Hydrogen energy unmanned aerial vehicle intelligent obstacle avoidance method based on online identification
Through online identification and 3D data processing, the intelligent obstacle avoidance method for hydrogen-powered drones solves the problem that traditional algorithms cannot identify obstacles in complex environments, achieving real-time obstacle recognition and safe flight.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2025-10-21
- Publication Date
- 2026-03-24
AI Technical Summary
Traditional path planning algorithms are unable to intelligently identify and avoid unexpected situations in complex environments during the flight of hydrogen-powered drones, which affects flight safety.
The intelligent obstacle avoidance method for hydrogen-powered drones based on online identification acquires 3D maps and 3D point cloud data, combines historical mission routes and current mission information, identifies and plans detours or accelerations to pass obstacles in real time, and constructs a speed-position objective function to optimize the obstacle avoidance scheme.
It enables real-time obstacle recognition and intelligent obstacle avoidance for hydrogen-powered drones in complex environments, reducing energy consumption, ensuring flight safety, and optimizing path planning.
Smart Images

Figure CN120993954B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The application relates to the technical field of three-dimensional position control, and in particular to an intelligent obstacle avoidance method for a hydrogen energy unmanned aerial vehicle based on online identification. BACKGROUND
[0002] The hydrogen energy unmanned aerial vehicle is an unmanned aerial vehicle using a hydrogen fuel cell as a power source, has the advantages of long endurance, zero emission and strong low-temperature adaptability, and has great potential in the fields of power inspection, environmental monitoring and emergency rescue. Due to the strong environmental adaptability, the hydrogen energy unmanned aerial vehicle usually performs tasks in complex environments. In addition to the harsh weather environment, in the fields of power inspection and emergency rescue, the hydrogen energy unmanned aerial vehicle also needs to face the influence of complex geological environments such as complex terrains. Rapid obstacle identification and intelligent obstacle avoidance can ensure the normal operation of the hydrogen energy unmanned aerial vehicle.
[0003] During the flight of the hydrogen energy unmanned aerial vehicle in performing a task, due to the strong environmental adaptability and the wide application in the field of emergency rescue, the working environment will be in a complex weather environment and geological environment. The traditional path planning algorithm cannot intelligently identify the sudden conditions in the flight process of the hydrogen energy unmanned aerial vehicle and subsequently avoid obstacles. Due to the change of the working posture and the flight speed, the identification and obstacle avoidance process of the hydrogen energy unmanned aerial vehicle will be affected by the working posture and the flight speed, so that the path planning in advance cannot accurately intelligently avoid obstacles at the changing speed, thereby interfering with the safety problem of the flight process of the hydrogen energy unmanned aerial vehicle. SUMMARY
[0004] The application provides an intelligent obstacle avoidance method for a hydrogen energy unmanned aerial vehicle based on online identification, to solve the problem of obstacle identification caused by the change of the working posture and the speed of the unmanned aerial vehicle in a complex environment. The technical scheme adopted is as follows:
[0005] The application provides an intelligent obstacle avoidance method for a hydrogen energy unmanned aerial vehicle based on online identification, to solve the problem of obstacle identification caused by the change of the working posture and the speed of the unmanned aerial vehicle in a complex environment. The technical scheme adopted is as follows:
[0006] A three-dimensional map of the current task of the hydrogen energy unmanned aerial vehicle is obtained, the three-axis speed of the unmanned aerial vehicle at each time is recorded, and the three-dimensional point cloud data near the unmanned aerial vehicle is obtained in real time through a laser radar. A large number of historical tasks of the hydrogen energy unmanned aerial vehicle of the same type are obtained.
[0007] It is judged whether there is a same historical task for the current task. If there is, the planning route of the current task is obtained according to the flight route distribution of the historical task. If there is not, the planning route of the current task is obtained on the basis of the shortest path from the starting point to the ending point of the three-dimensional map and the current task, combined with the working process of the current task. Based on the three-dimensional point cloud data and the flight speed of the unmanned aerial vehicle, a plurality of fixed obstacles and mobile obstacles on the planning route of the current task are obtained.
[0008] Based on the changes in the position of moving obstacles, determine whether the moving obstacles on the planned route can be passed quickly, and formulate an acceleration obstacle avoidance plan accordingly.
[0009] For moving and fixed obstacles that cannot be overcome by speed, a speed-position objective function is constructed based on the planned route, the workflow of the current task, and the possible collision relationship between the drone and the obstacle. The optimization yields a detour obstacle avoidance scheme, which, combined with the planned route, enables intelligent obstacle avoidance for hydrogen-powered drones.
[0010] Optionally, if such a route exists, the planned route for the current mission is obtained based on the flight path distribution of historical missions. Specific methods include:
[0011] Obtain a large number of identical historical tasks for the current task, and use the three-dimensional spatial coordinates of each position in the flight path of any identical historical task as elements. Arrange several elements into a sequence according to the order of their positions in the flight path of the identical historical task, and use this sequence as the flight path sequence of the identical historical task.
[0012] Calculate the DTW distance for any two flight path sequences of the same historical mission. The historical mission corresponding to the flight path sequence with the smallest average DTW distance to other flight path sequences is taken as the reference mission for the current mission, and the flight path of the reference mission is taken as the planned route for the current mission.
[0013] Optionally, if the above does not exist, the planned route for the current task is obtained based on the 3D map and the starting and ending points of the current task, combined with the workflow of the current task, and based on the shortest path from the starting point to the ending point. Specific methods include:
[0014] The system obtains the drone's flight altitude, the start and end points of the current task, and several targets to be monitored in the current task's workflow. The drone flies from the start point to the end point at the flight altitude, passing through each target to be monitored, and obtains the shortest path that meets the conditions, which is then used as the initial route for the current task.
[0015] Based on the obstacles encountered by the initial route in the 3D map, the planned route for the current task is obtained by adjusting the initial route.
[0016] Optionally, the method for adjusting the initial route to obtain the planned route for the current task includes:
[0017] Based on the 3D map, the part of the initial route of the UAV with obstacles at the flight altitude is obtained as the route to be avoided in the initial route, and the obstacle area corresponding to the obstacle is obtained; the starting point and ending point of the route to be avoided corresponding to any obstacle area are obtained, and several routes that do not pass through the obstacle area are obtained between the starting point and the ending point based on the 3D map, as several alternative routes for the route to be avoided.
