A robust multi-robot path dynamic margin planning method and system based on delay evaluation.

Abstract

This invention discloses a multi-robot path dynamic margin robust planning method and system based on delay evaluation. The method includes: given a map and robots, each robot in the map has a start point and an end point; setting delay probabilities and reliability requirements; establishing a global timetable for each node and initializing it to blank; assigning path planning priorities to each robot in the map; and sequentially selecting a robot as the current robot to be planned according to priority, until all robots have completed planning. This invention dynamically adjusts the delay conflict constraint interval during the planning process, effectively reducing the risk of conflicts that may occur during path execution, and uses a dynamic adjustment strategy for the robustness coefficient to ensure that the robot path meets the expected reliability requirements, overcoming the reliability deficiency problem caused by high path coupling in existing technologies. Further simulations show that this invention can improve reliability requirements under the same path time cost, significantly improve the solution speed under high reliability requirements, and thus reduce computational costs.

Description

Technical Field

[0001] This invention relates to a robust planning method and system for dynamic margin of multi-robot paths based on delay evaluation, belonging to the field of multi-robot path planning. Background Technology

[0002] Multi-robot path planning has numerous engineering applications in fields such as warehousing and logistics, autonomous driving systems, and airport transportation. The problem is to find conflict-free paths for multiple robots given a start point and an end point.

[0003] In the actual execution of a multi-robot system, various uncertainties may arise, causing deviations between the actual execution path and the planned path. This could lead to conflicts between robots and cause algorithm failure. When unexpected events occur, it may be necessary to adjust the plans of one or more robots to avoid collisions. However, replanning can require significant computational and communication resources, and it is difficult to guarantee that the planning will be completed before a collision occurs.

[0004] Currently, the k-robot robust planning algorithm is mainly used to ensure the reliability of multi-robot systems. However, the latency in the system is often difficult to determine, which makes it difficult to determine an appropriate k to deal with different scenarios. If k is set too large, efficiency and energy saving will be sacrificed for reliability. If k is set too small, it will be difficult to ensure the stable and reliable execution of the system. Therefore, it is necessary to consider a reliable and efficient robust path planning method. Summary of the Invention

[0005] This invention provides a multi-robot path dynamic margin robust planning method based on delay evaluation. Based on delay probability and combined with the single robot execution reliability requirements, it adopts a safe interval planning method to plan paths that meet reliability requirements for all robots according to priority order under safety constraints and delay conflict constraints.

[0006] The technical solution of this invention is:

[0007] According to a first aspect of the present invention, a multi-robot path dynamic margin robust planning method based on delay evaluation is provided, comprising the following steps:

[0008] Step 1: Given a map and robots, each robot on the map has a starting point and an ending point;

[0009] Step 2: Set the latency probability and reliability requirements, and create a global timetable for each node and initialize it to blank;

[0010] Step 3: Assign path planning priorities to each robot on the map; select a robot in order of priority as the current robot to be planned, until all robots have completed their path planning:

[0011] If the robot to be planned is of the highest priority, then the path planning algorithm is directly used to search and expand the nodes to find a path from the starting point to the end point, thus realizing the planning. The safety constraint interval and delay conflict constraint interval generated by each node on the path of the highest priority robot are inserted into the global timetable. The intervals other than the safety constraint interval and delay conflict constraint interval are the safety intervals. Among them, the delay conflict constraint interval is inserted sequentially after the safety constraint interval of the global timetable.

[0012] Otherwise, if the robot to be planned is not the highest priority, then based on the global timetable obtained after the previous planning of the robot to be planned, a path planning algorithm is used to search and expand the nodes according to the safety interval to find a path from the starting point to the end point, thus realizing the planning; and the safety constraint interval and delay conflict constraint interval generated by each node on the path of the currently planned robot are inserted into the global timetable. The intervals other than the safety constraint interval and delay conflict constraint interval are the safety intervals; among them, the delay conflict constraint interval is inserted sequentially after the safety constraint interval of the global timetable.

[0013] Furthermore, in step 3, the safety constraint interval generated by each node is the time step in which the robot passes through that node. Specifically, the delay conflict constraint interval generated by each node is calculated by incrementing the robustness coefficient k from the initial robustness coefficient by a preset step size and then calculating P(p...). i (t),k)), until P(p i (t),k)) is greater than the reliability requirement R, which will satisfy "P(p i The minimum robustness coefficient k when (t),k) is greater than the reliability requirement R” is used as the robot R i Within the delay conflict constraint interval of the current node.

