A method for generating a robot traction trajectory for braiding a bent structural member

Abstract

The present invention discloses a method for generating robot traction trajectories for the weaving of curved structural parts. The nonlinear geometric center line of the curved structural part in the robot for weaving the curved structural part is discretized into N+1 discrete points, and a local coordinate system is established for each discrete point; the angle between the X axes and the translation distance along the X and Z axes of the local coordinate systems of adjacent discrete points are calculated; a homogeneous transformation matrix between the local coordinate systems of adjacent discrete points is established; a weaving ring center coordinate system, a base coordinate system, and a flange coordinate system are established; the relative posture of the robot and the weaving machine is calibrated to obtain a homogeneous transformation matrix; a coordinate transformation relationship is constructed, and the coordinate transformation relationship is combined with a space closed motion chain to generate the robot terminal motion trajectory. The present invention makes full use of the shape feature information of the curved structural part and the robot's motion flexibility, effectively solves the technical problems of weaving and processing curved structural parts with curved shapes, effectively expands the types and range of woven products, and significantly improves their value.

Description

Technical Field

[0001] The present invention relates to a method for calculating a robot task space trajectory, in particular to a method for generating and calculating a motion trajectory during the weaving and traction process of a robot, and relates to a serial robot widely used in the field of carbon fiber composite material weaving. Background Art

[0002] The carbon fiber composite material weaving technology began in the 1960s. It is a forming technology in which multiple fiber bundles along the fabric forming direction are inclined and crossed according to a certain rule, so that the fiber bundles are intertwined with each other and cover the surface of the curved structural member to form different structures. The traditional ring weaving equipment based on a sliding table uses the single degree of freedom of the sliding table to realize linear reciprocating traction on the curved structural member, and is mostly used for processing simple linear shapes such as containers, pipelines, and cables. There is a limitation that the flexibility of the sliding table is insufficient and it cannot accurately weave the curved structural member.

[0003] With the development needs of the high-tech fields such as aerospace, modern transportation, and medical devices for composite material products showing complex shapes, diverse varieties, and flexible production, the application prospects of complex curved structural members with curved shapes have become increasingly broad. For example, some fuselage shells of large aircraft, landing gears of military aircraft, high-speed rail reversing guide rails, coronary stents and other high-value-added products all need to be manufactured based on the weaving of curved structural members.

[0004] Combining an industrial robot with a weaving machine and simulating the movement of a human arm can sensitively and conveniently change the orientation of the curved structural member, realize the flexible weaving and uniform covering of the fiber bundle, and is particularly suitable for the high-precision automatic weaving and forming of curved fiber products with three-dimensional complex shapes (such as curved brackets of high-speed rail reversing guide rails, variable cross-section shells of missiles, bumpers of lightweight automobiles, partial composite rotating bodies of aircraft wings and fuselages, turbine engine blades, etc.). Further improving the automation level and production efficiency of the weaving machine, applying robot technology to the weaving of curved structural members has become one of the development trends of the industry. Summary of the Invention

[0005] Generating a corresponding robot traction trajectory according to the shape characteristics of the curved structural member is an important prerequisite for realizing stable weaving of the robot. To solve the problem of generating a complex space traction trajectory of the robot, the present invention proposes a method for generating a robot traction trajectory for weaving a curved structural member, which effectively utilizes the shape characteristics of the curved structural member and the flexible characteristics of the multiple degrees of freedom of the robot, can ensure that the curved structural member is always in the best weaving position during the weaving process, improves the uniformity of fiber coverage, and enhances the accuracy of weaving and forming.

[0006] The present invention makes full use of the shape feature information of the bent structural member and the motion flexibility of the robot, effectively solves the technical problem of the braiding process of the bent structural member with a bent shape, can effectively expand the types and scope of braided products, significantly improve the comprehensive utilization rate and practical value of the equipment, and is applicable to the collaborative braiding equipment composed of a robot and a braiding machine.

[0007] The technical solution adopted by the present invention is to adopt the following steps:

[0008] The first step: For the bent structural member in the robot for braiding the bent structural member, establish a functional expression f(x, y, z) = 0 of the non-linear geometric center line of the bent structural member, where x, y, and z respectively represent the coordinate values of the X-axis, Y-axis, and Z-axis of the geometric center line of the bent structural member in the reference system O-XYZ, discretize the non-linear geometric center line into N + 1 discrete points, and determine the coordinate values P0(x0, y0, z0), …, P N (x N , y N , z N ) of each discrete point;

