A method for optimizing motion trajectory of distributed multi-agent based on entropy constraint

Abstract

The present application relates to the technical field of multi-agent motion optimization, in particular to a distributed multi-agent motion trajectory optimization method based on entropy constraint, comprising extracting the historical speed sequence of each agent and the historical communication interval sequence with each neighbor agent, calculating the space entropy, time entropy and communication entropy based on the semi-space constraint set, historical speed sequence and historical communication interval sequence respectively; using the historical speed sequence and historical communication interval sequence to dynamically match the entropy threshold vector, constructing the entropy cost function, combining the local space entropy index to switch the planning strategy, defining the entropy factor and dynamically adjusting the semi-space boundary at the bottleneck time, constructing the adjusted space-time distribution constraint; based on the historical space entropy value sequence to predict the trend, and constructing the objective function, outputting the optimized motion trajectory of the agent, the present application realizes the dynamic optimization of the feasible trajectory space under the premise of preserving the collision avoidance geometric lower bound.

Description

Technical Field

[0001] This invention relates to the field of multi-agent motion optimization technology, and in particular to a distributed multi-agent motion trajectory optimization method based on entropy constraints. Background Technology

[0002] With the widespread application of multi-agent systems in warehousing and logistics, intelligent transportation, and collaborative manufacturing, distributed asynchronous trajectory planning technology has become a core means to solve large-scale multi-agent cooperative motion problems. Existing distributed trajectory planning methods mainly include priority-based heuristic rule methods, model predictive control-based optimization methods, and spatiotemporal allocation-based methods. Among them, spatiotemporal allocation-based methods explicitly divide the feasible spatiotemporal regions between agents into half-space constraints by separating hyperplanes, transforming trajectory intersection constraints into linear inequality constraints. These methods offer strict collision avoidance guarantees in asynchronous communication environments and have become an important branch of current distributed multi-agent trajectory planning technology.

[0003] However, existing spatiotemporal allocation methods still have some shortcomings in practical applications. First, they lack the ability to quantitatively perceive the complexity of the situation. The planner only optimizes by minimizing the cost of reaching the target, and cannot assess the current complexity of the situation or predict future evolution trends. This leads to the agent passively satisfying half-space constraints in high-density scenarios and getting stuck in congestion bottlenecks. In addition, the half-space boundary offset is set based on a fixed geometric safety distance. The static safety margin is applied equally to all directions, all times, and all scenarios. In congested scenarios, this excessive conservatism significantly compresses the feasible trajectory space, resulting in a decrease in overall traffic efficiency. Finally, the situation assessment mechanism and threshold parameters are often tightly coupled with specific dynamic models. When deploying heterogeneous clusters with different dynamic structures such as dual integrators, Ackermans, and unicycles, parameter tuning is required for each model. This relies on human experience and requires repeated parameter tuning when switching scenarios, which seriously restricts the engineering promotion and application. At present, a distributed multi-agent motion trajectory optimization method based on entropy constraints is needed. Summary of the Invention

[0004] To address the problem that existing distributed multi-agent asynchronous trajectory planning methods suffer from low trajectory efficiency and difficulty in parameter tuning during heterogeneous cluster deployment due to a lack of quantitative perception and dynamic adjustment capabilities for situational complexity, this invention provides a distributed multi-agent motion trajectory optimization method based on entropy constraints.

[0005] This invention provides a distributed multi-agent motion trajectory optimization method based on entropy constraints, employing the following technical solution: A distributed multi-agent motion trajectory optimization method based on entropy constraints includes: Each agent obtains the trajectory information of its neighboring agents based on local communication, determines the set of half-space constraints it is subject to, and extracts its historical velocity sequence and historical communication interval sequence with each neighboring agent. Calculate spatial entropy, temporal entropy, and communication entropy based on the half-space constraint set, historical velocity sequence, and historical communication interval sequence, respectively. The entropy threshold vector is dynamically matched using historical velocity sequences and historical communication interval sequences, and adaptive weights are calculated based on the number of neighbors and the target distance. An entropy cost function is constructed based on spatial entropy, temporal entropy, and adaptive weights, and planning strategy switching is performed in conjunction with local spatial entropy indicators. Define an entropy factor and dynamically adjust the half-space boundary at the bottleneck moment to construct the adjusted spatiotemporal allocation constraint; Trend prediction is performed based on historical spatial entropy value sequences. The entropy increase cost of candidate trajectories is evaluated by combining spatiotemporal local entropy. An objective function consisting of the original cost, entropy cost, and entropy increase cost is constructed, and the optimized motion trajectory of the agent is output.

[0006] Furthermore, the calculation of spatial entropy, temporal entropy, and communication entropy respectively includes: Based on the direction information of the normal vectors of each half-space in the half-space constraint set, the two-dimensional workspace is divided into several uniformly oriented sectors. The number of half-space constraints in each sector is counted, the probability distribution of each sector is calculated, and the spatial entropy and its maximum value are calculated according to the Shannon information entropy definition. Based on historical velocity sequences, velocity values ​​are discretized into several velocity states using velocity threshold vectors. The frequency of each velocity state is counted and the probability distribution is calculated. The time entropy and its maximum value are calculated according to the Shannon information entropy definition. Based on historical communication interval sequences, the communication intervals are discretized into several communication intervals using the boundary vector of the communication intervals. The frequency of each communication interval is counted and the probability distribution is calculated. The communication entropy and its maximum value are obtained according to the Shannon definition of information entropy.

[0007] Furthermore, the dynamic matching of the entropy threshold vector using historical speed sequences and historical communication interval sequences includes historical speed sequences based on the historical speed buffer maintained by this agent, when... At that time, a velocity threshold vector is extracted from the historical velocity sequence using percentile statistics to be used for discretization calculation of time entropy. At that time, a preset default speed threshold vector is used; Based on the historical communication interval sequence in the historical communication interval buffer maintained by each neighboring agent, when the data volume of the historical communication interval buffer reaches the preset minimum sample size, the communication interval boundary vector is extracted from the historical communication interval sequence using the quartiles statistical method and fixed. When the communication interval exceeds the upper limit of the communication interval boundary vector, the communication interval is classified into the boundary interval. in, The amount of data in the historical speed buffer. This is the minimum sample size.

