Distributed spatio-temporal joint trajectory planning method for agent cluster

Abstract

A distributed spatio-temporal joint trajectory planning method for an intelligent agent cluster relates to the technical field of robot autonomous control, and comprises the following steps: planning the moving trajectory of each intelligent agent; collision conflict information between any intelligent agent and other intelligent agents in the cluster is detected in sequence, and the collision conflict information is sent to the other intelligent agents through network broadcasting; any agent generates a conflict graph after receiving the collision conflict information; based on the conflict graph, an approximate minimum vertex coverage algorithm is adopted to solve the minimum subset of the agents needing to re-plan the trajectory; re-planning the moving trajectory of the agents in the minimum agent subset at the same time; repeating the steps of collision conflict information detection, conflict graph generation, minimum agent subset construction and moving trajectory re-planning until the number of detected conflict information is zero, and determining the final moving trajectory of each agent; the method is used for solving the problems that traditional space-time coupling processing is poor, expandability is poor, dependence on a front-end path is high, and multi-constraint processing is complex.

Description

Technical Field

[0001] The present invention relates to the field of robot autonomous control technology, and in particular to a distributed spatiotemporal joint trajectory planning method for an intelligent agent cluster. Background Art

[0002] Swarms of robotic agents hold core value in strategic emerging industries, such as the "low-altitude economy." These applications include logistics and manned flight in urban air transportation; rapid disaster area surveys, precise material delivery, and coordinated search and rescue in emergency response; crop monitoring and precision spraying in smart agriculture; and automated inspections of large-scale infrastructure, such as bridges, power grids, and wind farms. In these scenarios, large numbers of robotic agents must collaborate in crowded, uncertain spaces. Therefore, developing a robust, scalable trajectory planning method capable of handling complex and dynamic environments while ensuring swarm safety and collaborative efficiency is a key technical bottleneck in moving the low-altitude economy from a visionary concept to a commercial reality.

[0003] Currently, existing technologies in the field of multi-agent trajectory planning can be mainly divided into the following categories: (1) Two-stage planning framework (front-end path search + back-end trajectory optimization): This is the most mainstream method.

[0004] Front-end path search: First, a preliminary, geometrically collision-free path is found in a discrete or continuous representation of the environment using a graph search or sampling algorithm such as A* or RRT*. This stage usually assumes that the environment is static.

[0005] Back-end trajectory optimization: Using the waypoints generated by the front-end as guidance, numerical optimization methods (such as Fast-Planner and EGO-Planner) are used to generate a smooth, time-parameterized trajectory that satisfies dynamic constraints. This stage addresses obstacle avoidance, typically by constructing safe flight corridors (SFCs) or using gradient-based penalty functions (e.g., using an ESDF map to calculate obstacle distances and gradients).

[0006] Problem: This decoupled framework has inherent limitations. The front-end path relies heavily on static environment assumptions, which can quickly fail in dynamic environments. This makes it difficult for back-end optimization to make significant spatiotemporal adjustments. The results of back-end optimization are highly dependent on the quality of the front-end path. If the initial path is far from the optimal solution, it will be difficult to find the global optimal trajectory.

[0007] (2) Centralized planning: Implementation method: Aggregate the status and target information of all intelligent agents to the central processor, build a joint state space, and then perform global unified planning. In theory, the global optimal solution can be found.

[0008] Problems: Computational complexity increases exponentially with the number of agents, resulting in the "curse of dimensionality" problem and making it unsuitable for large-scale clusters. Furthermore, the central node presents a high risk of "single point failure" and poor robustness.

[0009] (3) Decentralized sequential planning: Implementation: Agents are assigned a fixed priority order and each agent's trajectory is planned in turn. When planning for the current agent, the planned trajectories of all higher-priority agents are treated as dynamic obstacles to avoid. For example, EGO-Swarm employs chain planning at system startup.

[0010] Problems: The total planning time increases linearly with the number of agents, resulting in poor scalability. The quality of the planning results is heavily dependent on the preset priority order, making it difficult to ensure global optimality. Low-priority agents are prone to being "stuck" and unable to find a path.

[0011] (4) Local reactive obstacle avoidance based on speed obstacle method: Implementation: Each agent chooses a safe driving speed by calculating the speed obstacle space (i.e., the set of speeds that would lead to future collisions). This is a distributed local obstacle avoidance method.