[0009] According to the mathematical expression f(x, y, z) = 0 of the geometric center line of the bent structural member, construct a parametric equation expressed as: x = h(v), y = g(v), z = q(v). Set the increment of the dependent variable v as δ, discretize the center line into N + 1 discrete points, and for the i-th discrete point, the dependent variable v is: v i = v0 + δ × i, then the coordinate value P i of the corresponding discrete point is expressed as:

[0010]

[0011] The second step: Establish a local coordinate system O i -X i Y i Z i (i = 0, 1, …, N) for each discrete point, where O i -X i Y i Z i represents the local coordinate system of the i-th discrete point, so as to establish N + 1 local coordinate systems for all discrete points;

[0012] The third step: Calculate the included angle α i between the X-axes, the translation distance d xi along the X-axis, and the translation distance d zi along the Z-axis between the local coordinate systems of all adjacent discrete points, i = 0, 1, …, N;

[0013] Step 4: According to the result of Step 3, establish the homogeneous transformation matrix between the local coordinate systems of adjacent discrete points, i.e., the local coordinate system O i -X i Y i Z i and the local coordinate system O i+1 -X i+1 Y i+1 Z i+1 The homogeneous transformation matrix between them is:

[0014]

[0015] where trans(d xi , 0, d zi ) represents the translation matrix of the local coordinate system O i+1 -X i+1 Y i+1 Z i+1 of the (i + 1)-th discrete point relative to the local coordinate system O i -X i Y i Z i of the i-th discrete point, and roty(α i ) represents the rotation matrix of the local coordinate system O i+1 -X i+1 Y i+1 Z i+1 of the (i + 1)-th discrete point relative to the local coordinate system O i -X i Y i Z i about the Y i axis, d xi represents the translation distance between adjacent coordinate systems along the X-axis direction, and d zi represents the translation distance between adjacent coordinate systems along the Z-axis direction;

[0016] Step 5: Establish the knitting ring center coordinate system O b -X b Y b Z b with the center of the knitting ring of the knitting machine as the origin, establish the base coordinate system O r -X r Y r Z r with the base of the robot as the origin, and establish the flange coordinate system O f -X f Y f Z f ;

[0017] Step 6: Calibrate the relative pose of the robot and the knitting machine to determine the base coordinate system O of the robot r -X r Y r Z r and the center coordinate system O of the knitting loop of the knitting machine b -X b Y b Z b The rotation transformation angle and translation distance between them, and thus calculate the homogeneous transformation matrix according to the rotation transformation angle and translation distance

[0018] Step 7: Use the homogeneous transformation matrix to construct the coordinate transformation relationship, and then use the coordinate transformation relationship combined with the spatial closed kinematic chain to generate the motion trajectory of the center of the end flange of the robot in space.

[0019] In the first step described above, the bending structural member has a non-linear shape and its geometric center line has a clear function expression.

[0020] In the second step, specifically: according to the function expression of the non-linear geometric center line and the coordinate values of the discrete points, calculate the tangential vector of the non-linear geometric center line at the discrete points as the X-axis of the local coordinate system, calculate the reverse vector of the normal vector of the discrete points as the Z-axis of the local coordinate system, and finally determine the Y-axis of the local coordinate system according to the right-hand rule.

[0021] In the second step described above, calculate the first-order partial derivatives on the three axes according to the function expression of the non-linear geometric center line of the bending structural member and By substituting the numerical values of the discrete point P i (x i , y i , z i ) into the calculation, obtain the tangential vector of the discrete point P i as the X axis direction in the local coordinate system O i -X i Y i Z i In[[ID=�0]] i axis direction Calculate the second-order partial derivatives on the three axes according to the function expression of the non-linear geometric center line of the bending structural member and By substituting the numerical values of the discrete point P i (x i , y i , z i ) into the calculation, obtain the normal vector of the discrete point P i ​ Its reverse vector is used as the local coordinate system O i -X i Y i Z i The Z in i the axis direction is

[0022] Specifically, it can be: Calculate the tangential vector of the geometric center line of the bent structural member at the i-th discrete point P i here This tangential vector is the first-order partial derivative of the geometric center line function Substitute the coordinate values of the discrete point P i to calculate and obtain: Calculate the normal vector of the geometric center line of the bent structural member at the i-th discrete point P i here This normal vector is the second-order partial derivative of the geometric center line function Substitute the coordinate values of the discrete point P i to calculate and obtain: ... Take the discrete point as the origin O i , the tangential vector as X i axis, the reverse vector of the normal vector as Z i axis, determine the Y i axis according to the right-hand rule, and thus construct the local coordinate system O i -X i Y i Z i .

