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CN107398903A - The method for controlling trajectory of industrial machinery arm actuating station - Google Patents

The method for controlling trajectory of industrial machinery arm actuating station Download PDF

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Publication number
CN107398903A
CN107398903A CN201710787000.4A CN201710787000A CN107398903A CN 107398903 A CN107398903 A CN 107398903A CN 201710787000 A CN201710787000 A CN 201710787000A CN 107398903 A CN107398903 A CN 107398903A
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CN107398903B (en
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吴占雄
李忠伟
曾毓
杨宇翔
高明煜
何志伟
黄继业
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Rizhao Ruijing Software Technology Co ltd
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Hangzhou Dianzi University
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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
    • 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
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/40—Robotics, robotics mapping to robotics vision
    • G05B2219/40523—Path motion planning, path in space followed by tip of robot

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  • Engineering & Computer Science (AREA)
  • Robotics (AREA)
  • Mechanical Engineering (AREA)
  • Feedback Control In General (AREA)
  • Manipulator (AREA)
  • Numerical Control (AREA)

Abstract

本发明提供一种工业机械手臂执行端的轨迹控制方法，该方法包括获取工业机械手臂执行端的机械结构参数，根据机械结构参数确定雅克比矩阵并初始网格化精度ε；根据加工要求确定工业机械手臂执行端的运动轨迹；根据雅克比矩阵计算操作空间k+1时刻的参考位置变量以操作空间k+1时刻的参考位置变量为参数对目标函数进行约束二次优化逼近，求得k+1时刻实际操作空间位置变量Xk+1和k时刻关节空间的输入控制量uk；工业机械手臂执行端根据k+1时刻实际操作空间位置变量Xk+1和k时刻关节空间的输入控制量uk进行轨迹运动。

The invention provides a trajectory control method of the execution end of the industrial mechanical arm, the method includes obtaining the mechanical structure parameters of the execution end of the industrial mechanical arm, determining the Jacobian matrix and initial grid precision ε according to the mechanical structure parameters; determining the industrial mechanical arm according to the processing requirements The trajectory of the execution end; calculate the reference position variable at the moment k+1 in the operation space according to the Jacobian matrix The reference position variable at time k+1 in the operating space Constrained quadratic optimization approximation of the objective function for the parameters, and obtain the actual operating space position variable X k+1 at time k+1 and the input control variable u k of the joint space at time k; the execution end of the industrial robot arm is based on the actual Operate space position variable X k+1 and input control quantity u k of joint space at time k to perform trajectory motion.

Description

Track control method for industrial mechanical arm execution end
Technical Field
The invention relates to the field of industrial control, in particular to a track control method for an industrial mechanical arm execution end.
Background
The industrial mechanical arm has wide application in welding, painting, stacking and assembling, and becomes an essential intelligent device in industrial production. An industrial robot is a very complex multi-input multi-output nonlinear system with time-varying, strong coupling and nonlinear dynamics characteristics. The control is more complicated due to the influence of uncertain factors such as load change, mechanical disturbance and the like. The rapid development of industry 4.0 requires high quality industrial robot service. The control strategy aiming at stability and high efficiency becomes the difficulty of industrial robot research.
The motion discontinuity and the frequent switching of the control servo may cause the motion track of the execution end of the industrial robot to generate jitter, which may cause mechanical wear of the execution component and failure of the high frequency dynamic response. The control strategy of most industrial robots at present is to carry out PID control on independent joints, and the main defect of the control method is that the feedback gain is a predetermined constant and cannot be changed under the condition of change of a payload, and the dynamic effect of the robot joint is obvious when the robot joint rotates at a high speed.
Disclosure of Invention
The invention provides a control method of a motion track of an execution end of an industrial mechanical arm, which has high control precision and no jitter, and aims to overcome the obvious dynamic effect of the existing industrial robot control strategy.
