A multi-mobile robot path planning method with environmental self-adaptability

Abstract

The application provides a multi-mobile robot path planning method with environmental self-adaptability, and relates to the technical field of robot path planning. Firstly, in the spatial path planning stage, an improved light reflection RRT* algorithm is used to generate spatial paths for each robot, a dynamic step mechanism based on an artificial potential field gradient is introduced in the reference path generation stage, and a dynamic step mechanism fusing local expansion failure point density and the artificial potential field gradient is introduced in the tree expansion stage; arc length parameterized sampling is performed on the spatial paths of each robot, and characteristic information such as path conflict density, channel gap degree and path overlap interval is extracted; then adaptive landmark point selection is performed based on the path characteristic information, and a fixed number of key time control points of each robot are obtained; finally, the time parameters at the landmark points of each robot are optimized, so that the multi-mobile robot path planning result meeting the obstacle constraint, the speed constraint, the acceleration constraint, the entity size constraint and the safety distance constraint is obtained.

Description

Technical Field

[0001] This invention relates to the field of robot path planning technology, and in particular to a multi-mobile robot path planning method with environmental adaptability. Background Technology

[0002] With the rapid development of applications in warehousing and logistics, intelligent manufacturing, security inspection, and medical delivery, multi-mobile robot systems are widely used due to their high operational efficiency, flexible deployment, and strong adaptability. In multi-mobile robot systems, path planning is a key technology to ensure that each robot completes its tasks safely, orderly, and efficiently. This problem not only requires planning feasible paths for each robot that meet environmental constraints, but also comprehensively considering potential spatiotemporal conflicts that may arise among multiple robots in shared passageways, intersecting areas, and narrow corridors, thereby achieving a balance between overall task efficiency and operational safety.

[0003] Existing multi-robot path planning methods typically employ a "spatial path planning + temporal coordination optimization" approach. While this approach offers good engineering feasibility, in the spatial path planning stage, existing Rapidly-exploring Random Tree (RRT) sampling algorithms and their related improvements mostly use fixed-step expansion, making it difficult to adaptively adjust the expansion scale based on local environmental characteristics. This often leads to low search efficiency in open areas and high expansion failure rates in obstacle-rich areas and narrow passages, thus affecting the overall path generation efficiency and stability. On the other hand, in the temporal coordination stage, existing methods typically set several landmarks on each robot path and use the arrival time at each landmark as an optimization variable to adjust the robot's passage order and speed allocation along the path. However, existing landmarks are often set in a fixed number and evenly spaced along the path arc length, making it difficult to adaptively configure them based on key conflict locations such as path intersections, shared passage entrances and exits, and narrow areas. This can easily result in insufficient time adjustment capability in critical areas and redundant parameter configuration in non-critical areas, thus affecting conflict resolution effectiveness and overall optimization performance.

[0004] Therefore, existing multi-robot path planning methods still suffer from insufficient environmental adaptability in the spatial path planning stage and limited ability to represent key conflict areas in the time coordination stage, making it difficult to simultaneously ensure path quality, planning efficiency, and safety in complex environments. Based on this, it is necessary to propose a multi-robot path planning method with environmental adaptability to improve the efficiency and stability of spatial path generation in complex environments and enhance the ability to characterize key conflict areas in the time optimization stage, thereby improving the overall planning performance of multi-robot systems in complex scenarios. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a multi-mobile robot path planning method with environmental adaptability; it solves the problems of insufficient environmental adaptability of fixed step size in the spatial path planning stage, high failure rate in complex obstacle environments, and limited ability of equally spaced landmarks to represent key conflict areas in the time coordination stage of existing multi-mobile robot path planning.

[0006] On one hand, the present invention provides a multi-mobile robot path planning method with environmental adaptability, comprising the following steps:

[0007] Step 1: Construct a two-dimensional continuous spatial environment model for multi-mobile robot path planning and initialize robot parameters;

[0008] The two-dimensional continuous spatial environment model is specifically defined as follows: boundary walls, rectangular obstacles, and circular obstacles are set; the number of mobile robots in the environment is n; and a starting point is given for each robot. and the end point And set the robot radius and the minimum safe distance threshold d between robots. s ;

[0009] Step 2: Generate collision-free spatial paths for each robot based on a dynamic step size mechanism jointly driven by the artificial potential field gradient and the density of failure points.

[0010] Step 2.1: Construct multi-directional rays based on the origin and destination, and generate a reference path through light reflection propagation and cost evaluation;

[0011] For the i-th robot, first construct the main direction vector of the reference path based on the start and end points; the main direction vectors of the start and end points are respectively represented as:

[0012] ,(1);

[0013] (2);

[0014] in, As the starting coordinates, Let d be the starting coordinate. start Starting from the main direction, d goal The destination is the main direction.

[0015] Several auxiliary directions are superimposed on the main direction to form a bidirectional, multi-directional ray set; the number of rays is set to num_rays, the auxiliary directions on both sides of the main direction are uniformly distributed at angles, and the maximum deflection angle is set to θ. maxThe angular interval between adjacent auxiliary rays is set to Δθ. Rays are emitted simultaneously from the starting and ending points. If the ray propagates in free space, it continues to advance in the current direction. If the ray collides with the boundary of an obstacle, the propagation direction is updated according to the normal vector and tangential direction of the obstacle boundary, where the disturbance angle during collision reflection is set to θ. inter This process is continuously advanced to generate multiple candidate reference paths. The cost of all candidate paths leading to the target area is evaluated, and the path with the lowest total cost is selected as the reference path for the corresponding robot.

[0016] Step 2.2: Construct the total potential field of the environment and introduce the potential field gradient to guide the adaptive adjustment of the propagation step size;

[0017] The total potential field of the environment consists of the target attraction potential field and the obstacle repulsion potential field:

[0018] U(q) = U att (q)+U rep (q), (3);

[0019] Among them, the current position , where a is the x-coordinate of the robot's position, b is the y-coordinate of the robot's position, and U(q) is the total potential field of the environment. att (q) represents the target attractive potential field, U rep (q) represents the obstacle repulsion potential field.

[0020] The target attractive potential field is defined as:

[0021] (4);

[0022] Where, q g Let ζ be the target point location, and ζ be the gain coefficient of the attractive potential field, where ζ > 0;

[0023] The corresponding gradient of the attractive potential field is:

[0024] (5);

[0025] Let ρ(q) be the minimum distance from the obstacle to the current position q, and ρ0 be the distance at which the obstacle exerts its effect. Then the obstacle repulsive potential field is defined as:

[0026] (6);

[0027] Where η is the repulsive potential field gain coefficient, and η>0.