[0023] The specific content of the third step is:

[0024] 3.1. Calculate the rotation transformation angle and translation distance between the local coordinate system O i -X i Y i Z i of the i-th discrete point and the local coordinate system O i+1 -X i+1 Y i+1 Z i+1 of the (i + 1)-th discrete point. By calculating the angle between the tangential vectors and of adjacent discrete points, determine the X i -X i Y i Z i in the local coordinate system O iThe angle between the axis and the local coordinate system O of the (i + 1)-th discrete point i+1 -X i+1 Y i+1 Z i+1 and the X-axis in i+1 the angle α i is the angle of rotation around the Y i axis, and the specific calculation is as follows:

[0025]

[0026] 3.2. Calculate the translation distances of the local coordinate systems of adjacent discrete points along the X-axis and Z-axis. First, connect the origin O i of the local coordinate system of an adjacent discrete point with O i+1 to form a vector Calculate the angle β between the vector i and the X axis (tangential vector i ), and the specific calculation is as follows:

[0027]

[0028] where arccos() represents the inverse cosine trigonometric function, and O i represents the origin of the local coordinate system O i -X i Y i Z i ;

[0029] 3.3. Then, use the angle β i to calculate that the translation distance of the adjacent coordinate systems along the X-axis is |O i O i+1 |×cosβ i , and the translation distance along the Z-axis is

[0030] The specific content of the sixth step described above is:

[0031] Both the robot and the knitting machine are installed on the horizontal ground. By teaching, move the end flange of the robot to approach the center of the knitting loop in any posture, and make the center O f of the flange coincide with the center O b of the knitting loop. Read the coordinate value P f (x f , y f , z f ) of the center of the end flange of the robot through the teach pendant. Project the spatial topology formed by the robot and the knitting machine onto the ground to form a geometric constraint relationship, and the coordinate system O of the center of the knitting loopb -X b Y b Z b Relative to the base coordinate system O r -X r Y r Z r Rotating around the Z r axis by an angle of where atan() represents the arctangent trigonometric function, and the translation distance along the X r axis is d x = x f and the translation distance along the Y r axis is d y = y f and the translation distance along the Z r axis is d z = z f ; then obtain the coordinate system O of the center of the braiding ring b -X b Y b Z b Relative to the base coordinate system O r -X r Y r Z r The homogeneous transformation matrix is:

[0032]

[0033] where rotz(θ) represents the homogeneous transformation matrix for rotating by θ around the coordinate axis Z, and trans(d x , d y , d z ) represents the homogeneous transformation matrix for translating along the coordinate axes X, Y, and Z by d x , d y and d z respectively.

[0034] The specific content of the seventh step is as follows:

[0035] 7.1. Construct a spatial closed kinematic chain composed of a robot - a bending structural member - a braiding machine, and establish an equivalent equation for coordinate transformation [[ID=8l]]where represents the homogeneous transformation matrix of the center coordinate system O of the robot end flange r -X r Y r Z r relative to the robot base coordinate system O b -X b Y b Z b , represents the coordinate system O of the braiding ring center of the braiding machineb -X b Y b Z b With respect to the central coordinate system O of the robot end flange f -X f Y f Z f homogeneous transformation matrix of

[0036] The coordinate transformation equivalent equation in the tenth step described above is used for: with the base coordinate system O of the robot r -X r Y r Z r as the reference coordinate system, the base coordinate system O r -X r Y r Z r is transformed to the central coordinate system O of the robot end flange through a composite transformation of rotation and translation f -X f Y f Z f and further transformed to the central coordinate system O of the knitting loop of the knitting machine b -X b Y b Z b .

[0037] 7.2. Set the bending structural member to pass through the center of the knitting loop according to the knitting process, and the discrete points P of the geometric center line of the bending structural member N-i+1 origin O N-i+1 coincides with the center O of the knitting loop b and makes the tangent direction of the geometric center line of the bending structural member coincide with the radial direction of the knitting loop, that is, the local coordinate system X i axis coincides with the X b axis of the central coordinate system of the knitting loop, thus converting the coordinate transformation equivalent equation of the tenth step into

[0038] 7.3. Use the converted coordinate transformation equivalent equation to generate the homogeneous matrix of the robot end flange center under the reference of the robot base coordinate system:

[0039]

[0040] where f i represents the i-th discrete point of the robot traction trajectory, represents the homogeneous matrix of the robot end flange center under the reference of the robot base coordinate system when the (N - i + 1)-th discrete point R of the non-linear geometric center line of the bending structural member passes through the center of the knitting loop; N-i+1

[0041] ​Finally, the coordinates of the center of the flange at the end of the robot in the reference of the robot base coordinate system are extracted to obtain the coordinates of the motion trajectory of the center of the flange at the end of the robot, which are used as discrete trajectory points.

