的(b)是时延估计误差第二分量的观测曲线，图8中的(c)是时延估计误差第五分量的观测曲线。Fig. 8 is an observation curve of delay estimation error. Among them, (a) in Figure 8 is the observation curve of the first component of the delay estimation error, (b) in Figure 8 is the observation curve of the second component of the delay estimation error, and (c) in Figure 8 is the time delay The observed curve of the fifth component of the estimation error.

图1中：1.导轨2.底座3.行走驱动电机4.减速机5.移动滑块6.升降驱动电机7.连杆 8.从动轮9.主动轮10.连接杆11.车体12.翻转驱动电机13.电动缸In Figure 1: 1. Guide rail 2. Base 3. Walking drive motor 4. Reducer 5. Moving slider 6. Lifting drive motor 7. Connecting rod 8. Driven wheel 9. Driving wheel 10. Connecting rod 11. Car body 12 . Flip drive motor 13. Electric cylinder

具体实施方式Detailed ways

下面结合附图进一步说明本发明具体实施方式。The specific embodiments of the present invention will be further described below with reference to the accompanying drawings.

如图1-3所示，其中图1中各部件分别为：1.导轨2.底座3.行走驱动电机4.减速机5.移动滑块6.升降驱动电机7.连杆8.从动轮9.主动轮10.连接杆11.车体12.翻转驱动电机13.电动缸。首先，针对输送用并联机器人，采用解析法对其进行运动学逆解分析，进一步求得其运动学正解和雅克比矩阵；其次，根据汽车电泳涂装工艺要求，确定输送用并联机器人连接杆中点的期望运动轨迹，并结合运动学逆解求得主动关节期望运动轨迹；然后，采用时延估计技术获取并补偿输送用并联机器人系统中的非线性项和不确定项等未知动力学信息；进一步，设计一种输送用并联机器人系统的鲁棒精确微分器观测时延估计误差，提出一种输送用并联机器人无模型结合鲁棒精确微分器前馈补偿技术的有限时间收敛滑模控制方法；接着，采用分布式结构构建输送用并联机器人无模型结合鲁棒精确微分器前馈补偿技术的有限时间收敛滑模控制系统；最后，将计算得到的输送用并联机器人各主动关节的驱动控制量发送至各电机驱动器，以实现期望运动。具体方法如下：As shown in Figure 1-3, the components in Figure 1 are: 1. Guide rail 2. Base 3. Walking drive motor 4. Reducer 5. Moving slider 6. Lifting drive motor 7. Connecting rod 8. Driven wheel 9. Driving wheel 10. Connecting rod 11. Car body 12. Turning drive motor 13. Electric cylinder. Firstly, the inverse kinematics analysis of the parallel robot for conveying is carried out by analytical method, and its positive kinematics solution and Jacobian matrix are further obtained; The desired motion trajectory of the point is obtained and combined with the inverse kinematics solution to obtain the desired motion trajectory of the active joint; then, the time delay estimation technique is used to obtain and compensate the unknown dynamic information such as nonlinear terms and uncertain terms in the parallel robot system for conveying; Furthermore, a robust and precise differentiator for conveying parallel robot system is designed to observe the time delay estimation error, and a finite-time convergence sliding mode control method is proposed, which combines model-free parallel robot for conveying with robust precise differentiator feedforward compensation technology. Then, a distributed structure is used to construct a finite-time convergent sliding mode control system of the parallel robot for conveying, which is model-free and combined with robust accurate differentiator feedforward compensation technology. Finally, the calculated driving control variables of each active joint of the parallel robot for conveying are sent to to each motor drive to achieve the desired motion. The specific method is as follows:

1、采用解析法对输送用并联机器人进行运动学逆解分析，进一步求得其运动学正解和雅克比矩阵。1. The inverse kinematics analysis of the parallel robot for conveying is carried out by the analytical method, and the positive kinematics solution and Jacobian matrix are further obtained.