[0028] The corresponding repulsive potential gradient is:

[0029] (7);

[0030] Considering the need to further reduce the step size when approaching the target point to prevent crossing the target region, the following form of the total potential field gradient is adopted:

[0031] (8);

[0032] Where, ρ g The distance threshold for determining proximity to the target point;

[0033] Let the current propagation point be q. k Then its gradient magnitude is defined as:

[0034] (9);

[0035] In each propagation along the current direction d k Before proceeding, first determine the gradient magnitude g. k Calculate the propagation step size s k Specifically, the gradient magnitude g k After normalization, the step size is mapped to a scaling factor, and the final step size is constrained to the interval [s]. min s max Within this range, the next predicted propagation point is then obtained:

[0036] (10);

[0037] If from q k arrive If the line segments do not collide, the next predicted propagation point will be used as the new propagation point; if a collision occurs, the critical collision point location and reflection direction will be updated according to the original framework, and the propagation step size will be recalculated in the updated propagation state.

[0038] Step 2.3: Perform bias sampling within an adaptive range around the reference path with a preset probability;

[0039] Specifically, after obtaining the reference path, bias sampling is performed on the RRT* search process based on the reference path; that is, with a preset probability p bias Bias sampling is performed near the reference path with probability 1-p. bias Random sampling is performed within the global free space; the sampling range near the reference path is adaptively determined based on the distance between the current reference path point and local obstacles; the upper bound of the sampling radius near the reference path is set to r. max The distance d0 from the current reference path point to the nearest obstacle boundary is less than r. max When d0 is selected, the local sampling radius is taken; otherwise, r is selected. max As the local sampling radius;

[0040] Step 2.4: Combine the density of local expansion failure points with the gradient of the artificial potential field to dynamically adjust the step size of expanding new nodes in the tree;

[0041] Let the current expansion node be x. In each iteration, with x as the center, within a radius R... f The number of failed expansion points within the neighborhood is statistically analyzed; specifically, the geometric coverage area A of the danger zone formed by the failed points is estimated using the edge contour envelope algorithm. x The density of local failure points is defined as:

[0042] ,(11)

[0043] When the number of failure points is insufficient to form a valid edge contour envelope, a degenerate form is used:

[0044] (12);

[0045] Where N is the number of failure points in the neighborhood, r point The radius affected by a single failure point.

[0046] Simultaneously, calculate the gradient magnitude of the artificial potential field at the current extended node:

[0047] (13);

[0048] Where ▽U(x) is the magnitude of the gradient of the artificial potential field at the current extended node.

[0049] Based on the density of local failure points and the gradient of the artificial potential field, the step size of the current node is defined as:

[0050] (14);

[0051] in, For the natural constant An exponential function with base η base The lower bound of the basic step size, η max Let k1 and k2 be the upper bound of the maximum step size, respectively, the failure point density suppression coefficient and the artificial potential gradient suppression coefficient, and satisfy 0 < η. base <η max ;

[0052] Therefore, the new node update form of the tree expansion is:

[0053] (15);

[0054] Where, x near Let d be the current nearest neighbor node, and d be the node derived from x. near The unit direction vector pointing to the sampling point.

[0055] If the expansion is successful, the neighborhood reconnection and cost update of RRT* will continue; if the expansion fails, the failed position will be added to the set of failed points for subsequent calculation of local failure point density.

[0056] Step 2.5: Iteratively perform sampling and tree expansion, and prune and smooth the generated paths to output spatial paths;

[0057] Repeat steps 2.3 and 2.4 until a spatial path that satisfies the obstacle constraints is generated for each robot. For the backtracked paths, further pruning and smoothing are performed to remove redundant vertices and obtain a collision-free spatial path for time coordination optimization.

[0058] Step 3: Perform arc length parameterized sampling on the spatial path to extract multi-dimensional path feature information;

[0059] Step 3.1: Perform uniform arc length parameter sampling on the spatial path of each robot at fixed intervals;

[0060] Let the i-th robot path be π. i The total arc length is L i Uniform sampling is performed on the path at fixed arc length intervals δ; the number of sampling points is:

[0061] ,(16)

[0062] Where, N i N is the number of sampling points. min This represents the minimum number of sampling points.

[0063] The corresponding sampling arc length position is:

[0064] (17);

[0065] Let the arc length on the path be s. k The coordinates of the point are p. i (s k ), This represents the number of sampled arc lengths.

[0066] Step 3.2: Calculate the path conflict density based on the spatial proximity of the sampling point to other robot paths;

[0067] Define the spatial proximity H of a sampling point on the path to other robot paths. i (s k That is, the path conflict density is:

[0068] (18);

[0069] Where i represents the current robot, and j represents other robots. p represents the arc length at which the other robots are located. j ( ) represents the path points for other robots, d s For safe distance threshold, For indicator functions;

[0070] Step 3.3: Calculate the channel gap ratio based on the minimum distance from the sampling point to the nearest obstacle;

[0071] Define the distance C from a sampling point on the path to the nearest obstacle. i (s k That is, the channel gap is:

[0072] ,(19)

[0073] Where o is the point on the rectangular obstacle closest to the sampling point, and c is the point on the rectangular obstacle closest to the sampling point. Let O be the Euclidean distance from the sampling point to o. rect Let O be a set of rectangular obstacles. circ Let c be a set of circular obstacles. c and r c These are the center and radius of the circular obstacle, respectively.

[0074] The path conflict density and channel gap density are normalized to the [0,1] interval, respectively denoted as: and .

[0075] Step 3.4: Detect non-compliant sections of the safety distance between paths using scan lines, and merge and extract the set of overlapping path intervals.

[0076] For any robot pair (i, j), along path π i By step size Sampling is performed when sampling point p i (s) to path π j The minimum distance is less than the safe distance threshold d s At this point, the corresponding position is considered part of the overlapping interval; the starting arc length and ending arc length of the overlapping interval are recorded by scanning lines to obtain the set of overlapping segments of robot i relative to robot j. The starting arc length and ending arc length of the overlapping interval are recorded by scanning lines, and then all overlapping intervals are uniformly summarized, sorted, and greedily merged to obtain the set of key intervals:

[0077] (20);

[0078] Where r is the index number of the overlapping interval, I i For the set of key intervals extracted, a r and br These are the starting and ending boundaries of the overlapping interval, R. i This represents the total number of critical intervals.