[0042] In the above 7.3, the (N - i + 1)-th discrete point P of the non-linear geometric center line of the curved structural member N-i+1 When passing through the center of the braiding ring, the i-th discrete point of the robot traction trajectory, that is, the homogeneous matrix of the center of the flange at the end of the robot in the reference of the robot base coordinate system is expressed as:

[0043]

[0044] where represents the attitude matrix of the center of the flange at the end of the robot relative to the base coordinate system O r -X r Y r Z r and represents the coordinates of the center of the flange at the end of the robot relative to the robot base coordinate system, which are used as discrete trajectory points.

[0045] When the discrete point P of the geometric center line of the curved structural member N-i+1 coincides with the center O of the braiding ring b the coordinate value of the center of the flange at the end of the robot in the reference system of the base coordinate system is There are a total of N + 1 discrete points on the curved structural member, and thus the set of discrete trajectory points corresponding to the center of the flange at the end of the robot can be obtained as

[0046] Each discrete point on the geometric center line of the curved structural member corresponds to a discrete trajectory point in space of the center of the flange at the end of the robot. All the discrete trajectory points of the robot are linearly connected and combined to obtain the complete spatial traction motion trajectory of the robot during the braiding process.

[0047] The present invention utilizes the non-linear function expression of the geometric center line of the curved structural member, constructs a local coordinate system of a series of discrete points, obtains the transformation matrix between any adjacent local coordinate systems by calculating the rotation transformation angle and translation distance between adjacent coordinate systems. At the same time, the present invention calibrates the spatial relative pose between the robot and the braiding machine, constructs a closed motion chain composed of the robot - curved structural member - braiding machine, thereby obtaining the motion equivalent equation. Based on the requirements of the braiding process: the origin of the local coordinate system of the discrete geometric center line of the curved structural member and the tangential direction need to coincide with the origin of the braiding ring center and the radial direction respectively during the braiding process. By using the motion equivalent equation, the motion trajectory points of the center of the flange at the end of the robot in space are solved, and the trajectory points are combined to obtain the spatial traction trajectory of the robot during the braiding of the curved structural member.

[0048] The advantages and beneficial effects of the present invention are as follows:

[0049] 1. Traditional single-degree-of-freedom sliding tables or robots for braiding mainly achieve three-dimensional linear reciprocating traction of curved structural parts through a single degree of freedom, and are mostly used for processing simple shapes such as containers, pipelines, and cables. The range of products that can be processed is relatively narrow. The present invention makes full use of the shape feature information of curved structural parts and the flexible movement characteristics of multi-degree-of-freedom serial robots, and can be used for braiding and processing high-value-added curved-shaped products such as parts of the fuselage shell of large aircraft, landing gears of military aircraft, high-speed rail reversing guide rails, and coronary stents, effectively expanding the range and types of products that can be processed.

[0050] 2. The coverage of carbon fiber on the surface of curved structural parts has an important impact on the mechanical properties of products. The present invention avoids the problem of reduced uniformity of carbon fiber braiding coverage caused by the traditional linear traction mode that ignores the bending characteristics of curved structural parts, and can significantly improve the uniformity of carbon fiber braiding and the forming accuracy of processed products, ultimately improving the overall mechanical properties of products.

[0051] 3. Traditional sliding tables occupy a large area and lack flexibility, and cannot complete the work of other processes during carbon fiber braiding production through simple expansion, resulting in low overall equipment utilization rate. By replacing the single-degree-of-freedom sliding table with a robot, the site is saved and the overall equipment utilization efficiency is improved. Brief Description of the Drawings

[0052] Figure 1 is a flowchart of the method of the present invention;

[0053] Figure 2 is a schematic diagram of a curved structural part applicable in the present invention;

[0054] Figure 3 is a schematic diagram of discrete points on the geometric center line of a curved structural part in the present invention;

[0055] Figure 4 is a schematic diagram of the local coordinate system of discrete points on the geometric center line of a curved structural part in the present invention;

[0056] Figure 5 is a schematic diagram of the rotational transformation of the local coordinate system of adjacent discrete points of a curved structural part in the present invention;

[0057] Figure 6 is a schematic diagram of the translational transformation of the local coordinate system of adjacent discrete points of a curved structural part in the present invention;

[0058] Figure 7 is a schematic diagram of the coordinate system of the robot and the braiding machine in the present invention;

[0059] Figure 8It is a schematic diagram of the projection geometric relationship of the relative pose between the robot and the knitting machine in the present invention;

[0060] Figure 9 It is a schematic diagram of the closed kinematic chain composed of the robot - the bending structural member - the knitting machine in the present invention;

[0061] Figure 10 It is a schematic diagram of the discrete points of the robot traction trajectory in the present invention. Specific embodiments

[0062] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0063] As Figure 10 shown, the robot for bending structural member knitting includes a robot manipulator 1, a bending structural member 3, and a knitting loop 5; a rigid bending structural member 3 is fixed at the end of the robot manipulator 1, and a carbon fiber composite material is wound around the bending structural member 3 through the knitting loop 5 for knitting. The robot manipulator 1 needs to drive the bending structural member 3 to pass through the center 6 of the knitting loop of the knitting loop 5.