选取输送用并联机器人连接杆中点的位姿参数x＝(z，β)T作为系统广义坐标，其中，z (单位m)为连接杆中点在Z方向的位移，β(单位rad)为末端执行器绕Y轴逆时针旋转的角度。采用解析法对输送用并联机器人进行运动学逆解分析，求得位置逆解方程，对其求逆即得运动学正解。进一步，对运动学逆解方程两端进行求导，即得Select the pose parameter x=(z, β) T of the midpoint of the connecting rod of the parallel robot for conveying as the generalized coordinate of the system, where z (unit m) is the displacement of the midpoint of the connecting rod in the Z direction, β (unit rad) is The angle that the end effector rotates counterclockwise around the Y axis. Analytical method is used to analyze the kinematic inverse solution of the parallel robot for conveying, and the position inverse solution equation is obtained, and the inverse kinematics solution is obtained. Further, derivation of both ends of the kinematic inverse solution equation, that is,

Figure GDA0003475610710000071
Figure GDA0003475610710000071

式中，J即为输送用并联机器人系统的雅克比矩阵；

Figure GDA0003475610710000072
是输送用并联机器人主动关节位姿矢量，
Figure GDA0003475610710000073
是主动关节速度矢量；
Figure GDA0003475610710000074
是连接杆中点速度矢量。In the formula, J is the Jacobian matrix of the parallel robot system for conveying;
Figure GDA0003475610710000072
is the active joint pose vector of the parallel robot for conveying,
Figure GDA0003475610710000073
is the active joint velocity vector;
Figure GDA0003475610710000074
is the velocity vector at the midpoint of the connecting rod.

2、根据汽车电泳涂装工艺要求，设计输送用并联机器人连接杆中点的期望运动轨迹，并结合运动学逆解求得主动关节的期望运动轨迹。2. According to the requirements of the automotive electrophoretic coating process, the desired motion trajectory of the midpoint of the connecting rod of the parallel robot for conveying is designed, and the desired motion trajectory of the active joint is obtained by combining the inverse kinematics solution.

根据汽车白车身入槽、翻转、出槽的电泳涂装工艺要求，确定输送用并联机器人连接杆中点的期望运动轨迹xd＝(zd，βd)T，其中，zd(单位m)为连接杆中点在Z方向的期望位移，βd(单位rad)为末端执行器绕Y轴逆时针旋转的期望角度。结合运动学逆解方程，进一步求得主动关节的期望运动轨迹

Figure GDA0003475610710000075
(xdi单位m，
Figure GDA0003475610710000076
单位 rad)。According to the electrophoretic coating process requirements of the car body-in-white into the tank, turning over and out of the tank, determine the desired motion trajectory x d = (z d , β d ) T of the midpoint of the connecting rod of the parallel robot for conveying, where z d (unit m ) is the desired displacement of the midpoint of the connecting rod in the Z direction, and β d (in rad) is the desired angle of counterclockwise rotation of the end effector about the Y axis. Combined with the inverse kinematics solution equation, the desired motion trajectory of the active joint is further obtained
Figure GDA0003475610710000075
(x di unit m,
Figure GDA0003475610710000076
unit rad).

3、采用时延估计技术实时在线获取输送用并联机器人包含未知动力学、外界干扰和摩擦等不确定因素的动力学模型。3. The time delay estimation technology is used to obtain the dynamic model of the parallel robot for conveying in real time, including uncertain factors such as unknown dynamics, external interference and friction.

输送用并联机器人动力学模型的一般形式为：The general form of the dynamic model of the parallel robot for conveying is:

Figure GDA0003475610710000077
Figure GDA0003475610710000077

式中，M(q)为对称正定的惯性矩阵；

Figure GDA0003475610710000078
为哥氏力和离心力项；G(q)为重力项(单位 N.m)；
Figure GDA0003475610710000079
为摩擦力项(单位N.m)；τd为外界干扰项(单位N.m)；τ为控制力矩矢量(单位N.m)。where M(q) is a symmetric positive definite inertia matrix;
Figure GDA0003475610710000078
is the term of Coriolis force and centrifugal force; G(q) is the term of gravity (unit Nm);
Figure GDA0003475610710000079
is the friction term (unit Nm); τ d is the external disturbance term (unit Nm); τ is the control torque vector (unit Nm).

