Adaptive RRT storage AGV path planning method and system based on CVaR guidance

Abstract

The invention discloses an adaptive RRT storage AGV path planning method and system based on CVaR guidance, and the method comprises the steps: constructing a map for a storage scene, including a storage free space and an obstacle region, and abstracting the storage free space into a point-edge network diagram; taking the conditional risk value CVaR as an index for measuring the uncertainty of the driving time of the AGV, and establishing an optimization function with the purpose of minimizing the driving time of the AGV; optimizing a function target by adopting an RRT node extension mode, selecting a father node by taking the minimum CVaR as a principle, and rewiring; and performing path search by adopting target bias sampling and dynamic step length which are adaptively adjusted along with the obstacle density. According to the method, the uncertainty of the driving time of the AGV in the storage environment is considered, the CVaR serves as an index of the driving time uncertainty, and the'tail driving time risk 'is directly quantified and minimized in the planning stage.

Description

Technical Field

[0001] This invention relates to the field of industrial robot path planning technology, and in particular to an adaptive RRT* warehouse AGV path planning method and system based on CVaR guidance. Background Technology

[0002] In intelligent warehousing environments, Automated Guided Vehicles (AGVs) undertake core tasks such as cargo transfer and sorting. The rationality of their path planning directly affects the overall operational efficiency and cost control of the warehousing system. However, due to factors such as ground conditions, human influence, and fluctuations in AGV performance, the travel time of AGVs on fixed routes is uncertain. This uncertainty affects the accuracy of path planning, potentially leading to a significant decrease in efficiency or even delays in the actual execution of the originally planned optimal path. Currently, chance-constrained models are often used to handle uncertainty in stochastic path planning problems, but this method is often ineffective in dealing with extreme situations.

[0003] Traditional path planning algorithms, such as Dijkstra's algorithm, while simple to implement and robust, suffer from high time and space complexity and low computational efficiency, making them unsuitable for long-distance path planning in large-scale warehousing environments. Algorithm A, while highly scalable and possessing excellent search capabilities, suffers from slow solution speed due to its reliance on heuristic functions, hindering its performance in real-time obstacle avoidance scenarios. In contrast, the RRT* algorithm, as a sampling-based path planning method, has some applicability in complex environments and can find optimal paths. However, this algorithm has significant limitations: its high randomness and lack of effective guidance in generating sampling points lead to a large number of redundant sampling points, increasing computational resource consumption and slowing convergence, making it difficult to meet the real-time requirements of path planning in warehousing environments.

[0004] On the other hand, the core objective of route planning has gradually shifted from "shortest path" to "high on-time rate." However, current mainstream solutions still use "expected travel time" or "expected route length" as the sole optimization indicator, leading to a significant right-tail risk in the travel time distribution during peak order periods, mixed human-machine traffic, and temporary replenishment scenarios. If events that are "low-probability but result in long delays" (tail risks) occur in concentrated bursts, they directly reduce warehousing cycle time and increase operating costs, which traditional expectation models cannot predict or suppress.

[0005] In short, a three-level path optimization framework, such as the "pruning-optimized safety buffer," can quickly obtain feasible paths in static obstacle environments and address dynamic obstacles through online replanning. This method significantly shortens path length on average, but its cost function remains a deterministic scalar and does not model the uncertainty of travel time. Therefore, during periods of increased congestion or frequent dynamic obstacles, the number of replanning operations surges, and on-time performance remains difficult to guarantee.

[0006] Existing technologies also employ ant colony optimization (ACO) algorithms, which improve search efficiency and support multi-target cargo handling through bidirectional guidance from pheromones and random trees. However, their evaluation metrics still use the expected value model of "path length + smoothness," lacking quantitative means for the tail risk of time fluctuations; when environmental randomness increases, the algorithm requires more iterations to converge, limiting real-time performance.

[0007] Existing technologies have also solved the problems of static obstacle avoidance and dynamic obstacle replanning, but they share a common drawback: 1. The optimization objective only considers the first moment (expected distance / time), and cannot explicitly control the probability of task timeout; 2. There is no analytical expression for the uncertainty of travel time, which requires a large amount of sampling or iteration, making it difficult to make decisions in the millisecond level of the embedded controller; 3. The replanning trigger logic is based on deterministic collision detection, which can easily lead to frequent braking or detours in "passable but high-risk" areas, reducing overall efficiency.