[0064] The bending structural member 3 is a rod-shaped structure with a three-dimensional bent shape. The goal of the method is to generate the movement trajectory of the end of the robot manipulator 1 that can drive the bending structural member 3 as the robot traction trajectory 2, that is, the spatial traction movement trajectory, so that the knitting loop 5 can always pass through the center 6 of the knitting loop.

[0065] Therefore, the specific implementation is to establish a number of discrete points 4 of the geometric center line on the bending structural member 3, and then use the method of the present invention to generate the robot traction trajectory 2, and then control the movement of the end of the robot manipulator 1.

[0066] The basic principle of the present invention mainly lies in: First, decompose the geometric center line of the bent structural member 3 into a series of discrete points 4, and construct a local coordinate system at each discrete point 4. By calculating the rotation transformation angle and translation distance between adjacent local coordinate systems, construct the homogeneous transformation matrix between the coordinate systems. Establish a base coordinate system and a flange coordinate system at the robot base and the center of the flange respectively, and establish a coordinate system at the center of the knitting ring of the knitting machine. Calibrate the spatial relative pose of the robot and the knitting machine, and calculate the homogeneous transformation matrix of the coordinate system at the center of the knitting ring of the knitting machine relative to the robot base coordinate system. Based on the knitting process requirements, the discrete points of the geometric center of the bent structural member need to pass through the center of the knitting ring of the knitting machine in sequence and ensure that the tangential direction of the discrete points coincides with the radial direction of the knitting ring. Thus, a closed kinematic chain of the robot-bent structural member-knitting machine is constructed, a kinematic equivalent equation is established, and further through matrix operations, the pose matrix of the center of the flange at the end of the robot in space and the discrete traction trajectory points of the robot are obtained. Each discrete point of the geometric center line of the bent structural member corresponds to a discrete spatial traction trajectory point of the robot. Thus, the complete discrete points of the robot traction trajectory can be obtained according to the shape characteristics of the bent structural member.

[0067] Embodiment of the present invention:

[0068] Appendix Figure 1 The block diagram in it is the specific flowchart of the calculation method for the traction trajectory of the bent structural member knitting robot proposed by the present invention. As shown in Appendix Figure 7 shown, the present invention uses a 6-degree-of-freedom serial industrial robot and a horizontal knitting machine as processing equipment, and takes the bent structural member shown in Appendix Figure 2 shown as the processing and analysis object, and is described in combination with the embodiment. The angles involved are all expressed in degrees (°), and the units of the dimension lengths and distances involved are all millimeters (mm). The specific process of the present invention mainly includes the following steps:

[0069] The first step: As shown in Appendix Figure 2 and Appendix Figure 3 shown, the geometric center line of the bent structural member has the following parametric expression f(x, y, z):

[0070]

[0071] where v is the dependent variable v i = v0 + δ × i, and the value range is v ∈ [0, 90°]. The initial value of the dependent variable is v0 = 0°, and the increment is δ = 0.9°. Then the geometric center line of the bent structural member can be discretized into 101 points (N = 100).

[0072] The second step: As shown in Appendix Figure 4 shown, the first-order partial derivative of the geometric center line of the bent structural member is: h′(v i ) = 200cos(vi ), g′(v i ) = 0, q′(v i ) = -200sin(v i ), the coordinate values of the first discrete point P0 are: x0 = 200×sin(0°) = 0, y0 = 0, z0 = 200×cos(0°) = 200, that is, P0(0, 0, 200). Then the tangential vector at this point is: x′0 = 200×cos(0°) = 200, y′0 = 0, z′0 = -200×sin(0°) = 0, that is, the direction of X0 in the local coordinate system O0-X0Y0Z0 of the first discrete point is The second-order partial derivative of the geometric center line of the bent structural member is: h″(v i ) = -200sin(v i ), g″(v i ) = 0, q″(v i ) = -200cos(v i ), then the normal vector at point P0 is: x″0 = -200×sin(0°) = 0, y″0 = 0, z″0 = -200×cos(0°) = -200, that is, the direction of Z0 in the local coordinate system O0-X0Y0Z0 of the first discrete point is the reverse vector of the normal vector Finally, determine the direction of Y0 according to the right-hand rule.