为应用时延估计技术，引入正定常数对角阵

Figure GDA0003475610710000081
将动力学模型(1)简写为：In order to apply the delay estimation technique, a positive definite constant diagonal matrix is introduced
Figure GDA0003475610710000081
The kinetic model (1) is abbreviated as:

Figure GDA0003475610710000082
Figure GDA0003475610710000082

式中，

Figure GDA0003475610710000083
(单位N.m)表示包含输送用并联机器人非线性未知动力学、外界干扰和摩擦等不确定因素的动力学信息项。In the formula,
Figure GDA0003475610710000083
(unit Nm) represents the dynamic information item including uncertain factors such as nonlinear unknown dynamics, external disturbance and friction of the parallel robot for conveying.

采用时延估计技术实时在线获取输送用并联机器人系统动力学信息为：The dynamic information of the parallel robot system for conveying is obtained online in real time by using the time delay estimation technology as follows:

Figure GDA0003475610710000084
Figure GDA0003475610710000084

式中，

Figure GDA0003475610710000085
(单位N.m)是
Figure GDA0003475610710000086
的时延估计值，η(单位s)是延迟时间，η最小可设置为采样周期。In the formula,
Figure GDA0003475610710000085
(unit Nm) is
Figure GDA0003475610710000086
The delay estimate value of , η (unit s) is the delay time, and the minimum η can be set to the sampling period.

4、针对时延估计技术产生的时延估计误差，设计一种输送用并联机器人系统的鲁棒精确微分器在有限时间内对其进行观测。4. Aiming at the time-delay estimation error produced by time-delay estimation technology, a robust and precise differentiator for conveying parallel robot system is designed to observe it in a limited time.

时延估计技术由于采用时滞值

Figure GDA0003475610710000087
代替系统动力学信息项
Figure GDA0003475610710000088
由此产生的时延估计误差为：Delay estimation technique due to the use of delay value
Figure GDA0003475610710000087
In lieu of the system dynamics information item
Figure GDA0003475610710000088
The resulting delay estimation error is:

Figure GDA0003475610710000089
Figure GDA0003475610710000089

将动力学模型(2)两边同乘

Figure GDA00034756107100000810
并将式(4)代入，可得
Figure GDA00034756107100000815
的表达式为：Multiply both sides of the dynamic model (2)
Figure GDA00034756107100000810
Substitute into formula (4), we can get
Figure GDA00034756107100000815
The expression is:

Figure GDA00034756107100000811
Figure GDA00034756107100000811

式中，

Figure GDA00034756107100000812
(单位N.m)表示虚拟控制律，则实际控制律为：In the formula,
Figure GDA00034756107100000812
(unit Nm) represents the virtual control law, then the actual control law is:

Figure GDA00034756107100000813
Figure GDA00034756107100000813

定义主动关节的轨迹跟踪误差为：The trajectory tracking error of the active joint is defined as:

e＝q-qd e=qq d

选取滑模变量为：The sliding mode variables are selected as:

Figure GDA00034756107100000814
Figure GDA00034756107100000814

式中，A是正定对角矩阵。where A is a positive definite diagonal matrix.