In order to achieve the above object, the present invention provides a method for controlling a trajectory of an execution end of an industrial robot arm, the method comprising:
s1, obtaining mechanical structure parameters of the industrial mechanical arm execution end, determining a Jacobian matrix according to the mechanical structure parameters and initializing gridding precision;
step S2, determining the motion track of the executing end of the industrial mechanical arm according to the processing requirement, wherein the starting point is XstartEnd point is XterminalWhere X ═ { X, y, z, ωx,ωy,ωzThe position variable of k time of the operation space is used as the position variable;
step S3, calculating the reference position variable of the operating space at the time k +1 according to the Jacobian matrix
Step S4 to manipulate the reference position variable at time k +1 in spaceCarrying out constrained quadratic optimization approximation on the objective function for the parameters to obtain the actual operation space position variable X at the moment of k +1k+1And input control quantity u of joint space at time kk；
Step S5, the execution end of the industrial mechanical arm actually operates the space position variable X according to the k +1 momentk+1And input control quantity u of joint space at time kkCarrying out track motion;
wherein the objective function is:
the constraint conditions include:
the first constraint condition is:
the second constraint condition is as follows:
the third constraint condition is as follows: q. q.smin≤q≤qmax(ii) a And
the fourth constraint condition is as follows: u. ofmin≤uk≤umax；
Wherein,for the actual operating space position variable X at the time k +1k+1The differential of (a) is determined,reference position variable at time k +1Differentiation of (1); t issIs the state feedback interval time, the input control quantity of the joint space The acceleration of the angular velocity of the joint motor in the execution end is obtained; discrete Jacobian matrix Jk＝J(qk)；The upper limit of the motion speed of the execution end of the industrial mechanical arm is set; q. q.sminThe lower limit value of the motion angle of the joint motor; q. q.smaxThe upper limit value of the motion angle of the joint motor; u. ofminFor actuation of lower limit of end acceleration, umaxIs an execution end acceleration upper limit value.
According to an embodiment of the invention, a binary grid optimization algorithm is adopted to perform optimization approximation on an objective function, and the specific steps are as follows:
step S41, substituting the first constraint condition into the objective function to bring the objective function into the objective functionFinally obtain the product ofkIs an objective function of
Step S42, under the constraint of the fourth constraint condition, the u is paired at the interval delta ukPerforming equal-interval division;
step S43, calculatingAndtraversing and finding all lattice points which accord with the second constraint condition and the third constraint condition; if the two-dimensional gridding is not found, continuously carrying out two-dimensional gridding again at the interval of delta u/2;
step S44, calculating an objective function psi (u) according to the searched lattice points meeting the second constraint condition and the third constraint conditionk) To obtain the target function psi (u)k) Grid point corresponding to the minimum value of (1)
Step S45 toAt the center, in the rangeAt an interval of delta u/2lPerforming gridding, wherein l is a half grid number, re-executing the steps S43 to S44 whenWill control the quantityAs the controlled variable u at the time k +1kAnd (6) outputting.
According to an embodiment of the present invention, the Jacobian matrix is:
wherein q ═ { q ═ q1,q2,…,qiThe variable is a joint space angle variable, (x, y, z) is an execution end coordinate, (omega)x,ωy,ωz) Is the actuation end rotation angle.
According to an embodiment of the present invention, the mechanical structure parameters include a degree of freedom of an industrial robot arm execution end, a joint rotation angle, and an arm length.
According to an embodiment of the invention, the motion track of the executing end of the industrial mechanical arm is an arc line or a straight line.
In summary, the trajectory control method for the execution end of the industrial robot provided by the present invention predicts the position of the execution end at the next time by modeling the mechanical structure parameters of the execution end of the industrial robot and combining the motion trajectory determined by the processing requirement, and finally performs constraint optimization of the objective function with the predicted position as a parameter to obtain the input control quantity of the execution end. The control mode takes the mechanical structure parameters of the execution end and the current position as variables to calculate the parameters of the next spatial position in real time, the calculation real-time performance is very strong, the conformity with the actual motion track is very high, the control precision of the mechanical arm is high, the dynamic effect of the execution end of the mechanical arm in the motion process is effectively reduced, and the motion is more stable and efficient.
In order to make the aforementioned and other objects, features and advantages of the present invention comprehensible, preferred embodiments accompanied with figures are described in detail below.
Drawings
Fig. 1 is a flowchart illustrating a trajectory control method for an industrial robot actuator according to an embodiment of the present invention.