[0008] Furthermore, the calculation of the adaptive weights includes calculating adaptive spatial entropy weights and adaptive temporal entropy weights based on the number of neighbors and the distance to the target, respectively. The calculation formulas for the adaptive spatial entropy weights and adaptive temporal entropy weights are as follows: , , in, For adaptive spatial entropy weights, As the basic weight of spatial entropy, This is the spatial entropy weight scaling factor. For the number of neighbors, For adaptive time entropy weights, This is the time entropy weight scaling factor. As the basic weight of time entropy, The distance from the agent to the target. The target distance threshold.

[0009] Furthermore, the construction of the entropy cost function based on spatial entropy, temporal entropy, and adaptive weights includes normalizing the spatial and temporal entropies, and then combining the normalized spatial and temporal entropies with adaptive spatial and temporal entropy weights to construct the entropy cost function. The expression for the entropy cost function is as follows: , in, Let entropy cost function, For adaptive spatial entropy weights, For adaptive time entropy weights, To normalize the spatial entropy, This is the normalized time entropy.

[0010] Furthermore, the step of switching planning strategies by combining the local spatial entropy index includes calculating the minimum distance from the agent to each half-space boundary, calculating the local spatial entropy index based on the minimum value and the numerical stability term, evaluating the degree of constraint of the feasible region in the local space where the agent is located based on the spatial entropy and the local spatial entropy index, and adjusting the weight matrix of the optimal control problem and the entropy cost weight based on the degree of constraint of the feasible region to formulate corresponding trajectory planning strategies in different cost intervals. The expression of the local spatial entropy index is: , in, As a local spatial entropy index, Let be the distance from this agent to the boundary of the k-th half-space. For numerically stable terms, It is the minimum value among all half-space boundary distances.

[0011] Furthermore, the definition of the entropy factor and the dynamic adjustment of the half-space boundary at the bottleneck moment include calculating the distance from the agent to each half-space boundary. When the distance is less than a preset bottleneck identification distance threshold, the moment is marked as a bottleneck moment. The entropy factor is calculated using normalized spatial entropy and normalized temporal entropy. The boundary adjustment amount is calculated based on the half-space boundary distance at the bottleneck moment and the entropy factor. When a preset boundary adjustment trigger condition is met, the original half-space offset is corrected based on the boundary adjustment amount to obtain the adjusted half-space offset. The expression for the boundary adjustment amount is: , in, Let be the boundary adjustment amount for the k-th half-space. These are boundary adjustment coefficients based on physical constraints. The boundary adjustment coefficient is based on the entropy value. It is the entropy factor.

[0012] Furthermore, the construction of the adjusted spatiotemporal allocation constraint includes constructing a boundary-adjusted half-space based on the adjusted half-space offset, and combining the boundary-adjusted half-space with the corresponding time information to form the adjusted spatiotemporal allocation constraint. An extended objective function is constructed, incorporating both the original cost and entropy cost. The entropy cost weight is adaptively adjusted based on the number of neighbors and a neighborhood normalization factor. Under the adjusted spatiotemporal allocation constraints, the optimal planning for the current situation is determined based on the extended objective function. The expression for the extended objective function is as follows: , in, To expand the objective function, The original cost function, For agent i The planning status of secondary replanning. For the corresponding control input, For entropy cost weights, Let be the entropy cost function.

[0013] Furthermore, the trend prediction based on the historical spatial entropy value sequence includes each agent maintaining a historical spatial entropy value sequence, performing linear regression based on the time step index and the corresponding spatial entropy value, calculating the slope of entropy value change, and predicting future spatial entropy values ​​based on the slope of entropy value change. The workspace is discretized into a spatial grid. Based on the planned trajectory of each agent, the spatiotemporal local entropy of each grid cell at different times is calculated. A spatiotemporal local entropy distribution map is constructed by combining Gaussian weights. The entropy increase cost of candidate trajectories is evaluated using the spatiotemporal local entropy distribution map. Based on the future spatial entropy value and the cost of entropy increase, the motion trajectory of this intelligent agent is actively scheduled. The formula for calculating the future spatial entropy value is as follows: , in, The predicted future spatial entropy value, This represents the latest spatial entropy value in the historical sequence. The slope of the entropy change. To predict the time step, To plan the time step.

[0014] Furthermore, the active scheduling of the motion trajectory of the intelligent agent includes judging the high-entropy state of the intelligent agent based on the predicted spatial entropy value and the entropy increase cost of the candidate trajectory; When the predicted spatial entropy value exceeds the preset entropy value threshold, or the entropy increase cost of the candidate trajectory exceeds the preset entropy increase cost threshold, the suggested waiting time corresponding to the moment when the local entropy of the target area is at its lowest is determined based on the temporal evolution of the spatiotemporal local entropy distribution map. When the suggested waiting time is greater than zero and less than or equal to the preset maximum waiting time, control this intelligent agent to enter the waiting mode; When the suggested waiting time exceeds the preset maximum waiting time, the agent is triggered to replan its trajectory to find an alternative path. The formula for calculating the suggested waiting time is as follows: , in, Suggested waiting time To preset the maximum waiting time, This is the horizontal index of the target region in the grid coordinate system. This is the vertical index of the target region in the grid coordinate system. Grid index for target area The local entropy value at time t.

[0015] In summary, the present invention has the following beneficial technical effects: 1. This invention constructs an information entropy situation assessment framework based on spatial entropy, temporal entropy, and communication entropy, which enables multi-dimensional quantitative characterization of the spatial constraint distribution, motion state changes, and communication pattern patterns of multi-agent systems, thus solving the technical problem of the lack of quantitative perception capability of situation complexity in existing technologies.

[0016] 2. This invention achieves adaptive convergence of entropy calculation threshold to the actual motion and communication characteristics of heterogeneous dynamic models through dynamic matching of entropy threshold and adaptive weight calculation mechanism. It solves the technical problems of tight coupling between situation assessment parameters and specific dynamic models and large workload of parameter debugging when deploying heterogeneous clusters in the prior art.

[0017] 3. This invention achieves dynamic optimization of the feasible trajectory space while preserving the geometric lower bound for collision avoidance by constructing an entropy cost function, switching planning strategies guided by local spatial entropy indices, and dynamically adjusting the half-space boundary driven by entropy factors. This solves the technical problems of conservative trajectories and low overall cluster passage efficiency caused by static safety margins in existing technologies.