[0018] If there is no target to be monitored in the obstacle area, the shortest route among all the alternative routes to be avoided for the obstacle area will be used as the replacement route for the route to be avoided.
[0019] If there is a target to be monitored in the obstacle area, obtain the distance from each target to any alternative route in the obstacle area, and use the product of the mean and standard deviation of the distance as the distribution factor of the alternative route; use the product of the distribution factor and the length of the alternative route as the replacement factor of the alternative route; obtain all alternative routes corresponding to the route to be avoided in the obstacle area, and use the alternative route with the minimum replacement factor as the replacement route of the route to be avoided;
[0020] The routes to be avoided in the initial route are replaced by their alternative routes, and the result is used as the planned route for the current task.
[0021] Optionally, the specific method for obtaining several fixed and moving obstacles on the planned route of the current task includes:
[0022] For any 3D point cloud data of the UAV during its flight along the planned route of the current mission, obtain the line connecting any object in the 3D point cloud data at that moment to the UAV, and obtain the projected length of the line in the forward direction of the UAV at that moment, as the projected distance between the object and the UAV at that moment.
[0023] Obtain the projected distance between the object and the drone at the next adjacent moment, and the flight distance of the drone between the two moments. If the absolute value of the difference between the two projected distances is equal to the flight distance, the object is considered a fixed object at that moment; otherwise, the object is considered a moving object at that moment.
[0024] If any object is a fixed object at any given time in the 3D point cloud data, then the object is considered a fixed object; if the object is a moving object at at least one time, then the object is considered a moving object.
[0025] For any fixed object, obtain a 3D structural model of the fixed object and obtain the planned route space corresponding to the planned route of the current UAV mission; if there is an intersection between the 3D structural model and the planned route space, the intersection space is regarded as the intrusion space of the fixed object; if the 3D structural model is completely within the planned route space, the 3D structural model of the fixed object is regarded as the intrusion space, and the fixed object with the intrusion space is regarded as a fixed obstacle; if there is no intersection between the 3D structural model and the planned route space, the fixed object does not constitute a fixed obstacle.
[0026] Based on the positional changes of moving objects in 3D point cloud data, moving obstacles are identified in conjunction with the planned route for the current task.
[0027] Optionally, the method for determining moving obstacles based on the positional changes of moving objects in 3D point cloud data and the planned route of the current task includes:
[0028] For any moving object, the system acquires several moments in the 3D point cloud data at various times as the moving object's movement moments. Based on the moving object's position in the 3D point cloud data at each movement moment, it obtains the moving object's movement path. Combining this with the 3D structural modeling of the moving object, it obtains the moving object's movement path space. If the movement path space intersects with the planned path space, the time interval between the appearance of the intersection space and the disappearance of the intersection space is taken as the intrusion period of the moving object, and the moving object is considered a potential obstacle. If the movement path space does not intersect with the planned path space, the moving object does not constitute a moving obstacle.
[0029] During the flight of the UAV, based on the three-axis velocity of the UAV at several moments in flight, the three-axis velocity is predicted by the least squares method to obtain the three-axis velocity of the UAV at each moment in the intrusion period; combined with the planned route of the current mission, the predicted position of the UAV at each moment in the intrusion period is obtained, and then the predicted route and predicted route space of the UAV in the intrusion period are obtained; if there is an intersection between the predicted route space and the moving route space, the possible moving obstacle is regarded as a moving obstacle.
[0030] Optionally, the specific method for determining whether a moving obstacle on the planned route can be passed quickly includes:
[0031] For any moving obstacle, obtain the position and flight speed of the UAV at the first moment of movement of the moving obstacle, obtain the maximum flight speed of the UAV, and then obtain the time it takes for the UAV to accelerate from the flight speed to the maximum flight speed. Combined with the position of the UAV, obtain the time and position when the UAV reaches the maximum flight speed. Based on the time and position of the maximum flight speed, obtain the flight path space of the UAV during the intrusion time of the moving obstacle.
[0032] If the flight path space intersects with the intersection space, the moving obstacle cannot be accelerated through; if the flight path space does not intersect with the intersection space, the moving obstacle can be accelerated through, and the obstacle can be avoided by accelerating.
[0033] Optionally, the specific method for obtaining the accelerated obstacle avoidance scheme is as follows:
[0034] For any moving obstacle that can be accelerated through, a certain number of flight speeds between the drone's flight speed at the first moment of the obstacle's movement and the drone's maximum flight speed are all taken as the drone's acceleration scheme.
[0035] For any acceleration scheme, obtain the time and position of the UAV accelerating from the flight speed corresponding to the first movement moment to the flight speed corresponding to the acceleration scheme, maintain the flight speed corresponding to the acceleration scheme and fly, and obtain the moment when the UAV leaves the intersection space under the scheme, as the departure moment of the acceleration scheme.
[0036] The difference between the intrusion time of the moving obstacle and the takeoff time of the acceleration scheme is obtained as the takeoff time difference of the acceleration scheme. The difference between the flight speed corresponding to the acceleration scheme and the flight speed of the UAV at the first moving time is obtained as the acceleration metric of the acceleration scheme. The product of the takeoff time difference and the acceleration metric of the acceleration schemes with a takeoff time difference greater than or equal to 0 is inversely proportional to the result, which is used as the optimization factor of the acceleration scheme. The acceleration scheme corresponding to the maximum value among the optimization factors of all acceleration schemes with a takeoff time difference greater than or equal to 0 is used as the acceleration and obstacle avoidance scheme for the moving obstacle.
[0037] Optionally, the specific methods for constructing the velocity-position objective function and optimizing the obstacle avoidance scheme include:
[0038] For any fixed obstacle, several alternative routes are obtained as several detour schemes. The overall flight speed remains constant during the flight along the detour scheme, and the three-axis velocity is decomposed. The detour scheme is projected onto a planned route corresponding to the intrusion space of the fixed obstacle. The positions in the detour scheme that match several positions in the planned route are obtained through projection. Several positions of the detour scheme and several positions projected on the planned route are obtained as several projection position pairs of the detour scheme.
