Multi-uav low-energy consumption trajectory planning method and system based on spatiotemporal voxel map

Abstract

This invention relates to the field of UAV trajectory planning, and discloses a method and system for low-energy trajectory planning of multiple UAVs based on spatiotemporal voxel graphs. The method includes: constructing a spatiotemporal voxel graph based on urban low-altitude airspace data and defining an energy consumption-aware transfer cost; generating an initial low-energy trajectory based on the transportation task and the graph; identifying vertex and edge conflicts between trajectories and generating corresponding spatiotemporal vertex or edge constraints, adding them to the constraint set of the conflicting UAVs, and performing constraint replanning under the updated constraints with the goal of minimizing energy consumption; smoothing and verifying the executability of the replanned trajectory, and outputting a conflict-free, low-energy, and flyable four-dimensional trajectory for multiple UAVs. This invention, based on spatiotemporal voxel graphs and energy consumption-aware costs, generates safe, smooth, low-energy, and executable four-dimensional trajectories for multiple UAVs through conflict identification, constraint replanning, and trajectory smoothing, effectively improving the utilization efficiency of urban low-altitude airspace.

Description

Technical Field

[0001] This invention belongs to the field of unmanned aerial vehicle (UAV) trajectory planning, and specifically relates to a low-energy trajectory planning method and system for multiple UAVs based on spatiotemporal voxel maps. Background Technology

[0002] With the development of urban low-altitude economy and drone transportation applications, the demand for multiple drones to perform transportation, delivery, inspection, and emergency delivery tasks within the same low-altitude airspace is constantly increasing. In such scenarios, drones not only need to avoid buildings, obstacles, and no-fly zones, but also need to meet low-altitude airspace management requirements, mission time windows, flight performance constraints, and multi-drone safety spacing requirements. Therefore, how to generate safe, efficient, and executable trajectories for multiple drones under high-density low-altitude operation conditions has become a key technical problem supporting the large-scale operation of urban low-altitude intelligent transportation systems.

[0003] Existing research has proposed various 3D path planning methods by combining techniques such as grid modeling, topology modeling, heuristic search, and intelligent optimization, improving spatial obstacle avoidance capabilities and search efficiency in complex environments. However, most existing methods focus on spatial paths as the planning object, failing to adequately characterize the occupancy status of low-altitude airspace at different time periods, and making it difficult to uniformly describe the availability, occupancy, and reusability of airspace voxels in spatial and temporal dimensions. Some methods further incorporate temporal information, dynamic obstacle information, or task scheduling information, enabling path planning to adapt to environmental changes to some extent. However, these methods typically emphasize path generation before planning or local avoidance during operation, lacking adaptability to sudden conflicts, changes in local airspace occupancy, and the mutual influence of multiple aircraft trajectories during task execution. They also lack a processing mechanism for generating collaborative constraints based on spatiotemporal occupancy relationships and performing trajectory replanning, resulting in insufficient robustness of planning results under complex low-altitude operating conditions.

[0004] In addition, urban low-altitude transportation tasks are affected by multiple constraints such as the starting point, the destination, the safety interval, and the battery capacity. Existing methods mostly focus on path length, flight time, or local obstacle avoidance as the main optimization objectives, and do not adequately consider the differences in energy consumption of UAVs under different flight maneuvers such as horizontal flight, climb, descent, and turning. This can easily lead to problems such as the trajectory being feasible in space but having high energy consumption, and discrete paths being feasible but lacking continuous execution. As a result, the planned trajectory is not very energy-efficient in low-altitude transportation tasks with limited endurance.

[0005] It should be noted that the information disclosed in the background section above is only used to enhance the understanding of the background of the present invention, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0006] To address or at least mitigate one or more of the above problems, a low-energy trajectory planning method and system for multiple UAVs based on spatiotemporal voxel graphs is provided. This method can uniformly express the spatial occupancy, temporal occupancy, and trajectory transfer relationships in low-altitude airspace, reduce the risk of trajectory conflicts among multiple UAVs, and decrease energy consumption and safety risks during trajectory execution. This results in the generation of safe, smooth, low-energy, and executable four-dimensional trajectories for multiple UAVs, thereby improving the utilization efficiency of urban low-altitude airspace resources.

[0007] To achieve the above objectives, according to a first aspect of the present invention, a low-energy trajectory planning method for multiple unmanned aerial vehicles based on spatiotemporal voxel maps is provided, comprising the following steps: Acquire urban low-altitude airspace data, multiple drone transport mission data, and drone flight constraint data; A spatiotemporal voxel graph containing voxel time nodes and feasible transition edges is constructed based on urban low-altitude airspace data. Based on the flight maneuvers of the drone, determine the energy consumption perception transfer cost of each feasible transfer edge; Based on the spatiotemporal voxel map, energy consumption perception transfer cost, and the data of the multiple UAV transportation tasks, low-energy initial four-dimensional trajectories corresponding to multiple UAV transportation tasks are generated. Vertex and edge conflicts are identified based on the initial four-dimensional trajectories of each UAV; Based on the identified vertex or edge conflicts, vertex constraints are generated to prohibit conflicting drones from occupying specified voxels at specified time steps, or edge constraints to prohibit conflicting drones from performing specified transfer actions within specified time intervals. The vertex or edge constraints are added to the constraint set of the conflicting drones, and constraint replanning is performed under the updated constraint set. The constraint replanning aims to minimize the energy consumption-aware transfer cost, and prohibits passage only at the constrained voxel time nodes or transfer edges. The reprogrammed four-dimensional trajectory is smoothed and its feasibility is verified. Outputs low-energy, four-dimensional trajectories for multiple drones.

[0008] Furthermore, the urban low-altitude airspace data includes the urban low-altitude three-dimensional airspace range and its boundary values ​​in each coordinate axis direction of the three-dimensional spatial coordinate system, as well as the location information of buildings, static obstacles and no-fly zones; The data for the multiple drone transport missions includes the origin, destination, earliest takeoff time, and latest arrival time of multiple flight requests, with each flight request being executed by one drone. The UAV flight constraint data includes the UAV's maximum flight speed, maximum climb or descent rate, minimum safe interval, and minimum turning radius.

[0009] Furthermore, a spatiotemporal voxel graph containing voxel time nodes and feasible transition edges is constructed based on urban low-altitude airspace data, including: The urban low-altitude airspace is discretized into a three-dimensional voxel set, and the spatial index and center coordinates of each voxel are determined; obstacles and no-fly zones are expanded, and the passable voxel set is determined based on the expanded obstacles and no-fly zones. The planning timeframe is arranged according to time steps. Discretize into a discrete time set. Based on the set of traversable voxels and the set of discrete time, construct a set of voxel time nodes. Determine candidate transition edges between adjacent discrete time steps. For any traversable voxel, use six adjacent voxels and allow the UAV to hover in the current voxel. The spatiotemporal voxel graph is composed of all traversable voxel time nodes and the traversable transition edges obtained after screening the candidate transition edges.

[0010] Furthermore, the feasible transition edges obtained after screening the candidate transition edges include: Obtain the starting voxel center coordinates and ending voxel center coordinates, as well as the starting voxel height coordinates and ending voxel height coordinates for each candidate transition edge; Calculate the horizontal projection distance of the candidate transfer edge based on the coordinates of the starting voxel center and the ending voxel center; calculate the height change of the candidate transfer edge based on the height coordinates of the starting voxel and the ending voxel. If a candidate transfer edge simultaneously satisfies the following conditions: the horizontal distance is no greater than the product of the maximum flight speed and the time step, and the altitude change is no greater than the product of the maximum climb or descent rate and the time step, then the candidate transfer edge is retained as a feasible transfer edge; otherwise, it is excluded.

