A spatial heteromorphic trajectory transition method and system

Abstract

The application discloses a spatial non-planar trajectory transition method and system, and relates to the technical field of robot path trajectories. The method firstly solves the common perpendicular line of two non-planar straight lines, determines the intersection points of the common perpendicular line on the two straight lines, and projects one straight line to the plane where the other straight line is located. Then, the problem is converted into the transition of two straight lines in the same plane, and the transition of the straight line trajectory in the plane is solved. Finally, the transition trajectory is expanded from a two-dimensional plane trajectory to a three-dimensional space trajectory, so that the transition between spatial non-planar straight lines is realized. The application can realize the trajectory transition between spatial non-planar straight lines. Meanwhile, the application can use various transition trajectory types, and can meet different continuity requirements.

Description

Technical Field

[0001] This invention relates to the field of robot path trajectory technology, specifically to a method and system for transitioning spatial non-planar trajectories. Background Technology

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

[0003] A direct transition from one skew line segment to another can cause abrupt changes in the robot's speed and acceleration, resulting in significant impact and vibration. This not only affects the robot's positioning accuracy and operational quality but also accelerates the wear of its joint components, reducing the robot's lifespan. Therefore, an effective transition technology for skew linear trajectories in robot space is urgently needed to address these issues. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention discloses a spatial non-planar trajectory transition method and system to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a method for transitioning spatial non-planar trajectories, comprising the following steps:

[0006] Step S1: First, find the common perpendicular of the two skew lines, determine the intersection point of the common perpendicular on the two lines, and project one of the lines onto the plane containing the other line.

[0007] Step S2: Next, the problem is transformed into transitioning between two straight lines in the same plane, and the trajectory of the straight lines in the plane is solved.

[0008] Step S3: Finally, the transition trajectory is stretched from a two-dimensional planar trajectory to a three-dimensional spatial trajectory, thereby realizing the transition between skew lines in space.

[0009] Preferably, in step S1, it is assumed that two skew lines in space are respectively connected by points... , and points , Description: First, calculate the common perpendicular L_s of these two skew lines. The calculation process is as follows:

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

[0011]

[0012] in, This represents the direction vector of line 1. This represents the direction vector of line two; The direction vector of the common perpendicular;

[0013] 2) Calculate the length of the common perpendicular:

[0014]

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

[0016]

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

[0018] .

[0019] 5) Place the line on line two Projecting a point onto the plane containing a line:

[0020]

[0021] In turn, achieve , and The three points are in the same plane.

[0022] Preferably, in step S2, the solution for the transition of the circular arc trajectory in the plane includes the following steps:

[0023] First, establish a coordinate system centered on the circle. Indicates the center of the circle. This represents the y-axis direction in the coordinate system centered at the center of the circle, and the direction is determined by... Point of view point, If we denote the x-axis direction of the coordinate system centered at the center of the circle, then the formulas include the following:

[0024]

[0025]

[0026] center The coordinates are calculated using the following formula:

[0027]

[0028] in,

[0029] in, This represents the transition radius, a value specified by the user.

[0030] The x-axis of the circular coordinate system is calculated using the following formula:

[0031]

[0032] The position q of a point on the planar transition trajectory in space is calculated using the following formula:

[0033]

[0034] Where s represents the length of the current position on the transition trajectory.

[0035] Preferably, in step S3, the transition of the spatial skew straight line trajectory is solved, and the specific steps include:

[0036] To stretch the planar transition trajectory into a spatial transition trajectory, the planar transition trajectory is first stretched along the common perpendicular, with the stretching direction starting from point [point missing]. Point of view The final spatial transition point position q t It is calculated by the following formula:

[0037]

[0038] Wherein, the stretch distance is the length of the common perpendicular. .

[0039] The present invention also provides a spatial non-planar trajectory transition system, the system comprising the following modules:

[0040] Module 1: Find the common perpendicular of two skew lines, determine the intersection of the common perpendicular on the two lines, and project one of the lines onto the plane containing the other line.

[0041] Module 2: The problem is first transformed into a transition between two straight lines in the same plane, and then the trajectory of the straight lines in the plane is solved.

[0042] Module 3: Transitioning the transition trajectory from a two-dimensional planar trajectory to a three-dimensional spatial trajectory, thereby realizing the transition between non-planar straight lines in space.