[0018] 4. This invention achieves the early identification and avoidance of high-entropy regions and congestion bottlenecks by predicting the trend of historical spatial entropy value sequences and guiding the active scheduling strategy of spatiotemporal local entropy. It solves the technical problems of existing reactive decision-making mechanisms that cannot predict situation evolution, are prone to getting trapped in local optima and deadlock. Attached Figure Description

[0019] Figure 1 This is an overall schematic diagram of a distributed multi-agent motion trajectory optimization method based on entropy constraints according to an embodiment of the present invention.

[0020] Figure 2 This is a schematic diagram of the asynchronous planning loop of the distributed multi-agent motion trajectory optimization method under entropy constraints according to an embodiment of the present invention.

[0021] Figure 3 This is a schematic diagram of the circular opposing positions of eight heterogeneous intelligent agents according to an embodiment of the present invention; wherein, Figure 3 (a) is the accessibility version diagram. Figure 3 (b) Version with obstacles.

[0022] Figure 4 This is a schematic diagram of multiple intersection multi-agent trajectories according to embodiments of the present invention; wherein, Figure 4 (a) is a schematic diagram of the experimental trajectories of 13 Ackerman vehicles at a T-junction. Figure 4 (b) is a schematic diagram of the experimental trajectories of 12 Ackerman vehicles at an intersection. Figure 4(c) is a schematic diagram of the experimental trajectory of 10 vehicles on the roundabout section.

[0023] Figure 5 These are schematic diagrams illustrating unidirectional and bidirectional switching of the integrator according to embodiments of the present invention; wherein, Figure 5 Figure (a) is a schematic diagram of a one-way lane change. Figure 5 Figure (b) is a schematic diagram of two-way lane changing.

[0024] Figure 6 This is a schematic diagram of the circular exchange position of the 8 integrators according to an embodiment of the present invention. Detailed Implementation

[0025] The present invention will be further described in detail below with reference to the accompanying drawings.

[0026] Example 1 Reference Figure 1 This embodiment of a distributed multi-agent motion trajectory optimization method based on entropy constraints includes: Each agent obtains the trajectory information of its neighboring agents based on local communication, determines the set of half-space constraints it is subject to, and extracts its historical velocity sequence and historical communication interval sequence with each neighboring agent. Calculate spatial entropy, temporal entropy, and communication entropy based on the half-space constraint set, historical velocity sequence, and historical communication interval sequence, respectively. The entropy threshold vector is dynamically matched using historical velocity sequences and historical communication interval sequences, and adaptive weights are calculated based on the number of neighbors and the target distance. An entropy cost function is constructed based on spatial entropy, temporal entropy, and adaptive weights, and planning strategy switching is performed in conjunction with local spatial entropy indicators. Define an entropy factor and dynamically adjust the half-space boundary at the bottleneck moment to construct the adjusted spatiotemporal allocation constraint; Trend prediction is performed based on historical spatial entropy value sequences. The entropy increase cost of candidate trajectories is evaluated by combining spatiotemporal local entropy. An objective function consisting of the original cost, entropy cost, and entropy increase cost is constructed, and the optimized motion trajectory of the agent is output.

[0027] Specifically, a distributed multi-agent motion trajectory optimization method based on entropy constraints includes the following: like Figure 1 , Figure 2 As shown, S1, each agent obtains the trajectory information of its neighboring agents based on local communication, determines the set of half-space constraints it is subject to, and extracts its historical velocity sequence and historical communication interval sequence with each neighboring agent. In a distributed asynchronous execution architecture, each agent runs its planning loop independently, without the need for a global clock or a central node, coordinating solely through local neighbor communication. Each agent receives its set of neighbors via local communication. The trajectory information broadcast by each neighboring agent includes the predicted state sequence and control input sequence of the neighboring agents in the current planning time domain. Based on the separating hyperplane theorem, each agent calculates the feasible spatiotemporal region between itself and each neighboring agent, and determines the set of half-space constraints imposed on itself.

[0028] Specifically, for agent i at time... Half-space constraints from neighboring agent j , by normal vector and offset Define, satisfy ,in Let be the position vector and normal vector in two-dimensional space. The offset points to the feasible region of agent i. The sum of the geometric radii of the two agents is already included as the basic safety distance, forming a lower bound guarantee for collision avoidance. The set of half-space constraints imposed on agent i is denoted as... , where K is the total number of half-space constraints.

[0029] Meanwhile, each agent independently maintains a historical speed buffer. A sliding window mechanism is used to store the velocity sample values ​​of this agent in each replanning cycle. The historical velocity sequence is the set of velocity sample values ​​in this buffer, and the buffer data size is denoted as . Each agent independently maintains a historical communication interval buffer for each pair (i,j). Record the time interval between two adjacent allocation updates between agent i and neighbor agent j. When agent i completes a trajectory information exchange with neighbor agent j and updates the spatiotemporal allocation... Then, calculate the current time and the last updated time. Time difference The time difference is stored in a buffer, and the historical communication interval sequence is the set of time intervals in the buffer. The maximum length of the buffer is denoted as . The amount of data is denoted as In addition, each agent independently maintains a buffer of historical spatial entropy values. It is used to store the spatial entropy calculation values ​​of the most recent W planning periods, providing a data foundation for subsequent trend prediction.

[0030] In the above parameters, N represents the total number of agents, and i,j represents the agent index. W is the historical communication interval buffer, and W is the window length of the historical entropy value sequence. It is the normal vector of the half-space. This is the half-space offset. For a moment A two-and-a-half-dimensional space.

[0031] S2. Subsequently, based on the half-space constraint set, historical velocity sequence, and historical communication interval sequence, spatial entropy, temporal entropy, and communication entropy are calculated respectively. Regarding the spatial entropy calculation, the two-dimensional workspace is divided into... A uniformly oriented sector, corresponding to an angle range For each half-space normal vector in a given set of half-space constraints The pointing information, since the normal vector points inside the feasible region of agent i, the source direction of the neighbor constraint is... Statistics for each sector Number of half-space constraints within Calculate the probability distribution of each sector. ,in The total number of half-space constraints is used to calculate the spatial entropy based on Shannon's definition of information entropy. and its theoretical maximum value : , in, s represents the number of sectors in the direction, where s is the sector index in the direction. Let be the probability of the s-th sector.

[0032] In terms of time entropy calculation, the velocity sequence is extracted from the historical velocity buffer of agent i. Using the velocity threshold vector Discretize the continuous velocity value as There are several states. Define the velocity classification function. Map each velocity value to its corresponding discrete state. Count the frequency of each state and calculate the probability distribution. ,in The historical velocity buffer data volume is used to calculate the time entropy based on Shannon's definition of information entropy. and its theoretical maximum value : , in, For the first The frequency of each velocity state The total number of discrete states.