[0008] Therefore, there is an urgent need for a path planning method that can directly quantify and minimize the "tail-end travel time risk" during the planning phase, while maintaining real-time performance and embedded deployability, to fill the aforementioned gap. Summary of the Invention

[0009] The technical problem to be solved by this invention is to provide an adaptive RRT* warehouse AGV path planning method and system based on CVaR guidance, which directly quantifies and minimizes the "tail travel time risk" during the planning stage.

[0010] Furthermore, the present invention can also control the probability of task timeout below a specified confidence level within an acceptable increase in average time consumption.

[0011] Furthermore, the present invention can also maintain the real-time performance of the algorithm and its embedded deployability.

[0012] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: An adaptive RRT warehouse AGV path planning method based on CVaR guidance includes the following steps: S1. Construct a map of the warehouse scene, including the warehouse free space and obstacle area, and abstract the warehouse free space into a point-edge network graph; S2: Using the conditional risk value CVaR as an indicator to measure the uncertainty of AGV travel time, an AGV path segment travel time uncertainty model is established. S3: Establish an optimization function with the objective of minimizing the AGV's travel time; S4: The objective function is optimized using the RRT node expansion method. The parent node is selected and rewired based on the principle of minimizing the conditional risk value. Path search is performed using target bias sampling that is adaptive to obstacle density and dynamic step size. Iteration is performed until convergence, and the path with the minimum travel time from the starting point to the target point for the AGV with controllable on-time rate is output.

[0013] In the above technical solution, in step S2, the uncertainty model is as follows: For each fixed route that serves as an edge in the point-edge network, it is assumed that the travel time of the k-th path segment follows a normal distribution of conditional risk values. The travel time of high-risk path segments is quantified using conditional risk values, and the expected travel time of the selected segments is greater than or equal to a risk value threshold. The section of road.

[0014] In the above technical solution, in step S4, for each newly added node, the tail travel time from the root to that node is immediately evaluated using the conditional risk value, and the parent node with the smallest conditional risk value is selected for connection. This ensures that the entire node tree continuously converges towards the direction of "shortest tail time" or "shortest task completion time" during its growth process. This is unlike existing technologies that wait until the optimized path is generated before making posterior corrections.

[0015] In the above technical solution, in step S4, when selecting the parent node, the confidence level is first considered. Calculate the risk threshold of the domain and the path connected to all parent nodes within the domain, then calculate the conditional risk value, and finally select the node with the smallest conditional risk value as the parent node.

[0016] In the above technical solution, in step S4, when the node expansion toward the target is conflict-free, the target bias probability is incrementally increased; conversely, when an obstacle collision is detected during the node expansion process, the strategy reduces and resets the target bias probability.

[0017] In the above technical solution, during step S4, the bias probability of the sampling point towards the target point is dynamically adjusted to reduce the number of redundant sampling points.

[0018] In the above technical solution, in step S4, the target bias probability is continuously adjustable with the distance from the nearest node to the obstacle, and the upper limit does not exceed 0.9.

[0019] In the above technical solution, in step S4, when the node expansion tree is in an open area, the expansion step size is increased to speed up the algorithm convergence; when the expansion tree is in a narrow area with dense obstacles, the expansion step size is reduced to speed up the expansion tree to pass through the narrow area.

[0020] The above technical solution also includes step S5, which involves replanning obstacle avoidance by executing step S3 when the dynamic obstacle trajectory intersects with the planned path.

[0021] In other words, during the operation of the AGV, if a dynamic obstacle appears, it is determined whether the obstacle intersects with the path based on the trajectory of the obstacle. If the trajectory intersects, obstacle avoidance is achieved through replanning.

[0022] Based on the above method, the present invention also provides an electronic device or AGV control system or electronic device, including a processor, a memory, and a program stored in the memory and executable on the processor; when the program is executed by the processor, it implements the steps of any of the above methods.

[0023] Based on the above method, the present invention also provides a computer-readable storage medium storing a program, which, when executed by a processor, implements the steps of any of the above methods.

