An iterative optimization method for robot arm motion path based on batch collision detection

Abstract

The present invention discloses an iterative optimization method for a robot arm motion path based on batch collision detection. First, the robot arm's initial joint space motion path is sampled at equal distances to form a local candidate shortcut between any two sampling nodes. Then, each local candidate shortcut is interpolated at equal distances, and a gap neural network model is used to perform batch collision detection, thereby identifying collision-free local shortcuts; for collision-free local shortcuts, a shortest global optimization path is found; the above steps are iterated, and the initial sampling number is updated during each iteration. When the length of the optimized path or the optimization time meets the preset conditions, the iterative process ends, and finally a better robot arm global path is obtained. The robot arm joint space path length is adaptively optimized using an iterative optimization method to avoid the optimization effect being affected by the change in path length, thereby achieving efficient and rapid optimization of the robot arm motion path.

Description

Technical Field

[0001] This invention belongs to the field of robot motion optimization technology, and in particular relates to an iterative optimization method for the motion path of a robotic arm based on batch collision detection. Background Art

[0002] Optimizing the motion path of a robotic arm is a crucial step in the motion planning process. While sampling-based motion planning algorithms (RRT, PRM, etc.) can quickly find a collision-free path for the robotic arm, their random sampling method results in non-optimal path lengths, leaving significant room for optimization. Furthermore, real-time motion planning for robotic arms requires not only rapid path planning but also minimal optimization time. Existing path optimization methods, such as cubic spline interpolation, while finding smoother paths, often fail to meet the efficiency demands of real-time motion planning. The primary reason for this is the significant collision detection involved in the optimization process, which consumes considerable time. Therefore, how to quickly optimize the motion path after finding a collision-free path has become a critical technical challenge in real-time robotic arm motion planning.

[0003] Currently, some scholars have proposed learning-based motion path optimization methods to accelerate the motion path optimization process of robotic arms. However, these methods are greatly affected by the variation in the path length of the robotic arm, making them difficult to adapt to complex robotic arm motion path optimization tasks; further improvements are needed in optimization performance such as optimization time and path length. To address these problems and challenges, this invention proposes an iterative optimization method for robotic arm motion paths based on batch collision detection. Summary of the Invention

[0004] To address the above technical problems, this invention provides an iterative optimization method for robotic arm motion paths based on batch collision detection, aiming to solve the problems of low efficiency and difficulty in adapting to complex robotic arm motion path optimization tasks in existing methods.

[0005] The technical solution adopted by this invention to solve its technical problem is:

[0006] An iterative optimization method for the motion path of a robotic arm based on batch collision detection, the method comprising the following steps:

[0007] S100: Perform equidistant sampling of the initial joint spatial motion path of the robotic arm, with the number of sampling points being... A local candidate shortcut is formed between any two sampling nodes, resulting in a total of Local candidate shortcuts;

[0008] S200: For each local candidate shortcut, increment by step. Perform equidistant interpolation to obtain Interpolation points, Using interpolation points as input, a gap neural network model is used for batch collision detection to identify collisions. A collision-free local shortcut;

[0009] S300: For There are collision-free local shortcuts, each shortcut connecting two different robot joint space configuration points. The collision-free local shortcuts are regarded as edges of a graph, and each configuration point is a node of the graph. An initial distance value is assigned to each node, and a priority queue is created to explore the path. The shortest path is found and recorded, backtracked, and the backtracked path sequence and its total path length are output. The shortest globally optimized path found in the collision-free local shortcuts is obtained.

[0010] S400: Iterates from S100 to S300, updating the initial number of sampling points in each iteration. , , This is the incremental value of the number of sampling points in the iterative process. When the preset iteration termination condition is met, the iterative process ends, and a better global path for the robotic arm is finally obtained.

[0011] Preferably, S100 includes:

[0012] S110: An initial path in the joint space of the robotic arm obtained after preliminary motion planning is represented as follows: , The starting configuration node is The target configuration node is The joint space of the robotic arm is represented as ,in The initial configuration node of the robotic arm represents its degrees of freedom. and target configuration node In joint space, they are respectively represented as and , The initial path length is , The calculation method is as follows:

[0013] ;

[0014] in Indicates the initial path in the joint space of the robotic arm. The number of path nodes included; , express Any two adjacent joint space path nodes;

[0015] S120: Initial joint space motion path of the robotic arm Perform equidistant sampling, with the number of sampling points set to... That is, the sampling step size is Configure the starting point of the path and path target configuration points Including, a total One sampling node;

[0016] S130: Construct a local candidate shortcut between any two sampling nodes. A total of H local candidate shortcuts are constructed, of which... .