[0079] Step 4: Based on the path feature information, perform adaptive selection of waypoints;

[0080] Step 4.1: Extract the start and end points of the path, the boundary points of overlapping intervals, and the minimum value points of channel gaps to construct a candidate set of road sign points;

[0081] Initialize the set of selected waypoints, setting the path start point s=0 and the end point s=L. i As a mandatory waypoint, it is added to the set of selected waypoints; subsequently, the merged overlapping intervals [a r， b r The initial boundary a r and termination boundary b r Add to the candidate set.

[0082] Furthermore, in the channel gap degree signal The sliding window method is used to detect local minima to identify the location of narrow channels. Specifically, the window size is set... When the channel gap value of the center point is not greater than that of other sampling points within the window, it is determined to be a candidate point of local minimum; then, several points with the smallest gap value are selected from all local minimums and added to the candidate set.

[0083] Step 4.2: Filter candidate points based on comprehensive score and minimum interval constraint, and generate an adaptive landmark set through the maximum gap filling strategy.

[0084] For any candidate point s c Take the index of its nearest sampling point as k c The comprehensive scoring function is defined as follows:

[0085] ,(twenty one);

[0086] in, This indicates whether the candidate point is a boundary point of an overlapping interval; if so, the value is 1, otherwise it is 0. H w C w E These are the weights for the conflict intensity term, the narrowness term, and the boundary priority term, respectively.

[0087] Candidate points are sorted from highest to lowest score, and a minimum margin constraint is set:

[0088] ,(twenty two);

[0089] Where μ is the minimum interval scaling factor.

[0090] If the arc distance between the current candidate point and all points in the selected landmark set is not less than Δ min If the point is selected, add it to the set of selected waypoints; otherwise, skip the point.

[0091] If the number of selected landmarks is still less than the preset number K after the above screening, the maximum gap filling strategy is adopted: find the adjacent point pair with the largest arc length interval among the currently selected landmarks, and insert a new landmark at the midpoint; repeat this process until the number of landmarks reaches K.

[0092] Finally, the adaptive landmark set for the i-th robot is obtained:

[0093] ,(twenty three);

[0094] Among them, S i Let i be the set of adaptive landmarks for the i-th robot. Let be the arc length position corresponding to the Kth landmark in the set.

[0095] Step 5: Based on the selected adaptive landmarks, construct a multi-mobile robot time coordination optimization model that includes constraints on entity size and safety distance;

[0096] The specific multi-mobile robot time coordination optimization model is as follows: the arc length interval between adjacent landmarks is:

[0097] ,(twenty four);

[0098] Where, Δs k The arc length interval between adjacent road signs. and These are the arc length positions corresponding to the (k+1)th and kth landmarks of the i-th robot, respectively.

[0099] The feasibility constraints on the time parameters of adjacent road signs are calculated segment by segment and must satisfy:

[0100] (25);

[0101] in, and Let be the time when the i-th robot reaches the (k+1)-th and k-th waypoints, respectively. This represents the theoretical shortest running time for the robot between adjacent time landmarks.

[0102] Building upon this, the motion of multiple mobile robots is mapped onto a path-time space to construct path-time obstacles. A conventional path-time obstacle model is used for collision detection, and robot entity dimensions and safety margin requirements are incorporated into the model constraints. Simultaneously, an adaptive landmark set S is used. i As a reference point for arc length;

[0103] Step 6: Solve the multi-robot time coordination optimization model using optimization algorithms and output the multi-robot path planning results.

[0104] The optimization algorithm specifically involves: searching and optimizing the time parameters at each robot's adaptive landmark points, aiming to minimize the total completion time of the multi-robot team, and incorporating collision conflicts between robots into the objective function through a penalty function.

[0105] ,(26;

[0106] in, It is the objective function. It is the total completion time of the multi-robot team. It is the collision penalty function. These are the weighting coefficients of the penalty term. After optimization, the collision-free timetable parameters for each robot are obtained.

[0107] Finally, based on the optimized timetable parameters, the path-time trajectory of each robot along the spatial path is generated, and the multi-mobile robot path planning results that satisfy obstacle constraints, velocity constraints, acceleration constraints, entity size constraints and safety distance constraints are output.

[0108] On the other hand, this application proposes a computer-readable storage medium storing executable instructions that, when executed, cause a processor to perform the aforementioned multi-mobile robot path planning method with environmental adaptability.

[0109] Thirdly, this application proposes a computer program product, including a computer program or instructions that, when executed by a processor, implement the aforementioned multi-mobile robot path planning method with environmental adaptability.

[0110] The beneficial effects of adopting the above technical solution are as follows:

[0111] This invention provides a multi-mobile robot path planning method with environmental adaptability, which has the following advantages compared with the prior art;

[0112] 1. This invention improves the quality of reference path generation by introducing a dynamic step size mechanism based on artificial potential field gradient in the reference path generation stage, which makes the propagation of the reference path more stable in complex regions and the advancement more efficient in open regions.

[0113] 2. This invention introduces a dynamic step size mechanism that integrates the density of local failure points and the gradient of the artificial potential field during the tree expansion stage. This mechanism can simultaneously utilize environmental prior information and historical failure feedback information to adjust the expansion step size, reduce ineffective expansion and collisions, and improve the efficiency and stability of path search in complex obstacle environments.

[0114] 3. This invention introduces an adaptive landmark selection strategy based on conflict density, channel gap degree and overlapping interval boundary information, which prioritizes the allocation of limited time adjustment degrees of freedom to key conflict areas and narrow channel areas, thereby improving the ability of time schedule parameterization to express key sections. Attached Figure Description

[0115] Figure 1 This is a flowchart of a multi-mobile robot path planning method provided in an embodiment of the present invention;

[0116] Figure 2 This is a schematic diagram of the light reflection heuristic reference path according to an embodiment of the present invention;

[0117] Figure 3 This is a schematic diagram of dynamic step size adjustment according to an embodiment of the present invention;

[0118] Figure 4 This is a diagram illustrating the adaptive selection process of landmark points according to an embodiment of the present invention. Detailed Implementation

[0119] The specific implementation methods of this application will be further described in detail below with reference to the accompanying drawings and embodiments.