Detailed Description
As shown in fig. 1, the method for controlling a trajectory of an industrial robot actuator provided in this embodiment starts with step S1, obtaining mechanical structure parameters of the industrial robot actuator, determining a jacobian matrix according to the mechanical structure parameters, and initializing a meshing precision. In this embodiment, the mechanical structure parameters of the industrial robot actuator include the degree of freedom, the joint rotation angle, and the arm length of the industrial robot actuator. However, the present invention is not limited thereto. The Jacobian matrix determined from the mechanical structure parameters is as follows:
wherein q ═ { q ═ q1,q2,…,qiThe variable is a joint space angle variable, (x, y, z) is an execution end coordinate, (omega)x,ωy,ωz) Is the actuation end rotation angle.
Step S2, determining the motion track of the executing end of the industrial mechanical arm according to the processing requirement, wherein the starting point is XstartEnd point is XterminalWhere X ═ { X, y, z, ωx,ωy,ωzIs the position variable at the time instant of the operating space k. The motion trail of the execution end of the industrial mechanical arm is an arc line or a straight line, and is determined according to the shape of a product to be processed. In the present embodiment, after the step S1 is completed, the step S2 is executed. However, the present invention is not limited thereto. In other embodiments, step S2 may be performed first, and then step S1 may be performed; or steps S2 and S1 may be performed simultaneously.
Step S3 is executed to calculate the reference position variable at the time of k +1 in the operation space according to the Jacobian matrix
Step S4 is performed to manipulate the reference position variable at time k +1 in spaceConstrained quadratic optimization approximation is performed on the objective function for the parameters,obtaining the actual operation space position variable X at the moment of k +1k+1And input control quantity u of joint space at time kk. In this embodiment, the objective function is:
the constraint conditions include:
the first constraint condition is:
the second constraint condition is as follows:
the third constraint condition is as follows: q. q.smin≤q≤qmax(ii) a And
the fourth constraint condition is as follows: u. ofmin≤uk≤umax；
Wherein,for the actual operating space position variable X at the time k +1k+1The differential of (a) is determined,reference position variable at time k +1Differentiation of (1); t issIs the state feedback interval time, the input control quantity of the joint space The acceleration of the angular velocity of the joint motor in the execution end is obtained;discrete Jacobian matrix Jk＝J(qk)；The upper limit of the motion speed of the execution end of the industrial mechanical arm is set; q. q.sminThe lower limit value of the motion angle of the joint motor; q. q.smaxThe upper limit value of the motion angle of the joint motor; u. ofminFor actuation of lower limit of end acceleration, umaxIs an execution end acceleration upper limit value.
In this embodiment, a binary grid optimization algorithm is used to perform optimization approximation on the objective function, and the specific steps are as follows:
step S41, substituting the first constraint condition into the objective function to bring the objective function into the objective functionFinally obtain the product ofkIs an objective function of
Step S42, under the constraint of the fourth constraint condition, the u is paired at the interval delta ukAnd performing equal-interval division.
Step S43, calculatingAndtraversing and finding all lattice points which accord with the second constraint condition and the third constraint condition; and if the binary grid is not found, continuously carrying out binary grid again at the interval of delta u/2.
Step S44, calculating an objective function psi (u) according to the searched lattice points meeting the second constraint condition and the third constraint conditionk) To obtain the target function psi (u)k) Grid point corresponding to the minimum value of (1)
Step S45 toAt the center, in the rangeAt an interval of delta u/2lPerforming gridding, wherein l is a half grid number, re-executing the steps S43 to S44 whenWill control the quantityInput control quantity u as time k +1kAnd (6) outputting.
Such as when u is paired at intervals Δ u and Δ u/2 in step S43kWhen the equal-interval division is carried out, the lattice points meeting the conditions are not found, then the division is carried out by delta u/4, at the moment, the division frequency of the binary grid is 3 times, and therefore l is equal to 3 in the step S45.
Then, step S5 is executed, and the industrial robot execution end actually operates the spatial position variable X according to the time k +1k+1And input control quantity u of joint space at time kkPerforming a trajectory movement.
The trajectory control method for the execution end of the industrial mechanical arm provided by the embodiment calculates the input control quantity at the next moment by using the real-time data of the execution end, and the control has good real-time performance and accuracy. Furthermore, the binary grid optimization algorithm is accurate in calculation and small in calculation amount, can effectively avoid excessive CPU and memory resources, is suitable for being realized on an embedded control system, can meet the requirement of the existing industrial mechanical control system, and has good compatibility.