[0011] Furthermore, based on the flight maneuvers of the UAV, the energy consumption perception transfer cost of each feasible transfer edge is determined, including: The climb or descent altitude is determined based on the altitude change, and the flight path angle is determined based on the horizontal projection distance and altitude change. The horizontal flight cost is determined based on the horizontal projection distance, the climb cost is determined based on the climb altitude, the descent cost is determined based on the descent altitude, and the non-horizontal flight or turning penalty cost is determined based on the flight path angle. The energy consumption perceived transfer cost of each feasible transfer edge is obtained by weighted summing of the horizontal flight cost, climb cost, descent cost, and non-horizontal flight or turning penalty cost. For the discrete voxel time trajectory of each UAV, the energy consumption perception transfer costs of the feasible transfer edges at each time step are summed to obtain the total energy consumption perception trajectory cost of each UAV.

[0012] Furthermore, based on the spatiotemporal voxel map, energy consumption perception transfer cost, and the data from the multiple UAV transportation tasks, low-energy initial four-dimensional trajectories corresponding to multiple UAV transportation tasks are generated, including: For each flight request, it is executed by the corresponding UAV, with the starting voxel and the voxel time node corresponding to the earliest take-off time of each flight request as the starting node, and the ending voxel and the latest arrival time of each flight request as the target constraints. Based on voxel time nodes, feasible transition edges, and energy consumption-aware transition costs, an energy consumption-weighted spatiotemporal voxel graph is obtained; in the energy consumption-weighted spatiotemporal voxel graph, a feasible trajectory from the starting node to the voxel time node that satisfies the target constraint is searched. The feasible trajectory that minimizes the cumulative energy consumption perception transfer cost is used as the initial four-dimensional trajectory for each flight requirement.

[0013] Furthermore, based on the initial four-dimensional trajectories of each UAV, vertex and edge conflicts are identified, including: Based on the voxels occupied at each time step in each initial four-dimensional trajectory, construct a set of candidate trajectories for all UAVs; Spatiotemporal conflict detection is performed on the trajectories of different drones on a unified timeline: if two drones occupy the same voxel at the same time step, a vertex conflict is determined to have occurred; if two drones cross the same local transfer edge in opposite directions within the same time interval, or occupy the same local transfer edge in the same direction within the same time interval, an edge conflict is determined to have occurred.

[0014] Furthermore, based on the initial four-dimensional trajectories of each UAV, vertex and edge conflicts are identified, including: When a vertex conflict is detected, a vertex coordination constraint is generated to prevent one of the conflicting drones from occupying the conflicting voxel at the conflict time step. When an edge conflict is detected, an edge coordination constraint is generated that prohibits one of the conflicting drones from performing a conflict transfer action during the conflict time interval. The generated vertex coordination constraints or edge coordination constraints are added to the constraint set of the corresponding UAV, and constraint replanning is performed on the UAV under the updated constraint set to obtain the replanned trajectory. If replanning is successful, the original trajectory of the UAV is replaced with the replanned trajectory to obtain a low-energy, conflict-free four-dimensional trajectory; if replanning fails, the current constraint branch is abandoned; conflict detection, constraint generation and constraint replanning are repeated until there are no conflicts or feasible candidate solutions among the trajectories of all UAVs.

[0015] Furthermore, the reprogrammed four-dimensional trajectory is smoothed and its executability is verified, including: The discrete voxel time trajectory obtained after constrained replanning is obtained, the path point mapping and simplification are performed, the center position of each voxel is extracted as the trajectory point, and the key point sequence is obtained after removing redundant intermediate points. Estimate the local heading angle for each keypoint in the keypoint sequence, and form pose pairs by combining the positions and heading angles of adjacent keypoints; By using the Durbins curve to connect adjacent pose pairs while satisfying the minimum turning radius constraint, a smoothed planar trajectory is obtained, and the planar trajectory is then elevated to a three-dimensional geometric trajectory according to the arc length parameter. The three-dimensional geometric trajectory is parameterized in time to satisfy the velocity constraint and the rate of ascent constraint. If a local trajectory segment does not meet the velocity constraint or the rate of ascent constraint, the flight speed of the current local trajectory segment is reduced or a waiting segment is inserted to obtain an executable four-dimensional trajectory. The executable four-dimensional trajectory is validated for executability. The executability validation includes determining whether the trajectory maintains a preset safe distance from obstacles and no-fly zones, whether it meets the mission time window requirements, and whether it meets the minimum safe interval requirements between multiple UAVs. Finally, a set of low-energy executable four-dimensional trajectories for multiple UAVs is obtained.

[0016] To achieve the above objectives, according to a second aspect of the present invention, a low-energy trajectory planning system for multiple unmanned aerial vehicles based on spatiotemporal voxel maps is provided, comprising: The data acquisition module is used to acquire urban low-altitude airspace data, multiple drone transport mission data, and drone flight constraint data; The spatiotemporal voxel graph construction module is used to construct a spatiotemporal voxel graph containing voxel time nodes and feasible transition edges based on urban low-altitude airspace data. The energy consumption cost calculation module is used to determine the energy consumption perception transfer cost of each feasible transfer edge based on the flight action of the UAV. The initial trajectory generation module is used to generate low-energy initial four-dimensional trajectories corresponding to multiple UAV transportation tasks based on the spatiotemporal voxel map, energy consumption perception transfer cost and the multiple UAV transportation task data. The trajectory conflict identification module is used to identify vertex conflicts and edge conflicts based on the initial four-dimensional trajectory of each UAV. The collaborative constraint replanning module is used to generate vertex constraints that prohibit conflicting drones from occupying specified voxels at specified time steps, or edge constraints that prohibit conflicting drones from performing specified transfer actions within specified time intervals, based on the identified vertex or edge conflicts; add the vertex or edge constraints to the constraint set of the conflicting drones, and perform constraint replanning under the updated constraint set. The constraint replanning takes minimizing the energy consumption-aware transfer cost as the optimization objective, and prohibits passage only at the constrained voxel time nodes or transfer edges. The trajectory smoothing module is used to smooth the replanned four-dimensional trajectory and perform executability verification. The trajectory output module is used to output low-energy executable four-dimensional trajectories for multiple UAVs.

[0017] By adopting the above technical solution, the present invention has the following beneficial effects compared with the prior art: This invention constructs a spatiotemporal voxel map to uniformly express the spatial availability, temporal occupancy, and trajectory transfer states of airspace, enabling a more comprehensive characterization and utilization of low-altitude airspace resources. It employs a hierarchical collaborative mechanism combining conflict detection and constraint replanning, replanning only for UAVs affected by conflicts, maintaining a high planning success rate across various scenarios. Furthermore, it introduces energy consumption-aware transfer costs to uniformly model actions such as horizontal flight, climb, and descent, and smooths the trajectories after conflict resolution, generating low-energy-consumption executable four-dimensional trajectories that satisfy constraints on speed, climb rate, turning radius, and safety interval.

[0018] This invention constructs a spatiotemporal voxel graph, unifying the representation of low-altitude airspace voxels with discrete-time indices, enabling simultaneous description of airspace availability, temporal occupancy, and trajectory transition states. Example results show that, under the same scenario conditions, flight requirements, and parameter settings, the spatiotemporal airspace utilization rate of this invention reaches 74%, higher than the 60% of the optimal comparison method, indicating that the spatiotemporal voxel graph modeling method used in this invention can more fully characterize and utilize low-altitude airspace resources. This invention employs a hierarchical collaborative mechanism combining conflict detection and constraint replanning. It generates voxel temporal collaborative constraints based on vertex and edge conflicts, and only replans for UAVs affected by conflicts, avoiding redundant calculation of all UAV trajectories. Example results show that, under different airspace scales and flight requirement numbers, this invention can generate multi-UAV four-dimensional trajectories that satisfy constraints and are conflict-free, maintaining a 100% planning success rate under various low-level planners.