[0017] Preferably, S200 includes:

[0018] S210: For each local candidate shortcut, increment the step size. Perform equidistant interpolation. A total of local candidate shortcuts were obtained. One interpolation point;

[0019] S220: Assume the number of obstacles in the robotic arm's operating space is... One, using a trained gap neural network model to process the above Batch collision estimation is performed on each interpolation point to obtain... The gap prediction matrix corresponding to each interpolation point According to the gap prediction matrix Determine the configuration of the robotic arm joint as the first At each interpolation point, does the robotic arm collide with an obstacle?

[0020] S230: For any local candidate shortcut, if there is an interpolation point predicted as a "collision" in the local candidate shortcut, discard the local candidate shortcut; otherwise, retain it, thus ultimately identifying... A collision-free local shortcut.

[0021] Preferably, S220 includes:

[0022] Will Each interpolation point data point is input into the gap neural network model at once for batch data processing to obtain... The gap prediction matrix corresponding to each interpolation point ,in, for 3D matrix, k=1,2,… For matrices Each element in the array, if its value is less than the safety threshold If the condition is met, the element is set to 1; otherwise, it is set to 0.

[0023] For any gap prediction matrix If the matrix If all elements in the middle are 0, it means that the robotic arm joint is configured as the first... At each interpolation point, the robotic arm did not collide with the obstacle. If the matrix... If there is an element with a value of 1, it means that the robotic arm has collided with an obstacle;

[0024] After performing the aforementioned steps, you can obtain the desired results. Collision estimation results for each interpolation point.

[0025] Preferably, the gap inference network model comprises four sequentially forward-connected parts. The first part uses the robotic arm joint configuration node as initial input and employs a kernel function. The joint angles are encoded to increase the frequency of the input values, where... This represents the input robotic arm joint configuration node. This is an overclocking parameter. The output of the first part will serve as the input to the second part. The second part consists of a fully connected layer, a sigmoid activation function, and a dropout layer. The output of the second part will serve as the input to the third part. The third part consists of a fully connected layer, a sigmoid activation function, and a dropout layer. The output of the third part will serve as the input to the fourth part. The fourth part consists of a fully connected layer, and the output feature number is... The purpose is to achieve Mapping the gap distance in dimensional space to predict the distance from the robot arm to the workspace under the current joint configuration. The gap value of each obstacle.

[0026] Preferably, S300 includes:

[0027] S310: For the acquisition There are collision-free local shortcuts, each shortcut connecting two different robot joint space placement points. These collision-free local shortcuts are regarded as edges of a graph, and each placement point is regarded as a node of the graph.

[0028] S320: Initial Distance: Assigns an initial distance value to each node to record the distance from the starting configuration node of the robotic arm. The shortest path distance to this node, set the starting configuration node. The distance to the first node is 0, and the initial distances to all other nodes are set to infinity, indicating that they are not yet reachable.

[0029] S330: Create a priority queue: Create a priority queue for the initial configuration node. The node and its distance are added to the queue as the initial element. The priority queue will be arranged in ascending order of node distance so that the node with the smallest current distance can be processed each time.

[0030] S340: Perform path exploration until the target configuration point is found. The shortest path or priority queue is empty;

[0031] S350: Record the shortest path: While updating the distance, record the predecessor node of each node;

[0032] S360: Backtrack Path: When the priority queue has finished processing or the target configuration node... After finding the shortest path, record it using the predecessor node, from Going back to This generates a complete shortest path.

[0033] S370: Output Path: Outputs the path sequence obtained from backtracking and its total path length, obtaining the shortest globally optimized path found in the collision-free local shortcuts. .

[0034] Preferably, S340 includes:

[0035] S341: Retrieve the node with the smallest distance value from the priority queue, let's assume it's the current node. ;

[0036] S342: Check from All adjacent nodes from which the origin is located;

[0037] S343: For each adjacent node Calculate from arrive The path distance;

[0038] S344: If the distance of this path is greater than the current record If the distance is small, then update. The distance is calculated, and the node is reinserted into the priority queue with the updated distance value.

