Multi-robot motion planning method based on bidirectional discrete rapidly-exploring random tree

Abstract

A kind of multi-robot arm motion planning method based on bidirectional discrete rapid expansion random tree, comprising: 1, the route map of each robot arm is generated, and is combined into composite route map;2, each robot arm generates random tree in respective route map, to start point and target point as sampling point simultaneously expand two random trees;3, two random trees are expanded with the sampling point of the other party;4, select the node that meets the preset requirement, and judge whether it can pass through collision detection, is then enter 5, otherwise enter 3;5, traverse the near neighbor point of the selected node, judge whether the value of each near neighbor point is smaller with the selected node as parent node in 4, is then modify parent node as the selected node, otherwise judge whether two random trees are connected successfully;If connected successfully, end expansion, otherwise loop 3 to 5, until successfully connected.The present application helps to find solution for multi-robot arm motion planning problem, reduces the search of useless area, and speeds up the expansion speed of tree branch.

Description

Technical Field

[0001] This invention relates to the field of multi-robot motion planning technology, and in particular to a multi-robot motion planning method based on a bidirectional discrete fast expanding random tree. Background Technology

[0002] With the advent of the artificial intelligence era, more and more robotic arms are being integrated into the production process. They are liberating humans from heavy and repetitive labor. As the number of robotic arms increases and the demand for production flexibility grows, robotic arms will face greater collision risks and computational pressure in motion planning.

[0003] In traditional industrial sectors, such as automobile manufacturing, the working environment of robotic arms is typically known and predictable. This allows robotic arms to perform highly scripted operations through repetitive, predefined movements. However, as more and more robotic arms are added to production lines, the density of robotic arms in factories is increasing, and the objects on the assembly line are becoming increasingly complex. The paths planned for robotic arms should avoid collisions with other robotic arms or objects.

[0004] Planning the motion trajectories of multiple robotic arm systems simultaneously in a shared workspace is challenging. Most multi-robotic arm motion planning algorithms either become unsolvable as the number of robotic arms increases, or sacrifice algorithm completeness and path quality. Furthermore, the motion planning problem becomes particularly complex when the distances between the operations of each robotic arm are small. In this situation, operating multiple robotic arm systems in a decoupled manner is inefficient and cannot meet the demands of modern industrial production lines; therefore, it is necessary to synchronize the operations of multiple robotic arms in a complex configuration space. However, the difficulty of solving the motion planning problem increases exponentially with the dimensionality of the configuration space. In multi-robotic arm motion planning examples, the complex configuration space of multiple robotic arms is usually high-dimensional, requiring a comprehensive and high-resolution search, such as discretizing it using a grid and then searching it. In this context, handling the motion planning of multiple robotic arms in a shared workspace in an efficient and coupled manner is key to solving this problem. Summary of the Invention

[0005] This invention provides a multi-robot motion planning method based on a bidirectional discrete fast expanding random tree to solve the technical problems mentioned in the background art.

[0006] To achieve the above objectives, the technical solution of the present invention is implemented as follows:

[0007] This invention provides a multi-robotic arm motion planning method, comprising the following steps:

[0008] S1. Initialize the workspace environment, acquire obstacle information, determine the starting pose and target pose of each robotic arm, generate the route map of each robotic arm, and combine the route maps of each robotic arm into a composite route map through tensor product.

[0009] S2. Each robotic arm generates a random tree in its own route map, and expands two random trees simultaneously with the starting point and the target point as the root nodes.

[0010] S3. Both random trees are expanded using the sampling points of the other, and each expansion first expands the tree with fewer nodes.

[0011] S4. After expanding the two random trees to obtain new sampling points, find the node closest to the new sampling point on the random tree. Select the node that meets the preset requirements from the nearest neighbor of the nearest node according to the direction indicator function, and determine whether the selected node can pass the collision detection. If yes, proceed to S5; otherwise, proceed to S3.

[0012] S5. Traverse the nearest neighbors of the selected node and determine if the cost of each nearest neighbor is smaller with the selected node in S4 as its parent node. If it is smaller, change the parent node of the nearest neighbor to the selected node and determine if the two random trees of the robotic arm are successfully connected. If not, directly determine if the two random trees of the robotic arm are successfully connected. If the two random trees of the robotic arm are successfully connected, end the expansion. If they are not successfully connected, loop from S3 to S5 until the maximum iteration time is reached or the two random trees are successfully connected.