对式(8)中s关于时间求导，并将式(5)代入可得：Derivation of s in equation (8) with respect to time, and substituting equation (5) into equation (5) can be obtained:

Figure GDA0003475610710000091
Figure GDA0003475610710000091

根据式(9)，设计鲁棒精确微分器对时延估计误差ε进行观测：According to equation (9), a robust accurate differentiator is designed to observe the delay estimation error ε:

Figure GDA0003475610710000092
Figure GDA0003475610710000092

式中，z0，z1，z2∈R6，z1(单位N.m)是ε的观测值，z1将在有限时间内收敛到ε(单位N.m)； vj∈R6，j＝0，1，2；；λi＝diag(λi1，λi2，…，λi6)，(i＝0，1，2)；L＝diag(l1，l2，…，l6)是

Figure GDA0003475610710000093
(单位N.m/s) 的Lipshitz常数且li＞0，
Figure GDA0003475610710000094
设 x＝(x1，…，xn)T，定义符号sign(x)＝(sign(x1)，…，sign(xn))T， |x|qsign(x)＝(|x1|qsign(x1)，…，|xn|qsign(xn))T。In the formula, z 0 , z 1 , z 2 ∈ R 6 , z 1 (unit Nm) is the observed value of ε, z 1 will converge to ε (unit Nm) in a finite time; v j ∈ R 6 , j= 0, 1, 2; λ i =diag(λ i1 ,λ i2 ,...,λ i6 ),(i=0,1,2); L=diag(l 1 ,l 2 ,...,l 6 ) is
Figure GDA0003475610710000093
(unit Nm/ s ) Lipshitz constant and li > 0,
Figure GDA0003475610710000094
Let x=(x 1 ,..., x n ) T , define the sign sign(x) = (sign(x 1 ),..., sign(x n )) T , |x| 1 | q sign(x 1 ), …, |x n | q sign(x n )) T .

设观测误差σ0＝z0-s，σ1＝z1-ε，

Figure GDA0003475610710000095
则由(9)(10)两式得到观测误差动态：Let the observation error σ 0 =z 0 -s, σ 1 =z 1 -ε,
Figure GDA0003475610710000095
Then the observation error dynamics can be obtained from the equations (9) and (10):

Figure GDA0003475610710000096
Figure GDA0003475610710000096

则σ0，σ1，σ2将在有限时间内收敛至0。因此，z1在有限时间内收敛到时延估计误差ε的值。Then σ 0 , σ 1 , σ 2 will converge to 0 in a finite time. Therefore, z 1 converges to the value of the delay estimation error ε in a finite time.

5、基于时延估计误差ε(单位N.m)的有限时间观测值z1(单位N.m)，并结合式(6)，设计输送用并联机器人无模型结合鲁棒精确微分器前馈补偿技术的有限时间收敛滑模控制器为：5. Based on the finite-time observation value z 1 (unit Nm) of the delay estimation error ε (unit Nm), and combined with equation (6), the model-free parallel robot for conveying combined with the robust accurate differentiator feedforward compensation technology is designed. The time-convergent sliding mode controller is:

Figure GDA0003475610710000097
Figure GDA0003475610710000097

式中，m≥1，α1＝diag(α11，α12，…，α16)，α2＝diag(α21，α22，…，α26)。In the formula, m≥1, α 1 =diag(α 11 ,α 12 ,...,α 16 ), and α 2 =diag(α 21 ,α 22 ,...,α 26 ).

6、采用分布式结构构建输送用并联机器人无模型结合鲁棒精确微分器前馈补偿技术的有限时间收敛滑模控制系统。6. The distributed structure is used to construct a finite-time convergent sliding mode control system with a model-free parallel robot for conveying combined with a robust accurate differentiator feedforward compensation technology.