[0033] In terms of communication entropy calculation, for the historical communication interval sequence of agent pair (i,j), based on the allocation update sequence... Corresponding update time Calculate the time interval between adjacent updates m=1,2,…,M 1. Utilizing the communication interval boundary vector Discretize the communication interval as Define a communication interval classification function for each interval. Map each time interval to its corresponding discrete interval. Count the frequency of occurrence in each interval and calculate the probability distribution. Then, based on Shannon's definition of information entropy, the communication entropy is calculated. and its theoretical maximum value : , in, Assign an update time interval between the m-th and m+1-th updates. This represents the total number of communication updates. For the first The frequency of each communication interval, This represents the number of discrete intervals for the communication interval.

[0034] The above spatial entropy Time entropy and communication entropy Spatial entropy quantitatively characterizes the complexity of the local situation of an intelligent agent from three dimensions: space, time, and communication. It exhibits monotonicity, meaning that as the number of constraints increases and their distribution becomes more dispersed... Monotonically increasing when all constraints are concentrated in a single direction Take the minimum value when constraints exist in all directions and the number is equal. Take the maximum value. Time entropy. Communication entropy reflects the degree of drastic change in motion state. Characterizing the regularity of cooperation patterns among intelligent agents, the more regular the communication intervals, the more stable the neighbor negotiation.

[0035] S3. Regarding dynamic matching of entropy thresholds, since the calculation of spatial entropy, temporal entropy, and communication entropy all depend on threshold vectors, and the thresholds vary significantly under different dynamic models and task scenarios, traditional fixed threshold methods require manual parameter tuning for different models. Simply unifying the threshold will lead to entropy value distortion. Therefore, each agent dynamically matches the entropy calculation threshold based on historical data. Specifically, each agent maintains a historical velocity buffer. When the amount of data in the buffer meets The percentile statistical method is used to extract the velocity threshold vector from the historical velocity sequence. ,Right now: , in, The velocity threshold vector, used to discretize the time entropy, is a function that returns the q-th percentile of the dataset. These are the first, second, and third thresholds for speed discretization, when the amount of data in the buffer does not reach the minimum sample size. At that time, a preset default velocity threshold vector is used. The default value is set based on the typical speed range of common ground robots. As data accumulates, the above percentile statistical method automatically overrides the default value and converges to the actual speed distribution.

[0036] Similarly, each agent maintains a buffer for historical communication intervals. When the amount of data in the buffer meets At that time, the communication interval boundary vector was extracted from the historical communication interval sequence using the quartile statistical method. This will be fixed and will not be updated further. These are the first, second, and third interval boundary values ​​for the discretization of the communication interval, respectively. These communication interval boundary vectors are used for the discretization calculation of the communication entropy in step two. If an error occurs... Communication intervals within a certain range are automatically categorized into boundary intervals. During the learning phase, the quartiles of the current data are temporarily used as bins. Once the discrete interval boundaries of the communication intervals are fixed, subsequent entropy calculations remain stable, preventing drastic changes in entropy caused by small fluctuations in bins.

[0037] In terms of adaptive weight calculation, to dynamically adjust the importance of the entropy index according to the scenario, adaptive spatial entropy weights and adaptive temporal entropy weights are calculated based on the number of neighbors and the distance to the target, respectively. Specifically, the adaptive spatial entropy weights... Based on the number of neighbors The calculation involves increasing the spatial entropy weight as the number of neighbors increases to cope with more complex spatial constraints; and adaptive temporal entropy weighting. Based on the distance from the agent to the target Segmented calculation allows the agent to focus more on velocity stability as it approaches the target, avoiding trajectory oscillations near the endpoint. The calculation formula is as follows: , , in, For adaptive spatial entropy weights, As the basic weight of spatial entropy, This is the spatial entropy weight scaling factor. For the number of neighbors, For adaptive time entropy weights, This is the time entropy weight scaling factor. As the basic weight of time entropy, The distance from the agent to the target. The target distance threshold, Minimum sample size for the speed buffer. Minimum sample size for the communication buffer. For the velocity threshold vector, This is the default velocity threshold vector. The communication interval is discretized into interval boundary vectors.

[0038] S4. Regarding the construction of the entropy cost function, in order to facilitate the weighted combination of entropy values ​​under different scenarios, the spatial entropy is first calculated. and time entropy Normalization is performed. The normalized spatial entropy is obtained by dividing the spatial entropy by its theoretical maximum value. The normalized time entropy is obtained by dividing the time entropy by its theoretical maximum value. Normalized entropy value This facilitates subsequent weighted combination. Furthermore, the calculated adaptive spatial entropy weights are then used... With normalized spatial entropy Multiplication, with adaptive time entropy weights With normalized time entropy Multiply them, sum them, and construct the entropy cost function: , The higher the entropy value, the more complex the situation, and the higher the entropy cost the planner should pay.

[0039] Regarding strategy switching, to assess the degree of constraint on the feasible region of the local space in which the agent resides, the minimum distance from the agent to the boundary of each half-space is calculated, and the local space entropy index is calculated based on this minimum value and the numerical stability term. Specifically, for agent i at time... Half-space constraints Calculate the distance from this agent to the k-th half-space boundary: , in, For agent i at time... Location, This reflects the available space at that moment, and then the local spatial entropy index is calculated: , in It is the minimum value among all half-space boundary distances. For numerically stable terms, The larger the value, the closer the agent is to the boundary of the half-space, the higher the local spatial entropy, and the more severely the feasible region is restricted. Let entropy cost function, For adaptive spatial entropy weights, For adaptive time entropy weights, To normalize the spatial entropy, To normalize the time entropy, Let be the distance from this agent to the boundary of the k-th half-space. It is a local spatial entropy index.

[0040] Based on the calculated spatial entropy And the aforementioned local spatial entropy index The degree of constraint on the feasible region of the local space in which the agent resides is assessed. Based on this degree of constraint, the weight matrices Q and P of the optimal control problem, as well as the entropy cost weights, are adjusted. This enables the formulation of corresponding trajectory planning strategies within different cost ranges. Specifically, strategy switching is achieved by adjusting the OCP weight matrix and entropy cost weight, so that the agent adopts a conservative strategy in high-entropy regions and an efficient strategy in low-entropy regions, thereby proactively adjusting the planning behavior according to the current situation complexity.