[0013] Furthermore, the method for generating the route map for each robotic arm in S1 is as follows:

[0014] First, pose points are randomly generated individually in the workspace of each robotic arm. Collision detection is performed on each pose point, and pose points that will collide are eliminated. The remaining pose points are then connected, and the lines that come into contact with obstacles are deleted to obtain the route map for each robotic arm.

[0015] Furthermore, the roadmap is represented by a formula, as follows:

[0016] G i =(V i E i )

[0017] Among them, G i Indicates the robotic arm r i The route map, node V i Indicates the robotic arm r i Collision-free placement pose, edge E i Indicates the robotic arm r i The trajectory of collision-free motion.

[0018] Furthermore, step S2 specifically includes the following steps:

[0019] S21. First, generate an initial sampling point for each robotic arm on its respective route map;

[0020] S22. Each robotic arm expands two random trees simultaneously in its respective route map, with the starting point and the target point as the root nodes. Both trees expand in the direction of the initial sampling point. Each expansion first expands the tree with fewer nodes until an obstacle is encountered or the tree expands to the initial sampling point. If no obstacle is encountered or the tree expands to the initial sampling point, both trees expand in the direction of the previous initial sampling point.

[0021] Furthermore, step S3 specifically includes the following steps:

[0022] S31. Both random trees are expanded using the sampled points, and the tree with fewer nodes is expanded first in each expansion. The probability threshold P is initialized during the first run of S31. target =0;

[0023] S32. During the expansion process, determine whether the sampling point encounters an obstacle. If an obstacle is encountered, the probability threshold P is set. target Increase and generate a random value p. When the random value p is less than the probability threshold P... target At that time, the random point is used as the new sampling point Q. rand When the random value p is greater than or equal to the probability threshold, the target point is taken as the new sampling point Q. rand .

[0024] Furthermore, S32 is specifically expressed by the following formula:

[0025]

[0026] Among them, V goal The target point is used for sampling, and Sample() indicates random sampling.

[0027] Furthermore, step S4 specifically includes the following steps:

[0028] S41. A new sampling point Q is obtained by expanding the two random trees. rand Then, find the node V that is closest to the new sampling point on the random tree. near ;

[0029] S42, based on the direction indication function O d At node V near Select the nearest neighbor points V that best match the indicator function O. d The node is taken as node V new And satisfy (Vnear V new )∈E;

[0030] At node V near Select the nearest neighbor points V that best match the indicator function O. d The node specifically refers to node V. near Select a node V from all its nearest neighbors V. new This makes node V near To node V new The direction of the line connecting them is closest to node V. near New sampling point Q in S32 rand The direction indicated by the connection;

[0031] S43, if node V new If it is not in the random tree, then node V will be... new Add to the random tree, and add a path from node V. near To node V new The edge.

[0032] Furthermore, the direction indication function O in S42 d Specifically as follows:

[0033]

[0034] In the formula, ∠V near (Q ran d, V) represents the minimum angle between ray 1 and ray 2, where ray 1 originates from V. near Start and through Q rand , ray 2 from V near Starts and passes through V, where V represents node V. near The nearest neighbor; Adj(V) near G′) represents V in the route map G′ near The set of nearest neighbors, where argmin represents the minimum value.

[0035] The beneficial effects of this invention are:

[0036] 1. This invention proposes an efficient composite route graph that can handle scenarios with tightly coupled multiple robotic arms. The implicitly represented composite route graph enables us to efficiently solve the multi-robotic arm motion planning problem by searching only a portion of the configuration space. Furthermore, when planning the path for each robotic arm from its starting point to its target point, it avoids collisions with obstacles and with other robotic arms.

[0037] 2. This invention proposes a multi-robot motion planning method based on the dRRT*-Connect (bidirectional discrete fast expanding random tree optimization) algorithm. The proposed method involves two random trees that continuously expand alternately towards each other. Especially when the initial pose and target pose are within constrained regions, the two random trees can escape their respective constrained regions by rapidly expanding towards each other. This heuristic expansion makes the expansion of the random trees more greedy and explicit. Furthermore, by utilizing multiple sampling points, the dual-tree algorithm (i.e., the dRRT*-Connect algorithm) is more efficient than the single-tree algorithm, and the growth of the random trees is faster.

