Double-robot collaborative path planning method for aerospace product assembly

Abstract

The invention discloses a double-robot cooperative path planning method for aerospace product assembly, and the method comprises the steps: building a robot kinematic model, and generating a cooperative motion space of double robots through a Monte Carlo method; the robot structure is simplified and expanded based on capsule enveloping; the RRT * algorithm is optimized by adopting methods of bidirectional architecture, elliptical sampling, smoothing and the like; transplanting the optimized RRT * algorithm into a collision detection simulation program, continuously planning a robot pose time sequence until a collision-free optimal path is generated, and outputting a simulation result; and establishing communication with a control system to realize virtual-real mapping of the assembly scene. According to the automatic optimal pose time sequence planning method for double-robot assembly, the efficiency and stability of the assembly process are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of robot path planning, and in particular to a dual-robot collaborative path planning method for aerospace product assembly. Background Art

[0002] In the field of aerospace product assembly, cabin assembly faces challenges such as a wide variety of products, small batches, complex environments, and high assembly consistency requirements. This has led to a long-term reliance on manual labor, making it difficult to meet the increasingly stringent production and assembly requirements. More efficient and high-precision assembly methods are needed. With the continuous development of automation technology, robots have been widely used in production and assembly, providing a new automation approach for cabin assembly.

[0003] The cabin assembly process has the characteristics of high precision requirements, multiple types of collaborative tasks, and a complex external environment. The use of a single robot assembly method can only achieve a single type of assembly task and cannot meet the needs of multi-functional assembly tasks. Therefore, dual-robot collaboration is a future development trend and can greatly improve assembly quality and efficiency. For aerospace product assembly tasks, each robot is responsible for different tasks and needs to move synchronously in different spaces at the same time. Since current dual-robot collaborative path planning research mainly focuses on the same type of tasks and adopts a sequential assembly method, it is difficult to give full play to the performance of dual robots. Therefore, studying how to quickly plan safe, efficient, and smooth collaborative paths for dual robots is an urgent problem that needs to be solved. Summary of the Invention

[0004] In order to solve the above technical problems, the purpose of the present invention is to provide a dual-robot collaborative path planning method for aerospace product assembly. Through trajectory optimization, collision detection, and virtual-reality mapping, it solves the problems of low path efficiency, weak collaborative ability, and poor shared space security of dual robots during cabin assembly.

[0005] The technical solution to achieve the purpose of the present invention is: a dual-robot collaborative path planning method for aerospace product assembly, comprising:

[0006] Step 1: Establish a robot kinematic model and use the Monte Carlo method to generate the collaborative motion space of the two robots;

[0007] Step 2: Simplify and expand the robot structure based on the capsule geometry envelope method, and calculate the distance between the center lines of the two capsules to analyze the collision situation;

[0008] Step 3: Optimize the RRT* algorithm to calculate the path sequence covering the entire assembly area and solve the optimal motion path for the two robots;

[0009] Step 4: Transplant the optimized RRT* algorithm into the collision detection simulation program to generate the robot motion pose and verify the safety of the path. If there is no collision, the simulation result is output. If there is a collision, the motion pose sequence of the master robot is generated and the pose sequence of the slave robot is replanned until the optimal collision-free path is generated and the simulation result is output.

[0010] Step 5: Establish communication between the collision detection simulation program and the dual-robot control system to achieve virtual-real mapping of the planned path in the assembly scene.

