CN101612734A - Pipeline spraying robot and operation track planning method thereof - Google Patents

Abstract

The invention discloses a pipeline spraying robot with multiple redundant degrees of freedom and its operation trajectory planning method. The method includes steps: S1, importing the geometric model of the surface to be sprayed into a specific module of the drawing software, and the specific module automatically generates The non-collision spraying path of the spraying workpiece of the robot in the pipeline; S2, perform iterative calculation based on the projected gradient method, and plan the continuous motion trajectory of the joints of the robot; S3, perform collision inspection according to the continuous motion trajectory of the joints, if there is a collision, Then modify the weight coefficient of the optimization function, and return to step S2 to replan the continuous motion trajectory of the joint; otherwise, end the planning. The calculation amount of the method of the invention is small, and the inner wall of the special-shaped narrow and long pipeline can be sprayed after trajectory planning by using the method, which can ensure that the wall does not hit the wall, and has high spraying quality.

Description

Pipeline spraying robot and its operation trajectory planning method

technical field

The invention relates to the technical field of robots, in particular to a pipeline spraying robot with multiple redundant degrees of freedom and an operation trajectory planning method thereof.

Background technique

In the field of special industries, the inner walls of the narrow and long tubes of many complex workpieces need to be sprayed. Because the inner surfaces of these long and narrow tubes are relatively complex and the internal space is extremely narrow, it is difficult for spraying technicians to enter, so robots must be used for automatic spraying.

In the prior art, redundant degree-of-freedom robots are generally used for pipeline spraying operations. The meaning of "redundancy" is that in order for the robot to complete the spraying operation in the narrow and complicated pipeline, the degree of freedom of the robot must be increased, so that the robot body will not conflict with the environmental constraints while the robot end is tracking the spraying trajectory. In the trajectory planning of robot operations, inverse kinematics is usually used to solve the problem, which can be divided into two categories: local optimization method and global optimization method. The local optimization method depends on the current robot configuration, that is, starting from the current robot configuration, with the step size agreed in advance, searching for the extreme point of the optimization goal, and using it as the initial point of the next step, the local optimization method The feasible region of is a field U(q) of the current configuration; the feasible region of the global optimization method is the entire configuration space C(q) that satisfies the constraints, and the global optimal solution is found in C(q). Comparing local optimization and global optimization, the former requires less calculation and ensures convergence and stability in a small range, but may be unstable in a larger range; the latter guarantees global optimization, but has a large amount of calculation and slow convergence speed , does not even converge. For actual engineering, it is better to use local optimization method.

The methods in the prior art, such as extended Jacobian method, quadratic programming method, and key point obstacle avoidance method, are difficult to find a suitable optimization criterion, so they are not suitable for the planning of spraying operations on the inner wall of special-shaped narrow and long pipelines. For example, in the key point obstacle avoidance method, if the robot works on the inner wall of the narrow and long pipe, there must be many dangerous points of collision between the robot and the inner wall of the narrow and long pipe, and these dangerous points are not fixed, but change with the configuration of the robot. It is not feasible to find the danger point first and then optimize it. As another example, the extended Jacobian method is aimed at the robot with one redundant degree of freedom, which is obviously not applicable to the robot with multiple redundant degrees of freedom. As another example, in the quadratic programming method, it is necessary to write a quadratic optimization function, which contains a matrix, so the operation is complicated.

Therefore, the above method is not suitable for the multi-redundant degree of freedom robot to plan the spraying operation of the special-shaped narrow and long pipeline.

Contents of the invention

The object of the present invention is to provide a multi-redundant degree of freedom spraying robot and a trajectory planning method for spraying special-shaped long and narrow pipelines by using the robot to address the shortcomings of the prior art.

In order to achieve the above object, the present invention provides a trajectory planning method for pipeline spraying robots with multiple redundant degrees of freedom. The trajectory planning method refers to that the robot searches for a path from the starting point to The path of the end point enables the robot to complete the spraying operation on the inner wall of the pipeline without colliding with the inner wall of the pipeline as much as possible. For a redundant robot, the joint space dimension a is greater than the task space dimension b, given the end pose of the redundant robot, there are infinitely many points in the joint space corresponding to it, and the set of these points is an a-b dimension of the joint space Manifold, so that the redundant robot can achieve a given terminal posture, and can also change in this subspace to meet the requirements such as improving the flexibility of the robot, avoiding singularities, avoiding obstacles, avoiding joint limits and improving dynamic performance. Wait for the second goal.