[0014] Furthermore, the specific discrimination expression for the delay conflict constraint interval generated by each node is as follows:

[0015]

[0016] Wherein, P(p i (t),k)) represents the robot starting from point p. i (0) Execute to the current node p i (t), the probability of a delay within k time steps; n represents the probability of robot R. i Starting from p i (0) to the current node p i In (t), the delay time step is m, which represents the strict execution time step; T is the maximum time step; p d This represents the delay probability.

[0017] According to a second aspect of the present invention, a multi-robot path dynamic margin robust planning system based on delay evaluation is provided, comprising modules of any of the methods described above.

[0018] According to a third aspect of the present invention, a processor is provided for running a program, wherein the program, when running, executes the multi-robot path dynamic margin robust planning method based on delay evaluation as described in any one of the preceding claims.

[0019] According to a fourth aspect of the present invention, a computer-readable storage medium is provided, the computer-readable storage medium comprising a stored program that, when executed by a processor, causes the processor to implement the multi-robot path dynamic margin robust planning method based on delay evaluation as described above.

[0020] The beneficial effects of this invention are as follows: By dynamically adjusting the delay conflict constraint interval during the planning process, this invention effectively reduces the risk of conflicts that may arise during path execution. Furthermore, by employing a dynamic adjustment strategy for the robustness coefficient k, it ensures that the robot path meets the expected reliability requirements, overcoming the reliability deficiency problem caused by high path coupling in existing technologies. Simulation results further demonstrate that this invention can improve reliability requirements under the same path time cost, significantly increasing the solution speed under high reliability requirements, thereby reducing computational costs. This provides a more robust path planning scheme for multi-robot collaborative systems in complex scenarios such as logistics and autonomous driving. Attached Figure Description

[0021] Figure 1 This is a flowchart of the present invention;

[0022] Figure 2 These are three robot path planning maps provided in this embodiment of the invention;

[0023] Figure 3 These are three robot path planning time diagrams provided in this embodiment of the invention;

[0024] Figure 4 This is an example of a global timetable after inserting a barrier interval, provided in an embodiment of the present invention;

[0025] Figure 5 This is a diagram showing the cost-reliability comparison experiment results of this invention with other algorithms on a 32×32-20 random map;

[0026] Figure 6 This is a diagram showing the experimental results of the cost-reliability comparison between the present invention and other algorithms on a 48×48 empty map. Detailed Implementation

[0027] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of this application can be arbitrarily combined with each other.

[0028] Example 1: As Figures 1-6 As shown, according to a first aspect of the present invention, a multi-robot path dynamic margin robust planning method based on delay evaluation is provided, comprising the following steps:

[0029] Step 1: Given a map (G = V, E), where V represents the set of nodes in the map, E represents the set of edges in the map, and the map contains a set of n robots, U = {R1, R2, ... R...} n Each robot has a starting point and an ending point.

[0030] For example: with Figure 2 As shown, there are a total of 24 nodes in the 6×4 grid map, and the three robots are numbered R1, R2, and R3 respectively. Figure 2 In the diagram, S1, S2, and S3 are the grids where the starting points of the three robots are located, and G1, G2, and G3 are the grids where the ending points of the three robots are located. The black grids in the diagram represent impassable obstacle areas, and the white grids represent passable areas. It is known that at the initial time t = 0, each robot is at its starting point.

[0031] Step 2: Set the latency probability and reliability requirements, and create a global timetable for each node and initialize it to blank;

[0032] For example, a group of robots sets a delay probability p before planning their path. d =0.1, single robot reliability requirement R=98%; establish a global timetable for each node, the time of the timetable is from t=0,1,...T; in the embodiment of the present invention, T is 9, but can also be set to other values ​​as needed, each time step is 1, and the time represented by the time step is defined as needed.

[0033] Step 3: Assign path planning priorities to each robot on the map; select a robot in order of priority as the current robot to be planned, until all robots have completed their path planning:

[0034] If the robot to be planned is of the highest priority, the SIPP algorithm is directly used to search and expand the nodes to find a path from the starting point to the end point, thus realizing the planning. The safety constraint interval and delay conflict constraint interval generated by each node on the path of the highest priority robot are inserted into the global timetable. The intervals other than the safety constraint interval and delay conflict constraint interval are the safety intervals. The delay conflict constraint intervals are inserted sequentially after the safety constraint intervals in the global timetable.