如图4所示，针对输送用并联机器人，构建一种结合鲁棒精确微分器前馈补偿技术的有限时间收敛滑模分布式控制系统，该系统由“上位机PC+下位机UMAC多轴运动控制器”组成，其中上位机负责系统管理，下位机实现运动控制，两部分通过网络通讯实现信息交互，完成对并联机器人的运动控制。然后对并联机器人控制系统的硬件模块进行选型，主要包括个人计算机PC、多轴运动控制器UMAC、伺服控制系统和接近开关等部分。其中上位机PC配备Intel core i7-4790 3.60GHz处理器，主要实现系统初始化、数据处理、代码编译及机构运行状态实时监测等功能；下位机UMAC主要包括一块TURBO PMAC2 OPT-5C0型 CPU主板卡、两块ACC-24E2A型轴板卡、一块ACC-65E型I/O板卡、一块ACC-E1型电源板卡等；伺服驱动系统包括四台配置MR-J4-70A型伺服驱动器的HG-KR73BJ型交流伺服电机、四台配置MR-J4-100A型伺服驱动器的HG-SR102BJ型交流伺服电机，位置检测设备采用22 位(4194304pulses/rev)高分辨率绝对位置编码器。最后，构建控制系统软件平台，并完成上位机应用程序及下位机运动程序的开发。As shown in Figure 4, for the parallel robot for conveying, a finite-time convergence sliding mode distributed control system combined with robust accurate differentiator feedforward compensation technology is constructed. The upper computer is responsible for system management, the lower computer realizes motion control, and the two parts realize information exchange through network communication to complete the motion control of the parallel robot. Then the hardware modules of the parallel robot control system are selected, mainly including personal computer PC, multi-axis motion controller UMAC, servo control system and proximity switches. The upper computer PC is equipped with Intel core i7-4790 3.60GHz processor, which mainly realizes the functions of system initialization, data processing, code compilation and real-time monitoring of the running status of the organization; the lower computer UMAC mainly includes a TURBO PMAC2 OPT-5C0 CPU motherboard card, Two ACC-24E2A axis boards, one ACC-65E I/O board, one ACC-E1 power board, etc.; the servo drive system includes four HG-KR73BJ equipped with MR-J4-70A servo drives Type AC servo motors, four HG-SR102BJ AC servo motors equipped with MR-J4-100A servo drives, and the position detection equipment adopts 22-bit (4194304 pulses/rev) high-resolution absolute position encoders. Finally, build the control system software platform, and complete the development of the application program of the upper computer and the motion program of the lower computer.

7、将计算所得的输送用并联机器人各主动关节控制量发送至各电机驱动器，以实现期望运动。7. Send the calculated control quantities of each active joint of the parallel robot for conveying to each motor driver to achieve the desired motion.

通过Matlab仿真和输送用并联机器人样机系统实验，比较所提出无模型结合鲁棒精确微分器有限时间收敛滑模控制(FTSMC)和无模型一阶滑模控制(SMC)的控制效果，分别得到图5所示各主动关节轨迹跟踪曲线、图6所示各主动关节跟踪误差曲线、图7所示各主动关节对应电机驱动力矩曲线，以及图8所示时延估计误差观测曲线。Through Matlab simulation and parallel robot prototype system experiments for conveying, the control effects of the proposed model-free combined with robust precise differentiator finite-time convergence sliding mode control (FTSMC) and model-free first-order sliding mode control (SMC) are compared, respectively. The trajectory tracking curve of each active joint shown in Fig. 5, the tracking error curve of each active joint shown in Fig. 6, the corresponding motor driving torque curve of each active joint shown in Fig. 7, and the observation curve of time delay estimation error shown in Fig. 8.

图5和图6表明在外界干扰、摩擦和时延估计误差等不确定因素存在的情形下，本发明所提出的无模型结合鲁棒精确微分器有限时间收敛滑模控制方法使输送用并联机器人各关节具有更高的轨迹跟踪精度。这是因为其系统鲁棒性相对较强，对系统不确定性具有更强的抑制作用。图7表明所提控制方法对抖振具有显著的抑制效果，这是所得光滑滑模控制律带来的优势。图8表明所提控制方法能实现对时延估计误差的准确观测，表明了鲁棒精确微分器的有效性。Figures 5 and 6 show that in the presence of uncertain factors such as external interference, friction and time delay estimation error, the model-free combined with the robust precise differentiator finite-time convergence sliding mode control method proposed by the present invention makes the parallel robot for conveying Each joint has higher trajectory tracking accuracy. This is because its system robustness is relatively strong, and it has a stronger inhibitory effect on system uncertainty. Figure 7 shows that the proposed control method has a significant suppression effect on chattering, which is an advantage brought by the resulting smooth sliding mode control law. Figure 8 shows that the proposed control method can achieve accurate observation of the delay estimation error, demonstrating the effectiveness of the robust accurate differentiator.