[0038] 3. In this invention, once the starting point and target point are determined, the planned paths for both become crucial. Since random sampling lacks directionality, it leads to an abundance of useless nodes. This invention employs a probabilistic target-biased strategy (i.e., steps S31 to S32), which, without compromising the randomness of the target point, adds a certain directional constraint to the random tree, ensuring that the random tree always expands towards the target point, avoiding the generation of too many useless points, and accelerating the expansion speed of the branches. Attached Figure Description

[0039] Figure 1 This is a flowchart of the present invention;

[0040] Figure 2 This is the method for generating composite route maps in this invention;

[0041] Figure 3 For node V in this invention new Generation method;

[0042] Figure 4 This is a simulation diagram of the collaborative operation of two robotic arms in this invention. Detailed Implementation

[0043] To facilitate understanding of the present invention, a more complete description will be given below with reference to the accompanying drawings. Preferred embodiments of the invention are shown in the drawings. However, the invention can be implemented in many other different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided to provide a thorough and complete understanding of the disclosure of the invention.

[0044] To address the shortcomings mentioned in the background art, this invention provides a multi-robot motion planning method based on a bidirectional discrete fast expanding random tree. Primarily based on the dRRT*-Connect (Bidirectional Discrete Fast Expanding Random Tree Optimization) algorithm, this invention utilizes the implicit representation of the composite space to provide completeness and efficiency. Through bidirectional path search and a probabilistic target bias strategy between the starting and target points, it helps find solutions to high-dimensional multi-robot motion planning problems, reduces the search for useless regions, accelerates the expansion speed of the random tree branches, and prevents time waste caused by random sampling.

[0045] The present invention will now be described in detail:

[0046] Reference Figure 1 This application provides a multi-robot motion planning method based on a bidirectional discrete fast expanding random tree, comprising the following steps:

[0047] S1. Initialize the workspace environment, acquire obstacle information, determine the starting pose and target pose of each robotic arm, generate the route map of each robotic arm, and combine the route maps of each robotic arm into a composite route map through tensor product.

[0048] S2. Each robotic arm generates a random tree in its own route map, and expands two random trees simultaneously with the starting point and the target point as the root nodes.

[0049] S3. Both random trees are expanded using the sampling points of the other, and each expansion first expands the tree with fewer nodes.

[0050] S4. After expanding the two random trees to obtain new sampling points, find the node closest to the new sampling point on the random tree. Select the node that meets the preset requirements from the nearest neighbor of the nearest node according to the direction indicator function, and determine whether the selected node can pass the collision detection. If yes, proceed to S5; otherwise, proceed to S3.

[0051] S5. Traverse the nearest neighbors of the selected node and determine if the cost of each nearest neighbor is smaller with the selected node in S4 as its parent node. If it is smaller, change the parent node of the nearest neighbor to the selected node and determine if the two random trees of the robotic arm are successfully connected. If not, directly determine if the two random trees of the robotic arm are successfully connected. If the two random trees of the robotic arm are successfully connected, end the expansion. If they are not successfully connected, loop from S3 to S5 until the maximum iteration time is reached or the two random trees are successfully connected.

[0052] In some embodiments, the method for generating the route map for each robotic arm in S1 is as follows:

[0053] First, pose points are randomly generated individually in the workspace of each robotic arm. Collision detection is performed on each pose point, and pose points that will collide are eliminated. The remaining pose points are then connected, and the lines that come into contact with obstacles are deleted to obtain the route map for each robotic arm.

[0054] In some embodiments, the route map is represented by a formula, as follows:

[0055] G i =(V i E i )

[0056] Among them, G i Indicates the robotic arm r i The roadmap, vertex V i Indicates the robotic arm r i Placement location without collision, edge E i Indicates the robotic arm r i The trajectory of collision-free motion.

[0057] Route Map G i Embedded in the workspace Middle; i.e., route map G i It can be seen as a workspace Approximate value. Route map G i The construction is based on parameters n and r n The decision represents the number of samples and the connection radius, respectively.

[0058] The tensor product path graph is represented as G′=(E′,V′), where G1, ..., G R The tensor product between them. Each vertex of G′ describes the simultaneous placement of R robotic arms, and each edge of G′ describes the simultaneous movement of the robotic arms. Formally, It is each route map G i The Cartesian product of nodes. For two vertices V = (υ1, ..., υ2), ..., υ3, ..., υ4, ..., υ5, ..., υ6, ..., υ7, ..., υ8, ..., υ9, ..., υ1 ... m ), V′=(υ′1,...,υ′ m ),like or (v) i , v′ i )∈E i Then the edge set E′ contains the edge (V, V′).