[0011] Furthermore, in step 1, a robot kinematic model is established and the cooperative motion space of the two robots is generated using the Monte Carlo method, as follows:

[0012] 1-1) Based on the DH method, the transformation relationship between any adjacent link coordinate systems of the six-degree-of-freedom robot is obtained as follows:

[0013]

[0014] in i-1 T i is the coordinate system transformation matrix between the robot's i-1th and i-th manipulators; the coordinate system is defined as follows: the i-th joint axis is represented by z i Axis representation, take the common perpendicular line of two adjacent axes i and i+1, x i The direction of the common perpendicular line is determined by the right-hand rule. i axis, θ i Indicates the rotation angle around the z axis, z i Indicates the distance between two adjacent common perpendicular lines on the z-axis, a i represents the length of the common perpendicular, angle α i Represents the angle between two adjacent joint axes;

[0015] By multiplying the homogeneous transformation matrix, the robot end effector posture transformation matrix is ​​obtained:

[0016] 0 T n = 0 T1 1 T2… i-1 T i … n-1 T n

[0017] Where n is the number of robot joints.

[0018] 1-2) The selected assembly robot has 6 degrees of freedom, and the three joint axes of the assembly robot's end intersect at a point, satisfying the Pieper criterion in robotics mechanics. Therefore, a closed-form solution must exist. Therefore, a closed-form method is used to find the inverse kinematics solution. The inverse kinematics solution can be divided into two steps. First, θ1, θ2, and θ3 are solved based on the wrist position:

[0019] 0 T6→ 0 T w →θ1,θ2,θ3

[0020] in, 0 T6 is the coordinate transformation matrix from the robot base to the end. 0 T w is the coordinate transformation matrix from the robot base to the wrist center;

[0021] Then solve θ4, θ5, θ6 according to the wrist posture:

[0022] 3 R6(θ4,θ5,θ6)= 0 R3 -1 · 0 R6→θ4,θ5,θ6

[0023] in, 3 R6 is the rotation matrix from the base of the robot wrist to the end, 0 R3 is the rotation matrix from the robot base to the wrist base, 0 R6 is the rotation matrix from the robot base to the wrist base;

[0024] 1-3) The Monte Carlo method is used to simulate and analyze the dual-robot assembly space. The maximum number of randomizations is set, and the six joint angles are randomly generated within the limit. The end position is calculated based on the robot kinematics forward solution in 1-1) to obtain the collaborative assembly space range within the dual-robot compartment.

[0025] Furthermore, in step 2, the robot structure is simplified and expanded based on the capsule geometry envelope method to simplify the complexity of the collision detection algorithm. The distance between the center lines of the two capsules is calculated to analyze the collision situation. The details are as follows:

[0026] 2-1) Using the capsule-shaped envelope robot link to simplify and expand its structure, a dual-robot envelope structure is obtained;

[0027] 2-2) After the envelope processing in 2-1), the robot's collision detection is converted into the distance calculation between capsules. That is, the position of each capsule is obtained through the robot kinematics forward solution in 1-1), and the distance between each capsule is calculated. The position vector of any two points on the axis relative to the base coordinate system is:

[0028] l i=m i +k i (n i -m i )=m i +k i s i

[0029] Where: l i Represents the position vector of any point on the capsule body axis relative to the base coordinate system; m i and n i Respectively represent the position vectors of the starting point and end point of the i-th capsule axis relative to the base coordinate system; k i ∈[0,1] is a scalar parameter; s i =(n i -m i );

[0030] Therefore, the shortest distance between any two capsules is:

[0031] min(|l i -l j |-r i -r j )=min(|(m i +k i s i )-(m j +k j s j )|-r i -r j )

[0032] Where: r i Represents the radius of the i-th capsule; if the shortest distance between two capsules during movement is greater than the set safety distance, it is determined that the two robots have collided, and the spatial coordinates of the shortest distance point at this time are output, and the process goes to step 3.

[0033] Furthermore, the step 3 is to optimize the RRT* algorithm by using a bidirectional architecture, elliptical sampling, and smoothing processing methods, calculate a path sequence covering the entire assembly area, and solve the optimal motion path of the dual robots.