In summary, the trajectory control method for the execution end of the industrial robot provided by the present invention predicts the position of the execution end at the next time by modeling the mechanical structure parameters of the execution end of the industrial robot and combining the motion trajectory determined by the processing requirement, and finally performs constraint optimization of the objective function with the predicted position as a parameter to obtain the input control quantity of the execution end. The control mode takes the mechanical structure parameters of the execution end and the current position as variables to calculate the parameters of the next spatial position in real time, the calculation real-time performance is very strong, the conformity with the actual motion track is very high, the control precision of the mechanical arm is high, the dynamic effect of the execution end of the mechanical arm in the motion process is effectively reduced, and the motion is more stable and efficient.
Although the present invention has been described with reference to the preferred embodiments, it should be understood that various changes and modifications can be made therein by those skilled in the art without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (5)

1.一种工业机械手臂执行端的轨迹控制方法，其特征在于，包括：1. A trajectory control method of an industrial robot arm execution end, characterized in that, comprising: 步骤S1、获取工业机械手臂执行端的机械结构参数，根据机械结构参数确定雅克比矩阵并初始网格化精度ε；Step S1, obtain the mechanical structure parameters of the execution end of the industrial robot arm, determine the Jacobian matrix according to the mechanical structure parameters and initialize the meshing precision ε; 步骤S2、根据加工要求确定工业机械手臂执行端的运动轨迹，起始点为Xstart，终点为Xterminal，其中X＝{x,y,z,ωx,ωy,ωz}为操作空间k时刻的位置变量；Step S2. Determine the motion trajectory of the execution end of the industrial robot arm according to the processing requirements. The starting point is X start , and the end point is X terminal , where X={x,y,z,ω x ,ω y ,ω z } is the time k of the operation space the position variable; 步骤S3、根据雅克比矩阵计算操作空间k+1时刻的参考位置变量 Step S3, calculate the reference position variable at time k+1 in the operation space according to the Jacobian matrix 步骤S4、以操作空间k+1时刻的参考位置变量为参数对目标函数进行约束二次优化逼近，求得k+1时刻实际操作空间位置变量Xk+1和k时刻关节空间的输入控制量uk；Step S4, with the reference position variable at time k+1 in the operation space Perform constrained quadratic optimization approximation to the objective function for the parameters, and obtain the actual operating space position variable X k+1 at time k+1 and the input control quantity u k of the joint space at time k ; 步骤S5、工业机械手臂执行端根据k+1时刻实际操作空间位置变量Xk+1和k时刻关节空间的输入控制量uk进行轨迹运动；Step S5, the execution end of the industrial mechanical arm performs trajectory movement according to the actual operating space position variable X k+1 at time k+1 and the input control quantity u k of the joint space at time k; 