[0120] Example 1:

[0121] On the one hand, this invention provides a multi-mobile robot path planning method with environmental adaptability, such as... Figure 1 As shown, it includes the following steps:

[0122] Step 1: Construct a two-dimensional continuous spatial environment model for multi-mobile robot path planning and initialize robot parameters;

[0123] The two-dimensional continuous spatial environment model specifically includes boundary walls, rectangular obstacles, and circular obstacles to simulate typical obstacles such as walls, shelves, and columns in warehousing and logistics, intelligent manufacturing workshops, or indoor inspection environments. Let the number of mobile robots in the environment be n, and a starting point be given for each robot. and the end point And set the robot radius and the minimum safe distance threshold d between robots. s .

[0124] In this embodiment, the robot is no longer considered an ideal point mass, but rather its physical dimensions are taken into account for their impact on subsequent conflict detection and time coordination. Preferably, at least one shared passage area, one intersection area, and one narrow passage area are formed in the environment to fully reflect the complexity of path conflict and time coordination problems in multi-robot path planning;

[0125] Step 2: Generate collision-free spatial paths for each robot based on a dynamic step size mechanism jointly driven by the artificial potential field gradient and the density of failure points.

[0126] Step 2.1: Construct multi-directional rays based on the origin and destination, and generate a reference path through light reflection propagation and cost evaluation;

[0127] For the i-th robot, first construct the main direction vector of the reference path based on the start and end points; the main direction vectors of the start and end points are respectively represented as:

[0128] ,(1);

[0129] (2);

[0130] in, As the starting coordinates, Let d be the starting coordinate. start Starting from the main direction, d goal The destination is the main direction.

[0131] Several auxiliary directions are superimposed on the main direction to form a bidirectional, multi-directional ray set; in specific implementation, the number of rays is set to num_rays, the auxiliary directions on both sides of the main direction are uniformly distributed at angles, and the maximum deflection angle is set to θ. max The angular interval between adjacent auxiliary rays is set to Δθ. Rays are emitted simultaneously from the starting and ending points. If the ray propagates in free space, it continues to advance in the current direction. If the ray collides with the boundary of an obstacle, the propagation direction is updated according to the normal vector and tangential direction of the obstacle boundary, where the disturbance angle during collision reflection is set to θ. inter This process is continuously advanced to generate multiple candidate reference paths. The cost of all candidate paths leading to the target area is evaluated, and the path with the lowest total cost is selected as the reference path for the corresponding robot.

[0132] Figure 2 This is a schematic diagram of the heuristic reference path for generating light reflection in an embodiment of the present invention.

[0133] Step 2.2: Construct the total potential field of the environment and introduce the potential field gradient to guide the adaptive adjustment of the propagation step size;

[0134] The total potential field of the environment consists of the target attraction potential field and the obstacle repulsion potential field:

[0135] U(q) = U att (q)+U rep (q), (3);

[0136] Among them, the current position , where a is the x-coordinate of the robot's position, b is the y-coordinate of the robot's position, and U(q) is the total potential field of the environment. att (q) represents the target attractive potential field, U rep (q) represents the obstacle repulsion potential field.

[0137] The target attractive potential field is defined as:

[0138] (4);

[0139] Where, q g Let ζ be the target point location, and ζ be the gain coefficient of the attractive potential field, where ζ > 0;

[0140] The corresponding gradient of the attractive potential field is:

[0141] (5);

[0142] Let ρ(q) be the minimum distance from the obstacle to the current position q, and ρ0 be the distance at which the obstacle exerts its effect. Then the obstacle repulsive potential field is defined as:

[0143] (6);

[0144] Where η is the repulsive potential field gain coefficient, and η>0.

[0145] The corresponding repulsive potential gradient is:

[0146] (7);

[0147] In general, the gradient of the total potential field is:

[0148] ;

[0149] Considering the need to further reduce the step size when approaching the target point to prevent crossing the target region, the following form of the total potential field gradient is adopted:

[0150] (8);

[0151] Where, ρ gThe distance threshold for determining proximity to the target point;

[0152] Let the current propagation point be q. k Then its gradient magnitude is defined as:

[0153] (9);

[0154] In each propagation along the current direction d k Before proceeding, first determine the gradient magnitude g. k Calculate the propagation step size s k Specifically, the gradient magnitude g k After normalization, the step size is mapped to a scaling factor, and the final step size is constrained to the interval [s]. min s max Within this range, the next predicted propagation point is then obtained:

[0155] (10);

[0156] If from q k arrive If the line segments do not collide, the next predicted propagation point will be used as the new propagation point; if a collision occurs, the critical collision point location and reflection direction will be updated according to the original framework, and the propagation step size will be recalculated in the updated propagation state.

[0157] In this embodiment, the upper bound of the propagation step size is... Used to ensure propagation efficiency in open areas, propagating the lower bound of the step size. Used to ensure propagation stability in narrow regions. Target neighborhood threshold. Used to limit the propagation step size when approaching the target point, preventing the reference path from overshooting the target location.

[0158] Step 2.3: Perform bias sampling within an adaptive range around the reference path with a preset probability;

[0159] Specifically, after obtaining the reference path, bias sampling is performed on the RRT* search process based on the reference path; that is, with a preset probability p bias Bias sampling is performed near the reference path with probability 1-p. bias Random sampling is performed within the global free space; the sampling range near the reference path is adaptively determined based on the distance between the current reference path point and local obstacles; the upper bound of the sampling radius near the reference path is set to r. max The distance d0 from the current reference path point to the nearest obstacle boundary is less than r. max When d0 is selected, the local sampling radius is taken; otherwise, r is selected. max As the local sampling radius;

[0160] Step 2.4: Combine the density of local expansion failure points with the gradient of the artificial potential field to dynamically adjust the step size of expanding new nodes in the tree;

[0161] Let the current expansion node be x. In each iteration, with x as the center, within a radius R... f The number of statistical expansion failure points within the neighborhood is calculated. To more accurately describe the spatial clustering range of failure points, this implementation specifically uses the edge contour envelope algorithm to estimate the geometric coverage area A of the danger zone formed by the failure points. x The density of local failure points is defined as:

[0162] ,(11)

[0163] When the number of failure points is insufficient to form a valid edge contour envelope, a degenerate form is used:

[0164] (12);

[0165] Where N is the number of failure points in the neighborhood, r point The radius affected by a single failure point.