[0012] Problems: This approach is inherently reactive and lacks long-term planning, which can easily lead to path oscillation or local optimality (deadlock). The resulting trajectories are often non-smooth and conservative, sacrificing efficiency.

[0013] Therefore, we propose a trajectory planning method that is suitable for large-scale clusters, can handle complex dynamic scenes, and simplifies calculations. Summary of the Invention

[0014] The purpose of the present invention is to provide a distributed spatiotemporal joint trajectory planning method for a cluster of intelligent agents, which is used to solve the problems of poor spatiotemporal coupling processing, poor scalability, strong dependence on front-end paths, and complex multi-constraint processing in traditional methods.

[0015] The present invention is achieved through the following technical solutions: A distributed spatiotemporal joint trajectory planning method for a cluster of intelligent agents, specifically comprising: Plan the trajectory of each agent in the agent cluster; Based on the running trajectory of each agent, the collision information between any agent in the cluster and other agents is detected in turn, and the collision information is sent to other agents through network broadcast; After any agent receives collision information, it generates an independent and decentralized conflict graph; Based on the conflict graph, an approximate minimum vertex cover algorithm is used to find the minimum subset of agents that need to replan their trajectories. Simultaneously replan the trajectory of the agents in the minimum agent subset; Repeat the steps of collision information detection, conflict graph generation, minimum agent subset construction, and trajectory replanning until the number of detected conflict information is zero, and determine the final trajectory of each agent.

[0016] Furthermore, the specific steps of planning the running trajectory of each agent in the agent cluster are as follows: Set the agent's starting state and target state ; Define multiple spatiotemporal control points, and the spatiotemporal control points include Intermediate space control points, ,in ,as well as Duration of time period , the duration of any time period ; Using standard spline fitting operators , according to the initial state of the agent , target state , and space-time control points , generate the initial trajectory ; Based on spatiotemporal control points and the initial trajectory Constructing a unified cost function ; By optimizing the engine Minimize the unified cost function to obtain the optimal solution ; According to the initial state of the agent , target state , and the optimal solution , generate running trajectory .

[0017] Furthermore, if the trajectory time needs to be precisely controlled, the initial trajectory is generated When the time allocation ratio vector

[0018] Replacement Segment Duration ; When minimizing the uniform cost function, the actual duration of each segment is calculated as:

[0019] Where, is the total time of the desired trajectory.

[0020] Furthermore, the unified cost function is:

[0021] Where, As the main optimization goal, To unify the collision avoidance cost, is the dynamic constraint cost, is the time constraint cost, is the cost of reaching the target point, 、 、 、 and are the weights of the corresponding costs respectively.

[0022] Furthermore, the main optimization goal , if the time is minimized , the calculation formula is:

[0023] If the energy consumption of the trajectory is minimized , the calculation formula is: .

[0024] Furthermore, the unified collision avoidance cost The calculation formula is:

[0025] Where, is the indicator function, For the obstacle at time The three-dimensional space area occupied by For obstacles At the moment The three-dimensional space occupied by a

[0026] Furthermore, the dynamic constraint cost The calculation formula is:

[0027]

[0028]

[0029] Where, For speed penalty, is the acceleration penalty, and are the weights of speed penalty and acceleration penalty respectively, is the preset maximum speed, is the preset maximum acceleration.

[0030] Furthermore, the target point reaches the cost The calculation formula is:

[0031] Where, The trajectory at the end time location, The target point at the end time location.

[0032] Furthermore, the optimal solution The calculation formula is:

[0033] Where, is a unified cost function, is the optimization vector Dimensions, and They are the optimization vectors The lower and upper bounds of is the population size of the metaheuristic algorithm, is the maximum number of iterations.

[0034] Furthermore, the re-planning of the trajectory of the agents in the minimum agent subset is performed simultaneously, and the specific steps are as follows: Treat the agent trajectories that are not selected for replanning as fixed dynamic obstacles; The current optimal solution As a new space-time control point, combined with fixed dynamic obstacles, the trajectory of the intelligent body is replanned.

[0035] The technical solution of the present invention has at least the following advantages and beneficial effects: The present invention discloses a distributed spatiotemporal joint trajectory planning method for a cluster of intelligent agents. It adopts a distributed conflict resolution strategy based on a conflict graph and approximate minimum vertex cover. By allowing only a minimum subset of conflicting intelligent agents to perform parallel replanning, it fundamentally solves the efficiency bottleneck of traditional sequential planning and demonstrates excellent scalability.