[0039] Preferably, S400 includes:

[0040] S410: For the found optimized path The process iterates from S100 to S300, updating the number of sampling points in each iteration. ,in , The initial value is That is, the number of sampling points increases in each iteration. ;

[0041] S420: The iteration process ends when the length of the optimized path and the optimization time meet one of the following preset conditions, ultimately obtaining a better global path for the robotic arm; otherwise, the aforementioned iterative optimization process continues. The preset conditions include:

[0042] ,in This represents the length of the robotic arm path before optimization. This represents the length of the robotic arm path before optimization. This can be set by the user; or the cumulative optimization time may exceed a preset time. .

[0043] This invention proposes an iterative optimization method for robotic arm motion paths based on batch collision detection. By constructing multiple local candidate shortcuts, the likelihood of finding shorter paths is increased. Simultaneously, a gap neural network model is used for batch collision detection, accelerating the path optimization process. Furthermore, this invention employs an iterative optimization approach to adaptively optimize the path length in the robotic arm joint space, avoiding the impact of path length variations on the optimization effect, thus achieving efficient and rapid optimization of the robotic arm motion path. Attached Figure Description

[0044] Figure 1 This is a flowchart of an iterative optimization method for the motion path of a robotic arm based on batch collision detection, according to an embodiment of the present invention.

[0045] Figure 2 This is a schematic diagram of a local candidate shortcut in the joint space of a robotic arm in one embodiment of the present invention;

[0046] Figure 3 This is a schematic diagram of a robotic arm and environmental obstacles in one embodiment of the present invention;

[0047] Figure 4 This is an example diagram of an optimized robotic arm motion path in one embodiment of the present invention. Detailed Implementation

[0048] To enable those skilled in the art to better understand the technical solution of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings.

[0049] In one embodiment, such as Figure 1 As shown, an iterative optimization method for the motion path of a robotic arm based on batch collision detection is described, the method comprising the following steps:

[0050] S100: Perform equidistant sampling of the initial joint spatial motion path of the robotic arm, with the number of sampling points being... A local candidate shortcut is formed between any two sampling nodes, resulting in a total of Local candidate shortcuts;

[0051] S200: For each local candidate shortcut, increment by step. Perform equidistant interpolation to obtain Interpolation points, Using interpolation points as input, a gap neural network model is used for batch collision detection to identify collisions. A collision-free local shortcut;

[0052] S300: For There are collision-free local shortcuts, each shortcut connecting two different robot joint space configuration points. The collision-free local shortcuts are regarded as edges of a graph, and each configuration point is a node of the graph. An initial distance value is assigned to each node, and a priority queue is created to explore the path. The shortest path is found and recorded, backtracked, and the backtracked path sequence and its total path length are output. The shortest globally optimized path found in the collision-free local shortcuts is obtained.

[0053] S400: Iterates from S100 to S300, updating the initial number of sampling points in each iteration. , , The incremental value of the number of sampling points in the iteration process is preset by the user. When the preset iteration termination condition is met, the iteration process ends, and a better global path for the robotic arm is finally obtained.

[0054] In one embodiment, such as Figure 2 As shown, S100 includes:

[0055] S110: An initial path in the joint space of the robotic arm obtained after preliminary motion planning is represented as follows: , The starting configuration node is The target configuration node is The joint space of the robotic arm is represented as ,in The initial configuration node of the robotic arm represents its degrees of freedom. and target configuration node In joint space, they are respectively represented as and , The initial path length is , The calculation method is as follows:

[0056] ;

[0057] in Indicates the initial path of the UR5 robotic arm joint space. The number of path nodes included; , express Any two adjacent joint space path nodes;

[0058] S120: Initial joint space motion path of the robotic arm Perform equidistant sampling, with the number of sampling points set to... That is, the sampling step size is Configure the starting point of the path and path target configuration points Including, a total One sampling node;

[0059] S130: Construct a local candidate shortcut between any two sampling nodes. A total of H local candidate shortcuts are constructed, of which... .