[0166] Simultaneously, calculate the gradient magnitude of the artificial potential field at the current extended node:

[0167] (13);

[0168] Where ▽U(x) is the magnitude of the gradient of the artificial potential field at the current extended node.

[0169] Based on the density of local failure points and the gradient of the artificial potential field, the step size of the current node is defined as:

[0170] (14);

[0171] in, For the natural constant An exponential function with base η base The lower bound of the basic step size, η max Let k1 and k2 be the upper bound of the maximum step size, respectively, the failure point density suppression coefficient and the artificial potential gradient suppression coefficient, and satisfy 0 < η. base <η max ;

[0172] Therefore, the new node update form of the tree expansion is:

[0173] (15);

[0174] Where, x near Let d be the current nearest neighbor node, and d be the node derived from x. near The unit direction vector pointing to the sampling point.

[0175] If the expansion is successful, the neighborhood reconnection and cost update of RRT* will continue; if the expansion fails, the failed position will be added to the set of failed points for subsequent calculation of local failure point density. Figure 3 This is a schematic diagram of dynamic step size adjustment in this embodiment.

[0176] Step 2.5: Iteratively perform sampling and tree expansion, and prune and smooth the generated paths to output spatial paths;

[0177] Repeat steps 2.3 and 2.4 until a spatial path that satisfies the obstacle constraints is generated for each robot. For the backtracked paths, further pruning and smoothing are performed to remove redundant vertices and obtain a collision-free spatial path for time coordination optimization.

[0178] Step 3: Perform arc length parameterized sampling on the spatial path to extract multi-dimensional path feature information;

[0179] Step 3.1: Perform uniform arc length parameter sampling on the spatial path of each robot at fixed intervals;

[0180] Let the i-th robot path be π. i The total arc length is L i Uniform sampling is performed on the path at fixed arc length intervals δ; the number of sampling points is:

[0181] ,(16)

[0182] Where, N i N is the number of sampling points. min This represents the minimum number of sampling points.

[0183] The corresponding sampling arc length position is:

[0184] (17);

[0185] Let the arc length on the path be s. k The coordinates of the point are p. i (s k ), This represents the number of sampled arc lengths.

[0186] Step 3.2: Calculate the path conflict density based on the spatial proximity of the sampling point to other robot paths;

[0187] Define the spatial proximity H of a sampling point on the path to other robot paths. i (s k That is, the path conflict density is:

[0188] (18);

[0189] Where i represents the current robot, and j represents other robots. p represents the arc length at which the other robots are located. j ( ) represents the path points for other robots, d s For safe distance threshold, For indicator functions. H i (s k The larger the value, the higher the potential conflict risk near that arc length location.

[0190] Step 3.3: Calculate the channel gap ratio based on the minimum distance from the sampling point to the nearest obstacle;

[0191] Define the distance C from a sampling point on the path to the nearest obstacle. i (s k That is, the channel gap is:

[0192] ,(19)

[0193] Where o is the point on the rectangular obstacle closest to the sampling point, and c is the point on the rectangular obstacle closest to the sampling point. Let O be the Euclidean distance from the sampling point to o. rect Let O be a set of rectangular obstacles. circ Let c be a set of circular obstacles. c and r c C represents the center and radius of the circular obstacle, respectively. i (s k The smaller the value, the narrower the passage and the more limited the space for local avoidance.

[0194] To facilitate subsequent scoring, path conflict density and channel gap density are normalized to the [0,1] interval, and denoted as follows: and .

[0195] Step 3.4: Detect non-compliant sections of the safety distance between paths using scan lines, and merge and extract the set of overlapping path intervals.

[0196] For any robot pair (i, j), along path π i By step size Sampling is performed when sampling point p i (s) to path π j The minimum distance is less than the safe distance threshold d sAt this point, the corresponding position is considered part of the overlapping interval; the starting arc length and ending arc length of the overlapping interval are recorded by scanning lines to obtain the set of overlapping segments of robot i relative to robot j. The starting arc length and ending arc length of the overlapping interval are recorded by scanning lines, and then all overlapping intervals are uniformly summarized, sorted, and greedily merged to obtain the set of key intervals:

[0197] (20);

[0198] Where r is the index number of the overlapping interval, I i For the set of key intervals extracted, a r and b r These are the starting and ending boundaries of the overlapping interval, R. i This represents the total number of critical intervals.

[0199] Step 4: Based on the path feature information, perform adaptive selection of waypoints;

[0200] Step 4.1: Extract the start and end points of the path, the boundary points of overlapping intervals, and the minimum value points of channel gaps to construct a candidate set of road sign points;

[0201] Initialize the set of selected waypoints, setting the path start point s=0 and the end point s=L. i As a mandatory waypoint, it is added to the set of selected waypoints; subsequently, the merged overlapping intervals [a r， b r The initial boundary a r and termination boundary b r Add to the candidate set.

[0202] Furthermore, in the channel gap degree signal The sliding window method is used to detect local minima to identify the location of narrow channels. Specifically, the window size is set... When the channel gap value of the center point is not greater than that of other sampling points within the window, it is determined to be a candidate point of local minimum; then, several points with the smallest gap value are selected from all local minimums and added to the candidate set.

[0203] Step 4.2: Filter candidate points based on comprehensive score and minimum interval constraint, and generate an adaptive landmark set through the maximum gap filling strategy.

[0204] For any candidate point s c Take the index of its nearest sampling point as k c The comprehensive scoring function is defined as follows:

[0205] ,(twenty one);

[0206] in, This indicates whether the candidate point is a boundary point of an overlapping interval; if so, the value is 1, otherwise it is 0. H w C w E These are the weights for the conflict intensity term, the narrowness term, and the boundary priority term, respectively.

[0207] Candidate points are sorted from highest to lowest score, and a minimum margin constraint is set:

[0208] ,(twenty two);

[0209] Where μ is the minimum interval scaling factor.

[0210] If the arc distance between the current candidate point and all points in the selected landmark set is not less than Δ min If the point is selected, it is added to the set of selected landmarks; otherwise, the point is skipped to avoid excessive clustering of landmarks in a local area.

[0211] If the number of selected landmarks after the above screening is still less than the preset number K, then the maximum gap filling strategy is adopted: find the adjacent point pair with the largest arc length interval among the currently selected landmarks, and insert the new landmark at its midpoint; repeat this process until the number of landmarks reaches K. In this embodiment... Figure 4 A diagram illustrating the adaptive selection process of landmarks for each mobile robot's path.