[0036] In addition, by directly optimizing the spatiotemporal control points, tight coupling and joint planning of the spatiotemporal dimensions are achieved; this abandons the dependence on the front-end static path and gives the optimizer excellent global adjustment capabilities, enabling it to flexibly cope with complex dynamic scenarios that are difficult to handle with traditional two-stage methods.

[0037] Due to the global search capability of the metaheuristic algorithm and the guidance of a unified cost function, the method of the present invention can explore a wider solution space and find high-quality safe trajectories.

[0038] In addition, the unified cost function integrates multiple complex constraints such as static obstacles, dynamic obstacles, collisions with other intelligent agents, and its own dynamic limitations into a unified optimization objective, greatly simplifying the complexity of system design and multi-constraint processing. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 A schematic flow chart of a method of the present invention is shown; Figure 2 Schematic diagram of the precise time tracking of dynamic target points and spatial control points and time distribution for a single agent in a two-dimensional dynamic environment for 20 seconds; Figure 3 Schematic diagram of the optimization process for collision avoidance cost; Figure 4 Schematic diagram of the optimization process for dynamic constraint cost; Figure 5 Schematic diagram of the process of solving the minimum vertex cover based on the maximum degree greedy algorithm; Figure 6 A schematic diagram showing the process of a swarm of 20 agents crossing a narrow passage and exchanging positions; Figure 7 A schematic diagram is shown for the minimum spacing curve; Figure 8 Schematic diagram of the process of 10 intelligent agents traversing a narrow channel and accurately landing on a recovery platform in 32 seconds; Figure 9 Schematic diagram of the process of 100 intelligent agents traversing a dynamic environment and landing on a mobile recovery platform. Figure 10 The speed curve diagram of 10 agents uniformly sampled from 100 agents; Figure 11 Schematic diagram of a typical experimental scenario for 80,000 experiments. DETAILED DESCRIPTION

[0040] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations.

[0041] Example 1 like Figure 1As shown in FIG, a distributed spatiotemporal joint trajectory planning method for a cluster of intelligent agents specifically includes: Plan the trajectory of each agent in the agent cluster; In addition, the specific steps of planning the running trajectory of each agent in the agent cluster are as follows: The agent The three-dimensional trajectory is parameterized by The present invention adopts the quintic spline to ensure the continuity of high order: velocity, acceleration, jerk, and acceleration are continuous, that is, Continuous; a cubic polynomial can also be used, and the trajectory satisfies the continuity of velocity and acceleration. continuous.

[0042] Then set the initial state of the agent , including position, velocity, acceleration, etc., as well as target state ; Define multiple spatio-temporal control points (STP), and the spatio-temporal control points include Intermediate space control points, ,in ,and means the set of real numbers in three-dimensional space, and Duration of time period , the duration of any time period This spatiotemporal control point effectively eliminates reliance on static front-end paths, giving the optimizer superior global adjustment capabilities, enabling it to flexibly handle complex dynamic scenarios that are difficult to handle with traditional two-stage methods. Using standard spline fitting operators , according to the initial state of the agent , target state , and space-time control points , generate the initial trajectory , the trajectory is uniquely determined, satisfies all interpolation points and boundary conditions, and is high-order continuous everywhere; In addition, combined with the Figure 2 , demonstrated the spatiotemporal optimization effect of a single agent in a two-dimensional example case. Through precise spatiotemporal joint planning, the spatial shape and velocity distribution of the trajectory were adjusted, and the dynamic target point was tracked in exactly 20 seconds while avoiding dynamic and static obstacles. In addition, in time-sensitive tasks such as urban logistics, in order to strictly meet the preset total flight time , a precise time control mechanism can be introduced, that is: If you need to accurately control the trajectory time, generate the initial trajectory When the time allocation ratio vector

[0043] Replacement Segment Duration ; When minimizing the uniform cost function, the actual duration of each segment is calculated as:

[0044] Where, is the total time of the expected trajectory; thus, the total time of the expected trajectory Hengcheng achieves precise control of flight time.

[0045] Based on spatiotemporal control points and the initial trajectory Constructing a unified cost function ; The unified cost function is:

[0046] Where, As the main optimization goal, To unify the collision avoidance cost, is the dynamic constraint cost, is the time constraint cost, is the cost of reaching the target point, which means that when precise time control is not adopted, this item is used to punish the deviation between the total flight time and the expected time, and , is the cost of reaching the target point, 、 、 、 and are the weights of the corresponding costs respectively.