[0043] Preferably, in module one, it is assumed that two skew lines in space are respectively connected by points... , and points , Description: First, calculate the common perpendicular L_s of these two skew lines. The calculation process is as follows:

[0044] 1) Calculate the direction vector of the common perpendicular:

[0045]

[0046] in, This represents the direction vector of line 1. This represents the direction vector of line two; The direction vector of the common perpendicular;

[0047] 2) Calculate the length of the common perpendicular:

[0048]

[0049] 3) Calculate the intersection point of the common perpendiculars on line 1:

[0050]

[0051] 4) Calculate the intersection point of the common perpendiculars on line 2:

[0052]

[0053] 5) Place the line on line two Projecting a point onto the plane containing a line:

[0054]

[0055] In turn, achieve , and The three points are in the same plane.

[0056] Preferably, in module two, the specific steps for solving the transition of the circular arc trajectory in the plane include:

[0057] First, establish a coordinate system centered on the circle. Indicates the center of the circle. This represents the y-axis direction in the coordinate system centered at the center of the circle, and the direction is determined by... Point of view point, If we denote the x-axis direction of the coordinate system centered at the center of the circle, then the formulas include the following:

[0058]

[0059]

[0060] center The coordinates are calculated using the following formula:

[0061]

[0062] in,

[0063] in, This represents the transition radius, a value specified by the user.

[0064] The x-axis of the circular coordinate system is calculated using the following formula:

[0065]

[0066] The position q of a point on the planar transition trajectory in space is calculated using the following formula:

[0067]

[0068] Where s represents the length of the current position on the transition trajectory.

[0069] Preferably, in module three, the specific steps for solving the transition of spatially skewed straight-line trajectories include:

[0070] To stretch the planar transition trajectory into a spatial transition trajectory, the planar transition trajectory is first stretched along the common perpendicular, with the stretching direction starting from point [point missing]. Point of view The final spatial transition point position q t It is calculated by the following formula:

[0071]

[0072] Wherein, the stretch distance is the length of the common perpendicular. .

[0073] The present invention also provides a spatial non-planar trajectory transition processing device, including 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 can execute the above-described method by calling the program instructions.

[0074] The present invention also provides a computer-readable storage medium storing computer instructions that cause the computer to perform the above-described method.

[0075] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0076] This invention can realize trajectory transition between spatially skew lines; at the same time, this invention can use a variety of different transition trajectory types to meet different continuity requirements. Attached Figure Description

[0077] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0078] In the attached diagram:

[0079] Figure 1 This is a schematic diagram of the arc transition trajectory in the plane of the present invention;

[0080] Figure 2 This is a schematic diagram of the spatial non-planar straight line transition through the trajectory of the present invention. Detailed Implementation

[0081] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0082] Example: A method for transitioning spatial non-planar trajectories, specifically including the following steps:

[0083] I. Assume two skew lines in space are connected by points respectively. , and points , Description. First, calculate the common perpendicular L_s of these two skew lines. The calculation process is as follows:

[0084] 1) Calculate the direction vector of the common perpendicular.

[0085]

[0086] in, This represents the direction vector of line 1. This represents the direction vector of line 2. This represents the direction vector of the common perpendicular.

[0087] 2) Calculate the length of the common perpendicular.

[0088]

[0089] 3) Calculate the intersection point of the common perpendicular on line 1.

[0090]

[0091] 4) Calculate the intersection point of the common perpendicular on line 2.

[0092]

[0093] 5) Place the line on line two Projecting a point onto a plane containing a line

[0094]

[0095] This leads to , and The three points lie in the same plane. The problem is then transformed into a transitional problem of finding the trajectories of two straight lines in the plane.

[0096] II. Solving the problem of linear trajectory transition in a plane. This embodiment takes the circular arc transition trajectory as an example. Figure 1 As shown, it includes the following steps:

[0097] First, establish a coordinate system centered on the circle. Indicates the center of the circle. This represents the y-axis direction in the coordinate system centered at the center of the circle, and the direction is determined by... Point of view point, This represents the x-axis direction in the coordinate system centered at the center of the circle. Then...

[0098]

[0099]

[0100] in, This represents the transition radius, a value specified by the user.