[0039] For any pair of projected positions, the sum of the absolute values of the differences between the three axes of velocity in the pair of projected positions is obtained as the velocity change of the pair of projected positions; several targets to be monitored are obtained in the planned route segment; the difference between the distance between the location of the detour scheme in the pair of projected positions and any target to be monitored, minus the distance between the projected location and the target to be monitored, is obtained as the distance change between the pair of projected positions and the target to be monitored; the sum of the distance changes corresponding to each target to be monitored in the planned route segment is obtained as the monitoring change of the pair of projected positions.
[0040] Based on the velocity change and monitoring change of all projected position pairs in the detour scheme, and combined with the difference between the path length of the detour scheme and the length of the corresponding planned route segment, a velocity-position objective function for several detour schemes with fixed obstacles is constructed. The output value of the objective function is negatively correlated with the velocity change, the monitoring change, and the difference in length.
[0041] For moving obstacles that cannot be accelerated through, the velocity-position objective function is obtained by combining the collision relationship of their intersection space with the velocity-position objective function of the fixed obstacle.
[0042] The obstacle avoidance scheme is the one that corresponds to the maximum value of the objective function output among several detour schemes for any fixed obstacle or a moving obstacle that cannot be passed by speed.
[0043] Optionally, the specific method for obtaining the velocity-position objective function includes:
[0044] For any moving obstacle that cannot be accelerated through, several detour schemes are obtained based on the intersection space of the moving obstacle; several projection position pairs of any detour scheme are obtained, as well as the velocity change and monitoring change of the projection position pairs; for any position in the detour scheme, the time corresponding to the position and the distance between the position and the moving obstacle are obtained by combining the three-dimensional point cloud data, which is used as the collision amount of the projection position pair corresponding to the position.
[0045] If the collision amount of all projected position pairs in any detour scheme is non-negative, construct a velocity-position objective function for them; based on the velocity-position objective function with fixed obstacles, combine the inverse proportional normalization result of the sum of collision amounts of all projected position pairs to obtain the velocity-position objective function.
[0046] The beneficial effects of this invention are as follows: This invention generates a planned route by combining the current task of the UAV with the same historical tasks. If there are no similar historical tasks, the planned route is determined by comprehensively considering the UAV's workflow and flight distance. Based on the real-time acquisition of 3D point cloud data by the UAV's deployed LiDAR, obstacles on the planned route are identified. The distance change relationship between the object and the UAV is used to determine whether it has moved. Combined with the planned route and the distribution and movement changes of objects, it is determined whether the object has intruded into the planned route, providing a basis for subsequent obstacle avoidance analysis. Fixed obstacles do not require acceleration to pass; a detour obstacle avoidance scheme is directly selected. Moving obstacles, which may collide during flight based on the planned route, are assessed by accelerating and then determining whether the obstacle has intruded into the planned route. If the drone cannot avoid moving obstacles even after reaching its maximum flight speed, it will choose to detour. If it can avoid obstacles, it will reduce the speed change to minimize fuel consumption after acceleration, thus obtaining the optimal acceleration obstacle avoidance scheme, while ensuring no collision occurs. For detour obstacle avoidance schemes, the length of the detour path and the changes in position and speed relative to the planned route need to be considered. Since the planned route is the optimal flight scheme obtained based on the workflow, the detour scheme with smaller changes is closer to the optimal flight scheme. At the same time, it is necessary to consider whether the detour process affects the normal operation of the drone, so as to construct a detour scheme with minimal interference to the operation of the target to be monitored, thereby realizing real-time obstacle recognition and intelligent obstacle avoidance of hydrogen-powered drones. Attached Figure Description
[0047] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0048] Figure 1 This is a schematic diagram of a method for intelligent obstacle avoidance of hydrogen-powered drones based on online identification, provided as an embodiment of the present invention. Detailed Implementation
[0049] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0050] Please see Figure 1The diagram illustrates a flowchart of an intelligent obstacle avoidance method for hydrogen-powered drones based on online identification, according to an embodiment of the present invention. The method includes the following steps:
[0051] Step S001: Obtain a 3D map of the current mission of the hydrogen-powered drone, record the three-axis velocity of the drone at each moment, and obtain 3D point cloud data near the drone in real time through LiDAR, and obtain a large number of historical missions of the same model of hydrogen-powered drone.
[0052] The purpose of this embodiment is to enable hydrogen-powered drones to quickly identify obstacles and perform intelligent obstacle avoidance based on real-time speed and attitude during flight in complex working environments. This requires acquiring the task that the hydrogen-powered drone is currently performing, as well as a real-time 3D map. The drone's movement speed along the x, y, and z axes is measured in real time using a three-axis velocity sensor, while a lidar system acquires 3D point cloud data of the area ahead of the drone in real time for obstacle monitoring. Furthermore, the flight processes of a large number of historical tasks that are the same as the current task can provide a reference for the current task to perform subsequent real-time intelligent obstacle avoidance.
[0053] Specifically, the current task to be performed by the hydrogen-powered drone is obtained as the drone's current task. Based on the starting and ending points of the current task, a 3D map of the area between the starting and ending points is obtained. The 3D map acquisition represents the current flight process of the drone, which will not be elaborated further in this embodiment. Three-axis velocity sensors are deployed in the drone to measure the drone's velocity in the x, y, and z axes in real time, with the acquisition time interval set to record the three-axis velocity once per second. At the same time, all historical tasks of the same drone model as the current drone are obtained from the drone flight database, representing a large number of historical tasks of the same model of hydrogen-powered drone.
[0054] It should be further noted that during the flight of the drone, it is necessary to monitor changes in the surrounding terrain in real time, such as fixed obstacles like mountains and buildings, or possible moving obstacles like flying sand and rocks in harsh environments, as well as moving obstacles such as other aircraft. In such cases, it is necessary to deploy lidar to monitor the three-dimensional point cloud data of the direction of travel in real time in order to achieve rapid obstacle avoidance.
[0055] Specifically, a lidar is deployed in front of the hydrogen-powered drone (corresponding to the direction of travel). The lidar acquires three-dimensional point cloud data of the drone's direction of travel in real time. The acquisition cycle of the three-dimensional point cloud data is set by the lidar itself. When the drone's flight direction changes, it needs to be re-acquired. The specific process is existing technology and will not be described in detail in this embodiment.