[0047] The main optimization goals , such as minimizing trajectory time or energy consumption, if it is to minimize time , the calculation formula is:

[0048] If the energy consumption of the trajectory is minimized , usually approximated by the integral square of higher-order derivatives, such as minimizing the square integral of jerk, the calculation formula is: .

[0049] In addition, the unified collision avoidance cost , which is one of the core of the present invention, will uniformly handle the collision risk with static obstacles, dynamic obstacles and other intelligent bodies. Its value is defined as the penalty path length of the trajectory passing through these obstacles (and their safe expansion zones), such as Figure 3 As shown in Figure 2, this not only determines whether there is a collision, but also provides the optimizer with gradient information about the collision depth, guiding the trajectory to "push away" from the obstacle area; its calculation formula is:

[0050] Where, is the characteristic function, which means that when the agent Entering obstacles The space-time occupied area , or enter an obstacle The space-time occupied area , takes 1, otherwise it takes 0, For this obstacle At the moment The three-dimensional space area occupied by For obstacles At the moment In addition, to simplify the calculation and ensure the safety margin, in actual collision detection, the volume of the agent itself is usually equivalently attached to the occupied area of ​​the obstacle or other agents.

[0051] As needed, combine with Figure 4 , dynamic constraint cost To ensure that the generated trajectory is physically executable, the calculation formula is:

[0052]

[0053]

[0054] Where, For speed penalty, is the acceleration penalty, and are the weights of speed penalty and acceleration penalty respectively, is the preset maximum speed, is the preset maximum acceleration, where is the speed penalty term, if , , there is no punishment; if , , then the penalty value is proportional to the speeding amount; the acceleration penalty term This is consistent with the judgment logic of the speed penalty item.

[0055] In addition, the target point arrival cost , this is to ensure that the agent can reach its designated target point, and in our spatiotemporal joint planning framework, the target point itself can also be dynamic. Assuming that the agent The trajectory of the target point at time is (For static target points, is a constant vector). The cost of reaching the target point can be defined as the trajectory at the end time Location The target point position at this time The Euclidean distance between them is calculated as follows:

[0056] Where, The trajectory at the end time location, The target point at the end time In actual optimization, if the agent can Within the limit, and accurately reach the target point under the dynamic constraints, it means that the end position constraint , can be directly used as the last spatial control point in spline fitting or forced to be realized through the end boundary condition, which can reduce the optimization variables. However, if it cannot be reached accurately due to dynamic limitations or insufficient time, then Still valid as a soft constraint.

[0057] By optimizing the engine Minimize the unified cost function to obtain the optimal solution ; Among them, the optimization engine For meta-heuristic optimization algorithms, such as artificial bee colony algorithm ABC, gradient optimization algorithm GBO, etc., the engine will control the time and space points Treat it as a high-dimensional decision vector and perform a global search in the preset search space with the goal of minimizing the above unified cost function, and finally give the optimal solution found; And the optimal solution The calculation formula is:

[0058] Where, is a unified cost function, is the optimization vector Dimensions, for Intermediate spatial control points and time period (or scaling factor), , and They are the optimization vectors The lower and upper bounds are used to constrain the search range of spatial control points and the value range of time periods (or scale factors). is the population size of the metaheuristic algorithm, is the maximum number of iterations, which serves as one of the main termination conditions.

[0059] In this framework, the optimizer groups spatiotemporal control points As an abstract dimensional vector , without directly understanding its specific physical meaning (i.e. spatial point or time). Cost function Acting as a “black box”, it receives a candidate solution , which is parsed into specific spatiotemporal control points (or ), and then through the spline fitting operator Generate trajectories , and finally calculate the comprehensive cost value of the trajectory.

[0060] According to the initial state of the agent , target state , and the optimal solution , generate running trajectory ; Therefore, combining the construction of the unified cost function and the optimization process of the optimization engine, the generation of the running trajectory can be regarded as an iterative cycle: 1. Initialization: Randomly generate a population containing multiple candidate solutions (each solution is a group); 2. Evaluation: For each candidate solution, generate a trajectory through spline fitting and calculate its cost function value; 3. Update: Update the population according to specific algorithmic rules (such as ABC bee search behavior) to generate better candidate solutions; 4. Termination: When the maximum number of iterations is reached or a satisfactory solution that satisfies all constraints is found, the optimization ends and the optimal spatiotemporal control points are output, thus obtaining the final collision-free, dynamically feasible smooth trajectory.