[0060] In one embodiment, such as Figure 2 As shown, S200 includes:

[0061] S210: For each local candidate shortcut, increment the step size. Perform equidistant interpolation. A total of local candidate shortcuts were obtained. One interpolation point;

[0062] S220: Assume the number of obstacles in the robotic arm's operating space is... One, using a trained gap neural network model to process the above Batch collision estimation is performed on each interpolation point to obtain... The gap prediction matrix corresponding to each interpolation point According to the gap prediction matrix Determine the configuration of the robotic arm joint as the first At each interpolation point, does the robotic arm collide with an obstacle?

[0063] S230: For any local candidate shortcut, if there is an interpolation point predicted as a "collision" in the local candidate shortcut, discard the local candidate shortcut; otherwise, retain it, thus ultimately identifying... A collision-free local shortcut.

[0064] In one embodiment, S220 includes:

[0065] Will Each interpolation point data point is input into the gap neural network model at once for batch data processing to obtain... The gap prediction matrix corresponding to each interpolation point ,in, for 3D matrix, k=1,2,… For matrices Each element in the array, if its value is less than the safety threshold ( If the value is user-configurable, then the element is set to 1; otherwise, it is set to 0.

[0066] For any gap prediction matrix If the matrix If all elements in the middle are 0, it means that the robotic arm joint is configured as the first... At each interpolation point, the robotic arm did not collide with the obstacle. If the matrix... If there is an element with a value of 1, it means that the robotic arm has collided with an obstacle;

[0067] After performing the aforementioned steps, you can obtain the desired results. Collision estimation results for each interpolation point.

[0068] In one embodiment, the gap inference network model comprises four sequentially forward-connected parts. The first part takes robotic arm joint configuration nodes as initial input and uses a kernel function. The joint angles are encoded to increase the frequency of the input values, where... This represents the input robotic arm joint configuration node. This is an overclocking parameter. The output of the first part will serve as the input to the second part. The second part consists of a fully connected layer, a sigmoid activation function, and a dropout layer. The output of the second part will serve as the input to the third part. The third part consists of a fully connected layer, a sigmoid activation function, and a dropout layer. The output of the third part will serve as the input to the fourth part. The fourth part consists of a fully connected layer, and the output feature number is... The purpose is to achieve Mapping the gap distance in dimensional space to predict the distance from the robot arm to the workspace under the current joint configuration. The gap value of each obstacle.

[0069] In one embodiment, S300 includes:

[0070] S310: For the acquisition There are collision-free local shortcuts, each shortcut connecting two different robot joint space placement points. These collision-free local shortcuts are regarded as edges of a graph, and each placement point is regarded as a node of the graph.

[0071] S320: Initial Distance: Assigns an initial distance value to each node to record the distance from the starting configuration node of the robotic arm. The shortest path distance to this node, set the starting configuration node. The distance to the first node is 0, and the initial distances to all other nodes are set to infinity, indicating that they are not yet reachable.

[0072] S330: Create a priority queue: Create a priority queue for the initial configuration node. The node and its distance (0) are added to the queue as the initial element. The priority queue will be arranged in ascending order of node distance so that the node with the smallest current distance can be processed each time.

[0073] S340: Perform path exploration until the target configuration point is found. The shortest path or priority queue is empty;

[0074] S350: Record the shortest path: While updating the distance, record the predecessor node of each node;

[0075] S360: Backtrack Path: When the priority queue has finished processing or the target configuration node... After finding the shortest path, record it using the predecessor node, from Going back to This generates a complete shortest path.

[0076] S370: Output Path: Outputs the path sequence obtained from backtracking and its total path length, obtaining the shortest globally optimized path found in the collision-free local shortcuts. .

[0077] In one embodiment, S340 includes:

[0078] S341: Retrieve the node with the smallest distance value from the priority queue, let's assume it's the current node. ;

[0079] S342: Check from All adjacent nodes of the origin (i.e., those with) Other configuration nodes that are directly connected);

[0080] S343: For each adjacent node Calculate from arrive The path distance;

[0081] S344: If the distance of this path is greater than the current record If the distance is small, then update. The distance is calculated, and the node is reinserted into the priority queue with the updated distance value.

[0082] In one embodiment, S400 includes:

[0083] S410: For the found optimized path The process iterates from S100 to S300, updating the number of sampling points in each iteration. ,in , The initial value is That is, the number of sampling points increases in each iteration. ;

[0084] S420: The iteration process ends when the length of the optimized path and the optimization time meet one of the following preset conditions, ultimately obtaining a better global path for the robotic arm; otherwise, the aforementioned iterative optimization process continues. The preset conditions include:

[0085] ,in This represents the length of the robotic arm path before optimization. This represents the length of the robotic arm path before optimization. This can be set by the user; or the cumulative optimization time may exceed a preset time. .

