Spatial different-plane track transition method and system

Abstract

The invention discloses a space different-plane track transition method and system, and relates to the technical field of robot path tracks.The method comprises the steps that firstly, a common perpendicular line of two different-plane straight lines is solved, the intersection point of the common perpendicular line on the two straight lines is determined, and one straight line is projected to the plane where the other straight line is located; secondly, the problem is converted into transition of two straight lines in the same plane, and linear track transition in the plane is solved; and finally, the transition track is expanded from a two-dimensional plane track to a three-dimensional space track, so that transition between straight lines in different planes in the space is realized. According to the invention, track transition between straight lines on different planes in space can be realized; meanwhile, various different transition track types can be used, and different continuity requirements can be met.

Description

Technical Field

[0001] The present invention relates to the field of robot path trajectory technology, and in particular to a spatial non-planar trajectory transition method and system. Background Art

[0002] With the widespread application of robotics in many fields such as industrial manufacturing, aerospace, and special operations, the demand for robots to perform complex spatial trajectory tasks is growing. In many cases, robots need to work on non-planar linear trajectories in space, such as in multi-station assembly, welding and processing of complex spatial structures, and other tasks.

[0003] If the robot is switched directly from one non-planar line segment to another, the robot's motion speed and acceleration may change suddenly, resulting in greater shock and vibration. This will not only affect the robot's positioning accuracy and work quality, but also accelerate the wear of the robot's joint components and reduce the robot's service life. Therefore, an effective robot spatial non-planar straight line trajectory transition technology is urgently needed to solve the above problems. Summary of the invention

[0004] In view of the deficiencies in the prior art, the present invention discloses a spatial non-planar trajectory transition method and system to solve the problems raised in the above background technology.

[0005] To achieve the above object, the present invention provides the following technical solution: a spatial non-planar trajectory transition method, comprising the following steps:

[0006] Step S1, first solve the common perpendicular line of two skew lines, determine the intersection point of the common perpendicular line on the two lines, and project one of the lines onto the plane where the other line is located;

[0007] Step S2, then convert the problem into transition between two straight lines in the same plane, and solve the transition of the straight line trajectory in the plane;

[0008] Step S3: Finally, the transition trajectory is expanded from the two-dimensional plane trajectory to a three-dimensional space trajectory, thereby realizing the transition between spatial non-coplanar straight lines.

[0009] Preferably, in step S1, it is assumed that two skew lines in space are described by points p1, p2 and points p3, p4 respectively; firstly, the common perpendicular line L_s of the two skew lines is calculated, and the calculation process is as follows:

[0010] 1) Calculate the direction vector of the common perpendicular line:

[0011]

[0012] Where D1 represents the direction vector of line 1, D2 represents the direction vector of line 2; N represents the direction vector of the common perpendicular line;

[0013] 2) Calculate the length of the common vertical line:

[0014]

[0015] 3) Calculate the intersection point of the common perpendicular line on line 1:

[0016]

[0017] 4) Calculate the intersection point of the common perpendicular line on line 2:

[0018]

[0019] 5) Project point p4 on line 2 to the plane where line 1 lies:

[0020]

[0021] Then P1, P2 and The three points are in the same plane.

[0022] Preferably, in step S2, solving the arc trajectory transition in the plane includes the following specific steps:

[0023] First, establish the center coordinate system, c i represents the center of the circle, Indicates the y-axis direction of the circle center coordinate system, and the direction is determined by q i-1 Point to q i point, Represents the x-axis direction of the circle center coordinate system, then the formula includes the following:

[0024]

[0025] Center c i The coordinates are calculated by the following formula:

[0026]

[0027] in,

[0028] Among them, l i Indicates the transition radius, which is specified by the user;

[0029] The x-axis of the center coordinate system is calculated by the following formula:

[0030]

[0031] Then the position q of the point on the plane transition trajectory in space is calculated by the following formula:

[0032]

[0033] Where s represents the length of the current position on the transition trajectory.

[0034] Preferably, in step S3, solving the transition of spatial non-planar straight line trajectories includes:

[0035] In order to transform the plane transition trajectory into a space transition trajectory, the plane transition trajectory is first stretched along the common vertical line, and the stretching direction is from point C1 to point C2. The final position of the space transition point q t Calculated by the following formula:

[0036]

[0037] Among them, the stretching distance is the length h of the common perpendicular line.

[0038] The present invention also provides a spatial non-planar trajectory transition system, the system comprising the following modules:

[0039] Module 1: Find the common perpendicular line of two skew lines, determine the intersection point of the common perpendicular line on the two lines, and project one of the lines onto the plane where the other line lies;

[0040] Module 2: First, transform the problem into transition between two straight lines in the same plane, and solve the transition of the straight line trajectory in the plane;

[0041] Module 3: Expand the transition trajectory from a two-dimensional plane trajectory to a three-dimensional space trajectory, thereby realizing the transition between non-coplanar straight lines in space.