[0061] Based on the running trajectory of each agent, the collision information between any agent in the cluster and other agents is detected in turn, and the collision information is sent to other agents through network broadcast; Each agent Detect its initial trajectory with all other agents Is there a space-time collision between the trajectories of Broadcasts its conflict information (i.e., which agents it collided with) to all other agents in the cluster via a low-bandwidth network.

[0062] After any agent receives collision information, it generates an independent and decentralized conflict graph; After receiving the conflict information from all other agents, each agent independently and decentralizedly constructs an identical conflict graph. . Among them, each node of the conflict graph Represents an agent, each edge Representative Agent and There is a risk of collision between the trajectories.

[0063] Based on the conflict graph, an approximate minimum vertex cover algorithm is used to find the minimum subset of agents that need to replan their trajectories. That is, the conflict resolution problem is transformed into finding an approximate minimum vertex cover (MVC) of the conflict graph G. MVC is a minimum subset of nodes. , so that every edge in the graph has at least one endpoint in In this embodiment, an efficient, deterministic maximum greedy algorithm is used to solve the approximate MVC, such as Figure 5 As shown: (a) Initialize an empty replanning set ; (b) Loop: As long as there are edges in the conflict graph, select the node with the largest degree (i.e., the most conflicts) in the current graph. join in , and remove all Connected edges. If the degrees are the same, they are selected based on predetermined rules such as agent ID to ensure determinism; (c) The loop ends and the output is .

[0064] Since all agents are based on the same global conflict information and the same deterministic algorithm, they can reach a set of counterweight plans without central coordination. unanimous decision.

[0065] Simultaneously replan the trajectory of the agents in the minimum agent subset; In addition, the aforementioned replanning of the trajectory of the agents in the minimum agent subset is performed simultaneously, and the specific steps are as follows: The trajectory of the agent that is not selected for replanning is regarded as a fixed dynamic obstacle; that is, the trajectory of the agent that is not replanned is fixed in time and space, and the space area it occupies is Becoming a time-varying restricted area; The current optimal solution As a new spatiotemporal control point, combined with fixed dynamic obstacles, the trajectory of the intelligent agent is replanned; That is, the replanned agents are forced to generate new trajectories that completely avoid these restricted areas, thereby ensuring that the final output trajectory of the entire cluster is absolutely conflict-free. The agents that maintain the original trajectory form a "mobile roadblock", and the replanning agents must detour or adjust their speed to avoid interspersing.

[0066] Repeat the steps of collision information detection, conflict graph generation, minimum agent subset construction, and trajectory replanning until the number of detected conflict information is zero, and determine the final trajectory of each agent.

[0067] Based on the content of this embodiment, a limit test of "20 intelligent agents cluster crossing a narrow channel and exchanging positions" was conducted. The test results are as follows: Figure 6 As shown, Figure 7 The minimum spacing curve in the test results shows that the distance between intelligent agents can always be maintained above the safety threshold of 0.3 meters while ensuring a smooth trajectory without excessive twists and turns. This proves the powerful ability of the present invention to achieve complex cluster behaviors by finely optimizing time and space in extremely crowded and strongly coupled scenarios.

[0068] in addition, Figure 8 and Figure 9 The task of an intelligent agent traversing a narrow passage and accurately landing on a recovery platform within 32 seconds is presented. This task requires the intelligent agent cluster to accurately land on a mobile recovery platform in an environment containing a large number of dynamic and static obstacles. Figure 8 (a) is the initial state; (b) shows the cluster passing through the narrow channel in an orderly manner and avoiding dynamic obstacles; (c) shows the cluster leaving the channel; (d) shows all agents accurately landing on the mobile recovery platform within the preset time of 35 seconds; Figure 9 (a) shows the agent cluster passing through a complex dynamic obstacle area and approaching the mobile recovery platform, and (b) shows all agents accurately landing at their respective target points on the mobile recovery platform within the preset 50 seconds. The trajectory planned by this embodiment enables the agent cluster to successfully complete the task, and through the innovative time allocation ratio optimization mechanism, strictly meets the preset arrival time (35 seconds and 50 seconds respectively). Figure 10 As shown in the speed curve, the agent's speed drops smoothly to zero when it reaches the target, demonstrating its precise time control and dynamic target tracking capabilities.