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</mrow> <mi>T</mi> </msup> <mrow> <mo>(</mo> <msub> <mover> <mi>X</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msubsup> <mover> <mi>X</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mrow> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msubsup> <mo>)</mo> </mrow> <mo>+</mo> <msubsup> <mover> <mi>q</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>k</mi> <mi>T</mi> </msubsup> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msubsup> <mi>X</mi> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mrow> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msubsup> <mo>)</mo> </mrow> <mo>+</mo> <msubsup> <mi>u</mi> <mi>k</mi> <mi>T</mi> </msubsup> <mrow> <mo>(</mo> <msub> <mover> <mi>X</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msubsup> <mover> <mi>X</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> <mrow> <mi>r</mi> <mi>e</mi> <mi>f</mi> </mrow> </msubsup> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "" close = ""><mtable><mtr><mtd><mrow><munder><mi>min</mi><msub><mi>u</mi><mi>k</mi></msub></munder><mi>&amp;psi;</mi><mrow><mo>(</mo><msub><mi>X</mi><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>,</mo><msubsup><mi>X</mi><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow><mrow><mi>r</mi><mi>e</mi><mi>f</mi></mrow></msubsup><mo>)</mo></mrow><mo>=</mo><msup><mrow><mo>(</mo><msub><mi>X</mi><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>-</mo><msubsup><mi>X</mi><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow><mrow><mi>r</mi><mi>e</mi><mi>f</mi></mrow></msubsup><mo>)</mo></mrow><mi>T</mi></msup><mrow><mo>(</mo><msub><mi>X</mi><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>-</mo><msubsup><mi>X</mi><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow><mrow><mi>r</mi><mi>e</mi><mi>f</mi></mrow></msubsup><mo>)</mo></mrow><mo>+</mo><msup><mrow><mo>(</mo><msub><mover><mi>X</mi><mo>&amp;CenterDot;</mo></mover><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>-</mo><msubsup><mover><mi>X</mi><mo>&amp;CenterDot;</mo></mover><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow><mrow><mi>r</mi><mi>e</mi><mi>f</mi></mrow></msubsup><mo>)</mo></mrow><mi>T</mi></msup><mrow><mo>(</mo><msub><mover><mi>X</mi><mo>&amp;CenterDot;</mo></mover><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>-</mo><msubsup><mover><mi>X</mi><mo>&amp;CenterDot;</mo></mover><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow><mrow><mi>r</mi><mi>e</mi><mi>f</mi></mrow></msubsup><mo>)</mo></mrow></mrow></mtd></mtr><mtr><mtd><mrow><mo>+</mo><mn>2</mn><msup><mrow><mo>(</mo><msub><mi>X</mi><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>-</mo><msubsup><mi>X</mi><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow><mrow><mi>r</mi><mi>e</mi><mi>f</mi></mrow></msubsup><mo>)</mo></mrow><mi>T</mi></msup><mrow><mo>(</mo><msub><mover><mi>X</mi><mo>&amp;CenterDot;</mo></mover><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>-</mo><msubsup><mover><mi>X</mi><mo>&amp;CenterDot;</mo></mover><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow><mrow><mi>r</mi><mi>e</mi><mi>f</mi></mrow></msubsup><mo>)</mo></mrow><mo>+</mo><msubsup><mover><mi>q</mi><mo>&amp;CenterDot;</mo></mover><mi>k</mi><mi>T</mi></msubsup><mrow><mo>(</mo><msub><mi>X</mi><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>-</mo><msubsup><mi>X</mi><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow><mrow><mi>r</mi><mi>e</mi><mi>f</mi></mrow></msubsup><mo>)</mo></mrow><mo>+</mo><msubsup><mi>u</mi><mi>k</mi><mi>T</mi></msubsup><mrow><mo>(</mo><msub><mover><mi>X</mi><mo>&amp;CenterDot;</mo></mover><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>-</mo><msubsup><mover><mi>X</mi><mo>&amp;CenterDot;</mo></mover><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow><mrow><mi>r</mi><mi>e</mi><mi>f</mi></mrow></msubsup><mo>)</mo></mrow></mrow></mtd></mtr></mtable></mfenced> 