[0056] It should be noted that after acquiring the 3D map, based on whether a large number of drones of the same model have performed tasks along the same route, route planning is performed for the drone in conjunction with the 3D map, initially avoiding fixed terrain obstacles. However, during the drone's flight, due to complex geological environments and possible drastic weather changes, sudden obstacles or objects may intrude into the planned route. It is necessary to identify and avoid obstacles in a timely manner. Therefore, based on the 3D point cloud data in the direction of travel, it is determined whether sudden obstacles will intrude into the planned route. The three-axis velocity comprehensively reflects the drone's flight attitude and speed. Based on the speed and the planned route, the collision risk is judged, and similarity analysis is performed by combining the speed space and the speed space of historical tasks. Through similar speed models, combined with the intrusion of obstacles into the planned route, a real-time obstacle avoidance route is obtained, and the hydrogen-powered drone is controlled to avoid obstacles.
[0057] Step S002: Determine whether there is a similar historical mission for the current mission. If there is, obtain the planned route for the current mission based on the flight path distribution of the historical mission. If there is no similar historical mission, obtain the planned route for the current mission based on the shortest path from the start to the end point of the current mission, according to the 3D map and the start and end points of the current mission, combined with the workflow of the current mission. Based on the 3D point cloud data and the flight speed of the UAV, obtain several fixed and moving obstacles on the planned route of the current mission.
[0058] Preferably, in one embodiment of the present invention, the method of determining whether there is a similar historical mission for the current mission, and if so, obtaining the planned route for the current mission based on the flight path distribution of the historical mission, includes the following specific methods:
[0059] Historical tasks with the same start and end points as the current task, and with the same workflow as the current task (the workflow for the target to be monitored, such as the high-voltage power poles to be inspected in power line inspection, where the high-voltage power poles are the target to be monitored), are considered the same historical tasks as the current task.
[0060] Furthermore, a large number of identical historical tasks are obtained for the current task, and the three-dimensional spatial coordinates of each position in the flight path of any identical historical task are used as elements. Several elements are arranged into a sequence according to the order of their positions in the flight path of the identical historical task, which is used as the flight path sequence of the identical historical task. The DTW distance between any two flight path sequences of identical historical tasks is calculated. The identical historical task corresponding to the flight path sequence with the smallest average DTW distance to other flight path sequences is used as the reference task for the current task, and the flight path of the reference task is used as the planned route for the current task.
[0061] It should be noted that if there are similar historical missions and the same workflow, the flight routes of the same historical missions can be used as a reference for the planning route of the current mission. At the same time, even if the workflow is the same, the routes may differ due to obstacle avoidance and other measures. The route with the smallest difference from other routes is used as the planning route, that is, the route with the least change during flight.
[0062] It should be further explained that if there are no identical historical tasks, then the first step is to connect the starting point and the first target to be monitored between the starting point and the ending point, taking into account the targets to be monitored in the workflow. The shortest path is obtained by connecting them one by one to ensure that the initial route passes through each target to be monitored. Then, obstacles in the initial route are avoided, namely obstacles such as terrain and buildings that are themselves shown as obstacles in the 3D map, in order to obtain the planned route.
[0063] Preferably, in one embodiment of the present invention, if the path does not exist, the planned route for the current task is obtained based on the shortest path from the start point to the end point, according to the 3D map and the start and end points of the current task, combined with the workflow of the current task. The specific method includes:
[0064] The system acquires the UAV's flight altitude, the start and end points of the current mission, and several targets to be monitored in the current mission's workflow. The UAV flies from the start point to the end point at the specified flight altitude, passing each target to be monitored, and obtains the shortest path that meets the conditions, which is then used as the initial route for the current mission. Based on a 3D map, the system identifies the obstacle sections in the initial route at the specified flight altitude, which are then used as routes to be avoided in the initial route, and the corresponding obstacle areas are obtained. The system acquires the start and end points of any obstacle area corresponding to the route to be avoided, and based on the 3D map, obtains several routes between the start and end points that do not pass through the obstacle area, serving as several alternative routes for the route to be avoided.
[0065] Furthermore, based on the 3D map, the parts of the initial route of the UAV at its flight altitude containing obstacles are obtained as the routes to be avoided in the initial route, and the obstacle areas corresponding to the obstacles are obtained (directly obtained based on the 3D map, the initial route, and the corresponding flight altitude, i.e., obstacles such as mountains and buildings that intrude into the flight altitude of the initial route and can be directly obtained from the 3D map); the starting point and ending point of the route to be avoided corresponding to any obstacle area are obtained, and several routes that do not pass through the obstacle area are obtained between the starting point and the ending point based on the 3D map, as several alternative routes for the route to be avoided (based on the terrain of the obstacle area, the shortest detour scheme in each direction under different directions is used as the alternative routes, which can be directly obtained based on the 3D map and will not be elaborated further); if the obstacle If no target is found in the obstacle area, the shortest alternative route among all candidate routes to be avoided for that obstacle area is selected as the replacement route. If a target is found in the obstacle area, the distance from each target to any candidate route is obtained, and the product of the mean and standard deviation of these distances is used as the distribution factor of the candidate route. The product of the distribution factor and the length of the candidate route is used as the replacement factor of the candidate route. All candidate routes to be avoided for that obstacle area are obtained, and the candidate route with the smallest replacement factor is selected as the replacement route. Each candidate route in the initial route is replaced by its replacement route, and the result is used as the planned route for the current task.
[0066] It should be noted that, in the absence of identical historical tasks, the shortest path between the starting point and the end point is obtained by ensuring that it passes through each target to be monitored, and this path is used as the initial route. Then, for the parts of the initial route that pass through obstacles, replacement is required, that is, obstacles that cannot be passed must be avoided, and each section that passes through obstacles is used as the route to be avoided. If there are multiple detour options for obstacle areas, and there are no targets to be monitored in the obstacle area, the shortest alternative route is used directly as the replacement. If there are targets to be monitored, it is necessary to ensure that the distance to the targets to be monitored during the detour is small enough and the distance fluctuation is small, and the length of the alternative route should also be as short as possible, in order to select alternative routes.
[0067] It should be further explained that during the flight of the hydrogen-powered drone along the planned route, it acquires three-dimensional point cloud data of the front in real time through lidar. Based on the three-dimensional point cloud data, it identifies objects within the flight route range and determines whether the objects have moved by using three-dimensional point cloud data at adjacent moments. For stationary objects, it is necessary to analyze their three-dimensional structure to determine whether they are on the planned route. If they are moving objects, it is necessary to analyze whether they have intruded into the planned route and the moment of intrusion by judging their speed and direction of movement.