[0041] S5. Regarding bottleneck identification and entropy factor calculation, firstly, the distance from the agent to the boundary of each half-space is calculated. For agent i at time... Half-space constraints Calculate the distance from the current agent to the boundary of the k-th half-space. ,in, It is the normal vector of the half-space. For agent i at time... Location, This is the original half-space offset. Set the bottleneck identification distance threshold. ,when When this moment is marked as the bottleneck moment, it indicates that the half-space constraint is significantly compressing the feasible space of this agent, and then based on the normalized spatial entropy obtained in step four... With normalized time entropy Calculate the entropy factor This entropy factor comprehensively reflects the spatial complexity of the current situation and the degree of drastic change in motion state.

[0042] Regarding boundary adjustment calculation and dynamic adjustment triggering, the half-space boundary distance at the bottleneck moment is used as the basis. With entropy factor Calculate boundary adjustment amount: , in, Let be the boundary adjustment amount for the k-th half-space. These are boundary adjustment coefficients based on physical constraints. The boundary adjustment coefficient is based on the entropy value. For numerically stable terms, As an entropy factor, this boundary adjustment consists of two parts: the first term Based on physical constraints, the smaller the space, the greater the expansion; the second term Based on entropy, the higher the entropy, the more it expands.

[0043] When the preset boundary adjustment trigger condition is met, i.e., the normal vector of the half-space constraint is... The direction of the agent toward the target is highly consistent with that of the agent, and the local spatial entropy is... At that time, among them The preset entropy threshold is used to trigger boundary adjustment and entropy trend prediction replanning, based on the aforementioned boundary adjustment amount and the original half-space offset. Make corrections to obtain the adjusted half-space offset. This adjusts the half-space to be slightly larger than the original half-space, allowing the agent to select trajectory points closer to its neighbors in that direction, thus traversing the bottleneck region via a more direct path. To ensure continuous smoothness near the bottleneck, the boundary adjustment is uniformly applied to five time steps, including the bottleneck moment and two time steps before and after it. This adjustment is made possible by the offset of the original half-space. The sum of the geometric radii of the two agents is already included as the basic safety distance, constituting a lower bound guarantee for collision avoidance, and The design has an upper bound, and the adjusted constraints still retain the basic geometric separation distance provided by the separating hyperplane, so that the collision avoidance property is not destroyed.

[0044] The above adjustments Triggered when a preset boundary adjustment trigger condition is met, wherein the boundary adjustment trigger condition is: (i) constraint normal vector (i) The direction of the agent toward the target is highly consistent, meaning this constraint is hindering a direct path toward the target; (ii) The local spatial entropy satisfies This means that the surrounding constraints are concentrated, but there is still usable space in other directions.

[0045] Regarding the construction of the adjusted spatiotemporal allocation constraints, based on the adjusted half-space offset... Constructing a half-space with adjusted boundaries The adjusted half-space with the corresponding time information is combined to form the adjusted spatiotemporal allocation constraint. This ensures that the planned trajectory of the intelligent agent is included within the adjusted spatiotemporal allocation.

[0046] Regarding the construction of the extended objective function and adaptive weight adjustment, in order to introduce entropy cost into trajectory optimization, an extended objective function containing both the original cost and entropy cost is constructed: , in, To expand the objective function, The original cost function, For agent i The planning status of secondary replanning. For the corresponding control input, For entropy cost weights, The entropy cost function is used to proactively adjust the impact of entropy cost based on scene density. The entropy cost weight is adaptively calculated based on the number of neighbors and the normalization factor for the number of neighbors. , in, Based on weights, For the number of neighbors, The neighbor number normalization factor ensures that the impact of entropy cost is more significant in high-density scenarios, while satisfying the adjusted spatiotemporal allocation constraints. Under the premise that, among them, For agent i The trajectory of secondary replanning. For the spatiotemporal allocation after boundary adjustment, the optimal plan under the current situation is determined based on the extended objective function. The trajectory in the high-entropy region is penalized by the entropy cost term to guide the agent to avoid the high-entropy situation. At the same time, the boundary adjustment provides greater margin at the bottleneck moment, reduces the collision risk and improves the trajectory smoothness. However, so far, these decisions are based only on the entropy value at the current moment and cannot predict the trend of situation evolution.

[0047] S6. Based on the historical spatial entropy value sequence, perform trend prediction, combine spatiotemporal local entropy to evaluate the entropy increase cost of candidate trajectories, construct an objective function composed of the original cost, entropy cost and entropy increase cost, and output the optimized motion trajectory of the agent.

[0048] In terms of entropy trend prediction, each agent maintains a historical spatial entropy value sequence. Where W is the preset window length. Given the latest value, a linear regression is performed on this sequence to predict the future evolution trend of entropy. A time step index is defined. Calculate the average value of time steps and the mean of entropy Then, the regression slope is calculated: , in, The slope of the linear regression of spatial entropy reflects the rate of change of the entropy value. This indicates that the entropy value is increasing and the situation is deteriorating. Conversely, according to The size of the value can be used to define trend judgment rules.

[0049] Based on this regression slope and the current spatial entropy value, predict the future. Spatial entropy value at time: , in, The predicted future spatial entropy value, This represents the latest spatial entropy value in the historical sequence. To predict the time step, To plan the time step, if If this happens, a replanning process will be triggered in advance, and a strategy of waiting or fast passage will be adopted.

[0050] As the number of constraints on the agent continues to increase, the spatial entropy... The spatial entropy exhibits a monotonically increasing trend, and its rate of change can be expressed as: When the number of constraints increases and the distribution becomes more uniform, i.e., the probability distribution... As the system moves from concentration to uniformity, the entropy increases monotonically. Within a short time window... If the rate of increase of constraints is approximately constant, then the entropy value grows approximately linearly, and the slope of the linear regression is... It can effectively capture this trend.