The above method comprises the following steps:

S1, the geometric model of the surface to be sprayed is imported into a specific module of the drawing software, and the specific module automatically generates a non-collision spraying path of the robot's sprayed workpiece in the pipeline;

S2, perform iterative calculation based on the projection gradient method, and plan the continuous motion trajectory of the robot's joints;

S3. Carry out a collision check according to the joint continuous motion trajectory. If there is a collision, modify the weight coefficient of the optimization function, and return to step S2 to replan the joint continuous motion trajectory; otherwise, end the planning.

Wherein, the step of "the specific module automatically generates the non-collision spraying path of the robot's spraying workpiece in the pipeline" in step S1 can be specifically:

A1, load the sprayed workpiece model of the robot, and draw the auxiliary surface of the sprayed surface according to the spraying process parameters;

A2, select the auxiliary surface and the sprayed workpiece, and generate the intersection line of the two, so as to obtain the spraying path of the sprayed workpiece;

A3, select the interpolation method, determine the number of path points for spraying the workpiece, form the path points in order into a path point sequence X ₀ , X ₁ ,...,X _i ,...,X _n , export the path point sequence for future reference The robot plans the joint trajectory, where X _i =[xi _, y _i , _zi ], xi _, y _i , _zi are the coordinate values of the path point X _i on the X, Y, and Z coordinate axes respectively, i=1,...,n, n is an integer.

Wherein, step S2 specifically may include:

B1, fit the central axis of the pipeline, the function of the central axis is

$\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>\end{array}\right.<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; x</span>}{<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

Among them, x _L and x _U are the starting point and the end point of the pipeline respectively;

B2. Let the initial value of the iteration number j be 0, the iteration step size be ΔT, and the initial value of the joint angle of the robot be q ₀ , where $q_0={[{\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="A2009100908270013H1.png"\; state="\{\{state\}\}">q</figure-callout>}}_{1_0},{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="A2009100908270013H1.png"\; state="\{\{state\}\}">q</figure-callout>}}_{2_0},...,q_{N_0}]}^T,$ N is the number of joints;

对X₀求导得到 $\stackrel{\&CenterDot;}{X}=\frac{X_0-\hat{X}}{\mathrm{\&Delta;t}};$ 在公式X₀＝X_j中，0代表路径点的序号，j代表迭代次数；B3, let the position of the first path point of the sprayed workpiece X ₀ =X _j , according to the forward kinematics equation, the position of the first path point of the sprayed workpiece corresponding to the initial value q ₀ of the joint angle of the robot is obtained as

Taking the derivative with respect to X ₀ gives $\stackrel{\&CenterDot;}{x}=\frac{x_0-\hat{x}}{\mathrm{\&Delta;t}};$ In the formula X ₀ =X _j , 0 represents the serial number of the path point, and j represents the number of iterations;

B4, obtain the sum H of the distances between each joint of the robot and the central axis, and use H as the optimization function:

$\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="2"\; label="y\; i"\; filenames="A2009100908270013H1.png"\; state="\{\{state\}\}">y</figure-callout></span><figure-callout\; id="2"\; label="y\; i"\; filenames="A2009100908270013H1.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; </span>}}^{\mathrm{<span\; class="notranslate">i</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$

Where w _i is the weight coefficient;

B5, take v as the negative gradient direction of the optimization function H, and take an appropriate gain k to minimize the optimization function H, then

$\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&dtri;</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; k</span>}{<span\; class="notranslate">\; [</span>\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; h</span>}}{<span\; class="notranslate">\; \&PartialD;</span>{\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; ]</span>}_{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

Inverse Kinematics Equations According to the Projected Gradient Method

Substituting formula (3) into formula (4), we get

代入式(4)，得到

则新的关节角度值 $q_1=q_0+\stackrel{\&CenterDot;}{q}\mathrm{\&Delta;T};$ B6, the derivative of the initial value _q0 of the joint angle of the robot and the position _X0 of the first path point of the sprayed workpiece

Substituting into formula (4), we get

Then the new joint angle value $q_{}$${}_1=q_0+\stackrel{\&Center\; Dot;}{q}\mathrm{\&Delta;T};$

B7, calculate the new spraying workpiece position corresponding to the new joint angle value q1 according to the forward kinematics equation ${\hat{x}}_1=f\left(q_1\right);$

B8, calculate $\mathrm{\&Delta;X}=\left|\right|x_0-{\hat{x}}_1\left|\right|,$ If ΔX>ξ, then return to step B2 until ΔX<ξ to obtain the value of the joint angle of the robot corresponding to the position X _j of the first path point of the sprayed workpiece; where ξ is a preset acceptable error value;

B9, make j=j+1, obtain the value of the joint angle of the robot corresponding to the next path point of the sprayed workpiece, until obtaining the value of the joint angle of the robot corresponding to all path points;

B10, perform interpolation on each joint according to the interpolation method, and obtain the continuous motion trajectory of the joint;

B11. According to the terminal pose and terminal velocity of the robot, check whether the fluctuations of the spraying distance and spraying speed meet the constraints, and verify whether the spraying distance and spraying speed meet the joint torque constraints through the dynamic equation. If the above conditions are met, the end of the step S2, otherwise return to step S1.