[0073] Step 3: Repeat the above calculations in Step 2. Take v1 = 0° + 0.9°×1 = 0.9°. The origin coordinates of the second point can be calculated as P1(3.1415, 0, 199.98), and the tangential vector (the direction of X1) The reverse vector of the normal vector (the direction of Z1) Determine the direction of Y1 according to the right-hand rule, and thus construct the local coordinate system O1-X1Y1Z1.

[0074] Step 4: As shown in the attachment Figure 5 , calculate the rotation angle existing between adjacent local coordinate systems. The rotation angle around the Y0 axis between the local coordinate system O0-X0Y0Z0 at the first discrete point P0 and the local coordinate system O1-X1Y1Z1 at the second discrete point P1

[0075] Step 5: As shown in the attachment Figure 6 , the vector is Then the vector and the included angle between the X0 axis can be obtained through The translational distances along the X, Y, and Z axes between the local coordinate system O1-X1Y1Z1 and the coordinate system O0-X0Y0Z0 can be calculated respectively as d x0 = |O0O1| × cosβ0 = 3.1416 × 0.99997 = 3.1415, d z0 = -|O0O1| × sinβ0 = -0.0247.

[0076] Step 6: Repeat Step 4 to Step 5 to calculate the angle α between the Xi axis of all adjacent local coordinate systems and Xi+1 i (i = 0, 1, …, N-1), the translational distance d i along the X xi axis (i = 0, 1, …, N-1) and the translational distance d i along the Z zi axis (i = 0, 1, …, N-1).

[0077] Step 7: The composite homogeneous transformation matrix between the adjacent coordinate systems O0-X0Y0Z0 and O1-X1Y1Z1 is:

[0078]

[0079] And so on, calculate respectively to obtain Then calculate to obtain the transformation matrix between the initial local coordinate system O0-X0Y0Z0 of the curved structural member and O 100 -X 100 Y 100 Z 100 is:

[0080]

[0081] Step 8: As shown in the appendix Figure 7 , establish a coordinate system O b -X b Y b Z b at the center of the knitting loop of the knitting machine, establish a base coordinate system O r -X r Y r Z r at the base of the robot, and establish a flange coordinate system O f -X f Y f Z f .

[0082] Step 9: Move the robot to approach the center of the knitting loop of the knitting machine in an arbitrary posture through teaching, and make the center O f of the flange coincide with the center O bCoincide, project the spatial topology formed by the robot and the knitting machine onto the ground to form a geometric constraint relationship. As shown in the appendix Figure 8 Read the coordinate value P of the center of the flange at the end of the robot through the teach pendant f (433.01, 250, 900). Therefore, the translation distance along the X r axis is d x = 433.01, and the translation distance along the Y r axis is d y = 250, and the translation distance along the Z r axis is d z = 900. The center coordinate system O of the knitting ring b -X b Y b Z b relative to the base coordinate system O r -X r Y r Z r The rotation angle around the Z r axis is Thus, the homogeneous transformation matrix of the center coordinate system O of the knitting ring b -X b Y b Z b relative to the base coordinate system O r -X r Y r Z r is as follows is:

[0083]

[0084] Step 10: As shown in the appendix Figure 9 Construct a spatial closed kinematic chain composed of the robot - bending structural member - knitting machine, and establish an equivalent coordinate transformation equation

[0085] Step 11: According to the knitting process requirements, the bending structural member passes through the center of the knitting ring. When the origin O of the discrete points P on the geometric center line of the bending structural member 100 coincides with the center O of the knitting ring 100 At this time b The pose matrix representation of the first discrete point of the robot traction trajectory in space relative to the base coordinate system O -X b -X b Y b Z b is:

[0086]

[0087] The coordinate value of the first discrete trajectory point of the obtained robot traction trajectory is

[0088] The bending structural member continues to move. When the discrete point P on the geometric center line of the bending structural member 99 passes through the center of the braiding ring, at this time, the transformation relationship between the local coordinate system O0-X0Y0Z0 of the starting point of the bending structural member and the local coordinate system O 99 -X 99 Y 99 Z 99 is as follows: Substituting the data for calculation, we get:

[0089]

[0090] According to the motion equivalence equation, the homogeneous matrix of the second discrete point of the robot traction trajectory in space is obtained therefrom: Calculating, we get:

[0091]

[0092] Therefore, the coordinate value of the second discrete trajectory point of the robot traction trajectory is

[0093] Repeating the above calculation steps, the set of all corresponding discrete trajectory points of the robot traction can be obtained as

[0094] It can be seen from this that the method of the present invention can accurately calculate and obtain the robot spatial traction motion trajectory during the braiding process of the bending structural member. And in specific implementation, compared with the traditional straight trajectory, the present invention fully considers the bending characteristics of the bending structural member and the large-range motion characteristics of the robot, has high calculation accuracy, can be applied to the processing of bending structural members widely existing, and has remarkable technical effects in the field of robot braiding.