[0024] In summary, this invention considers the uncertainty of AGV travel time in a warehousing environment and uses CVaR as an indicator of travel time uncertainty. By adjusting the confidence level, the path selection of the AGV can be flexibly controlled. Compared with traditional methods based on expectation and chance constraints, this method improves operational efficiency and task success rate.

[0025] (1) The core innovation of this method lies in introducing Conditional Value at Risk (CVaR) as a quantitative indicator of the uncertainty of AGV travel time. As a robust risk measurement method, CVaR can overcome the limitations of traditional mean or variance indicators and flexibly cover the full range of risk assessments from the overall distribution average (lowest risk) to the extreme worst case (highest risk). By introducing CVaR as a risk measurement indicator, the risk level of different paths can be assessed more accurately, thereby selecting more robust and safer paths.

[0026] (2) By incorporating CVaR into the objective function rather than treating it as a constraint, this approach enhances the flexibility of risk preference.

[0027] (3) To further balance the efficiency and accuracy of path planning, the method integrates two key optimization strategies: one is dynamic target bias sampling, which reduces the number of redundant sampling points by dynamically adjusting the bias probability of sampling points to target points during the path search process, thus avoiding the problem of low search efficiency caused by random sampling in large-scale environments of traditional RRT* algorithm; the other is adaptive dynamic step size, which adjusts the sampling step size in real time according to the risk level of the current path and the complexity of the search area (such as obstacle density).

[0028] Compared with the prior art, the beneficial effects of this invention are: First, traditional methods often use expectation or chance constraints to handle time uncertainty, making it difficult to balance average performance with extreme risks. This invention uses CVaR as the core indicator. By calculating the expected travel time of a path segment at a specific confidence level, it can flexibly express various risk measures ranging from the average of the entire distribution (i.e., the lowest risk scenario) to the worst-case scenario (i.e., the highest risk scenario).

[0029] Secondly, addressing the redundant computation and slow convergence issues caused by random sampling in traditional RRT* algorithms, this invention proposes a dual optimization mechanism: dynamic target bias sampling dynamically adjusts the target bias probability by detecting the conflict state between the extended path and obstacles (increasing the probability to enhance directional search when there is no conflict, and decreasing the probability to expand the exploration range when there is a conflict), reducing invalid sampling points; adaptive dynamic step size adaptively adjusts the expansion step size based on the distance between nodes and obstacles (using the maximum step size to accelerate convergence in open areas, and using a decaying step size to ensure obstacle avoidance accuracy in narrow areas). The combination of these two mechanisms improves the convergence speed of the algorithm in complex warehouse environments while ensuring path quality, overcoming the limitation of traditional RRT* algorithms in balancing exploration and utilization.

[0030] Third, this invention utilizes the confidence level parameter of CVaR (such as...) (Value), allowing for flexible control over the risk preference of the path. For example, in emergency replenishment tasks, a low confidence level (such as...) can be set. =0.7) Prioritize routes with shorter average times; in high-priority transportation tasks, increase confidence levels (e.g., =0.95) to mitigate the risk of extreme delays. This flexibility allows the algorithm to adapt to the risk requirements of different tasks, while traditional methods often use fixed risk metrics, making it difficult to meet the diverse task priority requirements in warehousing scenarios. Attached Figure Description

[0031] The present invention will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings: Figure 1 This is a flowchart illustrating the steps of the adaptive RRT* warehouse AGV path planning method based on CVaR guidance of the present invention.

[0032] Figure 2 This is a flowchart of the CVaR-ARRT* algorithm of the present invention.

[0033] Figure 3 This is a warehouse environment map for the path planning of this invention.

[0034] Figure 4 The number of nodes required to find the initial path for different algorithms in this invention.

[0035] Figure 5 This is one example of an AGV's path under different risk profiles.

[0036] Figure 6 This is the path for one embodiment at a high confidence level.