Wherein, the robot may have multiple redundant degrees of freedom, for example, 2 redundant degrees of freedom.

Wherein, the drawing software may be DELMIA software, and correspondingly, the specific module is an ArcWelding module.

Among them, the interpolation method is quintic spline interpolation.

Among them, the spraying process parameters include spraying distance, spraying width and spraying width.

Among them, the spraying workpiece is the end spray gun.

The present invention also provides a pipeline spraying robot with multiple redundant degrees of freedom for operation planning using the above trajectory planning method, including a spraying workpiece and multiple joints connected with the spraying workpiece.

The above-mentioned technical scheme has the following advantages:

1. The scheme of the present invention belongs to the local optimization method, and the amount of calculation is small;

2. The solution of the present invention is suitable for multi-redundant degree-of-freedom robots to plan spraying operations for special-shaped narrow and long pipes. Therefore, on the one hand, it can ensure that it does not hit the wall, and on the other hand, it can achieve high spraying quality, such as uniform spraying and high accuracy.

Description of drawings

Fig. 1 is the method flowchart of the embodiment of the present invention;

Fig. 2 is an inverse kinematics solution model of a pipeline spraying robot with multiple redundant degrees of freedom according to an embodiment of the present invention.

Detailed ways

The specific implementation manners of the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

Fig. 1 is a method flow chart of an embodiment of the present invention; Fig. 2 is an inverse kinematics solution model of a pipeline spraying robot with multiple redundant degrees of freedom according to an embodiment of the present invention. As shown in Fig. 1 and Fig. 2, the operation trajectory planning method of the pipeline spraying robot with multiple redundant degrees of freedom according to the present invention comprises the following steps:

S1, import the geometric model of the surface to be sprayed into a specific module of the drawing software, such as the Arc Welding module of DELMIA software, and the Arc Welding module automatically generates the non-collision spraying path of the spraying workpiece (such as the end spray gun) of the robot in the pipeline;

S2, perform iterative calculation based on the projection gradient method, and plan the continuous motion trajectory of the robot's joints;

S3. Carry out a collision check according to the continuous motion trajectory of the joints. If there is a collision, modify the weight coefficient of the optimization function, and return to step S2 to replan the continuous motion trajectory of the joints; otherwise, end the planning. For example, the collision test in the ProE environment can be carried out. If there is a collision, the weight coefficient corresponding to the collision joint in the optimization function H is modified, and then the continuous motion trajectory planning of the robot joint is carried out in step S2 until the collision test is passed, and finally the result is sent to to the robot control system, which generates robot control commands.

In this embodiment, the step of "the Arc Welding module automatically generates the non-collision spraying path of the end spray gun of the robot in the pipeline" in step S1 may specifically include:

A1, load the end spray gun model of the robot, and draw the auxiliary surface of the sprayed surface according to the spraying process parameters (for example, spraying distance, spray width and spray overlap);

A2, select the auxiliary surface and the end spray gun, and generate the intersection line of the two, so as to obtain the spraying path of the end spray gun;

A3, select an interpolation method (such as quintic spline interpolation) according to needs (for example, according to the movement speed of the end spray gun), determine the number of path points of the end spray gun, and form the path point sequence X ₀ , X ₁ in order, …,X _i ,…,X _n , export the sequence of waypoints for planning the joint trajectory of the robot, where Xi _i =[xi _, y _i , _zi ], xi _, y _i , _zi respectively is the coordinate value of the path point X _i on the three coordinate axes of X, Y, and Z (as shown in FIG. 2 ), i=1, . . . , n, where n is an integer.