[0101] The coordinates of the center are calculated using the following formula.

[0102]

[0103] in,

[0104] The x-axis of the central coordinate system is calculated using the following formula.

[0105]

[0106] The position of a point on the planar transition trajectory in space is calculated using the following formula.

[0107]

[0108] Where s represents the length of the current position on the transition trajectory.

[0109] III. Solving the transition problem of spatial skew line trajectories, such as... Figure 2 As shown, it includes the following steps:

[0110] To stretch the planar transition trajectory into a spatial transition trajectory, the planar transition trajectory needs to be stretched along the common perpendicular, with the stretching direction starting from point [point missing]. Point of view The final spatial transition point position q t It is calculated by the following formula:

[0111]

[0112] Wherein, the stretch distance is the length of the common perpendicular. .

[0113] The present invention also provides a spatial non-planar trajectory transition system, the system comprising the following modules:

[0114] Module 1: Find the common perpendicular of two skew lines, determine the intersection of the common perpendicular on the two lines, and project one of the lines onto the plane containing the other line.

[0115] In module one, it is assumed that two skew lines in space are respectively connected by points... , and points , Description: First, calculate the common perpendicular L_s of these two skew lines. The calculation process is as follows:

[0116] 1) Calculate the direction vector of the common perpendicular:

[0117]

[0118] in, This represents the direction vector of line 1. This represents the direction vector of line two; The direction vector of the common perpendicular;

[0119] 2) Calculate the length of the common perpendicular:

[0120]

[0121] 3) Calculate the intersection point of the common perpendiculars on line 1:

[0122]

[0123] 4) Calculate the intersection point of the common perpendiculars on line 2:

[0124]

[0125] 5) Place the line on line two Projecting a point onto the plane containing a line:

[0126]

[0127] In turn, achieve , and The three points are in the same plane.

[0128] Module 2: The problem is first transformed into a transition between two straight lines in the same plane, and then the trajectory of the straight lines in the plane is solved.

[0129] In module two, the solution for the transition of circular arc trajectories in the plane includes the following steps:

[0130] First, establish a coordinate system centered on the circle. Indicates the center of the circle. This represents the y-axis direction in the coordinate system centered at the center of the circle, and the direction is determined by... Point of view point, If we denote the x-axis direction of the coordinate system centered at the center of the circle, then the formulas include the following:

[0131]

[0132]

[0133] center The coordinates are calculated using the following formula:

[0134]

[0135] in,

[0136] in, This represents the transition radius, a value specified by the user.

[0137] The x-axis of the circular coordinate system is calculated using the following formula:

[0138]

[0139] The position q of a point on the planar transition trajectory in space is calculated using the following formula:

[0140]

[0141] Where s represents the length of the current position on the transition trajectory.

[0142] Module 3: Transitioning the transition trajectory from a two-dimensional planar trajectory to a three-dimensional spatial trajectory, thereby realizing the transition between non-planar straight lines in space.

[0143] In module three, the solution for the transition of spatial non-planar straight-line trajectories includes the following steps:

[0144] To stretch the planar transition trajectory into a spatial transition trajectory, the planar transition trajectory is first stretched along the common perpendicular, with the stretching direction starting from point [point missing]. Point of view The final spatial transition point position q t It is calculated by the following formula:

[0145]

[0146] Wherein, the stretch distance is the length of the common perpendicular. .

[0147] The present invention also provides a spatial non-planar trajectory transition processing device, including 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 can execute the above-described method by calling the program instructions, which can efficiently and accurately process the spatial non-planar trajectory transition problem.

[0148] The present invention also provides a computer-readable storage medium that stores computer instructions that cause the computer to perform the above-described method. The storage medium provides a convenient and efficient way for storing and distributing programs.