约束条件包括：Constraints include: 第一约束条件： First constraint: 第二约束条件： The second constraint: 第三约束条件：qmin≤q≤qmax；以及The third constraint condition: q min ≤ q ≤ q max ; and 第四约束条件：umin≤uk≤umax；The fourth constraint condition: u min ≤ u k ≤ u max ; 其中，为k+1时刻实际操作空间位置变量Xk+1的微分，为k+1时刻的参考位置变量的微分；Ts是状态反馈间隔时间，关节空间的输入控制量 为执行端内关节电机角速度的加速度；离散雅可比矩阵Jk＝J(qk)；为工业机械手臂执行端运动速度的上限；qmin为关节电机运动角度下限值；qmax为关节电机运动角度上限值；umin为执行端加速度下限值，umax为执行端加速度上限值。in, is the differential of the actual operating space position variable X k+ 1 at time k+1, is the reference position variable at time k+1 The differential of ; T s is the state feedback interval time, the input control quantity of the joint space is the acceleration of the angular velocity of the joint motor in the actuator; the discrete Jacobian matrix J k ＝J(q k ); is the upper limit of the motion speed of the industrial robot arm; q min is the lower limit of the motion angle of the joint motor; q max is the upper limit of the motion angle of the joint motor; u min is the lower limit of the acceleration of the execution end, and u max is the upper limit of the acceleration of the execution end limit. 2.根据权利要求1所述的工业机械手臂执行端的轨迹控制方法，其特征在于，采用二分网格优化算法对目标函数进行优化逼近，具体步骤如下：2. the trajectory control method of the execution end of industrial mechanical arm according to claim 1, is characterized in that, adopts bisection grid optimization algorithm to carry out optimization approximation to objective function, concrete steps are as follows: 步骤S41、将第一约束条件代入目标函数带入目标函数最终得到关于uk的目标函数 Step S41, Substituting the first constraint condition into the objective function into the objective function Finally, the objective function about u k is obtained 步骤S42、在第四约束条件的约束下以间隔Δu对uk进行等间距划分；Step S42, under the constraints of the fourth constraint condition, u k is equally spaced with the interval Δu; 步骤S43、计算与遍历查找出符合第二约束条件和第三约束条件的所有格点；若没有查找到则以Δu/2为间隔不断的重新进行二分网格化；Step S43, calculation and Traverse to find all the grid points that meet the second and third constraints; if not found, continue to re-grid with Δu/2 as the interval; 步骤S44、根据查找到的符合第二约束条件和第三约束条件的格点计算目标函数ψ(uk)，得到目标函数ψ(uk)的最小值对应的格点 Step S44, calculate the objective function ψ(u k ) according to the found grid points meeting the second constraint condition and the third constraint condition, and obtain the grid point corresponding to the minimum value of the objective function ψ(u k ) 步骤S45、以为中心，在范围内以间隔Δu/2l进行网格化，其中l为二分网格次数，重新执行步骤S43至S44，当时将控制量作为k+1时刻的控制量uk输出。Step S45, with centered on the range Gridding is carried out at intervals Δu/2 l , where l is the number of bisection grids, re-execute steps S43 to S44, when control amount It is output as the control quantity u k at time k+1. 3.根据权利要求1所述的工业机械手臂执行端的轨迹控制方法，其特征在于，所述雅克比矩阵为：3. The trajectory control method of the execution end of the industrial mechanical arm according to claim 1, wherein the Jacobian matrix is: <mrow> <mi>J</mi> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mo>&amp;part;</mo> <mi>x</mi> <mo>/</mo> <mo>&amp;part;</mo> <msub> <mi>q</mi> <mn>1</mn> </msub> </mrow> </mtd> <mtd> <mrow> <mo>&amp;part;</mo> <mi>x</mi> <mo>/</mo> <mo>&amp;part;</mo> <msub> <mi>q</mi> <mn>2</mn> </msub> </mrow> </mtd> <mtd> <mn>...