[0069] In addition, based on the trajectory planning method of this embodiment, 80,000 large-scale cluster experiments were conducted. The experimental scenarios are as follows: Figure 11 The experimental results are shown in Table 1: Table 1 Performance comparison of 80,000 experiments

[0070] The data shows that when the number of agents increases from 16 to 100, the average number of iterations required to resolve all conflicts increases only slightly, from 2.07 to 3.78 (using MetaPlanner-ABC as an example), remaining at an extremely low level and not experiencing explosive growth with cluster size. This demonstrates that our method successfully decouples planning overhead from cluster size. Furthermore, while the average initial planning time and average replanning time increase with the number of agents, they remain at the millisecond level, with a gentle growth trend, fully meeting the real-time planning requirements of large-scale clusters. The lack of a significant increase in replanning time also demonstrates the effectiveness of the "hot start" mechanism. This stands in stark contrast to the traditional chain planning approach, where the total planning time increases linearly with the number of agents.

[0071] Example 2 As an embodiment, for the step of generating the initial trajectory, any mathematical tool that can describe a smooth and continuous trajectory using a finite set of parameters can be used as an alternative to this step: Alternative curve types: In addition to polynomial splines, you can also use B-splines, Bézier curves, or non-uniform rational B-splines (NURBS). These curve types are also defined by a set of control points and have good local control properties. By optimizing the positions of their control points, smooth trajectories can also be generated.

[0072] Alternative function bases: The trajectory can also be represented as a linear combination of a set of orthogonal function bases, such as Fourier series or Chebyshev polynomials. The optimization process becomes optimizing the coefficients of these function bases, which can also generate smooth trajectories that meet the requirements.

[0073] Example 3 As an example, in Example 1, all constraints are integrated into a single cost function as weighted penalty terms. There are also multiple equivalent alternative forms: Alternative collision cost form: The embodiment of the present invention calculates the length of the trajectory within the obstacle. Similarly, the collision cost can be defined as: The inverse of the minimum distance between the trajectory and the obstacle.

[0074] The maximum depth or volume of an obstacle that a track intrudes into.

[0075] Based on the artificial potential field method, obstacles are modeled as repulsive sources, and the cost is the sum of potential energy on the trajectory.

[0076] Alternative constraint handling methods: In addition to the weighted sum of soft constraints, you can also use: Hard constraints: During the optimization process, any solution that violates collision or dynamic constraints is directly assigned an infinite cost value and is thus discarded by the optimizer.

[0077] Lexicographic or hierarchical optimization: prioritize constraints. For example, first find a subset of solutions that satisfy safety (no collisions), then find solutions that satisfy dynamic constraints within this subset, and finally optimize for the primary objective, such as time or energy consumption.

[0078] Example 4 As an example, the initial trajectory planned in Example 1 needs to be optimized. The Artificial Bee Colony (ABC) algorithm and the Gradient Based Optimizer (GBO) can be used as optimizers. However, any optimization algorithm capable of performing global or local search in complex, high-dimensional spaces can be used to solve the cost function proposed in this invention. Therefore, other evolutionary algorithms, such as Genetic Algorithm (GA), Differential Evolution (DE), and Particle Swarm Optimization (PSO), can be used. These algorithms all follow the iterative paradigm of "population initialization-evaluation-update" and can seamlessly replace the optimizer in this example.

[0079] Other random search algorithms, such as simulated annealing (SA) and covariance matrix adaptive evolution strategy (CMA-ES), explore the solution space through different random strategies and are also suitable for solving the “black box” cost function of the present invention.

[0080] Example 5 As an example, in Example 1, the replanning set is determined based on the conflict graph and the approximate minimum vertex cover (MVC). This decentralized decision-making mechanism also has multiple alternatives: Alternative graph theory problem models: Conflict resolution can be modeled not only as MVC, but also as other graph theory problems, such as maximum independent set: finding the largest set of conflict-free agents in the graph, while agents outside this set need to be replanned.

[0081] Minimum Dominating Set: Find the fewest agents that can “cover” all other agents’ conflicts.

[0082] Alternative approximation algorithms: To solve the approximate MVC, in addition to the maximum greedy algorithm, other efficient deterministic or random approximation algorithms can also be used, such as the classic 2-approximation algorithm (that is, continuously selecting an edge and adding its two endpoints to the covering set).