[0212] Finally, the adaptive landmark set for the i-th robot is obtained:

[0213] ,(twenty three);

[0214] Among them, S i Let i be the set of adaptive landmarks for the i-th robot. Let be the arc length position corresponding to the Kth landmark in the set.

[0215] Step 5: Based on the selected adaptive landmarks, construct a multi-mobile robot time coordination optimization model that includes constraints on entity size and safety distance;

[0216] The specific multi-mobile robot time coordination optimization model is as follows: the arc length interval between adjacent landmarks is:

[0217] ,(twenty four);

[0218] Where, Δs k The arc length interval between adjacent road signs. and These are the arc length positions corresponding to the (k+1)th and kth landmarks of the i-th robot, respectively.

[0219] The feasibility constraints on the time parameters of adjacent road signs are calculated segment by segment and must satisfy:

[0220] (25);

[0221] in, and Let be the time when the i-th robot reaches the (k+1)-th and k-th waypoints, respectively. This represents the theoretical shortest running time for the robot between adjacent time landmarks.

[0222] Building upon this, the motion of multiple mobile robots is mapped onto a path-time space to construct path-time obstacles. A conventional path-time obstacle model is used for collision detection, and robot entity dimensions and safety margin requirements are incorporated into the model constraints. Simultaneously, an adaptive landmark set S is used. i As a reference point for arc length, the piecewise time curve construction method in the original algorithm is used to ensure speed continuity.

[0223] Step 6: Solve the multi-robot time coordination optimization model using optimization algorithms and output the multi-robot path planning results.

[0224] The optimization algorithm specifically involves: searching and optimizing the time parameters at each robot's adaptive landmark points, aiming to minimize the total completion time of the multi-robot team, and incorporating collision conflicts between robots into the objective function through a penalty function.

[0225] ,(26;

[0226] in, It is the objective function. It is the total completion time of the multi-robot team. It is the collision penalty function. These are the weighting coefficients of the penalty term. After optimization, the collision-free timetable parameters for each robot are obtained.

[0227] Finally, based on the optimized timetable parameters, the path-time trajectory of each robot along the spatial path is generated, and the multi-mobile robot path planning results that satisfy obstacle constraints, velocity constraints, acceleration constraints, entity size constraints and safety distance constraints are output.

[0228] Example 2:

[0229] Figure 2This diagram illustrates a light reflection-based heuristic reference path. As shown, when a ray encounters a rectangular or irregular obstacle during propagation, it can update its path by reversing direction based on the obstacle's boundary normal and tangential directions, similar to 'light reflection'. This diagram visually demonstrates that during the preprocessing stage, candidate reference paths that bypass obstacles can be quickly generated without requiring a costly global search.

[0230] Figure 3 This diagram illustrates the dynamic step size adjustment, highlighting a comparison of the expansion performance of the traditional fixed step size strategy and the dynamic step size strategy of this invention at obstacle edges. As shown in the figure, in the fixed step size mode on the left, when a node expands towards a random sampling point, the fixed step size easily leads to it directly crossing the safety boundary and colliding with the black obstacle (indicated by the red arrow). In contrast, in the dynamic step size mode on the right, the algorithm integrates the artificial potential field gradient and the density of local failure points. When approaching an obstacle, it adaptively reduces the expansion step size, effectively avoiding collisions and significantly improving the tree expansion success rate in narrow and complex environments.

[0231] Figure 4 The flowchart illustrates the technical solution for the adaptive selection of landmarks. As shown, landmark generation involves a rigorous filtering funnel: first, the spatial paths generated based on dynamic step sizes are sampled using arc length scaling; then, multi-dimensional features reflecting environmental complexity (path conflict density, channel gaps, and path overlap intervals) are extracted; subsequently, candidate points are comprehensively scored and ranked based on these feature indicators, and a minimum arc length interval constraint is introduced for preliminary filtering; finally, when the number of landmarks satisfying the constraints is less than a preset value, maximum gap filling is performed. This demonstrates that the present invention can accurately and adaptively allocate a finite number of landmarks to the critical areas of the system most prone to conflict.

[0232] Example 3:

[0233] This embodiment proposes a computer-readable storage medium that stores executable instructions. When these instructions are executed, if they are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium.

[0234] The computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the multi-mobile robot path planning method with environmental adaptability described in the various embodiments of this application.

[0235] The aforementioned storage media include: flash memory, hard disk, multimedia card, card-type memory (e.g., SD (Secure Digital Memory Card) or DX (Memory Data Register, MDR) memory, random access memory (RAM), static random access memory (SRAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), programmable read-only memory (PROM), magnetic memory, disk, optical disk, server, APP (Application) application store, and other media capable of storing program verification codes. These media store computer programs, which, when executed by a processor, can implement the various steps of the aforementioned multi-mobile robot path planning method with environmental adaptability.

[0236] Example 4:

[0237] This embodiment proposes a computer program product, including a computer program or instructions, which, when executed by a processor, implements the aforementioned multi-mobile robot path planning method with environmental adaptability.

[0238] Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or part of the technical solution, can be embodied in the form of a computer program product.

[0239] The various embodiments in this application are described in a progressive manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on describing the differences from other embodiments.

[0240] The scope of protection of this application is not limited to the embodiments described above. Obviously, those skilled in the art can make various modifications and variations to this disclosure without departing from the scope and spirit of this disclosure. If such modifications and variations fall within the scope of the methods disclosed herein and their equivalents, then the intent of this disclosure also includes such modifications and variations.

Claims

1. A path planning method for multiple mobile robots with environmental adaptability, characterized in that, Includes the following steps: Step 1: Construct a two-dimensional continuous spatial environment model for multi-mobile robot path planning and initialize robot parameters; Step 2: Generate collision-free spatial paths for each robot based on a dynamic step size mechanism jointly driven by the artificial potential field gradient and the density of failure points. Step 3: Perform arc length parameterized sampling on the spatial path to extract multi-dimensional path feature information; Step 4: Based on the path feature information, perform adaptive selection of waypoints; Step 5: Based on the selected adaptive landmarks, construct a multi-mobile robot time coordination optimization model that includes constraints on entity size and safety distance; Step 6: Solve the multi-robot time coordination optimization model using optimization algorithms and output the multi-robot path planning results.