[0019] This invention introduces an energy consumption-aware transfer cost, uniformly modeling the penalties for horizontal flight, climb, descent, and non-horizontal flight. This allows the trajectory planning process to prioritize low-energy-consumption feasible edge transfer methods. Simultaneously, the discrete voxel time trajectory after conflict resolution is made continuous and smoothed to generate an executable four-dimensional trajectory that satisfies speed constraints, climb rate constraints, minimum turning radius constraints, and safety interval constraints. Example results show that, under the same scenario, environmental parameters, and flight requirements, the total energy consumption cost of this invention is reduced by approximately 8.45%, 32.21%, 12.59%, and 11.19% compared to four comparative methods, respectively. This demonstrates that this invention can reduce the energy consumption cost of multi-UAV four-dimensional trajectories and improve trajectory smoothness and continuous executability.

[0020] The specific embodiments of the present invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0021] The accompanying drawings, as part of this invention, are provided to further illustrate the invention. The illustrative embodiments and descriptions of the invention are used to explain the invention, but do not constitute an undue limitation thereof. Clearly, the drawings described below are merely some embodiments; those skilled in the art can obtain other drawings based on these drawings without any creative effort.

[0022] In the attached diagram: Figure 1 This is a schematic diagram of the overall process of the low-energy trajectory planning method for multiple UAVs based on spatiotemporal voxel maps in this specific embodiment; Figure 2 This is a schematic diagram of spatiotemporal trajectory planning in a multi-UAV low-altitude transportation scenario in this specific embodiment; Figure 3 This is a schematic diagram of the three-dimensional voxels and six adjacent voxels in this specific embodiment; Figure 4 This is a schematic diagram of voxel time nodes and feasible transition edges in this specific embodiment; Figure 5 This is a schematic diagram illustrating the calculation of energy consumption perception transfer costs in this specific implementation embodiment; Figure 6 This is a schematic diagram of multi-UAV trajectory conflict recognition in this specific embodiment. (a) is a schematic diagram of vertex conflict, (b) is a schematic diagram of reverse edge conflict, and (c) is a schematic diagram of forward edge conflict. Figure 7 This is a schematic diagram of the trajectory replanning process based on voxel-time collaborative constraints in this specific embodiment; Figure 8 This is a schematic diagram of the structure of the multi-UAV low-energy trajectory planning system based on spatiotemporal voxel graphs in this specific embodiment. Detailed Implementation

[0023] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments will be clearly and completely described below with reference to the accompanying drawings. The following embodiments are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0024] In the following description, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0025] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of embodiments of the present invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0026] Please see Figure 1 , Figure 1 This invention demonstrates the overall process of starting from inputting flight requirements, urban low-altitude airspace information, and UAV motion constraints, and sequentially proceeding through 1) spatiotemporal voxel map construction, 2) multi-UAV trajectory collaborative planning, and 3) trajectory smoothing and executable processing, ultimately outputting a set of low-energy executable four-dimensional trajectories for multiple UAVs.

[0027] This invention provides a low-energy trajectory planning method for multiple unmanned aerial vehicles (UAVs) based on spatiotemporal voxel maps, comprising the following steps: Acquire urban low-altitude airspace data, multiple drone transport mission data, and drone flight constraint data; A spatiotemporal voxel graph containing voxel time nodes and feasible transition edges is constructed based on urban low-altitude airspace data. Based on the flight maneuvers of the drone, determine the energy consumption perception transfer cost of each feasible transfer edge; Based on spatiotemporal voxel maps, energy consumption perception transfer costs, and data from multiple UAV transportation missions, low-energy initial four-dimensional trajectories are generated for multiple UAV transportation missions. Vertex and edge conflicts are identified based on the initial four-dimensional trajectories of each UAV; Based on the identified vertex or edge conflicts, generate vertex constraints that prohibit conflicting drones from occupying specified voxels at specified time steps, or edge constraints that prohibit conflicting drones from performing specified transfer actions within specified time intervals; add the vertex or edge constraints to the constraint set of the conflicting drones, and perform constraint replanning under the updated constraint set. The constraint replanning aims to minimize the energy-aware transfer cost, and prohibits passage only at the constrained voxel time nodes or transfer edges. The reprogrammed four-dimensional trajectory is smoothed and its feasibility is verified. Outputs low-energy, four-dimensional trajectories for multiple drones.

[0028] In some embodiments, urban low-altitude airspace data includes the urban low-altitude three-dimensional airspace range and its boundary values ​​in each coordinate axis direction of the three-dimensional spatial coordinate system, as well as the location information of buildings, static obstacles, and no-fly zones; multiple UAV transport mission data includes the start point, destination, earliest take-off time, and latest arrival time of multiple flight requests, with each flight request executed by one UAV; UAV flight constraint data includes the maximum flight speed, maximum climb or descent rate, minimum safety interval, and minimum turning radius of the UAV.

[0029] Step 1: Obtain low-altitude airspace data, flight demand data, and drone motion constraint data for the target city.

[0030] The target city's low-altitude airspace is represented as ,in, Indicates the three-dimensional airspace range of the city's low altitude. , , , , and These represent the boundary values ​​of the airspace in the three coordinate directions. Buildings, static obstacles, and no-fly zones are represented as a set of obstacles and no-fly zones. The flight demand set is represented as .in, Represents the set of flight demand. This indicates the quantity of flight demand. For any given flight demand... It includes the origin voxel. endpoint voxels and task time window , and These represent the earliest takeoff time and the latest arrival time for the flight request. The group of drones is denoted as... .in, Indicates a collection of drones. This represents the drones executing the 1st, 2nd, ..., Nth flight requests. Each flight request is executed by one drone. Drone motion constraint data includes maximum flight speed. Maximum rate of ascent or descent Minimum safety interval and minimum turning radius .

[0031] In some embodiments, a spatiotemporal voxel graph containing voxel time nodes and feasible transition edges is constructed based on urban low-altitude airspace data, including: The urban low-altitude airspace is discretized into a three-dimensional voxel set, and the spatial index and center coordinates of each voxel are determined; obstacles and no-fly zones are expanded, and the passable voxel set is determined based on the expanded obstacles and no-fly zones. The planning timeframe is arranged according to time steps. Discretize into a discrete time set. Based on the set of traversable voxels and the set of discrete time, construct a set of voxel time nodes. Determine candidate transition edges between adjacent discrete time steps. For any traversable voxel, use six adjacent voxels and allow the UAV to hover in the current voxel. The spatiotemporal voxel graph is composed of all traversable voxel time nodes and the traversable transition edges obtained after screening the candidate transition edges.

[0032] Step 2: Construct a spatiotemporal voxel map of the city's low-altitude airspace.

[0033] First, the continuous urban low-altitude airspace According to voxel resolution Discretized into a three-dimensional voxel set .in, , and Representing voxels , and Dimensions in direction. Each spatial point. For a given voxel index, the index is calculated as follows: ; ; ; For voxels Its central coordinates Represented as: ; Furthermore, the planning timeframe is divided into time steps. Discrete into time sets , Represents a discrete-time set; Indicates the length of the planning time domain; the first The consecutive times corresponding to each time index are: .