[0042] Preferably, in the module 1, it is assumed that two skew lines in space are described by points p1, p2 and points p3, p4 respectively; firstly, the common perpendicular line L_s of the two skew lines is calculated, and the calculation process is as follows:

[0043] 1) Calculate the direction vector of the common perpendicular line:

[0044]

[0045] Where D1 represents the direction vector of line 1, D2 represents the direction vector of line 2; N represents the direction vector of the common perpendicular line;

[0046] 2) Calculate the length of the common vertical line:

[0047]

[0048] 3) Calculate the intersection point of the common perpendicular line on line 1:

[0049]

[0050] 4) Calculate the intersection point of the common perpendicular line on line 2:

[0051]

[0052] 5) Project point p4 on line 2 to the plane where line 1 lies:

[0053]

[0054] Then P1, P2 and The three points are in the same plane.

[0055] Preferably, in the module 2, the arc trajectory transition in the plane is solved, and the specific steps include:

[0056] First, establish the center coordinate system, c i represents the center of the circle, Indicates the y-axis direction of the circle center coordinate system, and the direction is determined by q i-1 Point to q i point, Represents the x-axis direction of the circle center coordinate system, then the formula includes the following:

[0057]

[0058] Center c i The coordinates are calculated by the following formula:

[0059]

[0060] in,

[0061] Among them, l i Indicates the transition radius, which is specified by the user;

[0062] The x-axis of the center coordinate system is calculated by the following formula:

[0063]

[0064] Then the position q of the point on the plane transition trajectory in space is calculated by the following formula:

[0065]

[0066] Where s represents the length of the current position on the transition trajectory.

[0067] Preferably, in the module 3, the transition of the spatial non-planar straight line trajectory is solved, and the specific steps include:

[0068] In order to transform the plane transition trajectory into a space transition trajectory, the plane transition trajectory is first stretched along the common vertical line, and the stretching direction is from point C1 to point C2. The final position of the space transition point q tCalculated by the following formula:

[0069]

[0070] Among them, the stretching distance is the length h of the common perpendicular line.

[0071] The present invention also provides a spatial non-planar trajectory transition processing device, comprising at least one processor and at least one memory communicatively connected to the processor, wherein: the memory stores program instructions executable by the processor, and the processor calls the program instructions to execute the above method.

[0072] The present invention also provides a computer-readable storage medium, wherein the computer-readable storage medium stores computer instructions, and the computer instructions enable the computer to execute the above method.

[0073] Compared with the prior art, the present invention has the following beneficial effects:

[0074] The present invention can realize the trajectory transition between non-planar straight lines in space; at the same time, the present invention can use a variety of different transition trajectory types to meet different continuity requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention and do not constitute a limitation of the present invention.

[0076] In the attached picture:

[0077] Figure 1 It is a schematic diagram of the arc transition trajectory in the plane of the present invention;

[0078] Figure 2 It is a schematic diagram of the transition of the spatial non-planar straight line through the trajectory of the present invention. DETAILED DESCRIPTION

[0079] The preferred embodiments of the present invention are described below in conjunction with the accompanying drawings. It should be understood that the preferred embodiments described herein are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0080] Embodiment: A spatial non-planar trajectory transition method specifically comprises the following steps:

[0081] 1. Assume that two non-coplanar lines in space are described by points p1, p2 and p3, p4 respectively. First, calculate the common perpendicular line L_s of the two non-coplanar lines. The calculation process is as follows:

[0082] 1) Calculate the direction vector of the common perpendicular line

[0083]

[0084] Wherein, D1 represents the direction vector of line 1, D2 represents the direction vector of line 2, and N represents the direction vector of the common perpendicular line.

[0085] 2) Calculate the length of the common vertical line

[0086]

[0087] 3) Calculate the intersection point of the common perpendicular line on line 1

[0088]

[0089] 4) Calculate the intersection point of the common perpendicular line on line 2

[0090]

[0091] 5) Project point p4 on line 2 to the plane where line 1 lies

[0092]

[0093] Then P1, P2 and The three points are in the same plane, and the problem is transformed into a problem of finding the transition between two straight line trajectories in the plane.

[0094] 2. Solving the problem of straight line trajectory transition in a plane. This embodiment takes the arc transition trajectory as an example. Figure 1 As shown, the following steps are included:

[0095] First, establish the center coordinate system, c i represents the center of the circle, Indicates the y-axis direction of the circle center coordinate system, and the direction is determined by q i-1 Point to q i point, represents the x-axis direction of the circle center coordinate system.