</mn> </mtd> <mtd> <mrow> <mo>&amp;part;</mo> <mi>x</mi> <mo>/</mo> <mo>&amp;part;</mo> <msub> <mi>q</mi> <mi>i</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>&amp;part;</mo> <mi>x</mi> <mo>/</mo> <mo>&amp;part;</mo> <msub> <mi>q</mi> <mn>1</mn> </msub> </mrow> </mtd> <mtd> <mrow> <mo>&amp;part;</mo> <mi>x</mi> <mo>/</mo> <mo>&amp;part;</mo> <msub> <mi>q</mi> <mn>2</mn> </msub> </mrow> </mtd> <mtd> <mn>...</mn> </mtd> <mtd> <mrow> <mo>&amp;part;</mo> <mi>x</mi> <mo>/</mo> <mo>&amp;part;</mo> <msub> <mi>q</mi> <mi>i</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>&amp;part;</mo> <mi>y</mi> <mo>/</mo> <mo>&amp;part;</mo> <msub> <mi>q</mi> <mn>1</mn> </msub> </mrow> </mtd> <mtd> <mrow> <mo>&amp;part;</mo> <mi>y</mi> <mo>/</mo> <mo>&amp;part;</mo> <msub> <mi>q</mi> <mn>2</mn> </msub> </mrow> </mtd> <mtd> <mn>...</mn> </mtd> <mtd> <mrow> <mo>&amp;part;</mo> <mi>y</mi> <mo>/</mo> <mo>&amp;part;</mo> <msub> <mi>q</mi> <mi>i</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>&amp;part;</mo> <mi>z</mi> <mo>/</mo> <mo>&amp;part;</mo> <msub> <mi>q</mi> <mn>1</mn> </msub> </mrow> </mtd> <mtd> <mrow> <mo>&amp;part;</mo> <mi>z</mi> <mo>/</mo> <mo>&amp;part;</mo> <msub> <mi>q</mi> <mn>2</mn> </msub> </mrow> </mtd> <mtd> <mn>...</mn> </mtd> <mtd> <mrow> <mo>&amp;part;</mo> <mi>z</mi> <mo>/</mo> <mo>&amp;part;</mo> <msub> <mi>q</mi> <mi>i</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;omega;</mi> <mi>x</mi> </msub> <mo>/</mo> <mo>&amp;part;</mo> <msub> <mi>q</mi> <mn>1</mn> </msub> </mrow> </mtd> <mtd> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;omega;</mi> <mi>x</mi> </msub> <mo>/</mo> <mo>&amp;part;</mo> <msub> <mi>q</mi> <mn>2</mn> </msub> </mrow> </mtd> <mtd> <mn>...</mn> </mtd> <mtd> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;omega;</mi> <mi>x</mi> </msub> <mo>/</mo> <mo>&amp;part;</mo> <msub> <mi>q</mi> <mi>i</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;omega;</mi> <mi>y</mi> </msub> <mo>/</mo> <mo>&amp;part;</mo> <msub> <mi>q</mi> <mn>1</mn> </msub> </mrow> </mtd> <mtd> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;omega;</mi> <mi>y</mi> </msub> <mo>/</mo> <mo>&amp;part;</mo> <msub> <mi>q</mi> <mn>2</mn> </msub> </mrow> </mtd> <mtd> <mn>...</mn> </mtd> <mtd> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;omega;</mi> <mi>y</mi> </msub> <mo>/</mo> <mo>&amp;part;</mo> <msub> <mi>q</mi> <mi>i</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;omega;</mi> <mi>z</mi> </msub> <mo>/</mo> <mo>&amp;part;</mo> <msub> <mi>q</mi> <mn>1</mn> </msub> </mrow> </mtd> <mtd> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;omega;</mi> <mi>z</mi> </msub> <mo>/</mo> <mo>&amp;part;</mo> <msub> <mi>q</mi> <mn>2</mn> </msub> </mrow> </mtd> <mtd> <mn>...</mn> </mtd> <mtd> <mrow> <mo>&amp;part;</mo> <msub> <mi>&amp;omega;</mi> <mi>z</mi> </msub> <mo>/</mo> <mo>&amp;part;</mo> <msub> <mi>q</mi> <mi>i</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow> <mrow><mi>J</mi><mo>=</mo><mfenced open = "[" close = "]"><mtable><mtr><mtd><mrow><mo>&amp;part;</mo><mi>x</mi><mo>/</mo><mo>&amp;part;</mo><msub><mi>q</mi><mn>1</mn></msub></mrow></mtd><mtd><mrow><mo>&amp;part;</mo><mi>x</mi><mo>/</mo><mo>&amp;part;</mo><msub><mi>q</mi><mn>2</mn></msub></mrow></mtd><mtd><mn>...</mn></mtd><mtd><mrow><mo>&amp;part;</mo><mi>x</mi><mo>/</mo><mo>&amp;part;</mo><msub><mi>q</mi><mi>i</mi></msub></mrow></mtd></mtr><mtr><mtd><mrow><mo>&amp;part;</mo><mi>x</mi><mo>/</mo><mo>&amp;part;</mo><msub><mi>q</mi><mn>1</mn></msub></mrow></mtd><mtd><mrow><mo>&amp;part;</mo><mi>x</mi><mo>/</mo><mo>&amp;part;</mo><msub><mi>q</mi><mn>2</mn></msub></mrow></mtd><mtd><mn>...