A geodesic curvature calculation method for automatic wire laying trajectory based on trajectory point set

Abstract

The present invention discloses a method for calculating the geodesic curvature of an automatic wire laying trajectory based on a trajectory point set, which belongs to the field of trajectory planning. Specifically, the method comprises the following steps: traversing three adjacent trajectory points P in sequence. i‑1 , P i and P i+1 ; Based on the middle point P i The coordinates and normal vector of the point P are calculated i The tangent plane S; then, the middle point P i Two points before and after P i‑1 and P i+1 Project onto the tangent plane S to obtain the corresponding projection point P′ i‑1 and P′ i+1 ; Based on the projection point P′ i‑1 and P′ i+1 Calculate the curvature radius, that is, get the middle point P i The geodesic curvature radius R, the reciprocal of which is the geodesic curvature; the value of i increases by 1, and the three trajectory points are deferred to P i , P i+1 and P i+2 Repeat the above steps until the geodesic curvature of each trajectory point, excluding the starting and ending points, is obtained. Finally, the fiber placement trajectory is corrected according to the geodesic curvature of each trajectory point to prevent wrinkles in the fiber filaments caused by excessive geodesic curvature during placement. This method is suitable for situations where precise geodesic curvature is not required.

Description

Technical Field

[0001] The present invention belongs to the field of trajectory planning, and in particular relates to a method for calculating the geodesic curvature of an automatic wire laying trajectory based on a trajectory point set. Background Art

[0002] Placement trajectory planning involves pre-planning the placement path to control the movement of the placement head across the placement surface. Because the fiber filaments being laid have a certain width (common specifications include 6.35mm and 12.7mm), when laying a trajectory with large geodesic curvature, the displacement between the two fiber boundaries will produce a large difference, which can cause defects such as wrinkles.

[0003] According to document 1: Fang Yiwu. Research on automatic fiber placement technology of composite wing beam based on geodesic algorithm [D]. Nanjing University of Aeronautics and Astronautics, 2014. It is recorded that the minimum allowable geodesic curvature radius of CYCOM 5320-1FP / T40 / 800B fiber with a width of 6.35mm and a thickness of 0.125mm is about 1000mm.

[0004] To ensure that the geodesic curvature radius of the wire placement trajectory does not fall below the allowable value, the trajectory's geodesic curvature radius must be calculated. Traditionally, this method calculates the geodesic curvature through differentiation, then takes the inverse to obtain the geodesic curvature radius. However, wire placement trajectories are often stored as point sets with normal and tangent vector information. This method requires first fitting a curve and then performing differentiation, resulting in a complex process. Summary of the Invention

[0005] In response to the above problems, the present invention provides a method for calculating the geodesic curvature of an automatic wire laying trajectory based on a trajectory point set. The geodesic curvature is calculated directly through the point coordinates and vector information of the trajectory point set. Simulation shows that the absolute deviation between the straight line segment connected by the trajectory point set and the actual trajectory curve does not exceed 0.01 mm.

[0006] The method for calculating the geodesic curvature of the automatic wire laying trajectory based on the trajectory point set comprises the following specific steps:

[0007] Step 1: From each trajectory point that constitutes the trajectory, traverse the three adjacent trajectory points P in turn i-1 , P i and P i+1 ;

[0008] The initial value of i is 2;

[0009] Step 2: Based on the middle point P i The coordinate values ​​and normal vector of Calculate the point P i The tangent plane S;

[0010] The expression of the tangent plane S is: AX+BY+CZ+D=0;

[0011] A=N ix , B=N iy , C=N iz

[0012] D=-(AP ix +BP iy +CP iz )

[0013] Among them, (N ix , N iy , N iz ) is the normal vector Coordinates of (P ix , P iy , P iz ) is point P i The coordinate value of

[0014] Step 3: The middle point P i Two points before and after P i-1 and P i+1 Project onto the tangent plane S to obtain the corresponding projection point P′ i-1 and P′ i+1 ;

[0015] Step 4: Based on the projection point P′ i-1 and P′ i+1 Calculate the curvature radius, that is, get the middle point P i The geodesic curvature radius R of a point, its reciprocal is the geodesic curvature;