[0034] Furthermore, step 3 includes the following process:

[0035] 3-1) In the robot's joint space, select the initial point p init and target point p goal As the root node of the random expansion tree, the starting point and end point of the robot in the joint space are used as the focus to construct an elliptical area, and elliptical sampling is performed to avoid redundant branches. Each sampling point p rand They are all composed of 6 joint angle values, which are used as leaf nodes to expand the random tree;

[0036] 3-2) Detect sampling point p rand Is it in the obstacle space? If not, calculate the nearest point p near , if it is in the collision space, a new round of sampling is performed;

[0037] 3-3) From the nearest point p near According to the nearest point p near To sampling point p rand The vector direction of the robot joint space is expanded with a fixed step size step to obtain a new node p new ;

[0038] 3-4) With the new node p new Reconnect the center of the circle and expand the nearest point p in the tree near With the new node p new The initial path connection established is used as the current parent node, and all nodes within the radius r are traversed to calculate: from the current parent node, that is, the current closest point p near To the new node p new The path length is added to the starting point p init The distance from other nodes to the new node p new The path length is added to the starting point p init distance; select the node with the smallest path cost as p new The new parent node of the node establishes a connection edge, that is, from the starting point p init Go through each node to reach the new node p new The sum of the Euclidean distances is the smallest;

[0039] 3-5) For the nearest point p near With the new node p new Connect the edges and perform interpolation processing, and detect the collision between the robot end and the environment. If there is no collision, the new node p new Add to the point set V, add the connecting edge to the edge set E, otherwise re-sample;

[0040] 3-6) Check whether the number of sampling times reaches the set value and whether the distance between the sampling point and the target point is less than the predetermined threshold; if any of the above conditions are met, output the edge set E, otherwise re-sample.

[0041] Furthermore, when sampling in the joint space, the sampling points are represented by a six-dimensional array θ = [θ1, θ2, θ3, θ4, θ5, θ6], θ i Represents the angle value of the i-th joint, satisfying the constraints:

[0042] θ i =θ min +(θ max-θ min )·rand

[0043] Among them, θ min and θ max are the minimum and maximum values ​​allowed, respectively, and rand is a random number between 0 and 1; thus, the new node p new The calculation formula is:

[0044]

[0045] Where: step represents a fixed step size, |||| represents the Euler distance.

[0046] Furthermore, the step 3 further comprises:

[0047] 3-7) Use a third-order Bezier curve to smooth the obtained path. The calculation formula is:

[0048] p(t)=(1-t) 3 p0+3t(1-t) 2 p1+3t 2 (1-t)p2+t 2 p3,t∈[0,1]

[0049] Where: p(t) represents the coordinates of the time point t, p0, p1, p2, and p3 represent the coordinates of the control points of the Bezier curve, which respectively define the shape and path smoothness of the third-order Bezier curve.

[0050] A computer device comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the steps of the above method are implemented when the processor executes the program.

[0051] A computer-readable storage medium stores a computer program, which implements the steps of the above method when executed by a processor.

[0052] A computer program product comprises a computer program, which implements the steps of the above method when executed by a processor.

[0053] Compared with the prior art, the present invention has the following significant advantages:

[0054] (1) The present invention designs a method for planning efficient and reliable robot assembly paths, and based on the planned paths, assists in completing the virtual-real mapping between robot control and the assembly process. This path planning method overcomes the shortcomings of traditional methods, such as insufficient accuracy and poor portability. After the optimized RRT* algorithm and collision detection simulation program are developed, the assembly process trajectory can be generated by simply importing the designed assembly scene and setting the relevant parameters, which has good practicality.

[0055] (2) The RRT* algorithm was optimized by adopting methods such as bidirectional architecture, elliptical sampling, and smoothing processing, which effectively iterated and optimized the optimal path, thereby improving the computational efficiency and the flexibility of the robot execution process.

[0056] (3) The collision detection process increases the information processing dimension and improves the assembly efficiency of the planned path by analyzing the position and posture time series of the master and slave robots.