[0068] Preferably, in one embodiment of the present invention, based on three-dimensional point cloud data and the flight speed of the UAV, a number of fixed and moving obstacles on the planned route of the current task are obtained, including the following specific method:
[0069] For any given moment in the UAV's flight path during the current mission, the following steps are taken: 1) Obtain the line connecting any object in the 3D point cloud data to the UAV at that moment (objects identified in the 3D point cloud data from the LiDAR, excluding fixed objects in the 3D map). 2) Obtain the projected length of this line in the UAV's forward direction at that moment, which is used as the projected distance between the object and the UAV at that moment. 3) Obtain the projected distance between the object and the UAV at the next adjacent moment, and the UAV's flight distance between the two moments. If the absolute value of the difference between the two projected distances is equal to the flight distance, the object is considered a fixed object at that moment; otherwise, it is considered a moving object. 4) If any object is a fixed object at all corresponding moments in the 3D point cloud data, it is considered a fixed object. 5) If an object is a moving object at at least one moment, it is considered a moving object.
[0070] Furthermore, for any fixed object, a 3D structural model of the fixed object is obtained, and the planned route space corresponding to the planned route of the current mission of the UAV is obtained (the planned route has a certain width and height due to the volume of the hydrogen-powered UAV, that is, the planned route is represented by a cylindrical range); if there is an intersection space between the 3D structural model and the planned route space (the intersection of the planned route space and the 3D structural model, both of which are three-dimensional structures), the intersection space is regarded as the intrusion space of the fixed object; if the 3D structural model is completely within the planned route space, the 3D structural model of the fixed object is regarded as the intrusion space, and the fixed object with the intrusion space is regarded as a fixed obstacle; if there is no intersection space between the 3D structural model and the planned route space, the fixed object does not constitute a fixed obstacle.
[0071] Furthermore, for any moving object, several moments in the 3D point cloud data of the moving object at various times are obtained as the movement moments of the moving object. Based on the position of the moving object in the 3D point cloud data at each movement moment, the movement route of the moving object is obtained. Combined with the 3D structural modeling of the moving object, the movement route space of the moving object is obtained. If there is an intersection space between the movement route space and the planned route space, the time period from the time when the intersection space appears to the time when the intersection space disappears is taken as the intrusion period of the moving object, and the moving object is regarded as a possible moving obstacle. If there is no intersection space between the movement route space and the planned route space, the moving object does not constitute a moving obstacle.
[0072] It should be further explained that after determining the intrusion of real-time 3D point cloud data into the route, it is necessary to further determine whether there is a collision risk between the drone and possible moving obstacles. Fixed obstacles always pose a collision risk and must be avoided based on the collision risk; while for possible moving obstacles, it is necessary to analyze whether there is an intersection between the boundary space and the drone's movement on the planned route during the intrusion period, in order to obtain the moving obstacle.
[0073] Furthermore, during the drone's flight, based on the three-axis velocities of the drone at several moments in flight, the three-axis velocities are predicted using the least squares method to obtain the three-axis velocities of the drone at each moment in the intrusion period; combined with the planned route of the current mission, the predicted position of the drone at each moment in the intrusion period is obtained, thereby obtaining the predicted route and predicted route space of the drone in the intrusion period; if there is an intersection between the predicted route space and the moving route space, the possible moving obstacle is regarded as a moving obstacle.
[0074] At this point, a planned route is generated by combining the current task of the UAV with the same historical tasks. If there are no similar historical tasks, the planned route is determined by comprehensively considering the UAV's workflow and flight distance. Based on the real-time acquisition of three-dimensional point cloud data by the lidar deployed on the UAV, obstacles on the planned route are identified. The distance change relationship between the object and the UAV is used to determine whether the object has moved. Combined with the planned route and the distribution and movement changes of the object, it is determined whether the object has intruded into the planned route, thus providing a basis for subsequent obstacle avoidance analysis.
[0075] Step S003: Based on the changes in the position of the moving obstacle, determine whether the moving obstacle on the planned route can be passed quickly, and formulate an acceleration obstacle avoidance plan accordingly.
[0076] It should be noted that after a collision risk is identified, it is necessary to take measures to avoid the collision risk, including two avoidance options: acceleration and detour. The optimal obstacle avoidance route is obtained by comprehensively considering whether the distance to the monitored target is too far away, whether the distance changes too much, and the degree of change in the collision risk under different avoidance options, i.e., the change in the collision range, and then controlling the drone to perform intelligent obstacle avoidance.
[0077] Specifically, for any moving obstacle, the position and flight speed of the UAV at the first moment of movement of the moving obstacle are obtained, the maximum flight speed of the UAV is obtained, and then the time it takes for the UAV to accelerate from the stated flight speed to the maximum flight speed is obtained. Combined with the position of the UAV, the time and position when the UAV reaches the maximum flight speed are obtained. Based on the time and position of the maximum flight speed, the flight path space of the UAV during the intrusion time of the moving obstacle is obtained. If the flight path space intersects with the intersection space, the moving obstacle cannot be accelerated through; if the flight path space does not intersect with the intersection space, the moving obstacle can be accelerated through, and obstacle avoidance is performed by accelerating through the moving obstacle.
[0078] It should be further noted that for various acceleration schemes, all of them accelerate from the current speed to a certain speed and maintain a certain speed to pass through the boundary space. The smaller the change in the drone's speed, that is, the smaller the acceleration range, and the closer the time when the drone flies out of the intersection space is before the intrusion time period and the closer it is to the intrusion time period, the smaller the energy cost required for the corresponding acceleration scheme to achieve obstacle avoidance. In this way, the objective function is constructed and the acceleration obstacle avoidance scheme is obtained.
[0079] Specifically, for any moving obstacle that can be accelerated through, several flight speeds between the drone's flight speed at the first moment of movement and the drone's maximum flight speed are used as the drone's acceleration scheme (in this embodiment, the acceleration scheme is set every 1 km / h, i.e., the data collection interval is 1 km / h, starting from the flight speed corresponding to the first moment of movement and ending at the maximum flight speed); for any acceleration scheme, the time and position of the drone accelerating from the flight speed corresponding to the first moment of movement to the flight speed corresponding to the acceleration scheme are obtained, the drone maintains the flight speed corresponding to the acceleration scheme and flies, and the moment when the drone leaves the intersection space under the scheme is obtained as the departure moment of the acceleration scheme.