[0051] In addition to entropy trend prediction, a spatiotemporal local entropy predictor is introduced to assess the future entropy increase of different paths. Regarding the construction of spatiotemporal local entropy and the assessment of entropy increase costs, the spatiotemporal local entropy predictor discretizes the workspace into a spatial grid based on the planning trajectories of all agents. Based on the planning trajectories of each agent, it calculates the spatiotemporal local entropy of each grid cell at different times, constructing a spatiotemporal local entropy distribution map. For each grid cell… and time slices The number of times the trajectory is occupied by the agent is counted, and Gaussian weights are applied for smoothing to calculate the spatiotemporal local entropy. , Among them, the outer layer is a set of neighbors. Summing all agents in the inner layer Iterate through all time steps of the trajectory planned by agent i. , , These are the trajectory points of agent i. Spatial and temporal distance to the center of the grid , , The mapping functions from position and time to grid indices are defined as follows, and the Gaussian weights are defined as: , in, The standard deviation is Gaussian weighted. This spatiotemporal local entropy distribution map constructs a global view of the entropy increase trend. A higher value indicates a greater likelihood that the spatiotemporal region is simultaneously occupied by multiple agents, and a more significant increase in local entropy. Based on this distribution map, the agents are calculated. i The entropy cost of candidate trajectories. For a trajectory traverse all its trajectory points Query the local entropy of the corresponding grid Calculate the entropy increase cost based on the preset segmentation penalty rules: , in, As a price for increased entropy, The local entropy value of the grid corresponding to the k-th trajectory point is used. Low-entropy regions are not penalized; medium-entropy regions are linearly penalized; and high-entropy regions are non-linearly penalized. Entry into severely entropy-increasing regions is strongly avoided. Thresholds of 2.0 and 3.0 are determined by the local entropy value. Typical distribution quantile settings.

[0052] Regarding proactive scheduling strategies, based on predicted spatial entropy values... The cost of entropy increase with candidate trajectories The high-entropy state of this agent is assessed. When... Exceeding the preset entropy threshold ,or When the preset entropy increase cost threshold is exceeded, the suggested waiting time corresponding to the moment of minimum local entropy in the target region is determined based on the time evolution of the spatiotemporal local entropy distribution map: , in, Suggested waiting time To preset the maximum waiting time, This is the horizontal index of the target region in the grid coordinate system. This is the vertical index of the target region in the grid coordinate system. Grid index for target area The local entropy value at time t. This formula seeks the moment when the local entropy of the target region is minimized, allowing the agent to achieve the minimum local entropy. Once activated, it can pass through the target area during periods of low entropy.

[0053] Suppose that the local entropy of the target region fluctuates periodically with time, i.e., there exists a time... Make ,in The current moment is [time]. When the agent starts immediately, the time it takes to reach the target area is [time]. ,in The distance to the target. This is the average speed. If... High entropy levels will cause severe entropy increases for the agent. (This refers to computational latency.) This makes the new arrival time The corresponding local entropy is lowest. Because... exist When the time reaches its minimum value, the agent can pass through during low-entropy periods, thereby reducing the overall travel time.

[0054] When the suggested waiting time is met When, control this intelligent agent to enter waiting mode; when When this occurs, it indicates that the target area remains in a high-entropy state for an acceptable period of time, triggering the agent's trajectory replanning to find a detour path.

[0055] In terms of constructing the overall objective function and solving for optimal control, an overall objective function is constructed that includes the initial cost, entropy cost, and entropy increase cost: , in, Let be the overall objective function. The original cost function, For agent i The planning status of secondary replanning. For the corresponding control input, Let entropy cost function, As a price for increased entropy, For entropy cost weights, This represents the entropy increase cost weight. It applies to the adjusted spatiotemporal allocation constraints after construction. Under the premise of [condition], solve the optimal control problem so that the agent not only minimizes the original cost to the target, but also actively avoids the current high-entropy region and the future high-entropy-increasing region, and outputs the optimized motion trajectory of the agent.

[0056] Example 2 The difference between this embodiment and Embodiment 1 is that this embodiment provides a simulation experiment of a distributed multi-agent motion trajectory optimization method based on entropy constraints; In this embodiment, the OCP discretization problem is solved using Acadsoc, and the inter-agent communication mechanism is implemented based on RobotOperatingSystem. Distributed deployment is simulated through multi-process concurrent execution. The sampling time for each agent is uniformly set to... The planning time domain length is set to .

[0057] Experiment 1: Circular Exchange Scenario with 8 Heterogeneous Agents. Eight heterogeneous agents were deployed, each with a diameter of 0.4m and a maximum speed between 0.6m / s and 1.0m / s, encompassing three types of dynamic structures: bicycle, dual integrator, and unicycle. Agents were initialized on a circle with a diameter of 4.0m, each targeting the opposite side. The solution window and communication window lengths within each agent's asynchronous planning cycle were differentiated based on their dynamic characteristics. A total of 575 replanning operations were triggered during the experiment, with a maximum single solution time of 23.82ms and an average replanning runtime of 7.21ms. All agents reached their targets without collision, and the minimum agent spacing was consistently maintained at a safe distance of over 0.4m. The trajectory lengths of each agent were concentrated between 8.06m and 8.42m, with a standard deviation of 0.16m. The path efficiency remained balanced across different dynamic models, verifying the adaptability of the entropy threshold matching mechanism to heterogeneous clusters without manual parameter tuning.

[0058] Based on the same initial configuration, multiple static obstacles are introduced around the center of the circle. By combining the obstacle avoidance scheme with the entropy constraint mechanism, the agent dynamically adjusts the half-space boundary to bypass the obstacles while maintaining safety. The introduction of obstacles does not compromise the convergence and safety of the system.

[0059] Table 1 shows the agent parameters and simulation results for a circular exchange scenario involving heterogeneous agents. in, , Intelligent agent The lengths of the solution window and communication window within the asynchronous planning cycle; Replanning runtime, minimum / maximum, in milliseconds; : Trajectory length; : Movement time. The discrete-time step of OCP for all agents. s, planning time-domain steps The total number of weight planning iterations was 575. The dynamic models covered three categories: bicycle models (numbers 1 and 5), double integrator models (numbers 2, 4, and 6), and unicycle models (numbers 3, 7, and 8).

[0060] like Figure 3 As shown, the image is a combination of "screenshot of an experiment involving 8 heterogeneous intelligent agents exchanging positions in a circular array" and "screenshot of an experiment involving 8 heterogeneous intelligent agents exchanging positions in a circular array containing multiple obstacles". Figure 3 (a) is the accessible version. Figure 3 (b) is the version with obstacles.