[0083] Alternative decentralized decision-making mechanisms: Instead of relying on graph theory, other distributed coordination mechanisms can be used to determine the agent that should replan. For example, a strategy based on dynamic priorities can be used: all agents calculate a dynamic priority based on a globally consistent set of rules (such as distance to the target, ID size, and remaining energy). When a conflict occurs, the agent with the lower priority is responsible for replanning to avoid it.

[0084] Negotiation or auction-based mechanism: Conflicting intelligent agents can "negotiate" or "bid" through a simple communication protocol to determine who has path priority, and the losing party will replan.

[0085] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. A distributed spatiotemporal joint trajectory planning method for a cluster of intelligent agents, characterized in that: Specifically include: Plan the trajectory of each agent in the agent cluster; Based on the running trajectory of each agent, the collision information between any agent in the cluster and other agents is detected in turn, and the collision information is sent to other agents through network broadcast; After any agent receives collision information, it generates an independent and decentralized conflict graph; Based on the conflict graph, an approximate minimum vertex cover algorithm is used to find the minimum subset of agents that need to replan their trajectories. Simultaneously replan the trajectory of the agents in the minimum agent subset; Repeat the steps of collision information detection, conflict graph generation, minimum agent subset construction, and trajectory replanning until the number of detected conflict information is zero, and determine the final trajectory of each agent.

2. The distributed spatiotemporal joint trajectory planning method for an agent cluster according to claim 1, characterized in that: The specific steps of planning the running trajectory of each agent in the agent cluster are as follows: Set the agent's starting state and target state ; Define multiple spatiotemporal control points, and the spatiotemporal control points include Intermediate space control points ,in ,as well as Duration of time period , the duration of any time period ; Using standard spline fitting operators , according to the initial state of the agent , target state , and space-time control points , generate the initial trajectory ; Based on spatiotemporal control points and the initial trajectory Constructing a unified cost function ; By optimizing the engine Minimize the unified cost function to obtain the optimal solution ; According to the initial state of the agent , target state , and the optimal solution , generate running trajectory .

3. The distributed spatiotemporal joint trajectory planning method for an agent cluster according to claim 2, characterized in that: If precise control of trajectory time is required, generate the initial trajectory When the time allocation ratio vector Replacement Segment Duration ; When minimizing the uniform cost function, the actual duration of each segment is calculated as: Where, is the total time of the desired trajectory.

4. The distributed spatiotemporal joint trajectory planning method for an agent cluster according to claim 2, characterized in that: The unified cost function is: Where, As the main optimization goal, To unify the collision avoidance cost, is the dynamic constraint cost, is the time constraint cost, is the cost of reaching the target point, 、 、 、 and are the weights of the corresponding costs respectively.

5. The distributed spatiotemporal joint trajectory planning method for an agent cluster according to claim 4, characterized in that: Main optimization goals , if the time is minimized , the calculation formula is: If the energy consumption of the trajectory is minimized , the calculation formula is: 。 6. The distributed spatiotemporal joint trajectory planning method for an agent cluster according to claim 4, characterized in that: The unified collision avoidance cost The calculation formula is: Where, is the indicator function, The obstacle at time The three-dimensional space area occupied by For obstacles At the moment The three-dimensional space occupied by a 7. The distributed spatiotemporal joint trajectory planning method for an agent cluster according to claim 4, characterized in that: Dynamic constraint cost The calculation formula is: Where, For speed penalty, is the acceleration penalty, and are the weights of speed penalty and acceleration penalty respectively, is the preset maximum speed, is the preset maximum acceleration.

8. The distributed spatiotemporal joint trajectory planning method for an agent cluster according to claim 4, characterized in that: The cost of reaching the target point The calculation formula is: Where, The trajectory at the end time location, The target point at the end time location.

9. The distributed spatiotemporal joint trajectory planning method for an agent cluster according to claim 2, characterized in that: The optimal solution The calculation formula is: Where, is a unified cost function, is the optimization vector Dimensions, and They are the optimization vectors The lower and upper bounds of is the population size of the metaheuristic algorithm, is the maximum number of iterations.

10. The distributed spatiotemporal joint trajectory planning method for an agent cluster according to claim 2, characterized in that: The specific steps of simultaneously replanning the trajectory of the agents in the minimum agent subset are as follows: Treat the agent trajectories that are not selected for replanning as fixed dynamic obstacles; The current optimal solution As a new space-time control point, combined with fixed dynamic obstacles, the trajectory of the intelligent body is replanned.

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