Claims

1. A method for generating a robot traction trajectory woven for a bent structural member, characterized in that: The method comprises the following steps: Step 1: For the bent structural member of the robot end effector woven for the bent structural member, establish the functional expression f(x, y, z) = 0 of the non-linear geometric centerline of the bent structural member, where x, y, and z respectively represent the X-axis, Y-axis, and Z-axis coordinate values of the geometric centerline of the bent structural member in the reference system O-XYZ. Discretize the non-linear geometric centerline into N + 1 discrete points, and determine the coordinate values P0(x0, y0, z0), …, P N (x N , y N , z N ); Step 2: Establish a local coordinate system O for each discrete point i _X i Y i Z i (i = 0, 1, …, N), where O i _X i Y i Z i represents the local coordinate system of the i-th discrete point, thereby establishing N + 1 local coordinate systems for all discrete points; Step 3: Calculate the angle α between the X-axes of the local coordinate systems of all adjacent discrete points i , the translation distance d along the X-axis xi and the translation distance d along the Z-axis zi , where i = 0, 1, …, N; Step 4: According to the result of Step 3, establish a homogeneous transformation matrix between the local coordinate systems of adjacent discrete points: where, trans(d xi ,0,d zi ) represents the translation matrix of the local coordinate system O i+1 _X i+1 Y i+1 Z i+1 of the (i + 1)-th discrete point relative to the local coordinate system O i _X i Y i Z i of the i-th discrete point, and roty(α i ) represents the rotation matrix of the local coordinate system O i+1 _X i+1 Y i+1 Z i+1 of the (i + 1)-th discrete point relative to the local coordinate system O i _X i Y i Z i of the i-th discrete point about the Y i axis, d xi represents the translation distance of adjacent coordinate systems along the X-axis, and d zi represents the translation distance of adjacent coordinate systems along the Z-axis; Step 5: Establish a coordinate system O with the center of the knitting loop of the knitting machine as the origin b _X b Y b Z b , and establish a base coordinate system O with the base of the robot as the origin r _X r Y r Z r , and establish a flange coordinate system O with the center of the end flange of the robot as the origin f _X f Y f Z f ; Step 6: Calibrate the relative pose of the robot and the braiding machine to determine the base coordinate system O of the robot r _X r Y r Z r and the center coordinate system O of the braiding loop of the braiding machine b _X b Y b Z b to calculate the homogeneous transformation matrix based on the rotation transformation angle and the translation distance Step 7: Use the homogeneous transformation matrix to construct the coordinate transformation relationship, and then use the coordinate transformation relationship combined with the spatial closed kinematic chain to generate the motion trajectory of the robot end-effector in space; The specific content of the seventh step is as follows: 7.

1. Construct a spatial closed kinematic chain composed of a robot - a bending structural member - a knitting machine, and establish an equivalent coordinate transformation equation where represents the homogeneous transformation matrix of the center coordinate system O r _X r Y r Z r of the center of the end - effector flange of the robot with respect to the base coordinate system O b _X b Y b Z b ; represents the homogeneous transformation matrix of the center coordinate system O b _X b Y b Z b of the knitting loop center of the knitting machine with respect to the center coordinate system O f _X f Y f Z f of the end - effector flange of the robot; 7.

2. Set the bending structural member to pass through the center of the braiding ring according to the braiding process, and the discrete points P of the geometric center line of the bending structural member N-i+1 The origin O N-i+1 coincides with the center O of the braiding ring b and make the tangent direction of the geometric center line of the bending structural member coincide with the radial direction of the braiding ring, so as to convert the coordinate transformation equivalent equation into 7.

3. Generate a homogeneous matrix of the robot end under the reference of the robot base coordinate system by using the converted coordinate transformation equivalent equation: where, f i represents the i-th discrete point of the robot's towing trajectory, represents the (N - i + 1)-th discrete point P of the geometric centerline of the bending structural member N-i+1 is the homogeneous matrix of the robot's end at the time of passing through the center of the braiding ring under the reference of the robot base coordinate system; Finally, extract the coordinates of the motion trajectory of the robot end by using the homogeneous matrix of the robot end under the reference of the robot base coordinate system.