[0149] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for transitioning spatial skew trajectories, characterized in that, Includes the following steps: Step S1: Find the common perpendicular of two skew lines, determine the intersection point of the common perpendicular on the two lines, and project one of the lines onto the plane containing the other line. Step S2: First, transform the problem into a transition between two straight lines in the same plane, and then solve for the transition trajectory of the straight lines in the plane; Step S3: The transition trajectory is stretched from a two-dimensional planar trajectory into a three-dimensional spatial trajectory, thereby realizing the transition between skew lines in space; In step S1, it is assumed that two skew lines in space are respectively connected by points... , and points , Description: First, calculate the common perpendicular L_s of these two skew lines. The calculation process is as follows: 1) Calculate the direction vector of the common perpendicular: ； in, This represents the direction vector of line 1. This represents the direction vector of line two; The direction vector of the common perpendicular; 2) Calculate the length of the common perpendicular: ； 3) Calculate the intersection point of the common perpendiculars on line 1: ； 4) Calculate the intersection point of the common perpendiculars on line 2: ； 5) Place the line on line two Projecting a point onto the plane containing a line: ； In turn, achieve , and The three points are in the same plane; In step S2, the transition of the circular arc trajectory in the plane is solved, and the specific steps include: First, establish a coordinate system centered on the circle. Indicates the center of the circle. This represents the y-axis direction in the coordinate system centered at the center of the circle, and the direction is determined by... Point of view point, If we denote the x-axis direction of the coordinate system centered at the center of the circle, then the formulas include the following: ； ； center The coordinates are calculated using the following formula: ； in, ; in, This represents the transition radius, a value specified by the user. The x-axis of the circular coordinate system is calculated using the following formula: ； The position q of a point on the planar transition trajectory in space is calculated using the following formula: ； Where s represents the length of the current position on the transition trajectory.

2. The spatial non-planar trajectory transition method according to claim 1, characterized in that: In step S3, the transition of the spatial skew straight line trajectory is solved, and the specific steps include: To stretch the planar transition trajectory into a spatial transition trajectory, the planar transition trajectory is first stretched along the common perpendicular, with the stretching direction starting from point [point missing]. Point of view The final spatial transition point position q t It is calculated by the following formula: ； Wherein, the stretch distance is the length of the common perpendicular. .

3. A spatial non-planar trajectory transition system, characterized in that, The system includes the following modules: Module 1: Find the common perpendicular of two skew lines, determine the intersection of the common perpendicular on the two lines, and project one of the lines onto the plane containing the other line. Module 2: The problem is first transformed into a transition between two straight lines in the same plane, and then the trajectory of the straight lines in the plane is solved. Module 3: Transitioning the transition trajectory from a two-dimensional planar trajectory to a three-dimensional spatial trajectory, thereby realizing the transition between skew lines in space; In module one, it is assumed that two skew lines in space are respectively connected by points... , and points , Description: First, calculate the common perpendicular L_s of these two skew lines. The calculation process is as follows: 1) Calculate the direction vector of the common perpendicular: ； in, This represents the direction vector of line 1. This represents the direction vector of line two; The direction vector of the common perpendicular; 2) Calculate the length of the common perpendicular: ； 3) Calculate the intersection point of the common perpendiculars on line 1: ； 4) Calculate the intersection point of the common perpendiculars on line 2: ； 5) Place the line on line two Projecting a point onto the plane containing a line: ； In turn, achieve , and The three points are in the same plane; In module two, the solution for the transition of circular arc trajectories in the plane includes the following steps: First, establish a coordinate system centered on the circle. Indicates the center of the circle. This represents the y-axis direction in the coordinate system centered at the center of the circle, and the direction is determined by... Point of view point, If we denote the x-axis direction of the coordinate system centered at the center of the circle, then the formulas include the following: ； ； center The coordinates are calculated using the following formula: ； in, ; in, This represents the transition radius, a value specified by the user. The x-axis of the circular coordinate system is calculated using the following formula: ； The position q of a point on the planar transition trajectory in space is calculated using the following formula: ； Where s represents the length of the current position on the transition trajectory.

4. The spatial non-planar trajectory transition system according to claim 3, characterized in that: In module three, the solution for the transition of spatial non-planar straight-line trajectories includes the following steps: To stretch the planar transition trajectory into a spatial transition trajectory, the planar transition trajectory is first stretched along the common perpendicular, with the stretching direction starting from point [point missing]. Point of view The final spatial transition point position q t It is calculated by the following formula: ； Wherein, the stretch distance is the length of the common perpendicular. .

5. A spatial non-planar trajectory transition processing device, characterized in that, It includes 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 can execute the method as described in any one of claims 1 and 2 by invoking the program instructions.

6. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions that cause the computer to perform the method as described in any one of claims 1 and 2.

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