[0035] Otherwise, if the robot to be planned is not the highest priority, then based on the global timetable obtained after the previous planning of the robot to be planned, the SIPP algorithm is used to search and expand the nodes according to the safety interval to find a path from the starting point to the ending point, thus realizing the planning; and the safety constraint interval and delay conflict constraint interval generated by each node on the path of the currently planned robot are inserted into the global timetable. The intervals other than the safety constraint interval and delay conflict constraint interval are the safety intervals; wherein, the delay conflict constraint interval is inserted sequentially after the safety constraint interval of the global timetable; the SIPP algorithm is a well-known existing safety interval planning algorithm, and other similar planning algorithms can also be used instead of the SIPP algorithm in this invention.

[0036] Furthermore, in step 3, the safety constraint interval generated by each node is the time step in which the robot passes through that node. Specifically, the delay conflict constraint interval generated by each node is calculated by incrementing the robustness coefficient k from the initial robustness coefficient by a preset step size and then calculating P(p...). i (t),k)), until P(p i If the robustness coefficient k is greater than the reliability requirement R, it means that the current robustness coefficient k can plan a path with a reliability of at least R for a single robot, i.e., the robot's R... i The probability of collisions with other robots due to various nondeterministic delay perturbations will not exceed (1-R), satisfying "P(p i The minimum robustness coefficient k when (t),k) is greater than the reliability requirement R” is used as the robot R i Within the delay conflict constraint interval of the current node. In this embodiment of the invention, the preset step size is set to 1.

[0037] Furthermore, the specific discrimination expression for the delay conflict constraint interval generated by each node is as follows:

[0038]

[0039] Wherein, P(p i (t),k)) represents the robot's execution up to the current node p. i (t), the probability of a delay within k time steps; n represents the probability of robot R.i Starting from p i (0) to the current node p i In (t), the delay time step is m, which represents the strict execution time step; T is the maximum time step; p d Let k be the delay probability; k is the robot's R. i The robustness coefficient at the current node; R is the reliability requirement.

[0040] This example aims to find a path from the starting point to the ending point for each robot, and any two paths satisfy safety constraints and delay conflict constraints. That is, even if there is a delay disturbance within the robustness coefficient k between any two robots, a conflict-free path can still be obtained. By repeating the above single-robot planning process until all robots have completed planning, the resulting overall path scheme is the conflict-free path planning scheme of the multi-robot path dynamic margin robust planning method based on delay evaluation. The global path scheme finally generated by this invention optimizes the overall path time cost and execution efficiency while meeting reliability requirements.

[0041] According to a second aspect of the present invention, a multi-robot path dynamic margin robust planning system based on delay evaluation is provided, comprising modules of any of the methods described above. Specifically, it includes: a first module for providing a map, in which each robot has a start point and an end point; a second module for setting delay probabilities and reliability requirements, establishing a global timetable for each node and initializing it to blank; and a third module for assigning path planning priorities to each robot in the map; sequentially selecting a robot as the current robot to be planned according to priority order until all robots have completed their planning. For parts of the modules not described in detail above, please refer to the relevant descriptions in the embodiments.

[0042] According to a third aspect of the present invention, a processor is provided for running a program, wherein the program executes the multi-robot path dynamic margin robust planning method based on delay evaluation as described in any one of the preceding embodiments.

[0043] According to a fourth aspect of the present invention, a computer-readable storage medium is provided, the computer-readable storage medium including a stored program that, when executed by a processor, causes the processor to implement the multi-robot path dynamic margin robust planning method based on delay evaluation as described above.

[0044] In one exemplary embodiment, the aforementioned computer-readable storage medium may include, but is not limited to, various media capable of storing computer programs, such as a USB flash drive, read-only memory (ROM), random access memory (RAM), portable hard disk, magnetic disk, or optical disk.

[0045] The following explanation uses three machines as examples:

[0046] 1. Assign path planning priorities to each robot on the map. R1, R2, and R3 have priority numbers 1, 2, and 3, respectively, with lower numbers indicating higher priority. Therefore, the robot priorities are R1 > R2 > R3. First, perform path planning for the highest priority robot R1, resulting in the path for robot R1 as shown in Table 1.

[0047] Table 1

[0048] time t＝0 t＝1 t＝2 t＝3 t＝4 t＝5 t＝6 node (A,3) (A,2) (B,2) (C,2) (D,2) (E,2) (F,2)

[0049] II. Path Planning

[0050] In this embodiment, the time step required for the robot to enter and exit a node is set to 1. The initial robustness coefficient is 1, and the preset step size is 1.