</mn></mtd><mtd><mrow><mo>&amp;part;</mo><mi>x</mi><mo>/</mo><mo>&amp;part;</mo><msub><mi>q</mi><mi>i</mi></msub></mrow></mtd></mtr><mtr><mtd><mrow><mo>&amp;part;</mo><mi>y</mi><mo>/</mo><mo>&amp;part;</mo><msub><mi>q</mi><mn>1</mn></msub></mrow></mtd><mtd><mrow><mo>&amp;part;</mo><mi>y</mi><mo>/</mo><mo>&amp;part;</mo><msub><mi>q</mi><mn>2</mn></msub></mrow></mtd><mtd><mn>...</mn></mtd><mtd><mrow><mo>&amp;part;</mo><mi>y</mi><mo>/</mo><mo>&amp;part;</mo><msub><mi>q</mi><mi>i</mi></msub></mrow></mtd></mtr><mtr><mtd><mrow><mo>&amp;part;</mo><mi>z</mi><mo>/</mo><mo>&amp;part;</mo><msub><mi>q</mi><mn>1</mn></msub></mrow></mtd><mtd><mrow><mo>&amp;part;</mo><mi>z</mi><mo>/</mo><mo>&amp;part;</mo><msub><mi>q</mi><mn>2</mn></msub></mrow></mtd><mtd><mn>...</mn></mtd><mtd><mrow><mo>&amp;part;</mo><mi>z</mi><mo>/</mo><mo>&amp;part;</mo><msub><mi>q</mi><mi>i</mi></msub></mrow></mtd></mtr><mtr><mtd><mrow><mo>&amp;part;</mo><msub><mi>&amp;omega;</mi><mi>x</mi></msub><mo>/</mo><mo>&amp;part;</mo><msub><mi>q</mi><mn>1</mn></msub></mrow></mtd><mtd><mrow><mo>&amp;part;</mo><msub><mi>&amp;omega;</mi><mi>x</mi></msub><mo>/</mo><mo>&amp;part;</mo><msub><mi>q</mi><mn>2</mn></msub></mrow></mtd><mtd><mn>...</mn></mtd><mtd><mrow><mo>&amp;part;</mo><msub><mi>&amp;omega;</mi><mi>x</mi></msub><mo>/</mo><mo>&amp;part;</mo><msub><mi>q</mi><mi>i</mi></msub></mrow></mtd></mtr><mtr><mtd><mrow><mo>&amp;part;</mo><msub><mi>&amp;omega;</mi><mi>y</mi></msub><mo>/</mo><mo>&amp;part;</mo><msub><mi>q</mi><mn>1</mn></msub></mrow></mtd><mtd><mrow><mo>&amp;part;</mo><msub><mi>&amp;omega;</mi><mi>y</mi></msub><mo>/</mo><mo>&amp;part;</mo><msub><mi>q</mi><mn>2</mn></msub></mrow></mtd><mtd><mn>...</mn></mtd><mtd><mrow><mo>&amp;part;</mo><msub><mi>&amp;omega;</mi><mi>y</mi></msub><mo>/</mo><mo>&amp;part;</mo><msub><mi>q</mi><mi>i</mi></msub></mrow></mtd></mtr><mtr><mtd><mrow><mo>&amp;part;</mo><msub><mi>&amp;omega;</mi><mi>z</mi></msub><mo>/</mo><mo>&amp;part;</mo><msub><mi>q</mi><mn>1</mn></msub></mrow></mtd><mtd><mrow><mo>&amp;part;</mo><msub><mi>&amp;omega;</mi><mi>z</mi></msub><mo>/</mo><mo>&amp;part;</mo><msub><mi>q</mi><mn>2</mn></msub></mrow></mtd><mtd><mn>...</mn></mtd><mtd><mrow><mo>&amp;part;</mo><msub><mi>&amp;omega;</mi><mi>z</mi></msub><mo>/</mo><mo>&amp;part;</mo><msub><mi>q</mi><mi>i</mi></msub></mrow></mtd></mtr></mtable></mfenced></mrow> 其中q＝{q1,q2,…,qi}为关节空间角度变量，(x,y,z)为执行端坐标，(ωx,ωy,ωz)为执行端旋转角度。Where q={q 1 ,q 2 ,…,q i } is the joint space angle variable, (x,y,z) is the execution end coordinates, (ω x ,ω y ,ω z ) is the execution end rotation angle. 4.根据权利要求1所述的工业机械手臂执行端的轨迹控制方法，其特征在于，所述机械结构参数包括工业机械手臂执行端的自由度、关节旋转角度以及臂长。4. The trajectory control method of the execution end of the industrial robot arm according to claim 1, wherein the mechanical structure parameters include the degree of freedom, joint rotation angle and arm length of the execution end of the industrial robot arm. 5.根据权利要求1所述的工业机械手臂执行端的轨迹控制方法，其特征在于，工业机械手臂执行端的运动轨迹为弧线或直线。5. The trajectory control method of the executing end of the industrial robot arm according to claim 1, wherein the motion trajectory of the executing end of the industrial robot arm is an arc or a straight line.
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