In this embodiment, step S2 may specifically include:

B1, fit the central axis of the pipeline, the central axis is farthest from the inner wall of the pipeline, and its function is

$\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>\end{array}\right.<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

Among them, x _L and x _U are the starting point and the end point of the pipeline respectively;

B2. Let the initial value of the iteration number j be 0, the iteration step size be ΔT, and the initial value of the joint angle of the robot be q ₀ , where $q_0={[{\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="A2009100908270013H1.png"\; state="\{\{state\}\}">q</figure-callout>}}_{1_0},{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="A2009100908270013H1.png"\; state="\{\{state\}\}">q</figure-callout>}}_{2_0},...,q_{N_0}]}^T,$ N is the number of joints. In this embodiment, N=8. As shown in FIG. 2, each joint is joint 1 to joint 8;

对X₀求导得到 $\stackrel{\&CenterDot;}{X}=\frac{X_0-\hat{X}}{\mathrm{\&Delta;t}};$ 在公式X₀＝X_j中，0代表路径点的序号，j代表迭代次数；B3, let the position of the first path point of the end spray gun X ₀ =X _j , according to the forward kinematics equation, the position of the first path point of the end spray gun corresponding to the initial value q ₀ of the joint angle of the robot is obtained as

Taking the derivative with respect to X ₀ gives $\stackrel{\&Center\; Dot;}{x}=\frac{x_0-\hat{x}}{\mathrm{\&Delta;t}};$ In the formula X ₀ =X _j , 0 represents the serial number of the path point, and j represents the number of iterations;

B4, obtain the sum H of the distances between each joint of the robot and the central axis, and use H as the optimization function:

$\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="2"\; label="y\; i"\; filenames="A2009100908270013H1.png"\; state="\{\{state\}\}">y</figure-callout></span><figure-callout\; id="2"\; label="y\; i"\; filenames="A2009100908270013H1.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; </span>}}^{\mathrm{<span\; class="notranslate">i</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$

Where w _i is the weight coefficient;

B5, take v as the negative gradient direction of the optimization function H, and take an appropriate gain k to minimize the optimization function H, then

$\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&dtri;</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; k</span>}{<span\; class="notranslate">\; [</span>\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; h</span>}}{<span\; class="notranslate">\; \&PartialD;</span>{\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; ]</span>}_{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

Inverse Kinematics Equations According to the Projected Gradient Method

Substituting formula (3) into formula (4), we get

代入式(4)，得到

则新的关节角度值 $q_1=q_0+\stackrel{\&CenterDot;}{q}\mathrm{\&Delta;T};$ B6, the derivative of the initial value q ₀ of the joint angle of the robot and the position X ₀ of the first path point of the end spray gun

Substituting into formula (4), we get

Then the new joint angle value $q_{}$${}_1=q_0+\stackrel{\&Center\; Dot;}{q}\mathrm{\&Delta;T};$

B7, calculate the new tip gun position corresponding to the new joint angle value _q1 according to the forward kinematics equation ${\hat{x}}_1=f\left(q_1\right);$

B8, calculate $\mathrm{\&Delta;X}=\left|\right|x_0-{\hat{x}}_1\left|\right|,$ If ΔX>ξ, then return to step B2 until ΔX<ξ, to obtain the value of the joint angle of the robot corresponding to the position X _j of the first path point of the end spray gun; where ξ is a preset acceptable error value;

B9, make j=j+1, obtain the value of the joint angle of the robot corresponding to the next path point of the end spray gun, until obtaining the value of the joint angle of the robot corresponding to all path points;

B10, perform interpolation on each joint according to the interpolation method, and obtain the continuous motion trajectory of the joint;

B11. According to the terminal pose and terminal velocity of the robot, check whether the fluctuations of the spraying distance and spraying speed meet the constraints, and verify whether the spraying distance and spraying speed meet the joint torque constraints through the dynamic equation. If the above conditions are met, the end of the step S2, otherwise return to step S1.

In this embodiment, the robot may have multiple redundant degrees of freedom, for example, 2 redundant degrees of freedom.

The present invention also provides a pipeline spraying robot with multiple redundant degrees of freedom for operation planning using the above trajectory planning method, including a spraying workpiece and multiple joints connected with the spraying workpiece.

It can be seen from the above embodiments that the trajectory planning method of the embodiment of the present invention is suitable for the multi-redundant degree of freedom robot to plan the spraying operation of the special-shaped narrow and long pipeline, so on the one hand, it can ensure that it does not hit the wall, and on the other hand, it can achieve high spraying efficiency. Quality, such as uniform spraying, high precision. And this method belongs to the local optimization method, and the calculation amount is small.

The above is only a preferred embodiment of the present invention, it should be pointed out that for those of ordinary skill in the art, without departing from the technical principle of the present invention, some improvements and modifications can also be made, these improvements and modifications It should also be regarded as the protection scope of the present invention.