2. The multi-mobile robot path planning method with environmental adaptability according to claim 1, characterized in that, The two-dimensional continuous spatial environment model described in step 1 specifically involves setting boundary walls, rectangular obstacles, and circular obstacles. Let the number of mobile robots in the environment be n, and give each robot a starting point. and the end point And set the robot radius and the minimum safe distance threshold d between robots. s .

3. The multi-mobile robot path planning method with environmental adaptability according to claim 2, characterized in that, Step 2 specifically includes the following steps: Step 2.1: Construct multi-directional rays based on the origin and destination, and generate a reference path through light reflection propagation and cost evaluation; For the i-th robot, first construct the main direction vector of the reference path based on the start and end points; the main direction vectors of the start and end points are respectively represented as: ，（1）； ，（2）； in, As the starting coordinates, Let d be the starting coordinate. start Starting from the main direction, d goal The main direction of the destination; Several auxiliary directions are superimposed on the main direction to form a bidirectional, multi-directional ray set; the number of rays is set to num_rays, the auxiliary directions on both sides of the main direction are uniformly distributed at angles, and the maximum deflection angle is set to θ. max The angular interval between adjacent auxiliary rays is set to Δθ. Rays are emitted simultaneously from the starting and ending points. If the ray propagates in free space, it continues to advance in the current direction. If the ray collides with the boundary of an obstacle, the propagation direction is updated according to the normal vector and tangential direction of the obstacle boundary, where the disturbance angle during collision reflection is set to θ. inter This process is continuously advanced to generate multiple candidate reference paths. The cost of all candidate paths leading to the target area is evaluated, and the path with the lowest total cost is selected as the reference path for the corresponding robot. Step 2.2: Construct the total potential field of the environment and introduce the potential field gradient to guide the adaptive adjustment of the propagation step size; The total potential field of the environment consists of the target attraction potential field and the obstacle repulsion potential field: U(q)=U att (q)+U rep (q),(3); Among them, the current position , where a is the x-coordinate of the robot's position, b is the y-coordinate of the robot's position, and U(q) is the total potential field of the environment. att (q) represents the target attractive potential field, U rep (q) represents the obstacle repulsion potential field; The target attractive potential field is defined as: ，（4）； Where, q g Let ζ be the target point location, and ζ be the gain coefficient of the attractive potential field, where ζ > 0; The corresponding gradient of the attractive potential field is: ，（5）； Let ρ(q) be the minimum distance from the obstacle to the current position q, and ρ0 be the distance at which the obstacle exerts its effect. Then the obstacle repulsive potential field is defined as: ，（6）； Where η is the repulsive potential field gain coefficient, and η>0; The corresponding repulsive potential gradient is: ，（7）； Considering the need to further reduce the step size when approaching the target point to prevent crossing the target region, the following form of the total potential field gradient is adopted: ，（8）； Where, ρ g The distance threshold for determining proximity to the target point; Let the current propagation point be q. k Then its gradient magnitude is defined as: ，（9）； In each propagation along the current direction d k Before proceeding, first determine the gradient magnitude g. k Calculate the propagation step size s k Specifically, the gradient magnitude g k After normalization, the step size is mapped to a scaling factor, and the final step size is constrained to the interval [s]. min s max Within this range, the next predicted propagation point is then obtained: ，（10）； If from q k arrive If the line segments do not collide, the next predicted propagation point will be used as the new propagation point; if a collision occurs, the critical collision point location and reflection direction will be updated according to the original framework, and the propagation step size will be recalculated in the updated propagation state. Step 2.3: Perform bias sampling within an adaptive range around the reference path with a preset probability; Specifically, after obtaining the reference path, bias sampling is performed on the RRT* search process based on the reference path; that is, with a preset probability p bias Bias sampling is performed near the reference path with probability 1-p. bias Random sampling is performed within the global free space; the sampling range near the reference path is adaptively determined based on the distance between the current reference path point and local obstacles; the upper bound of the sampling radius near the reference path is set to r. max The distance d0 from the current reference path point to the nearest obstacle boundary is less than r. max When d0 is selected, the local sampling radius is taken; otherwise, r is selected. max As the local sampling radius; Step 2.4: Combine the density of local expansion failure points with the gradient of the artificial potential field to dynamically adjust the step size of expanding new nodes in the tree; Let the current expansion node be x. In each iteration, with x as the center, within a radius R... f The number of failed expansion points within the neighborhood is statistically analyzed; specifically, the geometric coverage area A of the danger zone formed by the failed points is estimated using the edge contour envelope algorithm. x The density of local failure points is defined as: ，（11）； When the number of failure points is insufficient to form a valid edge contour envelope, a degenerate form is used: ，（12）； Where N is the number of failure points in the neighborhood, r point The radius of influence for a single failure point; Simultaneously, calculate the gradient magnitude of the artificial potential field at the current extended node: ，（13）； Where ▽U(x) is the magnitude of the gradient of the artificial potential field at the current extended node; Based on the density of local failure points and the gradient of the artificial potential field, the step size of the current node is defined as: ，（14）； in, For the natural constant An exponential function with base η base The lower bound of the basic step size, η max Let k1 and k2 be the upper bound of the maximum step size, respectively, the failure point density suppression coefficient and the artificial potential gradient suppression coefficient, and satisfy 0 < η. base <η max ; Therefore, the new node update form of the tree expansion is: ，（15）； Where, x near Let d be the current nearest neighbor node, and d be the node derived from x. near The unit direction vector pointing to the sampling point; If the expansion is successful, the neighborhood reconnection and cost update of RRT* will continue; if the expansion fails, the failed position will be added to the set of failed points for subsequent calculation of local failure point density. Step 2.5: Iteratively perform sampling and tree expansion, and prune and smooth the generated paths to output spatial paths; Repeat steps 2.3 and 2.4 until a spatial path satisfying obstacle constraints is generated for each robot. For the backtracked path, further pruning and smoothing are performed to remove redundant inflections, resulting in a collision-free spatial path for time coordination optimization.