[0034] Please see Figure 2 , Figure 2 The spatiotemporal trajectory planning process for two drone flight requirements in a voxelized urban low-altitude environment is demonstrated. Figure 2 In the middle, the horizontal axis represents the spatial voxel index. Its corresponding actual spatial location is determined by the voxel center coordinates. Determined; the vertical axis represents the discrete time step. t Corresponding to actual time The gray area represents no-fly zones or obstacle voxels, and the red area represents spatiotemporal safety constraints; the blue and green trajectories represent the four-dimensional trajectories of the two drones flying from their respective starting voxels to their ending voxels.

[0035] To ensure a safety margin between drones and obstacles and no-fly zones, obstacles and no-fly zones... After expansion treatment, the following is obtained: .in, This indicates the expanded obstacles and no-fly zones. Indicates radius as The spherical safety margin area This represents the Minkowski sum operation. Based on the expanded obstacles and no-fly zones, the set of passable voxels is determined: If the body element If the corresponding spatial unit does not intersect with the expanded obstacles and no-fly zones, then the voxel belongs to the traversable voxel category. Within the traversable voxel set... and discrete-time sets Based on this, construct a set of voxel time nodes. in, Represents the set of voxel time nodes; Indicates the drone at time step Occupy passable voxels The state.

[0036] To construct feasible transition edges between adjacent time layers, first for any passable voxel... u The six-adjacency rule is adopted, and the hovering action of the drone is included in the candidate successor voxel set: 。

[0037] Please see Figure 3 , Figure 3 Showing the current voxels u Its six neighboring voxel sets Spatial relationships. Among them, Indicates voxel uA set of six adjacent voxels that share a common face; This indicates that the drone is hovering at the current voxel level; Voxel representation Candidate successor voxel set.

[0038] For any voxel time node The candidate transitions of its adjacent time layers are represented as follows: ; Please see Figure 4 , Figure 4 This demonstrates how candidate successor voxel relationships are expanded between adjacent discrete-time layers. Among them, The time indicates that the drone moves from voxel to voxel within a time step. Transfer to voxels , The time indicates that the drone remains hovering. The spatiotemporal voxel graph is composed of all feasible voxel time nodes and feasible transition edges: , Represents a spacetime voxel diagram. Let represent the set of feasible transition edges.

[0039] In some embodiments, the feasible transition edges obtained after screening candidate transition edges include: Obtain the starting voxel center coordinates and ending voxel center coordinates, as well as the starting voxel height coordinates and ending voxel height coordinates for each candidate transition edge; Calculate the horizontal projection distance of the candidate transfer edge based on the coordinates of the starting voxel center and the ending voxel center; calculate the height change of the candidate transfer edge based on the height coordinates of the starting voxel and the ending voxel. If a candidate transfer edge simultaneously satisfies the following conditions: the horizontal projection distance is not greater than the product of the maximum flight speed and the time step, and the altitude change is not greater than the product of the maximum climb or descent rate and the time step, then the candidate transfer edge is retained as a feasible transfer edge; otherwise, it is excluded.

[0040] Step 3: Determine the feasible edges for motion in the spacetime voxel graph.

[0041] For any candidate transition ,set up and Representing voxels and voxels The center coordinates, and Representing voxels and voxels The height coordinates. If the candidate transition simultaneously satisfies... If a candidate transition edge is found to be feasible, it is retained as a feasible transition edge; otherwise, the candidate transition is excluded. All retained feasible transition edges constitute... .

[0042] Based on feasible voxel time nodes and feasible transition edges, an energy-weighted spatiotemporal voxel graph is obtained for trajectory search, conflict detection, and constrained replanning. , This represents the set of energy consumption-aware transfer costs corresponding to feasible transfer edges.

[0043] In some embodiments, the energy consumption-aware transfer cost of each feasible transfer edge is determined based on the flight actions of the UAV, including: The climb or descent altitude is determined based on the altitude change, and the flight path angle is determined based on the horizontal projection distance and altitude change. The horizontal flight cost is determined based on the horizontal projection distance, the climb cost is determined based on the climb altitude, the descent cost is determined based on the descent altitude, and the non-horizontal flight or turning penalty cost is determined based on the flight path angle. The energy consumption perceived transfer cost of each feasible transfer edge is obtained by weighted summing of the horizontal flight cost, climb cost, descent cost, and non-horizontal flight or turning penalty cost. For the discrete voxel time trajectory of each UAV, the energy consumption perception transfer costs of the feasible transfer edges at each time step are summed to obtain the total energy consumption perception trajectory cost of each UAV.

[0044] Step 4: Calculate the energy-aware transfer cost of feasible transfer edges.

[0045] Unmanned aerial vehicles (UAVs) consume propulsion energy during low-altitude flight in urban areas. This invention uses a multi-rotor UAV propulsion power model to represent the relationship between UAV flight speed and power. Given the UAV's airspeed V, its propulsion power... It can be represented as: ; in, Indicates airspeed Propulsion power at that time; This represents the blade profile power constant during hovering. This represents the induced power constant during hovering. Indicates the rotor tip speed; This represents the average induced velocity during hovering. Indicates the fuselage drag ratio; Indicates air density; Indicates rotor solidity; This indicates the area of ​​the rotor disk.

[0046] For any feasible transition edge in the spacetime voxel graph Drone time step Internal body elements The center moves to the voxel The center, its average velocity The corresponding propulsion energy can be approximated as .

[0047] Since directly using the aforementioned propulsion energy model for optimization on a large-scale spatiotemporal voxel graph incurs significant computational overhead, this invention employs an energy proxy cost model to transform complex energy consumption assessments into computable transition edge costs applicable to replanning processes. For any feasible transition edge... Its energy consumption perception transfer cost is expressed as: ; in, These represent the costs of level flight, climb, descent, and penalties for non-level flight or turning, respectively. Voxel representation u and voxels w The horizontal projection distance between them; Indicates the altitude climbed; Indicates the descent altitude; Indicates the flight path angle; This represents the penalty function related to the flight path angle.

[0048] Please see Figure 5 , Figure 5 This demonstrates a local trajectory segment composed of continuous feasible transfer edges and its associated energy consumption perception cost. Edge 1 represents horizontal flight, edge 2 represents climbing flight, and edge 3 represents descent and turning flight. and These represent the projected distances of each flight edge on the horizontal plane. Indicates the altitude climbed. Indicates descent altitude. This indicates the flight path angle or turning angle between adjacent trajectory edges.

[0049] By weighting and combining the costs of horizontal flight, climb, descent, and turning, the energy consumption perception transfer cost corresponding to a local trajectory segment can be obtained. : ; in, and These represent the projected distances of each flight edge on the horizontal plane. These represent the costs of level flight, climb, descent, and penalties for non-level flight or turning, respectively.

[0050] For drones Its discrete-time voxel trajectory is represented as .in, and They represent drones The departure time step and the arrival time step; Indicates drone At time step t The available voxels occupied. and These are the starting and ending voxels, respectively. The remaining elements represent the voxels that the drone passes through sequentially during its flight from the starting point to the ending point. (Trajectory) Total energy consumption perceived cost Represented as: ; in, Indicates drone At time step t From voxels Transfer to voxels The resulting energy consumption perception transfer cost.

[0051] In some embodiments, based on spatiotemporal voxel maps, energy consumption-aware transfer costs, and multiple UAV transportation mission data, low-energy initial four-dimensional trajectories corresponding to multiple UAV transportation missions are generated, including: For each flight request, it is executed by the corresponding UAV, with the starting voxel and the voxel time node corresponding to the earliest take-off time of each flight request as the starting node, and the ending voxel and the latest arrival time of each flight request as the target constraints. Based on voxel time nodes, feasible transition edges, and energy consumption-aware transition costs, an energy consumption-weighted spatiotemporal voxel graph is obtained; in the energy consumption-weighted spatiotemporal voxel graph, a feasible trajectory from the starting node to the voxel time node that satisfies the target constraint is searched. The feasible trajectory that minimizes the cumulative energy consumption perception transfer cost is used as the initial four-dimensional trajectory for each flight requirement.