[0016] The formula is:

[0017]

[0018] Among them, the intermediate variable is the projection point P′ i-1 Point to the middle point P i vector, The middle point P i Pointing to the projection point P′ i+1 vector,

[0019] Step 5: Increment the value of i by 1 and defer the three trajectory points to P i , P i+1 and P i+2 , return to step 2, and repeat the above steps to continue to calculate the geodesic curvature of the current middle point until the geodesic curvature of each trajectory point except the starting point and the end point is obtained;

[0020] Step 6: Correct the fiber placement trajectory according to the geodesic curvature of each trajectory point to prevent wrinkles in the fiber filaments caused by excessive geodesic curvature during placement.

[0021] The advantages of the present invention are:

[0022] The present invention can directly solve the geodesic curvature based on the information of the trajectory point set, and is suitable for situations where precise acquisition of the geodesic curvature is not required. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 The present invention is a flow chart of a method for calculating geodesic curvature of an automatic wire laying trajectory based on a trajectory point set.

[0024] Figure 2 It is a schematic diagram of the projection of three consecutive points onto the tangent plane.

[0025] Figure 3 This is a schematic diagram for calculating the curvature radius from three consecutive points. DETAILED DESCRIPTION

[0026] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0027] The present invention proposes a method for calculating the geodesic curvature of an automatic wire laying trajectory based on a trajectory point set. The geodesic curvature of the middle point is calculated based on three consecutive trajectory points. Simulation verification shows that the absolute deviation between the straight line segment connected by the trajectory point set and the actual trajectory curve does not exceed 0.01 mm.

[0028] like Figure 1 As shown, the specific steps are:

[0029] Step 1: From each trajectory point that constitutes the trajectory, traverse the three adjacent trajectory points P1, P2 and P3 in sequence;

[0030] If a curve is selected, call the GCPnts_QuasiUniformDeflection class of the Opencascade engine to discretize the track into trajectory points.

[0031] Step 2: Based on the coordinate value and normal vector of the middle point P2 Calculate the tangent plane S of the point P2;

[0032] The expression of the tangent plane S is: AX+BY+CZ+D=0;

[0033] A=N 2x , B=N 2y , C=N 2z

[0034] D=-(AP 2x +BP 2y +CP2z )

[0035] Among them, (N 2x , N 2y , N 2z ) is the normal vector Coordinates of (P 2x , P 2y , P 2z ) is the coordinate value of point P2.

[0036] Step 3: The two points before and after the middle point P2 (P 1x , P 1y , P 1z ) and P3(P 3x , P 3y , P 3z ) is projected onto the tangent plane S, and the corresponding projection point P′1(P′ 1x , P′ 1y , P′ 1z ) and P′3(P′ 3x , P′ 3y , P′ 3z );

[0037] Step 4: Calculate the curvature radius based on the projection points P′1 and P′3, that is, obtain the geodesic curvature radius R of the middle point P2, and its reciprocal is the geodesic curvature;

[0038] The formula is:

[0039]

[0040] Among them, L1 and L2 are intermediate variables; is the vector from the projected point P′1 to the middle point P2; is the vector from the middle point P2 to the projection point P′3; because the central angle and the reverse circumferential angle are complementary, θ and The angles are equal.

[0041] Step 5: Return to step 1 and extend the three trajectory points to P2, P3, and P4, repeating the above steps to find the geodesic curvature of the intermediate points until the last three points of the trajectory are reached. The geodesic curvature of each trajectory point except the starting point and the end point is obtained.

[0042] Step 6: Correct the fiber placement trajectory according to the geodesic curvature of each trajectory point, such as selecting fiber filaments of other widths for placement (CN117238414A), to ensure that the fiber filaments will not cause wrinkles during placement due to excessive geodesic curvature.