[0086] The following is a specific example to demonstrate the simulation verification and analysis of the proposed method, using the following experimental parameters:

[0087] 1) Robotic arm simulation environment such as Figure 3 As shown, the verification was performed using the UR5 robotic arm, including three environmental obstacles ( );

[0088] 2) Initial value of the number of sampling points Z It is 5. s, =1.1, mm;

[0089] 3) The initial configuration node for the robotic arm is =[-2.1808, -1.0708, 1.1, -1.5708, -1.4,0], Target configuration node = [-1.2608, -1.0708, 1.1, -1.5708, -1.4, 0];

[0090] At the initial configuration node of the robotic arm and target configuration node Fifty collision-free motion paths were randomly generated, with an initial average path length of 9.8917 rad. After path optimization using the method proposed in this invention, the optimized average path length was 4.904 rad, and the average optimization time was 0.4619 s, demonstrating optimization efficiency far exceeding traditional robotic arm motion optimization methods. The optimization time was reduced by 89.16%. Figure 4 A set of optimized robotic arm motion paths is shown.

[0091] The above-mentioned iterative optimization method for robotic arm motion paths based on batch collision detection has the following beneficial effects:

[0092] (1) Compared with traditional robotic arm path optimization methods, the iterative optimization method proposed in this invention increases the possibility of finding a shorter path by simultaneously constructing multiple local candidate shortcuts; at the same time, the use of a gap neural network model for batch collision detection in this invention greatly shortens the time required for path optimization.

[0093] (2) Compared with existing learning-based robotic arm motion path optimization methods, the iterative optimization method proposed in this invention can adaptively adjust the number of optimizations and the number of local candidate shortcuts according to the path length after each optimization, and can be applied to robotic arm motion path optimization tasks with large changes in path length.

[0094] The foregoing has provided a detailed description of the iterative optimization method for robotic arm motion paths based on batch collision detection provided by this invention. Specific examples have been used to illustrate the principles and implementation methods of this invention. The descriptions of the embodiments above are merely for the purpose of helping to understand the core ideas of this invention. It should be noted that those skilled in the art can make various improvements and modifications to this invention without departing from its principles, and these improvements and modifications also fall within the protection scope of the claims of this invention.

Claims

1. A method for iterative optimization of robot arm motion paths based on batch collision detection, characterized in that: The method comprises the following steps: S100: Perform equidistant sampling on the initial joint space motion path of the robot arm. The number of sampling points is , forming a local candidate shortcut between any two sampling nodes, forming a total of local candidate shortcuts; S200: For each local candidate shortcut, Perform equidistant interpolation to obtain interpolation points, interpolation points as input, and use the gap neural network model to perform batch collision detection to identify collision-free local shortcuts; S200 includes: S210: For each local candidate shortcut, Perform equidistant interpolation. A total of local candidate shortcuts are obtained interpolation points; S220: Assume that the number of obstacles in the robot arm operation space is The trained gap neural network model is used to interpolation points for batch collision estimation, and obtain The gap prediction value matrix corresponding to the interpolation points , according to the gap prediction value matrix Determine whether the robot arm joint configuration is When the interpolation point is reached, whether the robot arm collides with an obstacle; S230: For any local candidate shortcut, if there is an interpolation point predicted as "collision" in the local candidate shortcut, the local candidate shortcut is discarded, otherwise it is retained, so as to finally identify collision-free local shortcuts; S220 includes: Will The interpolation point data is input into the gap neural network model at one time for batch data processing, and the The gap prediction value matrix corresponding to the interpolation points ,in, for dimensional matrix, k=1,2,…, ; For the matrix For each element in , if its value is less than the safety threshold , then the element is set to 1, otherwise it is set to 0; For any gap prediction value matrix , if the matrix If all the elements are 0, it means that the robot arm joint configuration is When the interpolation point is reached, the robot arm does not collide with the obstacle. If the matrix If there is an element with a value of 1 in , it means that the robot arm collides with an obstacle; After completing the above operations, you can obtain Collision estimation results of interpolation points; The gap reasoning network model consists of four parts that are forward connected in sequence. The first part uses the robot joint configuration node as the initial input and uses the kernel function Encode the joint angles and increase the frequency of the input values, where Represents the input robot joint configuration node, is an overclocking parameter. The output of the first part will be used as the input of the second part. The second part consists of a fully connected layer, an activation function Sigmoid, and a DropOut layer. The output of the second part will be used as the input of the third part. The third part consists of a fully connected layer, an activation function Sigmoid, and a DropOut layer. The output of the third part will be used as the input of the fourth part. The fourth part consists of a fully connected layer, and the output feature number is , the purpose is to achieve The mapping of the dimensional gap distance is used to predict the robot arm’s position in the operating space under the current joint configuration. The clearance value of obstacles; S300: For A collision-free local shortcut is created, each shortcut connects two different robot joint space configuration points, the collision-free local shortcut is regarded as an edge of a graph, each configuration point is regarded as a node of the graph, an initial distance value is assigned to each node, and a priority queue is created for path exploration, the shortest path is found and recorded, backtracked, and the path sequence obtained by backtracking and its total path length are output to obtain a shortest global optimization path found in the collision-free local shortcut; S400: Iterate S100-S300, and the number of initial sampling points will be updated during each iteration , , It is the incremental value of the number of sampling points in the iterative process. When the preset iteration termination condition is met, the iterative process ends, and finally a better global path of the robot arm is obtained.