[0096]

[0097] Among them, l i Indicates the transition radius, which is specified by the user.

[0098] The coordinates of the center of the circle are calculated by the following formula

[0099]

[0100] in,

[0101]

[0102] The x-axis of the center coordinate system is calculated by the following formula

[0103]

[0104] Then the position of the point on the plane transition trajectory in space is calculated by the following formula

[0105]

[0106] Where s represents the length of the current position on the transition trajectory.

[0107] 3. Solve the problem of transition of non-planar straight line trajectories in space, such as Figure 2 As shown, the following steps are included:

[0108] In order to transform the plane transition trajectory into a space transition trajectory, the plane transition trajectory needs to be stretched along the common vertical line, with the stretching direction from point C1 to point C2. The final position of the space transition point q t Calculated by the following formula:

[0109]

[0110] Among them, the stretching distance is the length h of the common perpendicular line.

[0111] The present invention also provides a spatial non-planar trajectory transition system, the system comprising the following modules:

[0112] Module 1: Find the common perpendicular line of two skew lines, determine the intersection point of the common perpendicular line on the two lines, and project one of the lines onto the plane where the other line lies;

[0113] In the module 1, it is assumed that two skew lines in space are described by points p1, p2 and points p3, p4 respectively; first, the common perpendicular line L_s of the two skew lines is calculated, and the calculation process is as follows:

[0114] 1) Calculate the direction vector of the common perpendicular line:

[0115]

[0116] Where D1 represents the direction vector of line 1, D2 represents the direction vector of line 2; N represents the direction vector of the common perpendicular line;

[0117] 2) Calculate the length of the common vertical line:

[0118]

[0119] 3) Calculate the intersection point of the common perpendicular line on line 1:

[0120]

[0121] 4) Calculate the intersection point of the common perpendicular line on line 2:

[0122]

[0123] 5) Project point p4 on line 2 to the plane where line 1 lies:

[0124]

[0125] Then P1, P2 and The three points are in the same plane.

[0126] Module 2: First, transform the problem into transition between two straight lines in the same plane, and solve the transition of the straight line trajectory in the plane;

[0127] In the module 2, the arc trajectory transition in the plane is solved, and the specific steps include:

[0128] First, establish the center coordinate system, c i represents the center of the circle, Indicates the y-axis direction of the circle center coordinate system, and the direction is determined by q i-1 Point to q i point, Represents the x-axis direction of the circle center coordinate system, then the formula includes the following:

[0129]

[0130] Center c i The coordinates are calculated by the following formula:

[0131]

[0132] in,

[0133] Among them, l i Indicates the transition radius, which is specified by the user;

[0134] The x-axis of the center coordinate system is calculated by the following formula:

[0135]

[0136] Then the position q of the point on the plane transition trajectory in space is calculated by the following formula:

[0137]

[0138] Where s represents the length of the current position on the transition trajectory.

[0139] Module 3: Expand the transition trajectory from a two-dimensional plane trajectory to a three-dimensional space trajectory, thereby realizing the transition between non-coplanar straight lines in space.

[0140] In the module 3, the transition of the spatial non-planar straight line trajectory is solved, and the specific steps include:

[0141] In order to transform the plane transition trajectory into a space transition trajectory, the plane transition trajectory is first stretched along the common vertical line, and the stretching direction is from point C1 to point C2. The final position of the space transition point q t Calculated by the following formula:

[0142]

[0143] Among them, the stretching distance is the length h of the common perpendicular line.

[0144] The present invention also provides a spatial non-planar trajectory transition processing device, comprising at least one processor and at least one memory communicatively connected to the processor, wherein: the memory stores program instructions executable by the processor, and the processor calls the program instructions to execute the above-mentioned method, so as to efficiently and accurately process the spatial non-planar trajectory transition problem.

[0145] The present invention also provides a computer-readable storage medium, which stores computer instructions, and the computer instructions enable the computer to execute the above method. The above storage medium provides a convenient and efficient way for storing and disseminating programs.

[0146] Finally, it should be noted that the above description is only a preferred example of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions described in the aforementioned embodiments or replace some of the technical features therein by equivalents. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A spatial non-planar trajectory transition method, characterized in that: The following steps are involved: Step S1, solving the common perpendicular line of two skew lines, determining the intersection point of the common perpendicular line on the two lines, and projecting one of the lines onto the plane where the other line is located; Step S2, converting the problem into transition between two straight lines in the same plane, and solving the transition of the straight line trajectory in the plane; Step S3: Expand the transition trajectory from a two-dimensional plane trajectory to a three-dimensional space trajectory, thereby realizing the transition between spatial non-coplanar straight lines.