2. A method for generating a robot traction trajectory for weaving a bent structural member according to claim 1, characterized in that: In the first step, the bending structural member has a non-linear shape and its geometric center line has a clear function expression.

3. A method for generating a robot traction trajectory for braiding a bent structural member according to claim 1, characterized in that: In the second step, specifically: according to the function expression of the non-linear geometric centerline and the coordinate values of the discrete points, calculate the tangential vector of the non-linear geometric centerline at the discrete points. As the X-axis of the local coordinate system, calculate the reverse vector of the normal vector of the discrete points. As the Z-axis of the local coordinate system, finally determine the Y-axis of the local coordinate system according to the right-hand rule.

4. A method for generating a robot traction trajectory for braiding a bent structural member according to claim 1, characterized in that: In the second step described above, calculate the first-order partial derivatives on the three axes according to the function expression of the non-linear geometric center line of the bending structural member and By substituting the numerical values of the discrete point P i (x i , y i , z i ) into the calculation, obtain the tangent vector of the discrete point P i as the X axis direction in the local coordinate system O i _X i Y i Z i i Calculate the second-order partial derivatives on the three axes according to the function expression of the non-linear geometric center line of the bending structural member and By substituting the numerical values of the discrete point P i (x i , y i , z i ) into the calculation, obtain the normal vector of the discrete point P i Reverse its vector as the Z i _X i Y i Z i axis direction in the local coordinate system O i ​​ 5. A method for generating a robot traction trajectory for braiding a bent structural member according to claim 4, characterized in that: The specific content of the third step is as follows: 3.

1. Calculate the local coordinate system O of the i-th discrete point i _X i Y i Z i and the local coordinate system O of the i+1th discrete point i+1 _X i+ 1Y i+1 Z i+1 The rotation transformation angle and translation distance between adjacent discrete points are calculated by and The angle between them determines the local coordinate system O of the i-th discrete point i _X i Y i Z i X in i The local coordinate system O between the axis and the i+1th discrete point i+1 _X i+1 Y i+1 Z i+1 X in i+1 The angle between the axes is calculated as: 3.

2. Calculate the translation distances of the local coordinate system of adjacent discrete points along the X-axis and Z-axis directions. First, take the origin O of the local coordinate system of adjacent discrete points i and O i+1 to form a vector Calculate the vector and the angle β i between the X-axis i . The specific calculation is as follows: where arccos( ) represents the inverse cosine trigonometric function, O i represents the origin of the discrete point local coordinate system O i _X i Y i Z i ; 3.

3. Reusing the included angle β i Calculate the translation distance d in the X-axis direction between adjacent coordinate systems xi = |O i O i+1 | × cosβ i , and the translation distance d in the Z-axis direction zi = -|O i O i+1 | × sinβ i , 6. A method for generating a robot traction trajectory for braiding a bent structural member according to claim 1, characterized in that: The specific content of the sixth step is as follows: The robot and the knitting machine are both installed on a horizontal ground. Through teaching, the end flange of the robot is moved close to the center of the knitting loop of the knitting machine in any posture, and the center O of the flange is made f coincide with the center O of the knitting loop b The coordinate value P of the center of the end flange of the robot is read through the teach pendant f (x f , y f , z f ). The spatial topology formed by the robot and the knitting machine is projected onto the ground to form a geometric constraint relationship. The coordinate system O b _X b Y b Z b of the center of the knitting loop is rotated by an angle of r _X r Y r Z r around the Z r axis relative to the base coordinate system O where atan( ) represents the arctangent trigonometric function, and the translation distance along the X r axis is d x = x f , the translation distance along the Y r axis is d y = y f , and the translation distance along the Z r axis is d z = z f ; Then the homogeneous transformation matrix b _X b Y b Z b of the coordinate system O r _X r Y r Z r of the center of the knitting loop relative to the base coordinate system O is as follows: Among them, rotz(θ) represents the homogeneous transformation matrix for rotating by θ around the Z-axis of the coordinate axis, and trans(d x ,d y ,d z ) represents the homogeneous transformation matrix for translating by d x , d y , and d z along the X, Y, and Z axes of the coordinate axis respectively.

7. A method for generating a robot traction trajectory for braiding a bending structural member according to claim 1, wherein: In the above 7.3, the (N - i + 1)-th discrete point P of the non-linear geometric center line of the bending structural member N-i+1 When passing through the center of the braided ring, the i-th discrete point of the robot traction trajectory, that is, the homogeneous matrix of the robot end in the reference of the robot base coordinate system is expressed as: Among them, represents the attitude matrix of the center of the robot's end flange relative to the base coordinate system O r _X r Y r Z r , and represents the coordinates of the center of the robot's end flange relative to the robot's base coordinate system.

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