综上，本发明的输送用并联机器人结合鲁棒精确微分器有限时间收敛滑模控制方法。首先，针对该输送用并联机器人进行运动学分析并给出期望运动轨迹；然后，采用时延估计技术实时在线获取包含输送用并联机器人未知动力学、外界干扰和摩擦等不确定因素的动力学模型；针对时延估计技术产生的时延估计误差，设计一种输送用并联机器人系统的有限时间收敛鲁棒精确微分器进行观测；进一步，基于时延估计误差观测值的前馈补偿作用，设计一种有限时间收敛滑模控制器。最后，通过软件编程，实现该输送用并联机器人结合鲁棒精确微分器前馈补偿技术的有限时间收敛滑模控制。本发明在无需输送用并联机器人动力学模型和系统不确定性信息的前提下，既能提高系统鲁棒性又对滑模控制抖振有显著的抑制效果，且滑模变量及其导数均有限时间收敛至原点，从而提高输送用并联机器人的运动跟踪精度。In conclusion, the parallel robot for conveying of the present invention combines the finite-time convergence sliding mode control method of a robust precise differentiator. Firstly, the kinematics analysis of the parallel robot for transportation is carried out and the expected motion trajectory is given; then, the dynamic model including the unknown dynamics of the parallel robot for transportation, external disturbance and friction and other uncertain factors are obtained online in real time by using the time delay estimation technology. ; Aiming at the time delay estimation error generated by the time delay estimation technology, a finite-time convergence robust precise differentiator for conveying parallel robot system is designed for observation; further, based on the feedforward compensation effect of the observation value of the time delay estimation error, a A finite-time convergent sliding mode controller. Finally, through software programming, the finite-time convergent sliding mode control of the conveying parallel robot combined with the robust precise differentiator feedforward compensation technology is realized. The invention can not only improve the robustness of the system but also have a significant suppressing effect on the chattering of the sliding mode control without the need for the dynamic model of the parallel robot for conveying and the uncertainty information of the system, and the sliding mode variables and their derivatives are limited. The time converges to the origin, thereby improving the motion tracking accuracy of the parallel robot for conveyance.

在本说明书的描述中，参考术语“一个实施例”、“一些实施例”、“示意性实施例”、“示例”、“具体示例”、或“一些示例”等的描述意指结合该实施例或示例描述的具体特征、结构、材料或者特点包含于本发明的至少一个实施例或示例中。在本说明书中，对上述术语的示意性表述不一定指的是相同的实施例或示例。而且，描述的具体特征、结构、材料或者特点可以在任何的一个或多个实施例或示例中以合适的方式结合。In the description of this specification, reference to the terms "one embodiment," "some embodiments," "exemplary embodiment," "example," "specific example," or "some examples", etc., is meant to incorporate the embodiments A particular feature, structure, material, or characteristic described by an example or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

尽管已经示出和描述了本发明的实施例，本领域的普通技术人员可以理解：在不脱离本发明的原理和宗旨的情况下可以对这些实施例进行多种变化、修改、替换和变型，本发明的范围由权利要求及其等同物限定。Although embodiments of the present invention have been shown and described, it will be understood by those of ordinary skill in the art that various changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, The scope of the invention is defined by the claims and their equivalents.