[0051] Table 2 shows the obstacle intervals (obstacle intervals are the safety constraint interval + delay conflict constraint interval) of robot R1's path. At time t=0, the probability that robot R1 will experience a delay of less than one time step when reaching the current node (A,3) exceeds 98%. Therefore, considering a robustness coefficient k=1 within this time interval, the reliability requirement R=98% can be met. Thus, time t=0 is the safety constraint interval, and time t=1 is the delay conflict constraint interval (i.e., the delay conflict constraint interval is sequentially inserted after the safety constraint interval; t=0 is the safety constraint interval, k=1, meaning the delay conflict constraint interval is one time step after the safety constraint interval); t=[0 The obstacle interval at position (A,3) is formed by the points [0,1]. This means that when the robot extends to node (A,3), it needs to perform path finding within the time interval outside the obstacle interval constraint of t=[0,1]. Similarly, at time t=5, considering the robustness coefficient k=1, it is no longer possible to meet the reliability requirement R=98%. Therefore, considering the robustness coefficient k=2, time t=5 is the safety constraint interval, and time t=[6,7] is the delay conflict constraint interval. t=[5,7] forms the obstacle interval at position (E,2). The same logic applies to other nodes. The obstacle interval of robot R1 is finally obtained as shown in column 3 of Table 2.

[0052] Table 2

[0053] time node obstacle zone t＝0 (A,3) t＝[0,1] t＝1 (A,2) t＝[1,2] t＝2 (B,2) t＝[2,3] t＝3 (C,2) t＝[3,5] t＝4 (D,2) t＝[4,6] t＝5 (E,2) t＝[5,7] t＝6 (F,2) t＝[6,8]

[0054] After the planning of robot R1 is completed, the next priority robot R2 is selected as the current robot to be planned. For R2, the SIPP algorithm is used to search and expand the nodes within the time interval outside the obstacle interval constraint to find a path from the starting point to the end point, thus realizing the planning. Then, the planning of R3 is realized.

[0055] According to Figure 2 The map shown above, when applied with the above technical solution, yields the following path planning results: Figure 3 As shown.

[0056] In the above path planning process, there is a conflict at the two nodes (B,2) and (E,2). To better understand this, the method of dividing the safety constraint interval and the delay conflict constraint interval proposed in this invention will be explained with reference to the accompanying drawings:

[0057] like Figure 4 As shown, robot R1 occupies position point (B,2) at t=2. At this time, the robustness coefficient of R1 is k=1, and t=[2,3] becomes the obstacle interval of position point (B,2). Robot R2 does not occupy this position point. Robot R3, which has a priority after robot R2, can only enter (B,2) within the safe interval t=[4,∞] of position point (B,2) to reserve a time margin of 1 time step between robots to cope with unexpected delays. Similarly, at t=5, robot R1 occupies position point (E,2). At this time, the robustness coefficient is k=2. At the same time, robot R2 occupies this position point on the path assigned to it. To ensure reliability, robot R2 can only enter (E,2) within the safe interval t=[8,∞]. Figure 4 From top to bottom, they are: the global timeline of robot R1 at (B,2) after the path planning is completed, the global timeline of robot R3 at (B,2) after the path planning is completed, the global timeline of robot R1 at (E,2) after the path planning is completed, and the global timeline of robot R2 at (E,2) after the path planning is completed.

[0058] III. Verification Instructions

[0059] 1) Selecting a typical random 32×32 map, with execution time as the termination condition, a maximum time limit of 120 seconds is set for a single solution; exceeding this limit is considered a solution failure. In the test, the AkR-SIPP algorithm proposed in this invention sets single-robot reliability requirements to 85%, 90%, and 95%, with initial robustness coefficients k = {1, 2, 3} for each reliability requirement. The existing kR-SIPP algorithm uses robustness coefficients k = {1, 2, 3, 4, 5, 6, 7, 8, 9}. The robustness coefficients of both algorithms increase in increments of 1. Randomly selecting 60 and 75 robots, 10,000 experiments are conducted according to the above parameters to determine the cost-reliability performance for different robot numbers. Figure 5 As shown in Table 3, with the same number of robots, the average running time and average maximum completion time of each algorithm are compared under different reliability ranges (the cost is the path length). (Running time is the time for multiple robots to complete path planning, and average running time is the average of multiple experiments; maximum completion time is the maximum completion time for multiple robots to run from the starting point to the end point according to the planned path, and average maximum completion time is the average of multiple experiments; M is the overall system execution reliability index obtained after the path scheme is verified by the Monte Carlo method).