[0037] Figure 7 The curves show the change in travel time of different algorithms with the number of iterations under extreme conditions. Detailed Implementation

[0038] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0039] Example 1 The adaptive RRT* warehouse AGV path planning method based on CVaR guidance implemented according to the present invention, such as Figure 1 As shown, based on the warehousing scenario, a map is constructed to find the path with the shortest travel time for the AGV from the starting point to the target point in free space, including the following steps: S1. Model the warehouse environment, set the map size and static obstacles, divide the environment into free space and obstacle area, and represent the free space as a set of points and edges.

[0040] S2. Using CVaR as an indicator to measure the uncertainty of AGV travel time, we obtain an expression for the AGV travel time on a fixed route.

[0041] S3. After modeling the uncertainty of AGV travel time on a fixed route in step 2, construct an optimization function with the objective of minimizing task completion time.

[0042] S4. Initialize the parameters of the CVaR-guided adaptive RRT* algorithm and execute the algorithm until the preset number of iterations is reached or the convergence condition is met.

[0043] In some cases, step S5 can be added: If a dynamic obstacle appears during the operation of the AGV, determine whether it intersects with the path based on the trajectory of the dynamic obstacle. If the trajectory intersects, perform replanning by executing step S3 to achieve obstacle avoidance.

[0044] S2 includes: 2-1. Assume that the travel time of an AGV on a fixed route follows a normal distribution with known mean and variance. Therefore, in free space, the _th__ k Segment Path p The travel time of [k] follows a normal distribution. .

[0045] in In the first k The average travel time for a segment of the route. Let be the variance. Therefore, the random variable... probability density function The expression is: ; 2-2. According to 2-1, the AGV is in the first... k Segment Path p Travel time of [k] After the expression, in order to evaluate the travel time of the AGV in each path segment, the following is used: Quantifying path segments using conditional risk values ​​at different levels p The travel time of [k], i.e. ,random variable of express Above the risk value Distribution under threshold The expectation, that is: ; in .

[0046] 2-3. Based on the linear transformation property of the normal distribution, let Then Z follows the standard normal distribution. Conditions can be set. Convert to ,so: ; in, It is the inverse cumulative distribution function of the standard normal distribution.

[0047] 2-4. Using the conditional expectation property of the standard normal distribution, we can obtain... The expression: ; In S3, the optimization function aimed at minimizing the AGV's travel time is represented by CVaR: ; in, p Let P represent the path that minimizes the travel time obtained by this algorithm, and let P represent the set of all paths in free space.

[0048] When executing this algorithm in S4, the selection of the parent node is first based on the confidence level. Paths connected to all parent nodes within the computational domain Then calculate Finally, the node with the lowest conditional risk value is selected as the parent node.

[0049] S4 employs a dynamic target bias sampling strategy. When the expansion toward the target is conflict-free, the probability is incrementally increased to enhance the efficiency of the orientation search. Conversely, when an obstacle collision is detected during node expansion, the strategy reduces and resets the target bias probability to expand random sampling for obstacle avoidance. The adaptive target bias sampling strategy selects random sampling points in the following manner. ; ; in, It is the probability of random sampling. It is the target bias sampling probability, calculated using the following formula: ; in, Let be the initial target bias probability. To adjust the coefficient, The nearest node in the tree The nearest Euclidean distance to the obstacle To be a small constant, to prevent Too small To extend the safe distance between tree nodes and obstacles, For the new node, This represents a set of obstacles in a warehouse environment. The maximum probability is set to 0.9 to allow for some exploration. When When the value is large, increase the target bias probability to guide the search towards the target direction; when... When the value is small, the target bias probability is reduced to avoid failure due to excessive bias towards the target in narrow areas.

[0050] S4 employs an adaptive dynamic step size strategy. When the tree is in an open area, the step size is increased to accelerate algorithm convergence; when the tree is in a narrow area with dense obstacles, the step size is decreased to speed up the tree's passage through the narrow area. Adaptive Step Size The calculation method is as follows: ; in, For the maximum allowable step size, For the minimum allowable step size, This is for adjusting the coefficient.

[0051] In step S1, the warehouse environment is modeled, and information such as map size and static obstacles is set. The environment is divided into free space and obstacle area, and the free space is represented as a set of points and edges.