[0059] Tensor product roadmap has There are nodes. Considering the given route graph G. i Middle node v i The neighborhood of Adj(v) is i G i In the tensor product path graph G′, the nodes V = {u1, ..., v} R The neighborhood size of} is Using smaller G1, ..., G R Constructing G′ online is computationally advantageous.

[0060] like Figure 2 As shown, given a single robotic arm's route map G i and G j As shown on the left, the tensor product path graph G ij This appears as shown in the diagram on the right. For each pair of nodes, one of them originates from route graph G. i Choose one from route map G. j Select from the options. If the constituent nodes in the path graph of a single robotic arm also share an edge, then the two nodes in the tensor product path graph share an edge. For example, nodes 1A and 3C in G... ij Nodes 1 and 3 do not share an edge because nodes 1 and 3 do not share an edge.

[0061] In some embodiments, the process of generating the composite route map in S1 is as follows:

[0062] First, before path planning, let r i ,...,r m A total of m robotic arms are in the initial configuration s i and target configuration t i Working in workspace C, enabling G i =(V i E i For a single robotic arm r i The route map, node V i Indicates the robotic arm r i Collision-free placement pose, edge E i Indicates the robotic arm r i The trajectory of collision-free motion. (Assumption) Then s i , t i All are on the route map G i In the same connected component. Given a set of route graphs G1, ..., G... m Composite route graphs can be constructed in two different ways—one is by performing a Cartesian product on individual route graphs, and the other is by using a tensor product. In a composite route graph G = (V, E), node V represents all combinations of collision-free placement of m robotic arms, and edge E represents the trajectory of simultaneous collision-free movement of the m robotic arms. Formally, the set of m robotic arm configurations is C = (v1, ..., v...). m ) is a node of G, if for every i(v) i ∈V i When each robotic arm r i Placed in v iIn this process, pairwise collisions do not occur between robotic arms. The edge types in the route graphs generated by the Cartesian product and tensor product are different. If the Cartesian product is used, then (C, C′) ∈ E, where C = (v1, ..., v1). m ), C′=(v′1,...,v′ m If there exists i such that (v i , v′ i )∈E i For each j ≠ i, v j =v′ j Both are true, robotic arm r i From v i Move to v′ i At that time, it will not be related to node v j =v′ j Collisions occur with other robotic arms at that location. The tensor product path graph will generate more connections; for each i, if (v...) i , v′ i )∈E i Then (C, C′)∈E, and the robotic arm will remain collision-free as it moves along its respective path.

[0063] In some embodiments, S2 specifically includes the following steps:

[0064] S21. First, generate an initial sampling point for each robotic arm on its respective route map;

[0065] S22. Each robotic arm expands two random trees simultaneously in its respective route map, with the starting point and the target point as the root nodes. Both trees expand in the direction of the initial sampling point. Each expansion first expands the tree with fewer nodes until an obstacle is encountered or the tree expands to the initial sampling point. If no obstacle is encountered or the tree expands to the initial sampling point, both trees expand in the direction of the previous initial sampling point.

[0066] Two random trees expand alternately towards each other. In one iteration, both random trees expand towards the same sampling point, accelerating the connection establishment between the two random trees. The difference between bidirectional and unidirectional random trees is not only in bidirectional growth, but also in their more "greedy" approach. In unidirectional random trees, each time a sampling point is generated, if a collision detection is passed, the tree grows once in the direction of that sampling point, and then that sampling point is discarded. To continue growing the tree, a new sampling point must be generated, and each sampling point is used at most once. In contrast, bidirectional random trees first generate a sampling point, and then the tree grows in the direction of that sampling point until it encounters an obstacle or reaches that sampling point. In this way, a random point is used multiple times, accelerating the growth speed.

[0067] In some embodiments, S3 specifically includes the following steps:

[0068] S31. Both random trees are expanded using the sampled points, and the tree with fewer nodes is expanded first in each expansion. The probability threshold P is initialized during the first run of S31. target =0;

[0069] S32. During the expansion process, determine whether the sampling point encounters an obstacle. If an obstacle is encountered, the probability threshold P is set. target Increase and generate a random value p. When the random value p is less than the probability threshold P... target At that time, the random point is taken as the new sampling point Q. rand When the random value p is greater than or equal to the probability threshold, the target point is taken as the new sampling point Q. rand .

[0070] In some embodiments, S32 is expressed by the following formula:

[0071]

[0072] Among them, V goal The target point is used for sampling, and Sample() indicates random sampling.