Claims (10)

1. A trajectory planning method for a robot with multiple redundant degrees of freedom to carry out pipeline spraying operations, comprising the following steps: S1, importing the geometric model of the surface to be sprayed into a specific module of the drawing software, the specific module automatically generates a non-collision spraying path of the robot's sprayed workpiece in the pipeline; S2, performing iterative calculations based on the projection gradient method, and planning the continuous motion trajectory of the joints of the robot; S3, performing a collision check according to the continuous motion trajectory of the joint, if there is a collision, modify the weight coefficient of the optimization function, return to step S2 and replan the continuous motion trajectory of the joint; otherwise, end the planning. 2. The trajectory planning method according to claim 1, characterized in that the step of "the specific module automatically generates the collision-free spraying path of the robot's spraying workpiece in the pipeline" in the step S1 comprises: A1, loading the spraying workpiece model of the robot, and drawing the auxiliary surface of the sprayed surface according to the spraying process parameters; A2, select the auxiliary surface and the sprayed workpiece, and generate the intersection line of the two, so as to obtain the spraying path of the sprayed workpiece; A3, select the interpolation mode, determine the number of path points of the sprayed workpiece, form the path points in order into a path point sequence X ₀ , X ₁ ,...,X _i ,...,X _n , and combine the path points The sequence is derived in preparation for the planning of the joint trajectory of the robot, where X _i =[xi _, y _i , _zi ], _xi , y _i , _zi are respectively the path point _Xi in X, Y, Z The coordinate values of the three coordinate axes, i=1,...,n, where n is an integer. 3. The trajectory planning method according to claim 2, wherein said step S2 comprises: B1, fitting the central axis of the pipeline; B2, the initial value of the number of iterations j is 0, the iteration step size is ΔT, and the initial value of the joint angle of the robot is q ₀ ; B3, let the position of the first path point of the sprayed workpiece X ₀ =X _j , wherein 0 represents the sequence number of the path point, j represents the number of iterations, and obtain the initial joint angle corresponding to the robot according to the forward kinematics equation The position of the first path point of the sprayed workpiece with value q ₀ is $\hat{x}=f\left(q_0\right);$ B4, obtain the sum H of the distances between each joint of the robot and the central axis, and use H as an optimization function; B5, take v as the negative gradient direction of the optimization function H, and take the appropriate gain k, minimize the optimization function H, and calculate according to the inverse kinematic equation of the projected gradient method

B6, substitute the initial value _q0 of the joint angle of the robot and the derivative of the position _X0 of the first path point of the sprayed workpiece

get

Then the new joint angle value $q_1=q_0+\stackrel{\&Center\; Dot;}{q}\mathrm{\&Delta;T};$ B7, calculate the new spraying workpiece position corresponding to the new joint angle value _q1 according to the forward kinematics equation ${\hat{x}}_1=f\left(q_1\right);$ B8, calculate $\mathrm{\&Delta;X}=\left|\right|x_0-{\hat{x}}_1\left|\right|,$ If ΔX>ξ, then return to step B2 until ΔX<ξ to obtain the value of the joint angle of the robot corresponding to the position X _j of the first path point of the sprayed workpiece; where ξ is a preset acceptable error value; B9, make j=j+1, obtain the value of the joint angle of the robot corresponding to the next path point of the sprayed workpiece, until obtaining the value of the joint angle of the robot corresponding to all path points; B10, performing interpolation on each joint according to the interpolation method to obtain a continuous motion track of the joint; B11. Check whether the fluctuation of spraying distance and spraying speed satisfies the constraint, and verify whether the spraying distance and spraying speed satisfy the joint torque constraint through the dynamic equation. If the above conditions are satisfied, end step S2, otherwise return to step S1. 4. The trajectory planning method according to claim 1, wherein the robot has multiple redundant degrees of freedom. 5. The trajectory planning method according to claim 4, wherein the robot has two redundant degrees of freedom. 6. The trajectory planning method according to claim 1, wherein the drawing software is DELMIA software, and the specific module is an Arc Welding module. 7. The trajectory planning method according to claim 2, wherein the interpolation method is quintic spline interpolation. 8. The trajectory planning method according to claim 1, wherein the spraying process parameters include spraying distance, spraying width and spraying width. 9. The trajectory planning method according to any one of claims 1-8, characterized in that, the sprayed workpiece is an end spray gun. 10. A pipeline spraying robot with multiple redundant degrees of freedom, using the trajectory planning method described in any one of claims 1 to 8 for job planning, the robot includes a spraying workpiece and multiple joint.

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