[0052] Step 5: Generate low-energy initial four-dimensional trajectories for multiple drone transportation missions.

[0053] For each flight requirement By the corresponding drone Execution. In the energy-weighted spatiotemporal voxel plot In the middle, starting with voxels and earliest departure time Corresponding voxel time nodes Starting node, ending voxel and latest arrival time Assuming the objective is constrained, search for an initial four-dimensional trajectory that satisfies environmental, motion, and time window constraints. For unmanned aerial vehicles (UAVs) Its discrete voxel time trajectory Represented as: ; in, Indicates drone At time step Voxels occupied Indicates drone The time step to reach the endpoint voxel. Indicates drone The endpoint voxel occupied at the arrival time step satisfies: .set up Indicates drone exist Given the set of feasible trajectories in the given information, the initial trajectory search objective is to minimize the cumulative energy consumption perception transfer cost on the trajectory. ; in, Indicates drone At time step From voxels Transfer to voxels The cost of energy consumption perception transfer.

[0054] Due to the spacetime voxel map Since inaccessible voxels and local transfers that do not meet motion constraints have been eliminated, based on the above search process, a low-energy initial four-dimensional trajectory that meets the requirements of obstacle avoidance, no-fly zone avoidance, basic motion feasibility, and mission time window can be obtained.

[0055] In some embodiments, identifying vertex and edge conflicts based on the initial four-dimensional trajectories of each UAV includes: Based on the voxels occupied at each time step in each initial four-dimensional trajectory, construct a set of candidate trajectories for all UAVs; Spatiotemporal conflict detection is performed on the trajectories of different drones on a unified timeline: if two drones occupy the same voxel at the same time step, a vertex conflict is determined to have occurred; if two drones cross the same local transfer edge in opposite directions within the same time interval, or occupy the same local transfer edge in the same direction within the same time interval, an edge conflict is determined to have occurred.

[0056] Step 6: Identify spatiotemporal conflicts between the four-dimensional trajectories of multiple drones.

[0057] The set of candidate trajectories for all drones is represented as: On a unified timeline Spatiotemporal collision detection is performed on the trajectories of different drones. Conflict tuples are used. Represented as: ; in, and This refers to the two drones involved in the conflict; Indicates the type of conflict; Indicates conflicting voxel resources; This represents the discrete time step in which the conflict occurs.

[0058] Please see Figure 6 , Figure 6 (a) Figure 6 (b) and Figure 6 (c) in the diagram illustrates the methods for determining vertex conflicts, reverse edge conflicts, and forward edge conflicts.

[0059] When the conflict type When this occurs, it indicates a vertex collision. At this time, This indicates that the conflict occurred in the voxel. If two drones and At the same time step Occupy the same voxel ,Right now: Then determine the drone and At time step There is a vertex collision, and the corresponding collision tuple is represented as: .

[0060] When the conflict type At this time, it indicates that a border conflict has occurred. This indicates that the conflict involves voxels. With voxels Local transfer edges between two drones. and In time interval An edge conflict occurs when two edges cross the same local transition edge in opposite directions, or when they occupy local transition edges in the same direction within the same time interval. If the following conditions are met: (Reverse edge conflict), or satisfy: Then determine the drone and In time interval There are edge conflicts in memory, and the corresponding conflict tuple is represented as follows: .

[0061] By using the vertex and edge conflict detection methods described above, potential spatiotemporal conflicts among multiple UAVs in a shared low-altitude airspace can be identified before trajectory execution.

[0062] In some embodiments, identifying vertex and edge conflicts based on the initial four-dimensional trajectories of each UAV includes: When a vertex conflict is detected, a vertex coordination constraint is generated to prevent one of the conflicting drones from occupying the conflicting voxel at the conflict time step. When an edge conflict is detected, an edge coordination constraint is generated that prohibits one of the conflicting drones from performing a conflict transfer action during the conflict time interval. The generated vertex coordination constraints or edge coordination constraints are added to the constraint set of the corresponding UAV, and constraint replanning is performed on the UAV under the updated constraint set to obtain the replanned trajectory. If replanning is successful, the original trajectory of the UAV is replaced with the replanned trajectory to obtain a low-energy, conflict-free four-dimensional trajectory; if replanning fails, the current constraint branch is abandoned; conflict detection, constraint generation and constraint replanning are repeated until there are no conflicts or feasible candidate solutions among the trajectories of all UAVs.

[0063] Step 7: Generate coordination constraints based on the conflict type and perform constraint reprogramming.

[0064] Please see Figure 7 , Figure 7 This paper demonstrates a multi-UAV trajectory replanning process based on voxel-based temporal coordination constraints. First, an initial four-dimensional trajectory set of multiple UAVs is input, and a spatiotemporal occupancy set is constructed based on the voxel occupancy status of each UAV at different time steps. Then, trajectory conflicts are identified on a unified time axis. If no conflict exists, a conflict-free four-dimensional trajectory set is output, and the planning process ends. When a spatiotemporal conflict is detected, the UAV involved in the conflict, the conflicting voxel or transition edge, the conflicting time step, and the conflict type are extracted. When a spatiotemporal conflict is detected, the high-level coordination module generates candidate coordination constraints for the two UAVs involved in the conflict and adds these candidate constraints to the constraint sets of their respective UAVs. The low-level planning module performs constraint replanning under the corresponding candidate constraint sets to obtain candidate replanned trajectories. If multiple feasible candidate trajectories exist, the total energy consumption perceived cost of each candidate trajectory is calculated, and the candidate constraint with the minimum total cost and its corresponding trajectory are selected as the update result, ensuring that the trajectory after conflict resolution still has low energy consumption.

[0065] For vertex conflicts If constraints are applied to drones Then vertex coordination constraints are generated: .in, This indicates a coordination constraint; the constraint prohibits drones. At time step Voxel usage .

[0066] For edge conflict If constraints are applied to drones Then, edge coordination constraints are generated: This constraint prohibits drones. In time interval Internal execution from voxel To voxels The transfer action.

[0067] Add the corresponding drone based on the coordination constraints generated by the conflict. constraint set The updated constraint set is represented as follows: .in Indicates conflict Generate and apply to drones Coordination and constraints.

[0068] Subsequently, in the updated constraint set Below, for drones Reprogramming under constraints. The reprogramming problem is represented as: ; in, Indicates drone The replanning trajectory; This indicates that the starting point, ending point, time window, obstacle avoidance, motion constraints, and newly added coordination constraints are satisfied. The set of feasible trajectories.

[0069] If a feasible replanning trajectory is found, then use Replace the original trajectory This yields an updated set of multi-UAV trajectories. If no feasible trajectory is found, the candidate constraint branch is discarded.

[0070] Repeat the conflict detection, constraint generation, and constraint replanning processes until there are no remaining conflicts or feasible candidate solutions in the set of multiple UAV trajectories.