[0057] (4) The present invention makes it possible to map the virtual and real parts of the robot assembly process. With the help of simulation information, the flexibility of robot control and monitoring is greatly enhanced, and it has wide and good practicality. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 This is a flow chart of a dual-robot collaborative path planning method for aerospace product assembly according to the present invention.

[0059] Figure 2 This is a schematic diagram of the distance calculation principle between capsules in the present invention.

[0060] Figure 3 This is a flow chart of the optimized RRT* path planning algorithm in the present invention.

[0061] Figure 4 This is a diagram showing the path planning effect in 3D space using the optimized RRT* described in the present invention.

[0062] Figure 5 This is a flow chart of the dual-robot path collision detection method in the present invention.

[0063] Figure 6 This is a diagram of the collaborative assembly space within the dual-robot compartment of the present invention.

[0064] Figure 7 This is the simplified dual-robot envelope structure diagram using capsule bodies.

[0065] Figure 8 The invention uses the collision detection simulation program to generate a robot motion posture effect diagram. DETAILED DESCRIPTION

[0066] The present invention is further described in detail below with reference to the accompanying drawings.

[0067] Combine Figure 1 The dual-robot collaborative path planning method for aerospace product assembly described in the present invention comprises the following specific steps:

[0068] Step 1: Establish a robot kinematic model based on the DH method and use the Monte Carlo method to generate the collaborative motion space of the two robots in the cabin to ensure that the assembly task of this model cabin can be completed. The details are as follows:

[0069] 1-1) Based on the DH method, the transformation relationship between any adjacent link coordinate systems of the six-degree-of-freedom robot is obtained as follows:

[0070]

[0071] in i-1 T i is the coordinate system transformation matrix between the robot's i-1th and i-th manipulators; the coordinate system is defined as follows: the i-th joint axis is represented by z i Axis representation, take the common perpendicular line of two adjacent axes i and i+1, x i The direction of the common perpendicular line is determined by the right-hand rule. i axis, θ i Indicates the rotation angle around the z axis, z i Indicates the distance between two adjacent common perpendicular lines on the z-axis, a i represents the length of the common perpendicular, angle α i Represents the angle between two adjacent joint axes;

[0072] By multiplying the homogeneous transformation matrix, the robot end effector posture transformation matrix is ​​obtained:

[0073] 0 T n = 0 T1 1 T2… i-1 T i … n-1 T n

[0074] Where n is the number of robot joints;

[0075] The assembly robot selected in 1-2) has 6 degrees of freedom, and the three joint axes of the assembly robot intersect at one point, which satisfies the Pieper criterion in robot mechanism. There must be a closed-form solution, so the closed-form method is used to find the inverse solution. The inverse kinematics solution is divided into two steps. First, θ1, θ2, and θ3 are solved according to the wrist position (the wrist rotation angle is θ in the first, second, and third DH parameters). i ):

[0076] 0 T6→ 0 T w →θ1,θ2,θ3

[0077] in, 0 T6 is the coordinate transformation matrix from the robot base to the end.0 T w is the coordinate transformation matrix from the robot base to the wrist center;

[0078] Then solve θ4, θ5, θ6 according to the wrist posture:

[0079] 3 R6(θ4,θ5,θ6)= 0 R3 -1 · 0 R6→θ4,θ5,θ6

[0080] in, 3 R6 is the rotation matrix from the base of the robot wrist to the end, 0 R3 is the rotation matrix from the robot base to the wrist base, 0 R6 is the rotation matrix from the robot base to the wrist base;

[0081] 1-3) Use the Monte Carlo method to simulate and analyze the dual-robot assembly space. Set the maximum number of random attempts and randomly generate six joint angles within the limit. Calculate the end-user pose based on the robot kinematics forward solution in step 1-1) to obtain the collaborative assembly space within the dual-robot compartment.