2. The method according to claim 1, characterized in that S100 includes: S110: After preliminary motion planning, an initial path in the joint space of the robot arm is obtained, which is expressed as , The starting configuration node is , the target configuration node is , the robot arm joint space is represented as ,in represents the degrees of freedom of the robot arm, then the starting configuration node of the robot arm and the target configuration node In the joint space, they are expressed as and , The initial path length is , The calculation method is as follows: ； in Represents the initial path of the robot joint space The number of path nodes included; , express Any two adjacent joint space path nodes in ; S120: Initial joint space motion path of the robot arm Perform equidistant sampling, and set the number of sampling points to , that is, the sampling step length is , configure the path starting point and path target configuration points Including, a total of sampling nodes; S130: construct a local candidate shortcut between any two sampling nodes, and construct a total of H local candidate shortcuts, where .

3. The method according to claim 2, characterized in that S300 includes: S310: Acquired collision-free local shortcuts, each shortcut connects two different robot joint space configuration points, these collision-free local shortcuts are regarded as edges of a graph, and each configuration point is regarded as a node of the graph; S320: Initialization distance: Assign an initial distance value to each node, which is used to record the distance from the robot arm to the starting configuration node. The shortest path distance to the node, set the starting configuration node The distance of is 0, and the initial distance values ​​of all other nodes are set to infinity, indicating that they are not yet reachable; S330: Create a priority queue: Create a priority queue and start the configuration node and its distance as the initial element to be added to the queue. The priority queue will be arranged from small to large according to the node distance, so that the node with the smallest current distance can be processed each time; S340: Path exploration until the target configuration point is found The shortest path or priority queue is empty; S350: Record the shortest path: while updating the distance, record the predecessor node of each node; S360: Backtracking path: When the priority queue is processed or the target configuration node After the shortest path is found, the predecessor node record is used to Going back to , generate a complete shortest path; S370: Output path: Output the path sequence and total path length obtained by backtracking, and obtain the shortest global optimization path found in the collision-free local shortcut .

4. The method according to claim 3, characterized in that S340 includes: S341: Take the node with the smallest distance value from the priority queue and assume it is the current node ; S342: Check from All adjacent nodes of the starting point; S343: For each adjacent node , calculated from arrive Path distance; S344: If the path distance is longer than the currently recorded If the distance is small, update distance and reinsert the node with the updated distance value into the priority queue.

5. The method according to claim 4, characterized in that S400 includes: S410: For the found optimized path , iteratively execute S100-S300, and the number of sampling points will be updated during each iteration ,in , The initial value is , that is, the number of sampling points increases during each iteration ; S420: When the length of the optimized path and the optimization time meet one of the following preset conditions, the iterative process ends and a better global path of the robot arm is finally obtained, otherwise the aforementioned iterative process continues to be executed; the preset conditions include: ,in represents the path length of the robot arm before optimization, represents the path length of the robot arm before optimization, , set by the user; or the cumulative optimization time exceeds the preset time .

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