[0071] In some embodiments, the reprogrammed four-dimensional trajectory is smoothed and its executability is verified, including: The discrete voxel time trajectory obtained after constrained replanning is obtained, the path point mapping and simplification are performed, the center position of each voxel is extracted as the trajectory point, and the key point sequence is obtained after removing redundant intermediate points. Estimate the local heading angle for each keypoint in the keypoint sequence, and form pose pairs by combining the positions and heading angles of adjacent keypoints; By using the Durbins curve to connect adjacent pose pairs while satisfying the minimum turning radius constraint, a smoothed planar trajectory is obtained, and the planar trajectory is then elevated to a three-dimensional geometric trajectory according to the arc length parameter. The three-dimensional geometric trajectory is parameterized in time to satisfy the velocity constraint and the rate of ascent constraint. If a local trajectory segment does not meet the velocity constraint or the rate of ascent constraint, the flight speed of the current local trajectory segment is reduced or a waiting segment is inserted to obtain an executable four-dimensional trajectory. The executable four-dimensional trajectory is validated for executability. The executability validation includes determining whether the trajectory maintains a preset safe distance from obstacles and no-fly zones, whether it meets the mission time window requirements, and whether it meets the minimum safe interval requirements between multiple UAVs. Finally, a set of low-energy executable four-dimensional trajectories for multiple UAVs is obtained.

[0072] Step 8: Perform trajectory smoothing and executability processing on the discrete four-dimensional trajectory.

[0073] After constraint reprogramming, discrete voxel time trajectories that satisfy conflict constraints are obtained. Since directly connecting voxel centers will result in a broken trajectory, which may have problems such as sharp turns, abrupt changes in heading, and discontinuous velocity, the discrete trajectory needs to be smoothed and made executable.

[0074] For drones The final discrete trajectory obtained after conflict resolution is: ; in, Indicates drone At time step The corresponding voxel center location; Indicates drone The time step to reach the endpoint voxel. Indicates drone The next step after departure The corresponding center position of the voxel. Indicates drone At the time step The center position of the endpoint voxel. After removing redundant intermediate points, the keypoint sequence is obtained: , express One key point, This indicates the number of key points. For each key point... Estimate local heading angle And the pose pairs corresponding to adjacent keypoints are represented as: ; in, , Indicates the first The key point and the first The planar pose corresponding to each key point. , Indicates two key points atx Coordinates along the axis, , Indicates two key points at y Coordinates along the axis, , This indicates the heading angle at two key points.

[0075] Subsequently, a trajectory smoothing method based on the Durbins curve was adopted to meet the minimum turning radius. Under the given conditions, adjacent pose pairs are connected to obtain a smoothed planar trajectory. Then, according to the arc length parameter... Elevate the planar trajectory to a three-dimensional geometric trajectory ,in They represent drones At the arc length position s along x axis, y shaft and z Spatial coordinates along the axis. Parameterize the smooth trajectory in time, ensuring it satisfies velocity constraints and rate of ascent or descent constraints: , ; in, Indicates the position of the drone at the arc length. The speed at that location; This represents the rate of change of height with respect to the arc length parameter; Indicates the maximum flight speed; This indicates the maximum climb or descent rate. If a local trajectory segment does not meet the speed or climb rate constraints, the flight speed for that segment is reduced, or a short waiting period is inserted to ensure the trajectory's executability. The final result is the UAV... Executable four-dimensional trajectory: ; in, Represents continuous physical time; Indicates drone In continuous physical time The three-dimensional spatial position at that time.

[0076] Finally, the executable four-dimensional trajectory is validated for feasibility, including determining whether the trajectory maintains a preset safe distance from buildings, obstacles, and no-fly zones, whether it meets the mission time window requirements, and whether it meets the minimum safe interval requirements between multiple UAVs, thereby ensuring that the trajectory meets the actual flight execution requirements.

[0077] Step 9: Output a set of executable four-dimensional trajectories for multiple UAVs: ,in Indicates drone Executable four-dimensional trajectory, This represents the set of executable four-dimensional trajectories for all drones.

[0078] Each executable four-dimensional trajectory includes the UAV's spatial position, speed, heading, and mission arrival time at different times. Through the above steps, this invention can generate safe, smooth, low-energy, and executable multi-UAV four-dimensional trajectories in urban low-altitude multi-UAV transportation scenarios, satisfying constraints such as obstacle avoidance, no-fly zone avoidance, safety intervals, mission time windows, flight performance, and energy consumption.

[0079] Comparative experiment: To verify the technical effectiveness of this invention, four comparative methods were selected for performance analysis: Conflict-based Objective-oriented Prioritization (CBOP), which employs 3D grid search and priority conflict handling; Improved A* Algorithm, which uses grid occupancy and improved heuristic A* for path search; Meta-learning and Local-search Enhanced Genetic Algorithm (MLGA), which uses genetic search to generate multi-UAV trajectories; and 4D Fast Marching Square Method (4D-FM). 2 It generates a spacetime trajectory through four-dimensional arrival time propagation.

[0080] In the comparative experiment, three types of urban low-altitude scenarios were set up: small, medium, and large. The spatial ranges of the three scenarios were 600×700×100m, 1200×1400×200m, and 2400×2800×300m, respectively, with 60, 120, and 240 buildings respectively. Ten UAV transport missions were set up in each scenario, and six OD (Destination, Distance) levels were set based on the distance between the mission's origin (O) and destination. For simplicity, the maximum OD distance of each scenario was selected as the representative experimental condition, with the OD distances corresponding to the small, medium, and large scenarios being 500m, 1100m, and 2200m, respectively. Within the same scenario, all methods used completely identical building and no-fly zone distributions, mission origin and destination, mission time windows, maximum flight speeds, maximum climb or descent rates, minimum turning radii, and safe spacing between multiple UAVs. The energy consumption perception cost weight was set to... , , , To characterize the effective utilization of available voxel time resources by the planned trajectory, the spatiotemporal utilization rate is defined. It is represented as follows: ; in, This represents the number of non-repeating voxel time points that are effectively used in the planned trajectory set. This represents the total number of voxel time points available to the UAV within the mission-related airspace. Under the condition of ensuring no trajectory conflicts and satisfying the same safety constraints, The larger the value, the more fully the drone trajectory can utilize available low-altitude resources in both spatial and temporal dimensions.

[0081] The experimental platform consisted of Windows 11, an Intel Core i7-14700 2.10 GHz processor, and 64 GB of memory. Each experiment was run independently 15 times, and the statistical results are shown in Table 1. Table 1: Performance Comparison of Trajectory Planning Methods in Low-Altitude Scenarios of Different Cities ,

[0082] This invention achieves a 100% planning success rate in small, medium, and large scenarios. CBOP and Improved A* also maintain a 100% planning success rate; MLGA achieves a success rate of 67% in all three scenarios; 4D-FM² achieves a 100% success rate in small and medium scenarios, but drops to 91% in large scenarios. This demonstrates that this invention can still stably generate multi-UAV trajectories that meet constraints even with increased airspace size, increased number of buildings, and extended mission distance.

[0083] Regarding energy consumption, the perceived total energy cost of this invention in small, medium, and large scenarios is 6031.8934, 12065.3717, and 23758.1197, respectively, all being the lowest values ​​in their respective scenarios. In small scenarios, this invention reduces energy consumption by approximately 8.45%, 32.21%, 12.59%, and 11.19% compared to CBOP, Improved A*, MLGA, and 4D-FM², respectively; in medium scenarios, it reduces energy consumption by approximately 10.33%, 17.05%, 13.50%, and 5.26%; and in large scenarios, it reduces energy consumption by approximately 10.69%, 14.25%, 9.85%, and 0.22%. While the perceived energy cost of this invention is close to that of 4D-FM² in large scenarios, 4D-FM² does not always achieve successful planning and has a very high computational cost, resulting in overall performance inferior to this invention.