Claims (5)

1. A finite time convergence sliding mode control method for a parallel robot model-free combined robust accurate differentiator feedforward compensation technology for conveying is characterized by comprising the following steps of:
1) the parallel robot for conveying is used as a controlled object, the inverse kinematics solution analysis is carried out on the parallel robot for conveying by adopting an analytical method, and the positive kinematics solution and the Jacobian matrix are further obtained;
2) according to the requirements of the automobile electrophoretic coating process, an expected motion track of the midpoint of the connecting rods of the parallel robots for conveying is designed, and the expected motion track of the active joint is obtained by combining with inverse kinematics;
3) a time delay estimation technology is adopted to obtain a kinetic model of the parallel robot for conveying, which comprises unknown dynamics, external interference and friction, on line in real time;
the specific process of the step 3) is as follows:
the dynamic model of the parallel robot for conveying is as follows:
Figure FDA0003475610700000011
wherein M (q) is a symmetric positive definite inertial matrix;
Figure FDA0003475610700000012
are terms of Copenforces and centrifugal forces; g (q) is a gravity term;
Figure FDA0003475610700000013
is a friction force term; tau isdAn external interference item; tau is a control moment vector;
introducing positive definite constant diagonal matrix for applying time delay estimation technique
Figure FDA0003475610700000014
The kinetic model (1) is abbreviated as:
Figure FDA0003475610700000015
in the formula,
Figure FDA0003475610700000016
representing dynamic information items including nonlinear unknown dynamics, external interference and friction of the parallel robot for conveying;
the real-time online acquisition of the kinetic information of the parallel robot system for conveying by adopting the time delay estimation technology comprises the following steps:
Figure FDA0003475610700000017
in the formula,
Figure FDA0003475610700000018
is that
Figure FDA0003475610700000019
The delay estimate of (a); the variable with the subscript t-eta represents the value of the variable at this time, i.e., the time lag value of the variable, where eta is the delay time and the minimum value of eta can be set as the sampling period;
4) aiming at the time delay estimation error generated by the time delay estimation technology in the step 3), a robust accurate differentiator of the parallel robot system for conveying is designed to observe the time delay estimation error within a limited time;
in the step 4), designing a robust accurate differentiator of the parallel robot system for conveying to delay the estimation error in the observation within a limited time is specifically as follows:
when a time delay estimation technology is adopted to obtain a dynamic model of the parallel robot for conveying on line, a time delay estimation error is generated by using a sampling value at the previous moment to approximate the current values of a nonlinear item and an uncertain item of a parallel robot system for conveying, and the expression of the time delay estimation error is as follows:
Figure FDA0003475610700000021
wherein,
Figure FDA0003475610700000022
for a positive constant diagonal matrix, N ∈ R6Represents the dynamic information items including the nonlinear unknown dynamics, the external interference and the friction of the parallel robot for conveying,
Figure FDA0003475610700000023
is the delay estimate of N;
is provided with
Figure FDA0003475610700000024
And
Figure FDA0003475610700000025
defining the track tracking error of the active joint of the parallel robot for conveying as follows:
e(t)＝q(t)-qd(t)
selecting sliding mode variables of the parallel robot model-free combined robust accurate differentiator finite time convergence sliding mode control for conveying as follows:
Figure FDA0003475610700000026
wherein A is a positive definite diagonal matrix;
in order to obtain a finite time observation value of a time delay estimation error epsilon of a nonlinear term and an uncertain term of the parallel robot for conveying, a robust accurate differentiator of the parallel robot for conveying is designed as follows:
Figure FDA0003475610700000027
wherein u is a virtual control law, z0,z1,z2∈R6，z1Is an observed value of epsilon, z1Will converge to epsilon within a finite time; v. ofj∈R6，j＝0,1,2；λi＝diag(λi1，λi2，…，λi6)，i＝0,1,2；L＝diag(l1,l2,…,l6) Is that
Figure FDA0003475610700000028
Lipshitz constant and li＞0，
Figure FDA0003475610700000029
Let x be (x)1,…,xn)TThe symbol sign (x) is defined as1),…,sign(xn))T，|x|qsign(x)＝(|x1|qsign(x1),…,|xn|qsign(xn))T；