[0082] Step 2: Simplify and expand the robot structure based on the capsule geometry envelope method to reduce the complexity of the collision detection algorithm. Calculate the distance between the centerlines of the two capsules to analyze the collision situation. The details are as follows:

[0083] 2-1) Use the capsule envelope robot link to simplify and expand its structure to obtain a dual robot envelope structure.

[0084] 2-2) After the envelope processing in 2-1), the robot's collision detection can be converted into the distance calculation between capsules. That is, the position of each capsule is obtained through the robot kinematics solution in 1-1), and the distance between each capsule is calculated, such as Figure 2 As shown, the position vectors of any two points on the axis relative to the base coordinate system are:

[0085] l i =m i +k i (n i -m i )=m i +k i s i

[0086] Where: l i Represents the position vector of any point on the capsule body axis relative to the base coordinate system; m i and n iRespectively represent the position vectors of the starting point and end point of the i-th capsule axis relative to the base coordinate system; k i ∈[0,1] is a scalar parameter; s i =(n i -m i );

[0087] Therefore, the shortest distance between any two capsules is:

[0088] min(|l i -l j |-r i -r j )=min(|(m i +k i s i )-(m j +k j s j )|-r i -r j )

[0089] Where: r i Represents the radius of the i-th capsule; if the shortest distance between two capsules during movement is greater than the set safety distance, it is determined that the two robots have collided, and the spatial coordinates of the shortest distance point at this time are output, and the process goes to step 3.

[0090] Step 3: Use bidirectional architecture, elliptical sampling, smoothing and other methods to optimize the RRT* algorithm, calculate the path sequence covering the entire assembly area, and solve the optimal motion path of the dual robots. The algorithm flow is as follows: Figure 3 The details are as follows:

[0091] 3-1) In the robot's joint space, select the initial point p init and target point p goal As the root node of the random expansion tree, the starting point and end point of the robot in the joint space are used as the focus to construct an elliptical area, and elliptical sampling is performed to avoid redundant branches. Each sampling point p rand They are all composed of 6 joint angle values, which are used as leaf nodes to expand the random tree;

[0092] 3-2) Detect sampling point p rand Is it in the obstacle space? If not, calculate the nearest point p near , if it is in the collision space, a new round of sampling is performed;

[0093] 3-3) From the nearest point p near According to p near to p rand The vector direction of the robot joint space is expanded with a fixed step size step to obtain a new node p new ;

[0094] 3-4) With the new node p new Reconnect the center of the circle and expand the nearest point p in the tree near With the new node p new The initial path connection established is used as the current parent node, and all nodes within the radius r are traversed to calculate: from the current parent node, that is, the current closest point p near To the new node p new The path length is added to the starting point p init The distance from other nodes to the new node p new The path length is added to the starting point p init distance; select the node with the smallest path cost as p new The new parent node of the node establishes a connection edge, that is, from the starting point p init Go through each node to reach the new node p new The sum of the Euclidean distances is the smallest;

[0095] 3-5) For the nearest point p near With the new node p new Connect the edges and perform interpolation processing, and detect the collision between the robot end and the environment. If there is no collision, p new Add to the point set V, add the connecting edge to the edge set E, otherwise re-sample;

[0096] 3-6) Check whether the number of sampling times reaches the set value and whether the distance between the sampling point and the target point is less than the predetermined threshold. If any of the above conditions are met, output the edge set E, otherwise a new round of sampling is performed.

[0097] Among them, when sampling in the joint space, a six-dimensional array θ=[θ1,θ2,θ3,θ4,θ5,θ6] is used to represent the sampling points, θ i Represents the angle value of the i-th joint, satisfying the constraints:

[0098] θ i =θ min +(θ max -θ min )·rand

[0099] So the new node p new The calculation formula is:

[0100]

[0101] Where: step represents a fixed step size, |||| represents the Euler distance.

[0102] By fixing the step size step, the path is gradually expanded in the robot joint space, ensuring that the expansion direction is a unit vector, generating tree nodes, and avoiding direct jumps to sampling points far away from the current node, making the path expansion smoother and more controllable.