[0080] Furthermore, the difference between the first moment of the intrusion time of the moving obstacle and the departure time of the acceleration scheme is obtained as the departure time difference of the acceleration scheme; the difference between the flight speed corresponding to the acceleration scheme and the flight speed of the UAV at the first moment of movement is obtained as the acceleration metric of the acceleration scheme; the product of the departure time difference and the acceleration metric of the acceleration schemes with departure time differences greater than or equal to 0 is inversely proportionalized and used as the optimization factor of the acceleration scheme, that is, a departure time difference less than 0 indicates that the moving obstacle was not avoided and it is not considered for optimization; the acceleration scheme corresponding to the maximum value among the optimization factors of all acceleration schemes with departure time differences greater than or equal to 0 is used as the acceleration obstacle avoidance scheme for the moving obstacle; the acceleration obstacle avoidance schemes for each moving obstacle that can be accelerated through are obtained according to the above method.
[0081] At this point, fixed obstacles do not require acceleration to pass and the detour obstacle avoidance scheme is directly selected. For moving obstacles, since collisions may occur during flight based on the planned route, the flight is accelerated and then judged. If the moving obstacle cannot be avoided after reaching the maximum flight speed, the detour is also selected. If it can be avoided, the speed change is reduced to reduce the consumption of drone energy and fuel while ensuring that there is no collision after acceleration, thus obtaining the optimal acceleration obstacle avoidance scheme.
[0082] Step S004: For moving and fixed obstacles that cannot be passed quickly, based on the planned route, the current task workflow, and the possible collision relationship between the drone and the obstacle, a speed-position objective function is constructed, and the detour obstacle avoidance scheme is optimized. Combined with the planned route, intelligent obstacle avoidance of the hydrogen-powered drone is realized.
[0083] Specifically, for any fixed obstacle, following the method for obtaining alternative routes for the obstacle area during the route planning process, several alternative routes are obtained as several detour schemes for the fixed obstacle. During flight along the detour scheme, the overall flight speed remains constant, i.e., the scalar velocity in the flight speed does not change; only the flight direction changes, and the three-axis velocity is decomposed. The detour scheme is projected onto a segment of the planned route corresponding to the intrusion space of the fixed obstacle. Through projection, positions matching several locations in the detour scheme within the planned route segment are obtained (the number of locations in the planned route is fixed). This yields several positions of the detour scheme and several positions projected onto the planned route, serving as several projection position pairs of the detour scheme. For any... For a projected position pair, the sum of the absolute values of the differences in the three-axis velocities of the projected position pair is obtained. That is, the absolute value of the difference in the x-axis velocity between the position of the bypass scheme and the projected position in the projected position pair, and the absolute values of the differences in the y-axis and z-axis velocities are obtained and summed, which is taken as the velocity change of the projected position pair. Several targets to be monitored are obtained in the planned route segment. The difference between the distance between the position of the bypass scheme and any of the targets to be monitored in the projected position pair and the distance between the projected position and the target to be monitored is obtained, which is taken as the distance change between the projected position pair and the target to be monitored. The sum of the distance changes corresponding to each target to be monitored in the planned route segment is taken as the monitoring change of the projected position pair.
[0084] Furthermore, based on the speed change and monitoring change of all projected position pairs in the detour scheme, and combined with the difference between the path length of the detour scheme and the length of the corresponding planned route segment, a speed-position objective function for several detour schemes with fixed obstacles is constructed. The output value of the objective function is negatively correlated with the speed change, the monitoring change, and the difference in length (a negative correlation in the entire real number domain; the negative correlation is still satisfied even when the input is negative, i.e., the monitoring change and the difference in length may both be negative).
[0085] As an example, the mean of the velocity change for all projected position pairs in the detour scheme and the mean of all monitored changes are obtained. The product of the two means and the difference of the length is then inversely normalized to construct the velocity-position objective function.
[0086] Furthermore, the detour scheme corresponding to the maximum value of the objective function output among several detour schemes for the fixed obstacle is taken as the detour and obstacle avoidance scheme for the fixed obstacle.
[0087] It should be further explained that for moving obstacles that cannot be passed quickly, the same detour strategy as for fixed obstacles should be used to avoid them. In addition to the detour strategy for fixed obstacles, collision judgment should be performed based on the intersection space of moving obstacles to optimize the selection of detour strategies.
[0088] Specifically, for any moving obstacle that cannot be accelerated through, based on the intersection space of the moving obstacle, several detour schemes are obtained from the intersection space according to the method for generating detour schemes for fixed obstacles; and several pairs of projected positions for any detour scheme are obtained relative to the planned route, as well as the speed change and monitoring change of the projected position pairs; simultaneously, for any position in the detour scheme, since the flight speed scalar remains constant, the time corresponding to that position can be obtained during the UAV's flight along the detour scheme, and the position of the moving obstacle at that time can be determined through three-dimensional point cloud data, obtaining the distance between that position and the position of the moving obstacle at that time. If a collision occurs, the distance is set to -1; if no collision occurs, the minimum distance is 0. The unit is meters, and the distance is obtained based on the interaction between the lidar and the moving obstacle. The collision amount of the projected position pair corresponding to the given location is obtained. If the collision amount of all projected position pairs in any detour scheme is non-negative, a velocity-position objective function is constructed for them. If the collision amount of any projected position pair is negative, no velocity-position objective function is constructed for it. Based on the velocity-position objective function of the fixed obstacle, the velocity-position objective function is obtained by combining the inversely proportional normalized result of the sum of the collision amounts of all projected position pairs. That is, the velocity-position objective function of the detour scheme of the moving obstacle is the product of the velocity-position objective function of the fixed obstacle and the inversely proportional normalized result of the sum of the collision amounts of all projected position pairs in the detour scheme.