5) Based on the step 3) and the step 4), performing feedforward compensation by using an observed value obtained by the robust accurate differentiator, and designing a finite time convergence sliding mode controller for the parallel robot model-free combined robust accurate differentiator feedforward compensation technology for conveying;
in the step 5), an observed value z obtained by using a robust accurate differentiator of the parallel robot for conveying1Carrying out feedforward compensation, and designing a virtual control law u of model-free finite time convergence sliding mode control as follows:
Figure FDA0003475610700000031
wherein m is not less than 1, alpha1＝diag(α11,α12,…,α16)，α2＝diag(α21,α22,…,α26) W is an intermediate variable introduced when the virtual control law u is designed;
6) constructing a finite time convergence sliding mode control system of the parallel robot model-free combined robust accurate differentiator feed-forward compensation technology for conveying by adopting a distributed structure;
7) and sending the control quantity of each active joint of the parallel robot for conveying obtained by calculation to each motor driver so as to enable the parallel robot to move according to the expected track.
2. The finite time convergence sliding-mode control method of the parallel robot model-free combined robust accurate differentiator feed-forward compensation technology for conveying according to claim 1, characterized in that: in the step 1), two ends of the inverse kinematics solution equation are subjected to derivation, so that:
Figure FDA0003475610700000032
in the formula, J is a Jacobian matrix of the parallel robot for conveying;
Figure FDA0003475610700000033
is an active joint pose vector of the parallel robot for conveying, wherein x1,x2,x3,x4Respectively showing the displacement of four slide blocks of the parallel robot for conveying,
Figure FDA0003475610700000034
respectively showing the rotation angles of two driving wheels of the parallel robot for conveying,
Figure FDA0003475610700000035
is the active joint velocity vector;
Figure FDA0003475610700000036
is the connecting rod midpoint velocity vector.
3. The finite time convergence sliding-mode control method of the parallel robot model-free combined robust accurate differentiator feed-forward compensation technology for conveying according to claim 1, characterized in that: in the step 2), according to the electrophoretic coating process requirements of the automobile body-in-white groove, the overturning and the groove discharging, the expected motion track of the middle point of the connecting rod of the parallel robot for conveying is determined to be xd＝(zd,βd)TWherein z isdFor the desired displacement of the midpoint of the connecting rod in the Z direction, betadThe expected motion trail of the active joint is obtained for the expected angle of the end effector rotating around the Y axis in the anticlockwise direction by combining with the inverse solution equation of kinematics
Figure FDA0003475610700000037
Wherein xd1,xd2,xd3,xd4Respectively show the expected displacement of four sliding blocks of the parallel robot for conveying,
Figure FDA0003475610700000038
respectively showing the expected rotation angles of the two driving wheels of the parallel robot for conveying.
4. The finite time convergence sliding-mode control method of the parallel robot model-free combined robust accurate differentiator feed-forward compensation technology for conveying according to claim 1, characterized in that: step 5) also comprises the following steps:
at virtual control law u and observation z1Under the feedforward compensation action on the delay estimation error epsilon, the dynamic of the sliding mode variable s is as follows:
Figure FDA0003475610700000041
the variable of the sliding mode and the derivative thereof are converged to the origin within a limited time
Figure FDA0003475610700000042
Is continuous, so the virtual control law u is not only continuous but also smooth.
5. The finite time convergence sliding-mode control method of the parallel robot model-free combined robust accurate differentiator feedforward compensation technology for conveying according to claim 4, characterized in that: the step 5) further comprises the step of designing a finite time convergence sliding mode control law tau without a model and combined with a robust precise differentiator feedforward compensation technology according to a virtual control law u, wherein the finite time convergence sliding mode control law tau is as follows:
Figure FDA0003475610700000043
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