[0060] Table 3

[0061]

[0062] 2) Selecting a typical empty 48*48 map, with execution time as the termination condition, a maximum time limit of 120 seconds is set for a single solution; exceeding this limit is considered a solution failure. In the test, the AkR-SIPP algorithm proposed in this invention has reliability requirements of 85%, 90%, and 95%, with an initial robustness coefficient k = {1, 2, 3}. The existing kR-SIPP algorithm uses a robustness coefficient k = {1, 2, 3, 4, 5, 6, 7, 8, 9}. The robustness coefficients of both algorithms increase in increments of 1. Randomly selected 90 and 130 robots are used for 10,000 experiments each based on the above parameters. The cost-reliability performance for different robot numbers is as follows: Figure 6As shown in Table 4, under the same number of robots, the average running time and average maximum completion time of each algorithm are compared under different reliability intervals (running time is the time for multiple robots to complete path planning, and average running time is the average of multiple experiments; maximum completion time is the maximum completion time for multiple robots to run from the starting point to the ending point according to the planned path, and average maximum completion time is the average of multiple experiments). The results show that the method of the present invention can reduce the cost by 25% compared with kR-SIPP in the same high reliability interval, and improve the solution speed by 45% in the same high reliability interval (i.e., the overall system reliability M requires more than 33%). Especially in large-scale robot planning, the improvement in average running time of the present invention is more significant in the high reliability interval. Since the maximum completion time may be affected by many factors in real-world conditions, and the present invention mainly studies running time, the main indicator is still the average running time of path planning. Figure 6 As shown in Table 4, this invention provides a more efficient and reliable robust solution.

[0063] Table 4

[0064]

[0065] The specific embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A robust multi-robot path dynamic margin planning method based on delay evaluation, characterized in that, Includes the following steps: Step 1: Given a map and robots, each robot on the map has a starting point and an ending point; Step 2: Set the latency probability and reliability requirements, and create a global timetable for each node and initialize it to blank; Step 3: Assign path planning priorities to each robot on the map; select a robot in order of priority as the current robot to be planned, until all robots have completed their path planning: If the robot to be planned is of the highest priority, then the path planning algorithm is directly used to search and expand the nodes to find a path from the starting point to the end point, thus realizing the planning. The safety constraint interval and delay conflict constraint interval generated by each node on the path of the highest priority robot are inserted into the global timetable. The intervals other than the safety constraint interval and delay conflict constraint interval are the safety intervals. Among them, the delay conflict constraint interval is inserted sequentially after the safety constraint interval of the global timetable. Otherwise, if the robot to be planned is not the highest priority, then based on the global timetable obtained after the previous planning of the robot to be planned, a path planning algorithm is used to search and expand the nodes according to the safety interval to find a path from the starting point to the end point, thus realizing the planning; and the safety constraint interval and delay conflict constraint interval generated by each node on the path of the currently planned robot are inserted into the global timetable. The intervals other than the safety constraint interval and delay conflict constraint interval are the safety intervals; among them, the delay conflict constraint intervals are inserted sequentially after the safety constraint intervals in the global timetable. In step 3, the safety constraint interval generated by each node is the time step in which the robot passes through that node. Specifically, the delay conflict constraint interval generated by each node is: [The robustness coefficient is used to define the robustness coefficient]. k The calculation starts from the initial robustness coefficient and increments by a preset step size. P ( p i ( t ), k )) until P ( p i ( t ), k ()) greater than reliability requirements R , will satisfy P ( p i ( t ), k ()) greater than reliability requirements R The minimum robustness coefficient k of the robot at that time R i Within the delay conflict constraint range of the current node; The specific discrimination expression for the delay conflict constraint interval generated by each node is as follows: ； in, P ( p i ( t ), k )) indicates that the robot starts from the starting point p i (0) Execute to the current node p i ( t ),Appear k The probability of delay within a time step; n Represents robots R i From the starting point p i (0) to the current node p i ( t The delay time step in ) m This indicates that the time step must be strictly followed; T Maximum time step; p d This represents the delay probability.

2. A multi-robot path dynamic margin robust planning system based on delay evaluation, characterized in that, Includes modules based on the method of claim 1.

3. A processor, characterized in that, The processor is used to run a program, wherein the program executes the multi-robot path dynamic margin robust planning method based on delay evaluation as described in claim 1.

4. A computer-readable storage medium comprising a stored program, characterized in that: When the program is executed by the processor, it enables the processor to implement the multi-robot path dynamic margin robust planning method based on delay evaluation as described in claim 1.

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