[0052] First, we model the free space of the warehouse environment. Let non-empty compact sets represent the robot's configuration space (C-space), and let its barrier-free subset be represented as... ,in Represents the set of all obstacles in C-space, Use a tree This indicates that the tree consists of tuples. To indicate, and These represent the sets of nodes and edges of the tree, respectively.

[0053] Then, the path is modeled. and These represent the given starting and ending points, respectively. The path... Represented as A finite sequence of N edges, with symbol This represents the set of all paths. Path Connection starting point and target point ,Right now It is a set , where each path segment All are completely located middle, Indicates in Positive integers within the range.

[0054] In step S2, CVaR is used as an indicator to measure the uncertainty of AGV travel time, and an expression for the travel time of AGV on a fixed route is obtained.

[0055] First, based on the assumption that the AGV's travel time on a fixed route follows a Gaussian distribution with known mean and variance, the time in free space for the AGV is... k Segment Path p The travel time of [k] follows a normal distribution. .random variable probability density function The expression is: ; in In the first k The average travel time for a segment of the route. For variance, Indicates that the AGV is in the first... k The travel time of a segment of the route.

[0056] To evaluate the drone's travel time on each path segment, the following methods were used: Quantifying path segments using conditional risk values ​​at different levels p The travel time of [k], i.e. ,random variable of express Above the risk value Distribution under threshold The expectations, among which ,Right now: ; in, yes Distribution Quantiles It follows a normal distribution, and its expression is as follows: ; Based on the linear transformation property of the normal distribution, let Then Z follows the standard normal distribution. Conditions can be set. Convert to Therefore, the conditional expectation can be expressed as: ; Then, using the conditional expectation property of the standard normal distribution, we obtain: ; in, It is the inverse cumulative distribution function of the standard normal distribution.

[0057] Using the conditional expectation property of the standard normal distribution, we can obtain The expression: ; In step S3, after modeling the uncertainty of AGV travel time on a fixed route in step S2, an optimization function is constructed with the goal of minimizing the task completion time.

[0058] The derivation is obtained through step S2. Following the expression, we represent the objective function of this problem based on CVaR, as follows: ; In step S4, the parameters of the CVaR-guided adaptive RRT* algorithm are initialized, and the algorithm is executed until the preset number of iterations is reached or the convergence condition is met.

[0059] The CVaR-guided adaptive RRT* warehouse AGV path planning algorithm process includes: Initialization: Initialize an empty tree T, with its starting coordinates. End point coordinates Confidence level Initial target bias probability Trimming radius Maximum step size minimum step size Adaptive bias probability adjustment coefficient Adaptive step size adjustment coefficient ; Generate sampling node: Select a sampling node according to the adaptive target bias sampling strategy; Find the nearest node: Find the nearest node in tree T. The nearest node ; Expanding the tree: Based on an adaptive dynamic step-size strategy from Towards Expand in one direction to generate a new node. ; Validity check: If from arrive The extended connection has no obstacles (i.e., it is not in the set of obstacles). If the sample is in the middle, continue; otherwise, resample. Try reconnecting: Get In scope Given a set of neighboring nodes, construct a time cost distribution for each neighboring node and calculate the time cost for a given confidence level. of and The neighbor node with the lowest conditional risk value is selected as the optimal connection point.

[0060] Termination condition: The algorithm terminates and outputs the path when the preset number of iterations is reached or the convergence condition is met. .

[0061] In the aforementioned CVaR-guided adaptive RRT* warehouse AGV path planning algorithm, an adaptive dynamic bias sampling strategy is employed to select sampling nodes. When the expansion toward the target is conflict-free, the probability is incrementally increased to enhance the orientation search efficiency. Conversely, when an obstacle collision is detected during node expansion, the strategy reduces and resets the target bias probability to expand random sampling for obstacle avoidance. The adaptive target bias sampling strategy selects random sampling points in the following manner. ; ; in, It is the probability of random sampling. It is the target bias sampling probability or target bias probability, calculated using the following formula: ; in, Let be the initial target bias probability. To adjust the coefficient, The nearest node in the tree The nearest Euclidean distance to the obstacle To be a small constant, to prevent Too small To extend the safe distance between tree nodes and obstacles, For the new node, This represents a set of obstacles in a warehouse environment. The maximum probability is set to 0.9 to allow for some exploration. When When the value is large, increase the target bias probability to guide the search towards the target direction; when... When the value is small, the target bias probability is reduced to avoid failure due to excessive bias towards the target in narrow areas.