[0061] Five additional simulation experiments were then conducted to further verify the proposed method's ability to perceive and respond to situational complexity under different environmental structures. No collisions occurred in any of the experiments. Figure 4 The simulation results for three types of road network traffic scenarios are shown. In the T-junction scenario, 13 Ackerman model vehicles merge from three directions and coordinate their passage through the intersection. In the crossroads scenario, 12 Ackerman model vehicles complete the passage of four-way converging traffic. In the roundabout scenario, 10 Ackerman model vehicles complete the entire process of merging, bypassing, and exiting. In these three scenarios, the local high-density situation formed by multi-directional traffic flow in the intersection is precisely the congestion bottleneck problem addressed in this paper. Entropy-guided boundary adjustment enables the agent to predict the trend of situation deterioration and proactively adjust its planning strategy before entering the intersection, achieving orderly passage without centralized scheduling. This directly corresponds to the congestion bottleneck identification and avoidance mechanism described in the second contribution of this paper.

[0062] Figure 4 The images are a combination of screenshots from experiments involving 13 Ackermann vehicles at a T-junction, 12 Ackermann vehicles at a crossroads, and 10 vehicles at a roundabout, arranged from left to right. like Figure 5 As shown, Figure 5 Simulation results for lane-changing scenarios are presented. In a unidirectional lane-changing scenario, eight dual-integrator model agents start from the same side and complete lateral position exchanges. In a bidirectional lane-changing scenario, the scale expands to 16 dual-integrator agents, with the left and right groups pairing targets in a cyclic offset manner, and the trajectories forming a complex interactive structure with double-beam intersections in the middle. In the bidirectional scenario, opposing flows coexist and the number of agents doubles, significantly increasing the intensity of local spatial competition. When multiple agents converge on the same area, the entropy constraint evaluation framework, by quantifying local spatial entropy and communication mode uncertainty in real time, enables each agent to quantitatively assess the quality of the current half-space allocation and predict the future evolution of constraints, proactively adopting conservative strategies or adjusting the start sequence to avoid getting caught in a congested situation, which is consistent with the description of the quantitative assessment function of half-space quality in the first contribution.

[0063] Subsequently, the proposed method was quantitatively compared with five existing methods, such as... Figure 6 As shown, the dynamic model uniformly adopted a dual integrator, with the maximum velocity and acceleration set to 1.0 m / s² and 1.5 m / s², respectively. The planning time domain was uniformly set to 2.3 s. Eight agents completed the opposite position exchange on a circle with a diameter of 4.0 m. The experimental configuration and comparison method were completely consistent. The comparison results are summarized in Table 2.

[0064] Table 2 compares the performance of multiple methods in a circular exchange scenario using an 8-integrator. In synchronous planning methods, the replanning runtimes of IMPC-DR and DMPC are as high as 95 / 130ms and 51 / 90ms respectively, which are dozens of times longer than the minimum solution time of 4ms in this embodiment, reflecting the high computational cost of synchronous concurrent solution in multi-agent scenarios. Although LSC has a relatively low solution time, its movement time and trajectory length are the worst among synchronous methods. In asynchronous planning methods, MADER is affected by its conservative check-recheck mechanism, resulting in significantly higher movement time and trajectory length. This reflects the inherent limitation of planners tending to be conservative in high-density scenarios when quantitative situational awareness is lacking, which is the core problem addressed in this paper. Although the sequential planning method Ego-swarm has a low single-run solution time, its serial execution mechanism leads to a significantly higher overall movement time. In comparison, our method's movement time is 7.0–9.3 s, with both the minimum and maximum values ​​being optimal across the entire table. The maximum movement time of 9.3 s is also better than the ASTA method's 9.6 s. The trajectory length is 8.06–8.30 m, the shortest across the entire table, with a total of 501 replanning attempts. The minimum solution time of 4 ms is on par with Ego-swarm, which has the lowest computational cost, and significantly better than the synchronous methods IMPC-DR and DMPC. The maximum solution time of 23 ms is slightly higher than some methods, mainly due to the additional computations triggered by entropy prediction and boundary adjustment when the situation deteriorates, but it is still far lower than the planning cycle of 150 ms and does not affect real-time performance. These results demonstrate that the entropy trend prediction mechanism effectively avoids the agent falling into an inefficient passive waiting state by triggering trajectory re-optimization in advance before the situation deteriorates. It achieves optimal performance across the entire table in terms of movement time and trajectory quality, and is on par with the fastest method in terms of computational efficiency. This verifies the comprehensive improvement effect of the entropy constraint evaluation framework on traffic efficiency and planning quality.

[0065] The above are all preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Therefore, all equivalent changes made in accordance with the structure, shape and principle of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A distributed multi-agent motion trajectory optimization method based on entropy constraints, characterized in that, include: Each agent obtains the trajectory information of its neighboring agents based on local communication, determines the set of half-space constraints it is subject to, and extracts its historical velocity sequence and historical communication interval sequence with each neighboring agent. Calculate spatial entropy, temporal entropy, and communication entropy based on the half-space constraint set, historical velocity sequence, and historical communication interval sequence, respectively. The calculation of spatial entropy, temporal entropy, and communication entropy includes: Based on the direction information of the normal vectors of each half-space in the half-space constraint set, the two-dimensional workspace is divided into several uniformly oriented sectors. The number of half-space constraints in each sector is counted, the probability distribution of each sector is calculated, and the spatial entropy and its maximum value are calculated according to the Shannon information entropy definition. Based on historical velocity sequences, velocity values ​​are discretized into several velocity states using velocity threshold vectors. The frequency of each velocity state is counted and the probability distribution is calculated. The time entropy and its maximum value are calculated according to the Shannon information entropy definition. Based on the historical communication interval sequence, the communication interval is discretized into several communication intervals using the communication interval boundary vector. The frequency of each communication interval is counted and the probability distribution is calculated. The communication entropy and its maximum value are obtained according to the Shannon information entropy definition. The entropy threshold vector is dynamically matched using historical velocity sequences and historical communication interval sequences, and adaptive weights are calculated based on the number of neighbors and the target distance. The calculation of the adaptive weights includes calculating adaptive spatial entropy weights and adaptive temporal entropy weights based on the number of neighbors and the distance to the target, respectively. The calculation formulas for the adaptive spatial entropy weights and adaptive temporal entropy weights are as follows: ； in, For adaptive spatial entropy weights, As the basic weight of spatial entropy, This is the spatial entropy weight scaling factor. For the number of neighbors, For adaptive time entropy weights, This is the time entropy weight scaling factor. As the basic weight of time entropy, The distance from the agent to the target. The target distance threshold; An entropy cost function is constructed based on spatial entropy, temporal entropy, and adaptive weights, and planning strategy switching is performed in conjunction with local spatial entropy indicators. The method of switching planning strategies by combining local spatial entropy index includes calculating the minimum distance from the agent to each half-space boundary, calculating the local spatial entropy index based on the minimum distance and the numerical stability term, evaluating the degree of constraint of the feasible region of the agent's local space based on the spatial entropy and the local spatial entropy index, and adjusting the weight matrix and entropy cost weight of the optimal control problem based on the degree of constraint of the feasible region to formulate corresponding trajectory planning strategies within different cost intervals. The expression of the local spatial entropy index is as follows: ， in, As a local spatial entropy index, Let be the distance from this agent to the boundary of the k-th half-space. For numerically stable terms, It is the minimum value among all half-space boundary distances; Define an entropy factor and dynamically adjust the half-space boundary at the bottleneck moment to construct the adjusted spatiotemporal allocation constraint; Trend prediction is performed based on historical spatial entropy value sequences. The entropy increase cost of candidate trajectories is evaluated by combining spatiotemporal local entropy. An objective function consisting of the original cost, entropy cost, and entropy increase cost is constructed, and the optimized motion trajectory of the agent is output.