[0073] In some embodiments, S4 specifically includes the following steps:

[0074] S41. A new sampling point Q is obtained by expanding the two random trees. rand Then, find the node V that is closest to the new sampling point on the random tree. near ;

[0075] S42, based on the direction indication function O d At vertex V near Select the node that best matches the indicator function Od from all its nearest neighbors V as node V. new And satisfy (V near V new )∈E;

[0076] At vertex V near Select from all nearest neighbors V except the one that best matches the indicator function O d The node specifically refers to the node at vertex V. near Select a node V from all its nearest neighbors V. new Such that vertex V near To node V new The direction of the line connecting them is closest to vertex V. near New sampling point Q in S32 rand The direction indicated by the connection;

[0077] S43, if node V new If it is not in the random tree, then node V will be... new Add to the random tree, and add a path from vertex V. near To node V new The edge.

[0078] The specific implementation method is as follows: Let the new sampling point vertex For robotic arm i (1≤i≤R), the direction indication function O d From route map G i Extract Neighbors Make the expression minimize. Combining to obtain V near , Combining to obtain V new Since only the route map G needs to be traversed... i middle The search can be performed efficiently because it includes all of the neighbors.

[0079] In some embodiments, the direction indication function O in S42 d Specifically as follows:

[0080]

[0081] In the formula, ∠v near (Q rand V) represents the minimum angle between ray 1 and ray 2, where ray 1 originates from V. near Start and through Q rand , ray 2 from V near Starts and passes through V, where V represents node V. near The nearest neighbor; Adj(V) near G′) represents V in the route map G′ near The set of nearest neighbors, where arg min represents the minimum value.

[0082] Given node V near New sampling point Q rand Direction indicator function O d Middle node V new ∈V′, it is at the new sampling point Q rand Vertex V found in the direction near The neighbors (in G′). The key to this method lies in the direction indication function O. dSuch a neighbor can be found efficiently without relying on an explicit representation of G′. Let Q, Q′, Q"∈C, define ρ(Q, Q′) as the ray Q′ starting from point Q, and denoted as ∠Q(Q′, Q") as the minimum angle between ρ(Q, Q′) and ρ(Q, Q"). Using Adj(V near , G′) means that V in G′ near The set of neighboring nodes, that is, for each V∈Adj(V near (G), it believes (V) near If V)∈E, then O d The implementation method is as follows. Let For each robotic arm (1≤i≤R), the direction indication function O d From route map G i Extract Neighbors Make the expression Minimize. Note that this search can be performed efficiently because it only requires traversing the route graph G. i middle All nearest neighbors; all The combination yields V near .

[0083] To verify the feasibility of this invention, a dual-arm simulation platform was built in the ROS simulation environment. The dRRT*-Connect algorithm was used to plan the motion trajectories of the two arms in a task involving collaborative manipulation of an object by the dual arms. Figure 4 As shown.

[0084] To verify the efficiency of this invention, the OMPL open-source platform and its official test routines were used to compare the proposed algorithms with those included in OMPL, such as RRT, RRTConnect, RRTstar, pRRT, PRM, PRMstar, and LazyPRMstar. Each algorithm was run 200 times, and the average path length was calculated. The default parameters in the OMPL tests were used for each algorithm.

[0085] Table 1: Comparison results of dRRT*-Connect algorithm with RRT, RRTstar, and RRTConnect

[0086] RRT 100 0.021030 58.459516 RRTstar 100 1.114254 38.167264 RRT-Connect 100 0.015154 56.915798 dRRT*-Connect 100 0.018747 39.780084

[0087] The results show that the present invention has significant advantages over traditional planning algorithms in terms of planning time and planning path.

[0088] Of course, those skilled in the art will recognize that the present invention is not limited to the details of the exemplary embodiments described above, but also includes the same or similar methods that can be implemented in other specific forms without departing from the spirit or essential characteristics of the invention. Therefore, the embodiments should be considered exemplary and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, it is intended that all variations falling within the meaning and scope of equivalents of the claims be included within the present invention.