[0103] 3-7) Use a third-order Bezier curve to smooth the obtained path. The calculation formula is:

[0104] p(t)=(1-t) 3 p0+3t(1-t) 2 p1+3t 2 (1-t)p2+t 2 p3,t∈[0,1]

[0105] Where: p(t) represents the coordinates of the time point t, p0, p1, p2, and p3 represent the coordinates of the control points of the Bezier curve, which respectively define the shape and path smoothness of the third-order Bezier curve.

[0106] Output the final planned path and optimize the RRT* path planning effect in 3D space. Figure 4 As shown, go to step 4.

[0107] Step 4: Transplant the optimized RRT* algorithm into the collision detection simulation program, generate the robot motion posture and verify the safety of the path. If there is no collision, output the simulation result. If there is a collision, generate the motion posture sequence of the master robot and re-plan the posture sequence of the slave robot until the collision-free optimal path is generated and the simulation result is output. The collision detection process is as follows: Figure 5 As shown, the details are as follows:

[0108] 4-1) While the optimized RRT* algorithm can generate a collision-free path, it ensures the safety of the robot's end-points, but it does not guarantee collision-free joints. Therefore, the optimized RRT* algorithm was built as an API interface and ported into a collision detection simulation program to further generate robot motion poses to verify the safety of the path.

[0109] 4-2) Based on the robot collision detection simulation program planning in step 4-1), complete the full-process path planning simulation of the two robots, obtain the time series of the motion postures of the two robots, and output the simulation results if there is no collision;

[0110] 4-3) If the simulation results indicate a collision, the robot paths are replanned based on the collaborative assembly space within the dual-robot compartment from step 1-3). One robot is designated as the master robot and its pose sequence is not interfered with. The other robot is designated as the slave robot and its pose sequence is replanned. The master robot's final pose in the collaborative assembly space is added to the collision space. The slave robot replans the pose sequence in the collaborative assembly space, starting with the master robot completing the assembly task in the collaborative assembly space and ending with the master robot completing the assembly task. The robot collision detection simulation program from step 4-1) is then called to generate the pose sequence for the slave robot. If there is no collision, the simulation results are output.

[0111] Go to step 5.

[0112] Step 5: Establish communication between the collision detection simulation program and the dual-robot control system to achieve virtual-real mapping of the planned path in the assembly scene, as follows:

[0113] An industrial communication bus is established between the host computer, PLC, and robot systems, enabling real-time data exchange between the collision detection simulation program and the dual-robot control system. Based on the robot pose timing generated by the simulation program, this assists in robotic control during the aerospace product assembly process. Furthermore, during the assembly process, PLC and robot data are collected in real time, enabling the simulation program to map virtual reality to the real scene.

[0114] In order to illustrate the technical solution and technical purpose of the present invention, the present invention is further introduced below with reference to the accompanying drawings and specific embodiments.

[0115] The Monte Carlo method is used to generate the collaborative motion space of the two robots in the cabin. The results are as follows: Figure 6 As shown in the figure, by analyzing the dual-robot collaborative motion space and the aerospace product process flow, the reachability of the system and the final assembly posture can be determined.

[0116] The capsule envelope robot link is used to simplify and expand its structure, and the resulting dual robot envelope structure is as follows: Figure 7 As shown in the figure, the robot collision detection is converted into the distance calculation between capsules. If the distance is less than the set safety distance, it is considered a collision, thereby reducing the complexity of the algorithm.

[0117] The optimized RRT* algorithm is transplanted into the collision detection simulation program to generate the robot motion posture as follows Figure 8 As shown, it can be output directly if there is no collision.

[0118] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of improvement of the present invention.