2. The distributed multi-agent motion trajectory optimization method based on entropy constraints according to claim 1, characterized in that, The method of dynamically matching the entropy threshold vector using historical speed sequences and historical communication interval sequences includes historical speed sequences based on the historical speed buffer maintained by this agent, when... At that time, a velocity threshold vector is extracted from the historical velocity sequence using percentile statistics to be used for discretization calculation of time entropy. At that time, a preset default speed threshold vector is used; Based on the historical communication interval sequence in the historical communication interval buffer maintained by each neighboring agent, when the data volume of the historical communication interval buffer reaches the preset minimum sample size, the communication interval boundary vector is extracted from the historical communication interval sequence using the quartiles statistical method and fixed. When the communication interval exceeds the upper limit of the communication interval boundary vector, the communication interval is classified into the boundary interval. in, The amount of data in the historical speed buffer. This is the minimum sample size.

3. The distributed multi-agent motion trajectory optimization method based on entropy constraints according to claim 1, characterized in that, The construction of the entropy cost function based on spatial entropy, temporal entropy, and adaptive weights includes normalizing the spatial and temporal entropy, and then combining the normalized spatial and temporal entropy with adaptive spatial and temporal entropy weights to construct the entropy cost function. The expression for the entropy cost function is as follows: ， in, Let entropy cost function, For adaptive spatial entropy weights, For adaptive time entropy weights, To normalize the spatial entropy, This is the normalized time entropy.

4. The distributed multi-agent motion trajectory optimization method based on entropy constraints according to claim 1, characterized in that, The definition of the entropy factor and dynamic adjustment of the half-space boundary at the bottleneck moment includes calculating the distance from the agent to each half-space boundary. When the distance is less than a preset bottleneck identification distance threshold, the moment is marked as a bottleneck moment. The entropy factor is calculated using normalized spatial entropy and normalized temporal entropy. The boundary adjustment amount is calculated based on the half-space boundary distance at the bottleneck moment and the entropy factor. When a preset boundary adjustment trigger condition is met, the original half-space offset is corrected based on the boundary adjustment amount to obtain the adjusted half-space offset. The expression for the boundary adjustment amount is: ， in, Let be the boundary adjustment amount for the k-th half-space. These are boundary adjustment coefficients based on physical constraints. The boundary adjustment coefficient is based on the entropy value. It is the entropy factor.

5. The distributed multi-agent motion trajectory optimization method based on entropy constraints according to claim 4, characterized in that, The construction of the adjusted spatiotemporal allocation constraints includes constructing a boundary-adjusted half-space based on the adjusted half-space offset, and combining the boundary-adjusted half-space with the corresponding time information to form the adjusted spatiotemporal allocation constraints. An extended objective function is constructed, incorporating both the original cost and entropy cost. The entropy cost weight is adaptively adjusted based on the number of neighbors and a neighborhood normalization factor. Under the adjusted spatiotemporal allocation constraints, the optimal planning for the current situation is determined based on the extended objective function. The expression for the extended objective function is as follows: ， in, To expand the objective function, The original cost function, For agent i The planning status of secondary replanning. For the corresponding control input, For entropy cost weights, Let be the entropy cost function.

6. The distributed multi-agent motion trajectory optimization method based on entropy constraints according to claim 1, characterized in that, The trend prediction based on the historical spatial entropy value sequence includes each agent maintaining the historical spatial entropy value sequence, performing linear regression based on the time step index and the corresponding spatial entropy value, calculating the slope of entropy value change, and predicting future spatial entropy values ​​based on the slope of entropy value change. The workspace is discretized into a spatial grid. Based on the planned trajectory of each agent, the spatiotemporal local entropy of each grid cell at different times is calculated. A spatiotemporal local entropy distribution map is constructed by combining Gaussian weights. The entropy increase cost of candidate trajectories is evaluated using the spatiotemporal local entropy distribution map. Based on the future spatial entropy value and the cost of entropy increase, the motion trajectory of this intelligent agent is actively scheduled. The formula for calculating the future spatial entropy value is as follows: ， in, The predicted future spatial entropy value, This represents the latest spatial entropy value in the historical sequence. The slope of the entropy change. To predict the time step, To plan the time step.

7. The distributed multi-agent motion trajectory optimization method based on entropy constraints according to claim 6, characterized in that, The active scheduling of the motion trajectory of the intelligent agent includes judging the high-entropy state of the intelligent agent based on the predicted spatial entropy value and the entropy increase cost of the candidate trajectory. When the predicted spatial entropy value exceeds the preset entropy value threshold, or the entropy increase cost of the candidate trajectory exceeds the preset entropy increase cost threshold, the suggested waiting time corresponding to the moment when the local entropy of the target area is at its lowest is determined based on the temporal evolution of the spatiotemporal local entropy distribution map. When the suggested waiting time is greater than zero and less than or equal to the preset maximum waiting time, control this intelligent agent to enter the waiting mode; When the suggested waiting time exceeds the preset maximum waiting time, the agent is triggered to replan its trajectory to find an alternative path. The formula for calculating the suggested waiting time is as follows: ， in, Suggested waiting time To preset the maximum waiting time, This is the horizontal index of the target region in the grid coordinate system. This is the vertical index of the target region in the grid coordinate system. Grid index for target area The local entropy value at time t.

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