[0062] Furthermore, the aforementioned adaptive RRT* warehouse AGV path planning algorithm based on CVaR guidance also employs an adaptive dynamic step size strategy. When the expansion tree is in an open area, the expansion step size is increased to accelerate algorithm convergence; when the expansion tree is in a narrow area with dense obstacles, the expansion step size is decreased to accelerate the expansion tree's passage through the narrow area. Adaptive expansion step size. The calculation method is as follows: ; in, For the maximum allowable step size, For the minimum allowable step size, This is for adjusting the coefficient.

[0063] After executing the above algorithm, a feasible path from the starting point to the ending point can be generated. However, since the generated path is composed of a series of discrete nodes, there may be inflection points, resulting in a non-smooth path, which is not conducive to the actual execution of the robot. Therefore, a third-order Bézier curve is used to smooth the path generated by the above algorithm. A third-order Bézier curve defines a smooth curve through four control points, and its mathematical expression is: ; in, and These are the starting and ending points of the curve. and To control the midpoint of the curve shape.

[0064] During AGV operation, if a dynamic obstacle appears, it is determined whether the obstacle intersects the path based on its trajectory. If the trajectory intersects, the replanning module is called by executing step S3 to generate a collision-free path.

[0065] Example 2 like Figure 1-5 As shown, the present invention provides an adaptive RRT* warehouse AGV path planning method and system based on CVaR guidance, which has broad application scenarios in AGV path planning, scheduling and other fields in warehouse scenarios.

[0066] AGVs need to perform path planning in a warehouse environment. Warehouse environments are complex and changeable, and there are usually multiple obstacles, such as shelves, stacks, and fixed equipment. Considering the uncertainty of the travel time of AGVs on fixed routes in a warehouse environment, AGVs need to plan their routes from the starting point to the destination, while avoiding collisions with obstacles and optimizing the travel path as much as possible.

[0067] like Figure 1 and 2 As shown, the adaptive warehouse AGV path planning method based on CVaR guidance provided in this embodiment of the invention includes the following steps: Step 1: Model the warehouse environment, set the map size and static obstacles, divide the environment into free space and obstacle areas, and represent the free space as a set of points and edges.

[0068] The first step is to model the warehouse environment, setting information such as map size and static obstacles. The warehouse environment is represented as a collection of free space and obstacles. An example of this is the environment map. Figure 3 As shown.

[0069] Step 2: Using CVaR as an indicator to measure the uncertainty of AGV travel time, we obtain an expression for the AGV's travel time on a fixed route.

[0070] Step 3: After modeling the uncertainty of AGV travel time on a fixed route in Step 2, construct an optimization function with the objective of minimizing task completion time.

[0071] Step 4: Initialize the parameters of the CVaR-guided adaptive RRT* algorithm and execute the algorithm until the preset number of iterations is reached or the convergence condition is met.

[0072] Initialize algorithm parameters, initialize empty tree T, set the coordinates of the start and target points, and determine the confidence level based on the storage environment. The values ​​of are shown in Table 1, which are the main parameters of this embodiment: Table 1. Parameters of the CVaR-guided adaptive warehouse AGV path planning method

[0073] After modeling the environment and initializing relevant parameters, the starting and target nodes are input, and an adaptive warehouse AGV path planning algorithm guided by CVaR is executed: The first step involves selecting sampling nodes based on an adaptive dynamic step-size strategy. When the expansion toward the target is conflict-free, the probability is incrementally increased to enhance the efficiency of the orientation search. Conversely, when an obstacle collision is detected during node expansion, the strategy reduces and resets the target bias probability to expand random sampling for obstacle avoidance. The adaptive target bias sampling strategy selects random sampling points in the following manner. ; ; in, It is the probability of random sampling. It is the target bias sampling probability, calculated using the following formula: ; in, Let be the initial target bias probability. To adjust the coefficient, The nearest node in the tree The nearest Euclidean distance to the obstacle To be a small constant, to prevent Too small To extend the safe distance between tree nodes and obstacles, For the new node, This refers to a collection of obstacles in a warehouse environment.