Claims

1. A dual-robot collaborative path planning method for aerospace product assembly, characterized in that: include: Step 1: Establish a robot kinematic model and use the Monte Carlo method to generate the collaborative motion space of the two robots; Step 2: Simplify and expand the robot structure based on the capsule geometry envelope method, and calculate the distance between the center lines of the two capsules to analyze the collision situation; Step 3: Optimize the RRT* algorithm to calculate the path sequence covering the entire assembly area and solve the optimal motion path for the two robots; Step 4: Transplant the optimized RRT* algorithm into the collision detection simulation program to generate the robot motion pose and verify the safety of the path. If there is no collision, the simulation result is output. If there is a collision, the motion pose sequence of the master robot is generated and the pose sequence of the slave robot is replanned until the optimal collision-free path is generated and the simulation result is output. Step 5: Establish communication between the collision detection simulation program and the dual-robot control system to achieve virtual-real mapping of the planned path in the assembly scene.

2. A dual-robot collaborative path planning method for aerospace product assembly according to claim 1, characterized in that: Step 1: Establish a robot kinematic model and use the Monte Carlo method to generate the collaborative motion space of the two robots. The details are as follows: 1-1) Based on the DH method, the transformation relationship between any adjacent link coordinate systems of the six-degree-of-freedom robot is obtained as follows: in i-1 T i is the coordinate system transformation matrix between the robot's i-1th and i-th manipulators; the coordinate system is defined as follows: the i-th joint axis is represented by z i Axis representation, take the common perpendicular line of two adjacent axes i and i+1, x i The direction of the common perpendicular line is determined by the right-hand rule. i axis, θ i Indicates the rotation angle around the z axis, z i Indicates the distance between two adjacent common perpendicular lines on the z-axis, a i represents the length of the common perpendicular, angle α i Represents the angle between two adjacent joint axes; By multiplying the homogeneous transformation matrix, the robot end effector posture transformation matrix is ​​obtained: 0 T n = 0 T1 1 T2… i-1 T i … n-1 T n Where n is the number of robot joints; 1-2) The selected assembly robot has 6 degrees of freedom, and the three joint axes of the assembly robot's end intersect at a point, satisfying the Pieper criterion in robotics mechanics. This means there must be a closed-form solution, so a closed-form method is used to find the inverse kinematics solution. The inverse kinematics solution is divided into two steps. First, θ1, θ2, and θ3 are solved based on the wrist position: 0 T6→ 0 T w →θ1,θ2,θ3 in, 0 T6 is the coordinate transformation matrix from the robot base to the end. 0 T w is the coordinate transformation matrix from the robot base to the wrist center; Then solve θ4, θ5, θ6 according to the wrist posture: 3 R6(θ4,θ5,θ6)= 0 R3 -1 · 0 R6→θ4,θ5,θ6 in, 3 R6 is the rotation matrix from the base of the robot wrist to the end, 0 R3 is the rotation matrix from the robot base to the wrist base, 0 R6 is the rotation matrix from the robot base to the wrist base; 1-3) Use the Monte Carlo method to simulate and analyze the dual-robot assembly space. Set the maximum number of random attempts and randomly generate six joint angles within the limit. Calculate the end-user pose based on the robot kinematics forward solution in step 1-1) to obtain the collaborative assembly space within the dual-robot compartment.

3. The dual-robot collaborative path planning method for aerospace product assembly according to claim 2, characterized in that: Step 2: Simplify and expand the robot structure based on the capsule geometry envelope method to reduce the complexity of the collision detection algorithm. Calculate the distance between the center lines of the two capsules to analyze the collision situation. The details are as follows: 2-1) Using the capsule-shaped envelope robot link to simplify and expand its structure, a dual-robot envelope structure is obtained; 2-2) After the envelope processing in 2-1), the robot's collision detection is converted into the distance calculation between capsules. That is, the position of each capsule is obtained through the robot kinematics forward solution in 1-1), and the distance between each capsule is calculated. The position vector of any two points on the axis relative to the base coordinate system is: l i =m i +k i (n i -m i )=m i +k i s i Where: l i Represents the position vector of any point on the capsule body axis relative to the base coordinate system; m i and n i Respectively represent the position vectors of the starting point and end point of the i-th capsule axis relative to the base coordinate system; k i ∈[0,1] is a scalar parameter; s i =(n i -m i ); Therefore, the shortest distance between any two capsules is: min(|l i -l j |-r i -r j )=min(|(m i +k i s i )-(m j +k j s j )|-r i -r j ) Where: r i Represents the radius of the i-th capsule; if the shortest distance between two capsules during movement is greater than the set safety distance, it is determined that the two robots have collided, and the spatial coordinates of the shortest distance point at this time are output, and the process goes to step 3.