2. A spatial non-planar trajectory transition method according to claim 1, characterized in that: In step S1, it is assumed that two skew lines in space are described by points p1, p2 and points p3, p4 respectively; first, the common perpendicular line L_s of the two skew lines is calculated, and the calculation process is as follows: 1) Calculate the direction vector of the common perpendicular line: Where D1 represents the direction vector of line 1, D2 represents the direction vector of line 2; N represents the direction vector of the common perpendicular line; 2) Calculate the length of the common vertical line: 3) Calculate the intersection point of the common perpendicular line on line 1: 4) Calculate the intersection point of the common perpendicular line on line 2: 5) Project point p4 on line 2 to the plane where line 1 lies: Then P1, P2 and The three points are in the same plane.

3. A spatial non-planar trajectory transition method according to claim 2, characterized in that: In step S2, the arc trajectory transition in the plane is solved, and the specific steps include: First, establish the center coordinate system, c i represents the center of the circle, Indicates the y-axis direction of the circle center coordinate system, and the direction is determined by q i-1 Point to q i point, Represents the x-axis direction of the circle center coordinate system, then the formula includes the following: Center c i The coordinates are calculated by the following formula: in, Among them, l i Indicates the transition radius, which is specified by the user; The x-axis of the center coordinate system is calculated by the following formula: Then the position q of the point on the plane transition trajectory in space is calculated by the following formula: Where s represents the length of the current position on the transition trajectory.

4. A spatial non-planar trajectory transition method according to claim 3, characterized in that: In step S3, the spatial non-planar straight line trajectory transition is solved, and the specific steps include: In order to transform the plane transition trajectory into a space transition trajectory, the plane transition trajectory is first stretched along the common vertical line, and the stretching direction is from point C1 to point C2. The final position of the space transition point q t Calculated by the following formula: Among them, the stretching distance is the length h of the common perpendicular line.

5. A spatial non-planar trajectory transition system, characterized in that: The system includes the following modules: Module 1: Find the common perpendicular line of two skew lines, determine the intersection point of the common perpendicular line on the two lines, and project one of the lines onto the plane where the other line lies; Module 2: First, transform the problem into transition between two straight lines in the same plane, and solve the transition of the straight line trajectory in the plane; Module 3: Expand the transition trajectory from a two-dimensional plane trajectory to a three-dimensional space trajectory, thereby realizing the transition between non-coplanar straight lines in space.

6. A spatial out-of-plane trajectory transition system according to claim 5, characterized in that: In the module 1, it is assumed that two skew lines in space are described by points p1, p2 and points p3, p4 respectively; first, the common perpendicular line L_s of the two skew lines is calculated, and the calculation process is as follows: 1) Calculate the direction vector of the common perpendicular line: Where D1 represents the direction vector of line 1, D2 represents the direction vector of line 2; N represents the direction vector of the common perpendicular line; 2) Calculate the length of the common vertical line: 3) Calculate the intersection point of the common perpendicular line on line 1: 4) Calculate the intersection point of the common perpendicular line on line 2: 5) Project point p4 on line 2 to the plane where line 1 lies: Then P1, P2 and The three points are in the same plane.

7. A spatial out-of-plane trajectory transition system according to claim 6, characterized in that: In the module 2, the arc trajectory transition in the plane is solved, and the specific steps include: First, establish the center coordinate system, c i represents the center of the circle, Indicates the y-axis direction of the circle center coordinate system, and the direction is determined by q i-1 Point to q i point, Represents the x-axis direction of the circle center coordinate system, then the formula includes the following: Center c i The coordinates are calculated by the following formula: in, Among them, l i Indicates the transition radius, which is specified by the user; The x-axis of the center coordinate system is calculated by the following formula: Then the position q of the point on the plane transition trajectory in space is calculated by the following formula: Where s represents the length of the current position on the transition trajectory.

8. A spatial out-of-plane trajectory transition system according to claim 7, characterized in that: In the module 3, the transition of the spatial non-planar straight line trajectory is solved, and the specific steps include: In order to transform the plane transition trajectory into a space transition trajectory, the plane transition trajectory is first stretched along the common vertical line, and the stretching direction is from point C1 to point C2. The final position of the space transition point q t Calculated by the following formula: Among them, the stretching distance is the length h of the common perpendicular line.

9. A spatial non-planar trajectory transition processing device, characterized in that: It comprises at least one processor and at least one memory in communication with the processor, wherein the memory stores program instructions executable by the processor, and the processor calls the program instructions to execute any method according to claims 1 to 4.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores computer instructions, and the computer instructions enable the computer to execute the method according to any one of claims 1 to 4.

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