[0089] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Furthermore, the technical solutions of the various embodiments of the present invention can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A multi-robot motion planning method based on a bidirectional discrete fast expanding random tree, characterized in that, Includes the following steps: S1. Initialize the workspace environment, acquire obstacle information, determine the starting pose and target pose of each robotic arm, generate the route map of each robotic arm, and combine the route maps of each robotic arm into a composite route map through tensor product. S2. Each robotic arm generates a random tree in its own route map, and expands two random trees simultaneously with the starting point and the target point as the root nodes. S3. Both random trees are expanded using the sampling points of the other, and each expansion first expands the tree with fewer nodes. S4. After expanding the two random trees to obtain new sampling points, find the node closest to the new sampling point on the random tree. Select the node that meets the preset requirements from the nearest neighbor of the nearest node according to the direction indicator function, and determine whether the selected node can pass the collision detection. If yes, proceed to S5; otherwise, proceed to S3. S5. Traverse the nearest neighbors of the selected node and determine if the cost of each nearest neighbor is smaller with the selected node in S4 as its parent node. If it is smaller, change the parent node of the nearest neighbor to the selected node and determine if the two random trees of the robotic arm are successfully connected. If not, directly determine if the two random trees of the robotic arm are successfully connected. If the two random trees of the robotic arm are successfully connected, end the expansion. If they are not successfully connected, loop from S3 to S5 until the maximum iteration time is reached or the two random trees are successfully connected.

2. The multi-robotic arm motion planning method according to claim 1, characterized in that, The method for generating the route map for each robotic arm in S1 is as follows: First, pose points are randomly generated individually in the workspace of each robotic arm. Collision detection is performed on each pose point, and pose points that will collide are eliminated. The remaining pose points are then connected, and the lines that come into contact with obstacles are deleted to obtain the route map for each robotic arm.

3. The multi-robotic arm motion planning method according to claim 1, characterized in that, The route map is represented by a formula, as follows: G i =(V i ,E i ) Among them, G i Indicates the robotic arm r i The route map, node V i Indicates the robotic arm r i Collision-free placement pose, edge E i Indicates the robotic arm r i The trajectory of collision-free motion.

4. The multi-robotic arm motion planning method according to claim 1, characterized in that, S2 specifically includes the following steps: S21. First, each robotic arm generates an initial sampling point in its respective route map; S22. Each robotic arm expands two random trees simultaneously in its respective route map, with the starting point and the target point as the root nodes. The two trees expand in the direction of the initial sampling point. Each expansion first expands the tree with fewer nodes until an obstacle is encountered or the expansion reaches the initial sampling point. If no obstacle is encountered or the expansion reaches the initial sampling point, both trees expand using the direction of the previous initial sampling point as the sampling direction.

5. The multi-robotic arm motion planning method according to claim 1, characterized in that, S3 specifically includes the following steps: S31. Both random trees are expanded using the sampled points, and each expansion first expands the tree with fewer nodes. The probability threshold P is initialized during the first run of S31. target =0; S32. During the expansion process, determine whether the sampling point encounters an obstacle. If an obstacle is encountered, the probability threshold P is set. target Increase and generate a random value p. When the random value p is less than the probability threshold P, target At that time, the random point is used as the new sampling point Q. rand When the random value p is greater than or equal to the probability threshold, the target point is taken as the new sampling point Q. rand .

6. The multi-robotic arm motion planning method according to claim 5, characterized in that, The formula for S32 is as follows: Among them, V goal The target point is used for sampling, and Sample() indicates random sampling.

7. The multi-robotic arm motion planning method according to claim 5, characterized in that, S4 specifically includes the following steps: S41. A new sampling point Q is obtained by expanding the two random trees. rand Then, find the node V that is closest to the new sampling point on the random tree. near ; S42, based on the direction indication function O d At node V near Select the nearest neighbor points V that best match the indicator function O. d The node is taken as node V new And satisfy (V near V new )∈E; At node V near Select the nearest neighbor points V that best match the indicator function O. d The node specifically refers to node V near Select a node V from all its nearest neighbors V. new This makes node V near To node V new The direction of the line connecting them is closest to node V. near New sampling point Q in S32 rand The direction indicated by the connecting line; S43, if node V new If it is not in the random tree, then node V will be... new Add to the random tree, and add a path from node V. near To node V new The edge.

8. The multi-robotic arm motion planning method according to claim 7, characterized in that, The direction indication function O in S42 d Specifically as follows: In the formula, ∠v near (Q rand V) represents the minimum angle between ray 1 and ray 2, where ray 1 originates from V. near Start and through Q rand , ray 2 from V near Starts and passes through V, where V represents node V. near The nearest neighbor; Adj(V) near G′) represents V in the route map G′ near The set of nearest neighbors, where argmin represents the minimum value.

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