[0084] In terms of spatiotemporal utilization, the present invention achieves spatiotemporal utilization rates of 33%, 76%, and 74% in small, medium, and large scenarios, respectively, all of which are higher than the highest values ​​of 31%, 69%, and 60% of the comparative methods in the corresponding scenarios. This indicates that the present invention uses voxel-time nodes to uniformly represent the occupation status of UAVs on spatial and temporal resources, and utilizes conflict detection and coordination constraint replanning mechanisms to enable different UAVs to reuse the same or adjacent spatial resources at different times, thereby improving the spatiotemporal utilization efficiency of limited urban low-altitude resources.

[0085] Regarding planning time, the average planning times of this invention in small, medium, and large scenes are 48.0161 s, 91.1696 s, and 100.6470 s, respectively, all lower than the four comparison methods. Particularly in large scenes, the average planning time of 4D-FM² increases to 5307.9321 s, while that of this invention is only 100.6470 s. Although the energy consumption of this invention and 4D-FM² in large scenes is similar, 4D-FM² does not always succeed in planning, and its computational overhead is very high, resulting in overall performance inferior to this invention. This invention, by unifying the representation of voxel time nodes and performing constraint replanning only on UAVs affected by conflict constraints, can reduce unnecessary repeated searches and maintain high planning efficiency even when the scene scale expands.

[0086] In summary, this invention achieves a 100% planning success rate in small, medium, and large scenarios, while also achieving the lowest energy consumption, the highest spatiotemporal utilization rate, and the shortest average planning time, demonstrating excellent overall performance.

[0087] Based on the same inventive concept, please see Figure 8 The present invention also provides a low-energy trajectory planning system for multiple unmanned aerial vehicles based on spatiotemporal voxel maps, comprising: The data acquisition module is used to acquire urban low-altitude airspace data, multiple drone transport mission data, and drone flight constraint data; The spatiotemporal voxel graph construction module is used to construct a spatiotemporal voxel graph containing voxel time nodes and feasible transition edges based on urban low-altitude airspace data. The energy consumption cost calculation module is used to determine the energy consumption perception transfer cost of each feasible transfer edge based on the flight action of the UAV. The initial trajectory generation module is used to generate low-energy initial four-dimensional trajectories for multiple UAV transportation tasks based on spatiotemporal voxel maps, energy consumption perception transfer costs, and data from multiple UAV transportation tasks. The trajectory conflict identification module is used to identify vertex conflicts and edge conflicts based on the initial four-dimensional trajectory of each UAV. The collaborative constraint replanning module is used to generate vertex constraints that prohibit conflicting drones from occupying specified voxels at specified time steps, or edge constraints that prohibit conflicting drones from performing specified transfer actions within specified time intervals, based on the identified vertex or edge conflicts. The vertex or edge constraints are added to the constraint set of the conflicting drones, and constraint replanning is performed under the updated constraint set. The constraint replanning aims to minimize the energy consumption-aware transfer cost, and only prohibits passage at the constrained voxel time nodes or transfer edges. The trajectory smoothing module is used to smooth the replanned four-dimensional trajectory and perform executability verification. The trajectory output module is used to output low-energy executable four-dimensional trajectories for multiple UAVs.

[0088] Based on the same inventive concept, the present invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the multi-UAV low-energy trajectory planning method based on spatiotemporal voxel maps as described above.

[0089] The program product of the present invention for implementing the above-described method may employ a portable compact disk read-only memory and include program code, and may run on a terminal device, such as a personal computer. However, the program product of the present invention is not limited thereto. In the present invention, the readable storage medium may be any tangible medium containing or storing a program that may be used by or in conjunction with an instruction execution system, apparatus, or device.

[0090] It should be noted that a computer-readable storage medium may include data signals propagated in baseband or as part of a carrier wave, carrying readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A readable storage medium may also be any readable medium other than a readable storage medium, capable of transmitting, propagating, or transmitting programs for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the readable storage medium may be transmitted using any suitable medium, including but not limited to wireless, wired, optical fiber, RF, etc., or any suitable combination thereof.

[0091] Unless otherwise defined, the technical or scientific terms used in this invention shall have the general meaning understood by one of ordinary skill in the art to which this invention pertains. Words such as “a,” “an,” “an,” “the,” “the,” and “these” used in this invention do not indicate quantitative limitations and may be singular or plural. The terms “comprising,” “including,” “having,” and any variations thereof used in this invention are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or device that comprises a series of steps or modules (units) is not limited to the listed steps or modules (units) but may include steps or modules (units) not listed, or may include other steps or modules (units) inherent to these processes, methods, products, or devices. Words such as “connected,” “linked,” and “coupled” used in this invention are not limited to physical or mechanical connections but may include electrical connections, whether direct or indirect. “A plurality” used in this invention refers to two or more. “And / or” describes the relationship between related objects, indicating that three relationships may exist; for example, “A and / or B” can represent: A alone, A and B simultaneously, and B alone. Normally, the character " / " indicates that the objects before and after it are in an "or" relationship. In this invention, the terms "first," "second," "third," etc., are used only to distinguish similar objects and do not represent a specific order of objects.

[0092] Obviously, the accompanying drawings are merely some examples or embodiments of the present invention. Those skilled in the art can apply the present invention to other similar situations based on these drawings without any creative effort. Furthermore, it is understood that although the work done in this development process may be complex and lengthy, certain design, manufacturing, or production modifications made according to the technical content disclosed in the present invention are merely conventional technical means and should not be considered as insufficient disclosure of the present invention.

[0093] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-described technical content to create equivalent embodiments without departing from the scope of the present invention. The implementation schemes in the above embodiments can also be further combined or replaced. Any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A low-energy trajectory planning method for multiple unmanned aerial vehicles based on spatiotemporal voxel maps, characterized in that, Includes the following steps: Acquire urban low-altitude airspace data, multiple drone transport mission data, and drone flight constraint data; A spatiotemporal voxel graph containing voxel time nodes and feasible transition edges is constructed based on urban low-altitude airspace data. Based on the flight maneuvers of the drone, determine the energy consumption perception transfer cost of each feasible transfer edge; Based on the spatiotemporal voxel map, energy consumption perception transfer cost, and the data of the multiple UAV transportation tasks, low-energy initial four-dimensional trajectories corresponding to multiple UAV transportation tasks are generated. Vertex and edge conflicts are identified based on the initial four-dimensional trajectories of each UAV; Based on the identified vertex or edge conflicts, vertex constraints are generated to prohibit conflicting drones from occupying specified voxels at specified time steps, or edge constraints to prohibit conflicting drones from performing specified transfer actions within specified time intervals. The vertex or edge constraints are added to the constraint set of the conflicting drones, and constraint replanning is performed under the updated constraint set. The constraint replanning aims to minimize the energy consumption-aware transfer cost, and prohibits passage only at the constrained voxel time nodes or transfer edges. The reprogrammed four-dimensional trajectory is smoothed and its feasibility is verified. Outputs low-energy, four-dimensional trajectories for multiple drones.

2. The method according to claim 1, characterized in that, The urban low-altitude airspace data includes the urban low-altitude three-dimensional airspace range and its boundary values ​​in each coordinate axis direction of the three-dimensional spatial coordinate system, as well as the location information of buildings, static obstacles and no-fly zones; The data for the multiple drone transport missions includes the origin, destination, earliest takeoff time, and latest arrival time of multiple flight requests, with each flight request being executed by one drone. The UAV flight constraint data includes the UAV's maximum flight speed, maximum climb or descent rate, minimum safe interval, and minimum turning radius.