[0043] Example:

[0044] The specific steps are:

[0045] S100: Input the Kth trajectory point set P{n} with normal vector N and tangent vector t; i=0;

[0046] S110: Take three consecutive points P[i], P[i+1], P[i+2];

[0047] S120: Project P[i] and P[i+2] onto the tangent plane of P[i+1] to obtain P[i]' and P[i+2]';

[0048] S130: Calculate the curvature radius R of P[i+1] through the three points P[i]', P[i+1], and P[i+2]', and the reciprocal of the curvature radius R is the geodesic curvature of P[i+1];

[0049] S140: Add one to i and repeat steps S110-S130 to obtain the geodesic curvature radius of each point on the trajectory.

[0050] Figure 2 The figure shows a schematic diagram of the projection of three consecutive points onto the tangent plane described in S120. In the figure, P1, P2, and P3 are three consecutive points, plane S is the tangent plane of P2, P′1 is the projection of P1 on plane S, and P′3 is the projection of P3 on plane S. The calculation formula is:

[0051] P1(P 1x , P 1y , P 1z ), P2(P 2x , P 2y , P 2z ), P3(P 3x , P 3y , P 3z ), P′1(P′ 1x , P′ 1y , P′ 1z ), P′3(P′ 3x , P′ 3y , P′ 3z )

[0052] Tangent plane S: AX+BY+CZ+D=0, A=N 2x , B=N 2y , C=N 2z , D=-(AP 2x +BP 2y +CP 2z )

[0053] E=A 2 +B 2 +C 2

[0054] P′ 1x =((B2 +C 2 )*P 1x -A*(B*P 1y +C*P 1z +D)) / E

[0055] P′ 1y =((A 2 +C 2 )*P 1y -B*(A*P 1x +C*P 1z +D)) / E

[0056] P′ 1z =((B 2 +A 2 )*P 1z -C*(B*P 1y +A*P 1x +D)) / E

[0057] P′ 3x =((B 2 +C 2 )*P 3x -A*(B*P 3y +C*P 3z +D)) / E

[0058] P′ 3y =((A 2 +C 2 )*P 3y -B*(A*P 3x +C*P 3z +D)) / E

[0059] P′ 3z =((B 2 +A 2 )*P 3z -C*(B*P 3y +A*P 3x +D)) / E

[0060] Figure 3 The figure shows a schematic diagram of calculating the curvature radius from three consecutive points as described in S130. In the figure, P1, P2, and P3 are three consecutive points, namely P′1, P2, and P′3 after projection in S120. The calculation formula is:

[0061]

[0062]

Claims

1. A method for calculating geodesic curvature of an automatic wire laying trajectory based on a trajectory point set, characterized in that: The specific steps are as follows: Step 1: From each trajectory point that constitutes the trajectory, traverse the three adjacent trajectory points P in turn i-1 , P i and P i+1 ; The initial value of i is 2; Step 2: Based on the middle point P i The coordinate values ​​and normal vector of Calculate the point P i The tangent plane S; The expression of the tangent plane S is: AX+BY+CZ+D=0; A=N ix ,B=N iy ,C=N iz D=-(AP ix +BP iy +CP iz ) Among them, (N ix ,N iy ,N iz ) is the normal vector Coordinates of (P ix ,P iy ,P iz ) is point P i The coordinate value of Step 3: The middle point P i Two points before and after P i-1 and P i+1 Project onto the tangent plane S to obtain the corresponding projection point P′ i-1 and P′ i+1 ; Step 4: Based on the projection point P′ i-1 and P′ i+1 Calculate the curvature radius, that is, get the middle point P i The geodesic curvature radius R of a point, its reciprocal is the geodesic curvature; The formula is: Among them, the intermediate variable is the projection point P′ i-1 Point to the middle point P i vector, The middle point P i Pointing to the projection point P′ i+1 vector, Step 5: Increment the value of i by 1 and defer the three trajectory points to P i , P i+1 and P i+2 , return to step 2, and repeat the above steps to continue to calculate the geodesic curvature of the middle point until the geodesic curvature of each trajectory point except the starting point and the end point is obtained; Step 6: Correct the fiber placement trajectory according to the geodesic curvature of each trajectory point to prevent wrinkles in the fiber filaments caused by excessive geodesic curvature during placement.

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