[0074] Step 2: Distance within tree T The nearest node .

[0075] The third step involves calculating the current step size based on an adaptive dynamic step size strategy. When the expanded tree is in an open area, the expansion step size is increased to accelerate algorithm convergence. Conversely, when the expanded tree is in a narrow area with numerous obstacles, the expansion step size is decreased to expedite the tree's passage through the narrow area. (Adaptive expansion step size) The calculation method is as follows: ; in, For the maximum allowable step size, For the minimum allowable step size, This is for adjusting the coefficient.

[0076] Step 4, if from arrive The extended connection has no obstacles (i.e., it is not in the set of obstacles). If the result is positive, continue; otherwise, resample.

[0077] Step 5: Obtain In scope Given a set of neighboring nodes, construct a time cost distribution for each neighboring node and calculate the time cost for a given confidence level. of and The neighbor node with the lowest conditional risk value is selected as the optimal connection point.

[0078] Based on the assumption that the AGV's travel time on a fixed route follows a normal distribution with known mean and variance, the time in free space for the AGV is... k Segment Path p The travel time of [k] follows a normal distribution. .

[0079] in In the first k The average travel time for a segment of the route. Let Variance be the variance.

[0080] The above assumes that the AGV's travel time on a fixed route follows a normal distribution with known mean and variance. This embodiment will Represented as path segment Euclidean distance, ,use Quantifying path segments using conditional risk values ​​at different levels p The travel time of [k], i.e. ,random variable of express Above the risk value Distribution under threshold The expectations, among which ,Right now: ; in, yes Distribution Quantiles It follows a normal distribution, and its expression is as follows: ; Based on the linear transformation property of the normal distribution, let Then Z follows the standard normal distribution. Conditions can be set. Convert to Therefore, the conditional expectation can be expressed as: ; Then, using the conditional expectation property of the standard normal distribution, we obtain: ; in, It is the inverse cumulative distribution function of the standard normal distribution.

[0081] Using the conditional expectation property of the standard normal distribution, we can obtain The expression: ; according to , , The value can be calculated. The value, in Within the set of neighboring nodes, select the neighboring node with the lowest conditional risk value as the parent node.

[0082] Repeat the above steps. When the preset number of iterations is reached or the convergence condition is met, output the path and smooth the generated path using a third-order Bézier curve.

[0083] like Figure 4 The figure shows a box plot comparing the number of nodes required to find the initial path using the CVaR-guided adaptive RRT* algorithm (CVaR-ARRT*), the unmodified RRT* algorithm, and the chance-constrained RRT* algorithm in this embodiment. The comparison shows that the CVaR-ARRT* algorithm outperforms the unmodified RRT* and CC-RRT* algorithms in terms of both the mean number of nodes required to find the initial solution and the number of outliers.

[0084] like Figure 5 As shown in (a)-(c), this embodiment uses parameter adjustments. To obtain the AGV's path under different risk preferences, the initialization parameters in this embodiment are based on Table 1. The AGV starts from the origin and plans a path with the shortest travel time according to the confidence level. By adjusting... The value of can be used to flexibly select a suitable path planning strategy based on the uncertainty of the environment.

[0085] when When taking a smaller value, the AGV considers the probability distribution of the entire travel time, thus guiding the path selection of the planning algorithm to choose a more "aggressive" path, or tending to traverse areas with greater uncertainty, such as... Figure 5 As shown in (b) and (c); when When = 0, path planning degenerates into optimizing the expectation of random variables, corresponding to Figure 5 (a), that is .

[0086] when When taking a larger value, the AGV considers the tail of the entire probability distribution, in the worst case... In certain situations, choose a safer, more "conservative" path, such as... Figure 6 As shown in (a) and (b).

[0087] Table 2 shows the correlation with Figure 5 and Figure 6 The corresponding travel time of the AGV to the target point under different confidence levels, where EP-RRT* is based on the expected traditional RRT* algorithm. When When the value increases, path planning becomes more risk-averse, choosing a more conservative path. While this path selection strategy effectively reduces path risk, it also leads to longer flight times. Nevertheless, because this parameter is adjustable, various scenarios can be simulated to select the appropriate path. value.