[0089] Furthermore, the detour scheme corresponding to the maximum value of the objective function output among several detour schemes for the moving obstacle is taken as the detour and obstacle avoidance scheme for the moving obstacle; then all fixed and moving obstacles in the planned route are identified in a timely manner based on the three-dimensional point cloud data of LiDAR, and obstacle avoidance schemes are generated to detour or accelerate through, thereby realizing online obstacle identification and intelligent obstacle avoidance of hydrogen-powered drones. After passing through the obstacle, the drone returns to the original planned route to continue flying.
[0090] Therefore, for the detour obstacle avoidance scheme, it is necessary to comprehensively consider the length of the detour path, as well as the changes in position and speed relative to the planned route. Since the planned route is the optimal flight plan obtained based on the workflow, the detour scheme with smaller changes is closer to the optimal flight plan. At the same time, it is necessary to consider whether the detour process affects the normal working process of the drone, so as to construct the detour scheme with minimal interference to the working process of the target to be monitored, thereby realizing the real-time obstacle recognition and intelligent obstacle avoidance of the hydrogen-powered drone.
[0091] It should be noted that this embodiment adopts... The model is used to represent the inverse proportional relationship and for normalization processing. As input to the model, This represents an exponential function with the natural constant as the base. Implementers can set inverse proportional functions and normalization functions according to the actual situation.
[0092] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the principles of the present invention should be included within the protection scope of the present invention.
Claims
1. A method for intelligent obstacle avoidance of hydrogen-powered unmanned aerial vehicles based on online identification, characterized in that, The method includes the following steps: Acquire a 3D map of the current mission of the hydrogen-powered drone, record the three-axis velocity of the drone at each moment, and acquire 3D point cloud data near the drone in real time through LiDAR, and obtain a large number of historical missions of the same model of hydrogen-powered drone. The system determines whether there are any identical historical missions for the current mission. If so, it obtains the planned route for the current mission based on the flight path distribution of the historical missions. If not, it obtains the planned route for the current mission based on the shortest path from the start to the end point, using the 3D map and the start and end points of the current mission, combined with the workflow of the current mission. Based on the 3D point cloud data and the flight speed of the UAV, it obtains several fixed and moving obstacles on the planned route of the current mission. Based on the changes in the position of moving obstacles, determine whether the moving obstacles on the planned route can be passed quickly, and formulate an acceleration obstacle avoidance plan accordingly. For moving and fixed obstacles that cannot be passed quickly, a speed-position objective function is constructed based on the planned route, the workflow of the current task, and the possible collision relationship between the drone and the obstacle. The detour obstacle avoidance scheme is optimized and combined with the planned route to realize intelligent obstacle avoidance of hydrogen-powered drones. If no such path exists, the planned route for the current task is obtained based on the 3D map, the start and end points of the current task, and the workflow of the current task, using the shortest path from the start to the end point. The specific methods include: obtaining the UAV's flight altitude, the start and end points of the current task, and several targets to be monitored in the workflow of the current task; the UAV flies from the start point to the end point at the specified flight altitude, passing through each target to be monitored, obtaining the shortest path that meets the conditions and using it as the initial route for the current task; based on the 3D map, the parts of the initial route where obstacles exist are obtained, serving as the routes to be avoided in the initial route, and the obstacle areas corresponding to the obstacles are obtained; the start and end points of the routes to be avoided corresponding to any obstacle area are obtained, and several routes between the start and end points are obtained based on the 3D map that do not pass through the obstacle area. The route through the obstacle area is used as several alternative routes for the route to be avoided. If there is no target to be monitored in the obstacle area, the shortest route among all the alternative routes for the obstacle area is used as the replacement route. If there is a target to be monitored in the obstacle area, the distance from each target to any alternative route in the obstacle area is obtained, and the product of the mean and standard deviation of the distance is used as the distribution factor of the alternative route. The product of the distribution factor and the length of the alternative route is used as the replacement factor of the alternative route. All alternative routes for the obstacle area are obtained, and the alternative route with the minimum replacement factor is used as the replacement route. Each route to be avoided in the initial route is replaced by its replacement route, and the result is used as the planned route for the current task.
2. The intelligent obstacle avoidance method for hydrogen-powered unmanned aerial vehicles based on online identification according to claim 1, characterized in that, If such a route exists, the planned route for the current mission is obtained based on the flight route distribution of historical missions. Specific methods include: Obtain a large number of identical historical tasks for the current task, and use the three-dimensional spatial coordinates of each position in the flight path of any identical historical task as elements. Arrange several elements into a sequence according to the order of their positions in the flight path of the identical historical task, and use this sequence as the flight path sequence of the identical historical task. Calculate the DTW distance for any two flight path sequences of the same historical mission. The historical mission corresponding to the flight path sequence with the smallest average DTW distance to other flight path sequences is taken as the reference mission for the current mission, and the flight path of the reference mission is taken as the planned route for the current mission.
3. The intelligent obstacle avoidance method for hydrogen-powered unmanned aerial vehicles based on online identification according to claim 1, characterized in that, The specific method for obtaining several fixed and moving obstacles on the planned route of the current task includes: For any 3D point cloud data of the UAV during its flight along the planned route of the current mission, obtain the line connecting any object in the 3D point cloud data at that moment to the UAV, and obtain the projected length of the line in the forward direction of the UAV at that moment, as the projected distance between the object and the UAV at that moment. Obtain the projected distance between the object and the drone at the next adjacent moment, and the flight distance of the drone between the two moments. If the absolute value of the difference between the two projected distances is equal to the flight distance, the object is considered a fixed object at that moment; otherwise, the object is considered a moving object at that moment. If any object is a fixed object at any given time in the 3D point cloud data, then the object is considered a fixed object; if the object is a moving object at at least one time, then the object is considered a moving object. For any fixed object, obtain the 3D structural model of the fixed object and obtain the planned route space corresponding to the planned route of the current UAV mission. If there is an intersection between the three-dimensional structure modeling and the planned route space, the intersection space shall be regarded as the intrusion space of the fixed object; If the three-dimensional structure model is entirely within the planned route space, the three-dimensional structure model of the fixed object is regarded as the intrusive space, and the fixed object with intrusive space is regarded as the fixed obstacle. If there is no boundary between the three-dimensional structure modeling and the planned route space, the fixed object does not constitute a fixed obstacle; Based on the positional changes of moving objects in 3D point cloud data, moving obstacles are identified in conjunction with the planned route for the current task.