4. The multi-mobile robot path planning method with environmental adaptability according to claim 3, characterized in that, Step 3 specifically includes the following steps: Step 3.1: Perform uniform arc length parameter sampling on the spatial path of each robot at fixed intervals; Let the i-th robot path be π. i The total arc length is L i Uniform sampling is performed on the path at fixed arc length intervals δ; the number of sampling points is: ，（16）； Where, N i N is the number of sampling points. min This represents the minimum number of sampling points. The corresponding sampling arc length position is: ，（17）； Let the arc length on the path be s. k The coordinates of the point are p. i (s k ), This represents the number of sampled arc lengths; Step 3.2: Calculate the path conflict density based on the spatial proximity of the sampling point to other robot paths; Define the spatial proximity H of a sampling point on the path to other robot paths. i (s k That is, the path conflict density is: ，（18）； Where i represents the current robot, and j represents other robots. p represents the arc length at which the other robots are located. j ( ) represents other robot path points, d s For safe distance threshold, For indicator functions; Step 3.3: Calculate the channel gap ratio based on the minimum distance from the sampling point to the nearest obstacle; Define the distance C from a sampling point on the path to the nearest obstacle. i (s k That is, the channel gap is: ，（19）； Where o is the point on the rectangular obstacle closest to the sampling point, and c is the point on the rectangular obstacle closest to the sampling point. Let O be the Euclidean distance from the sampling point to o. rect Let O be a set of rectangular obstacles. circ Let c be a set of circular obstacles. c and r c These are the center and radius of the circular obstacle, respectively. The path conflict density and channel gap density are normalized to the [0,1] interval, respectively denoted as: and ; Step 3.4: Detect non-compliant sections of the safety distance between paths using scan lines, and merge and extract the set of overlapping path intervals; For any robot pair (i, j), along path π i By step size Sampling is performed when sampling point p i (s) to path π j The minimum distance is less than the safe distance threshold d s At this time, the corresponding position is considered as part of the overlapping interval; the starting arc length and ending arc length of the overlapping interval are recorded by scanning lines to obtain the set of overlapping segments of robot i relative to robot j; the starting arc length and ending arc length of the overlapping interval are recorded by scanning lines, and then all overlapping intervals are uniformly summarized, sorted and greedily merged to obtain the set of key intervals: ，（20）； Where r is the index number of the overlapping interval, I i For the set of key intervals extracted, a r and b r These are the starting and ending boundaries of the overlapping interval, R. i This represents the total number of critical intervals.

5. A multi-mobile robot path planning method with environmental adaptability according to claim 4, characterized in that, Step 4 specifically includes the following steps: Step 4.1: Extract the start and end points of the path, the boundary points of overlapping intervals, and the minimum value points of channel gaps to construct a candidate set of road sign points; Initialize the set of selected waypoints, setting the path start point s=0 and the end point s=L. i As a mandatory waypoint, it is added to the set of selected waypoints; subsequently, the merged overlapping intervals [a r， b r The initial boundary a r and termination boundary b r Add to candidate set; Furthermore, in the channel gap degree signal The sliding window method is used to detect local minima and identify the location of narrow channels; specifically, the window size is set... When the channel gap value of the center point is not greater than that of other sampling points within the window, it is determined to be a candidate point for a local minimum; then, several points with the smallest gap values ​​are selected from all local minimums and added to the candidate set. Step 4.2: Filter candidate points based on comprehensive score and minimum interval constraint, and generate an adaptive landmark set through the maximum gap point filling strategy; For any candidate point s c Take the index of its nearest sampling point as k c The comprehensive scoring function is defined as follows: ，（21）； in, This indicates whether the candidate point is a boundary point of an overlapping interval; if so, the value is 1, otherwise it is 0. H w C w E These are the weights for the conflict intensity term, the narrowness term, and the boundary priority term, respectively. Candidate points are sorted from highest to lowest score, and a minimum margin constraint is set: ，（22）； Where μ is the minimum interval scaling factor; If the arc distance between the current candidate point and all points in the selected landmark set is not less than Δ min If the point is selected, add it to the set of selected waypoints; otherwise, skip the point. If the number of selected landmarks is still less than the preset number K after the above filtering, the maximum gap filling strategy is adopted: find the adjacent point pair with the largest arc length interval among the currently selected landmarks, and insert a new landmark at the midpoint; repeat this process until the number of landmarks reaches K. Finally, the adaptive landmark set for the i-th robot is obtained: ，（23）； Among them, S i Let i be the set of adaptive landmarks for the i-th robot. Let be the arc length position corresponding to the Kth landmark in the set.

6. A multi-mobile robot path planning method with environmental adaptability according to claim 5, characterized in that, The multi-mobile robot time coordination optimization model described in step 5 is as follows: the arc length interval between adjacent landmarks is: ，（24）； Where, Δs k The arc length interval between adjacent road signs. and These are the arc length positions corresponding to the (k+1)th and kth landmarks of the i-th robot, respectively; The feasibility constraints on the time parameters of adjacent road signs are calculated segment by segment and must satisfy: ，（25）； in, and Let be the time when the i-th robot reaches the (k+1)-th and k-th waypoints, respectively. This represents the theoretical shortest running time for the robot between adjacent time landmarks; Building upon this, the motion of multiple mobile robots is mapped onto a path-time space to construct path-time obstacles. A conventional path-time obstacle model is used for collision detection, and robot entity dimensions and safety margin requirements are incorporated into the model constraints. Simultaneously, an adaptive landmark set S is used. i Used as a reference point for arc length.

7. A multi-mobile robot path planning method with environmental adaptability according to claim 6, characterized in that, The optimization algorithm described in step 6 specifically involves: searching and optimizing the time parameters at each robot's adaptive landmark point, with the goal of minimizing the total completion time of the multi-robot team, and incorporating collision conflicts between robots into the objective function through a penalty function. ，（26）； in, It is the objective function. It is the total completion time of the multi-robot team. It is the collision penalty function. These are the weighting coefficients of the penalty term; after optimization, the collision-free timetable parameters for each robot are obtained. Finally, based on the optimized timetable parameters, the path-time trajectory of each robot along the spatial path is generated, and the multi-mobile robot path planning results that satisfy obstacle constraints, velocity constraints, acceleration constraints, entity size constraints and safety distance constraints are output.

8. A computer-readable storage medium storing executable instructions, characterized in that, When the instruction is executed, it causes the processor to perform a multi-mobile robot path planning method with environmental adaptability as described in any one of claims 1-7.

9. A computer program product, comprising a computer program or instructions, characterized in that, When the computer program or instructions are executed by the processor, they implement the multi-mobile robot path planning method with environmental adaptability as described in any one of claims 1-7.

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