[0088] Table 2. Travel time of AGV to target point under different confidence levels.

[0089] Example 3 like Figure 7 As shown, in extreme cases, such as ground conditions, electromagnetic interference, and the AGV's own performance, the travel time on a fixed route is significantly affected. Traditional path planning algorithms based on expectation optimization and chance constraints have significantly longer travel times than the adaptive RRT* algorithm based on CVaR guidance proposed in this invention. CC-RRT* is the RRT* algorithm based on chance constraints. Table 3 shows the extreme cases... Figure 7 The driving time and failure rate of different algorithms in the corresponding embodiments.

[0090] Table 3. Driving time and failure rate of different algorithms

[0091] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. It should be understood that those skilled in the art can make improvements or modifications based on the above description, and all such improvements and modifications should fall within the scope of protection of the appended claims.

Claims

1. A CVaR-guided adaptive RRT warehouse AGV path planning method, characterized in that... Includes the following steps: S1. Construct a map of the warehouse scene, including the warehouse free space and obstacle area, and abstract the warehouse free space into a point-edge network graph; S2: Using the conditional risk value CVaR as an indicator to measure the uncertainty of AGV travel time, an AGV path segment travel time uncertainty model is established. S3: Establish an optimization function with the objective of minimizing the AGV's travel time; S4: The objective function is optimized using the RRT node expansion method. The parent node is selected and rewired based on the principle of minimizing the conditional risk value. Path search is performed using target bias sampling that is adaptive to obstacle density and dynamic step size. Iteration is performed until convergence, and the path with the minimum travel time from the starting point to the target point for the AGV with controllable on-time rate is output.

2. The adaptive RRT warehouse AGV path planning method based on CVaR guidance according to claim 1, characterized in that... In step S2, the uncertainty model is as follows: For each fixed route that serves as an edge in the point-edge network, it is assumed that the travel time of the k-th path segment follows a normal distribution of conditional risk values. The travel time of high-risk path segments is quantified using conditional risk values, and the expected travel time is selected if it is greater than or above the risk value threshold. The section of road.

3. The adaptive RRT warehouse AGV path planning method based on CVaR guidance according to claim 1, characterized in that... In step S4, for each new node, the tail travel time from the root to the node is immediately evaluated using the conditional risk value, and the parent node with the smallest conditional risk value is selected for connection.

4. The adaptive RRT warehouse AGV path planning method based on CVaR guidance according to claim 1, characterized in that... In step S4, when selecting the parent node, the confidence level is first considered. Calculate the risk threshold of the domain and the path connected to all parent nodes within the domain, then calculate the conditional risk value, and finally select the node with the smallest conditional risk value as the parent node.

5. The adaptive RRT warehouse AGV path planning method based on CVaR guidance according to claim 1, characterized in that... In step S4, when the node expansion toward the target is conflict-free, the target bias probability is incrementally increased; conversely, when an obstacle collision is detected during node expansion, the strategy reduces and resets the target bias probability.

6. The adaptive RRT warehouse AGV path planning method based on CVaR guidance according to claim 1, characterized in that... In step S4, during the path search process, the bias probability of the sampling point toward the target point is dynamically adjusted.

7. The adaptive RRT warehouse AGV path planning method based on CVaR guidance according to claim 1, characterized in that... In step S4, when the node expansion tree is in an open area, the expansion step size is increased to speed up the algorithm convergence; when the expansion tree is in a narrow area with dense obstacles, the expansion step size is reduced to speed up the expansion tree to pass through the narrow area.

8. The adaptive RRT warehouse AGV path planning method based on CVaR guidance according to claim 1, characterized in that... It also includes step S5, where when the dynamic obstacle trajectory intersects with the planned path, step S3 is executed to replan the obstacle avoidance.

9. An electronic device comprising a processor, a memory, and a program stored in the memory and executable on the processor, characterized in that: When the program is executed by the processor, it implements the steps of the method according to any one of claims 1-8.

10. A computer-readable storage medium, characterized in that, The storage medium stores a program that, when executed by a processor, implements the steps of the method described in any one of claims 1-8.

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