4. The intelligent obstacle avoidance method for hydrogen-powered unmanned aerial vehicles based on online identification according to claim 3, characterized in that, The method for determining moving obstacles based on the positional changes of moving objects in 3D point cloud data and the planned route of the current task includes the following specific methods: For any moving object, obtain several moments in the 3D point cloud data of the moving object at each moment, and take them as the moving moments of the moving object. Based on the position of the moving object in the 3D point cloud data at each moving moment, obtain the moving route of the moving object. By combining the three-dimensional structural model of the moving object, the spatial path of the moving object is obtained. If there is an intersection between the movement route space and the planned route space, the time period from the time the intersection appears to the time the intersection disappears shall be taken as the intrusion period of the moving object, and the moving object shall be regarded as a possible moving obstacle. If there is no boundary between the movement route space and the planned route space, the moving object does not constitute a movement obstacle; During the flight of the UAV, based on the three-axis velocity of the UAV at several moments in flight, the three-axis velocity is predicted by the least squares method to obtain the three-axis velocity of the UAV at each moment in the intrusion period; combined with the planned route of the current mission, the predicted position of the UAV at each moment in the intrusion period is obtained, and then the predicted route and predicted route space of the UAV in the intrusion period are obtained. If the predicted route space and the moving route space have an intersection, the possible moving obstacle is taken as a moving obstacle.
5. The intelligent obstacle avoidance method for hydrogen-powered unmanned aerial vehicles based on online identification according to claim 4, characterized in that, The specific methods for determining whether moving obstacles on the planned route can be passed quickly include: For any moving obstacle, obtain the position and flight speed of the UAV at the first moment of movement of the moving obstacle, obtain the maximum flight speed of the UAV, and then obtain the time it takes for the UAV to accelerate from the said flight speed to the maximum flight speed. Combined with the position of the UAV, obtain the time and position when the UAV reaches the maximum flight speed. Based on the time and location of maximum flight speed, obtain the flight path space of the UAV during the period of intrusion of the moving obstacle; If the flight path space intersects with the intersection space, the moving obstacle cannot be accelerated through; if the flight path space does not intersect with the intersection space, the moving obstacle can be accelerated through, and the obstacle can be avoided by accelerating.
6. The intelligent obstacle avoidance method for hydrogen-powered unmanned aerial vehicles based on online identification according to claim 5, characterized in that, The specific methods for obtaining the accelerated obstacle avoidance scheme are as follows: For any moving obstacle that can be accelerated through, a certain number of flight speeds between the drone's flight speed at the first moment of the obstacle's movement and the drone's maximum flight speed are all taken as the drone's acceleration scheme. For any acceleration scheme, obtain the time and position of the UAV accelerating from the flight speed corresponding to the first movement moment to the flight speed corresponding to the acceleration scheme, maintain the flight speed corresponding to the acceleration scheme and fly, and obtain the moment when the UAV leaves the intersection space under the scheme, as the departure moment of the acceleration scheme. The difference between the intrusion time of the moving obstacle and the take-off time of the acceleration scheme is obtained as the take-off time difference of the acceleration scheme; the difference between the flight speed corresponding to the acceleration scheme and the flight speed of the UAV at the first moving moment is obtained as the acceleration measure of the acceleration scheme. The product of the takeoff time difference and the acceleration metric of the acceleration scheme with a takeoff time difference greater than or equal to 0, and then processed inversely, is used as the optimal factor for that acceleration scheme. The acceleration scheme corresponding to the maximum value among the optimization factors of all acceleration schemes with takeoff time differences greater than or equal to 0 is used as the acceleration and obstacle avoidance scheme for the moving obstacle.
7. The intelligent obstacle avoidance method for hydrogen-powered unmanned aerial vehicles based on online identification according to claim 5, characterized in that, The specific methods for constructing the velocity-position objective function and optimizing the obstacle avoidance scheme include: For any fixed obstacle, several alternative routes are obtained as several detour schemes. The overall flight speed remains constant during the flight along the detour scheme, and the three-axis velocity is decomposed. The detour scheme is projected onto a planned route corresponding to the intrusion space of the fixed obstacle. The positions in the detour scheme that match several positions in the planned route are obtained through projection. Several positions of the detour scheme and several positions projected on the planned route are obtained as several projection position pairs of the detour scheme. For any pair of projection positions, obtain the sum of the absolute values of the differences between the three axes of velocity in the pair of projection positions, and use it as the velocity change of the pair of projection positions. The plan obtains several targets to be monitored contained in the planned route. The difference between the distance between the position of the detour scheme of the projected position pair and any of the targets to be monitored and the distance between the projected position and the target to be monitored is obtained as the distance change between the projected position pair and the target to be monitored. The sum of the distance changes corresponding to each target to be monitored contained in the planned route is used as the monitoring change of the projected position pair. Based on the velocity change and monitoring change of all projected position pairs in the detour scheme, and combined with the difference between the path length of the detour scheme and the length of the corresponding planned route segment, a velocity-position objective function for several detour schemes with fixed obstacles is constructed. The output value of the objective function is negatively correlated with the velocity change, the monitoring change, and the difference in length. For moving obstacles that cannot be accelerated through, the velocity-position objective function is obtained by combining the collision relationship of their intersection space with the velocity-position objective function of the fixed obstacle. The obstacle avoidance scheme is the one that corresponds to the maximum value of the objective function output among several detour schemes for any fixed obstacle or a moving obstacle that cannot be passed by speed.
8. The intelligent obstacle avoidance method for hydrogen-powered unmanned aerial vehicles based on online identification according to claim 7, characterized in that, The specific method for obtaining the velocity-position objective function is as follows: For any moving obstacle that cannot be accelerated through, several detour schemes are obtained based on the intersection space of the moving obstacle; several projection position pairs of any detour scheme are obtained, as well as the velocity change and monitoring change of the projection position pairs; for any position in the detour scheme, the time corresponding to the position and the distance between the position and the moving obstacle are obtained by combining the three-dimensional point cloud data, which is used as the collision amount of the projection position pair corresponding to the position. If the collision amount of all projected position pairs in any detour scheme is non-negative, construct a velocity-position objective function for them; based on the velocity-position objective function with fixed obstacles, combine the inverse proportional normalization result of the sum of collision amounts of all projected position pairs to obtain the velocity-position objective function.
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