4. The dual-robot collaborative path planning method for aerospace product assembly according to claim 1, characterized in that: In step 3, the RRT* algorithm is optimized using a bidirectional architecture, elliptical sampling, and smoothing methods to calculate a path sequence covering the entire assembly area and solve the optimal motion path of the dual robots.

5. The dual-robot collaborative path planning method for aerospace product assembly according to claim 4, characterized in that: Step 3 includes the following process: 3-1) In the robot's joint space, select the initial point p init and target point p goal As the root node of the random expansion tree, the starting point and end point of the robot in the joint space are used as the focus to construct an elliptical area and perform elliptical sampling. Each sampling point p rand They are all composed of 6 joint angle values, which are used as leaf nodes to expand the random tree; 3-2) Detect sampling point p rand Is it in the obstacle space? If not, calculate the nearest point p near , if it is in the collision space, a new round of sampling is performed; 3-3) From the nearest point p near According to the nearest point p near To sampling point p rand The vector direction of the robot joint space is expanded with a fixed step size step to obtain a new node p new ; 3-4) With the new node p new Reconnect the center of the circle and expand the nearest point p in the tree near With the new node p new The initial path connection established is used as the current parent node, and all nodes within the radius r are traversed to calculate: from the current parent node, that is, the current closest point p near To the new node p new The path length is added to the starting point p init The distance from other nodes to the new node p new The path length is added to the starting point p init distance; select the node with the smallest path cost as p new The new parent node of the node establishes a connection edge, that is, from the starting point p init Go through each node to reach the new node p new The sum of the Euclidean distances is the smallest; 3-5) For the nearest point p near With the new node p new Connect the edges and perform interpolation processing, and detect the collision between the robot end and the environment. If there is no collision, the new node p new Add to the point set V, add the connecting edge to the edge set E, otherwise re-sample; 3-6) Check whether the number of sampling times reaches the set value and whether the distance between the sampling point and the target point is less than the predetermined threshold; if any of the above conditions are met, output the edge set E, otherwise re-sample.

6. A dual-robot collaborative path planning method for aerospace product assembly according to claim 5, characterized in that: When sampling in the joint space, the sampling points are represented by a six-dimensional array θ = [θ1, θ2, θ3, θ4, θ5, θ6], θ i Represents the angle value of the i-th joint, satisfying the constraints: i i =θ min +(θ max -θ min )·rand Among them, θ min and θ max are the minimum and maximum values ​​allowed, respectively, and rand is a random number between 0 and 1; So the new node p new The calculation formula is: Where: step represents a fixed step size, |||| represents the Euler distance.

7. The dual-robot collaborative path planning method for aerospace product assembly according to claim 5, characterized in that: The step 3 further comprises: 3-7) Use a third-order Bezier curve to smooth the obtained path. The calculation formula is: p(t)=(1-t) 3 p0+3t(1-t) 2 p1+3t 2 (1-t)p2+t 2 p3,t∈[0,1] Where: p(t) represents the coordinates of the time point t, p0, p1, p2, and p3 represent the coordinates of the control points of the Bezier curve, which respectively define the shape and path smoothness of the third-order Bezier curve.

8. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the steps of the method according to any one of claims 1 to 7 are implemented.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

10. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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