3. The method according to claim 2, characterized in that, A spatiotemporal voxel graph containing voxel time nodes and feasible transition edges is constructed based on urban low-altitude airspace data, including: The urban low-altitude airspace is discretized into a three-dimensional voxel set, and the spatial index and center coordinates of each voxel are determined; obstacles and no-fly zones are expanded, and the passable voxel set is determined based on the expanded obstacles and no-fly zones. The planning timeframe is arranged according to time steps. Discretize into a discrete time set. Based on the set of traversable voxels and the set of discrete time, construct a set of voxel time nodes. Determine candidate transition edges between adjacent discrete time steps. For any traversable voxel, use six adjacent voxels and allow the UAV to hover in the current voxel. The spatiotemporal voxel graph is composed of all traversable voxel time nodes and the traversable transition edges obtained after screening the candidate transition edges.

4. The method according to claim 3, characterized in that, The feasible transition edges obtained after filtering candidate transition edges include: Obtain the starting voxel center coordinates and ending voxel center coordinates, as well as the starting voxel height coordinates and ending voxel height coordinates for each candidate transition edge; Calculate the horizontal projection distance of the candidate transfer edge based on the coordinates of the starting voxel center and the ending voxel center; calculate the height change of the candidate transfer edge based on the height coordinates of the starting voxel and the ending voxel. If a candidate transfer edge simultaneously satisfies the following conditions: the horizontal distance is no greater than the product of the maximum flight speed and the time step, and the altitude change is no greater than the product of the maximum climb or descent rate and the time step, then the candidate transfer edge is retained as a feasible transfer edge; otherwise, it is excluded.

5. The method according to claim 4, characterized in that, Based on the drone's flight maneuvers, determine the energy consumption perception transfer cost for each feasible transfer edge, including: The climb or descent altitude is determined based on the altitude change, and the flight path angle is determined based on the horizontal projection distance and altitude change. The horizontal flight cost is determined based on the horizontal projection distance, the climb cost is determined based on the climb altitude, the descent cost is determined based on the descent altitude, and the non-horizontal flight or turning penalty cost is determined based on the flight path angle. The energy consumption perceived transfer cost of each feasible transfer edge is obtained by weighted summing of the horizontal flight cost, climb cost, descent cost, and non-horizontal flight or turning penalty cost. For the discrete voxel time trajectory of each UAV, the energy consumption perception transfer costs of the feasible transfer edges at each time step are summed to obtain the total energy consumption perception trajectory cost of each UAV.

6. The method according to claim 5, characterized in that, Based on the spatiotemporal voxel map, energy consumption perception transfer cost, and the data from the multiple UAV transportation tasks, low-energy initial four-dimensional trajectories corresponding to multiple UAV transportation tasks are generated, including: For each flight request, it is executed by the corresponding UAV, with the starting voxel and the voxel time node corresponding to the earliest take-off time of each flight request as the starting node, and the ending voxel and the latest arrival time of each flight request as the target constraints. Based on voxel time nodes, feasible transition edges, and energy consumption-aware transition costs, an energy consumption-weighted spatiotemporal voxel graph is obtained; in the energy consumption-weighted spatiotemporal voxel graph, a feasible trajectory from the starting node to the voxel time node that satisfies the target constraint is searched. The feasible trajectory that minimizes the cumulative energy consumption perception transfer cost is used as the initial four-dimensional trajectory for each flight requirement.

7. The method according to claim 1, characterized in that, Vertex and edge conflicts are identified based on the initial four-dimensional trajectories of each UAV, including: Based on the voxels occupied at each time step in each initial four-dimensional trajectory, construct a set of candidate trajectories for all UAVs; Spatiotemporal conflict detection is performed on the trajectories of different drones on a unified timeline: if two drones occupy the same voxel at the same time step, a vertex conflict is determined to have occurred; if two drones cross the same local transfer edge in opposite directions within the same time interval, or occupy the same local transfer edge in the same direction within the same time interval, an edge conflict is determined to have occurred.

8. The method according to claim 7, characterized in that, Vertex and edge conflicts are identified based on the initial four-dimensional trajectories of each UAV, including: When a vertex conflict is detected, a vertex coordination constraint is generated to prevent one of the conflicting drones from occupying the conflicting voxel at the conflict time step. When an edge conflict is detected, an edge coordination constraint is generated that prohibits one of the conflicting drones from performing a conflict transfer action during the conflict time interval. The generated vertex coordination constraints or edge coordination constraints are added to the constraint set of the corresponding UAV, and constraint replanning is performed on the UAV under the updated constraint set to obtain the replanned trajectory. If replanning is successful, the original trajectory of the UAV is replaced with the replanned trajectory to obtain a low-energy, conflict-free four-dimensional trajectory; if replanning fails, the current constraint branch is abandoned; conflict detection, constraint generation and constraint replanning are repeated until there are no conflicts or feasible candidate solutions among the trajectories of all UAVs.

9. The method according to claim 1, characterized in that, The reprogrammed four-dimensional trajectory is smoothed and its feasibility is verified, including: The discrete voxel time trajectory obtained after constrained replanning is obtained, the path point mapping and simplification are performed, the center position of each voxel is extracted as the trajectory point, and the key point sequence is obtained after removing redundant intermediate points. Estimate the local heading angle for each keypoint in the keypoint sequence, and form pose pairs by combining the positions and heading angles of adjacent keypoints; By using the Durbins curve to connect adjacent pose pairs while satisfying the minimum turning radius constraint, a smoothed planar trajectory is obtained, and the planar trajectory is then elevated to a three-dimensional geometric trajectory according to the arc length parameter. The three-dimensional geometric trajectory is parameterized in time to satisfy the velocity constraint and the rate of ascent constraint. If a local trajectory segment does not meet the velocity constraint or the rate of ascent constraint, the flight speed of the current local trajectory segment is reduced or a waiting segment is inserted to obtain an executable four-dimensional trajectory. The executable four-dimensional trajectory is validated for executability. The executability validation includes determining whether the trajectory maintains a preset safe distance from obstacles and no-fly zones, whether it meets the mission time window requirements, and whether it meets the minimum safe interval requirements between multiple UAVs. Finally, a set of low-energy executable four-dimensional trajectories for multiple UAVs is obtained.

10. A low-energy trajectory planning system for multiple unmanned aerial vehicles based on spatiotemporal voxel maps, characterized in that, include: The data acquisition module is used to acquire urban low-altitude airspace data, multiple drone transport mission data, and drone flight constraint data; The spatiotemporal voxel graph construction module is used to construct a spatiotemporal voxel graph containing voxel time nodes and feasible transition edges based on urban low-altitude airspace data. The energy consumption cost calculation module is used to determine the energy consumption perception transfer cost of each feasible transfer edge based on the flight action of the UAV. The initial trajectory generation module is used to generate low-energy initial four-dimensional trajectories corresponding to multiple UAV transportation tasks based on the spatiotemporal voxel map, energy consumption perception transfer cost and the multiple UAV transportation task data. The trajectory conflict identification module is used to identify vertex conflicts and edge conflicts based on the initial four-dimensional trajectory of each UAV. The collaborative constraint replanning module is used to generate vertex constraints that prohibit conflicting drones from occupying specified voxels at specified time steps, or edge constraints that prohibit conflicting drones from performing specified transfer actions within specified time intervals, based on the identified vertex or edge conflicts; add the vertex or edge constraints to the constraint set of the conflicting drones, and perform constraint replanning under the updated constraint set. The constraint replanning takes minimizing the energy consumption-aware transfer cost as the optimization objective, and prohibits passage only at the constrained voxel time nodes or transfer edges. The trajectory smoothing module is used to smooth the replanned four-dimensional trajectory and perform executability verification. The trajectory output module is used to output low-energy executable four-dimensional trajectories for multiple UAVs.

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