CN115617076A - Trajectory planning and dynamic obstacle avoidance method for near-earth search UAV - Google Patents
Trajectory planning and dynamic obstacle avoidance method for near-earth search UAV Download PDFInfo
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Abstract
Description
技术领域technical field
本发明属于无人机路径规划及轨迹优化领域,特别是一种近地搜索无人机的轨迹规划及动态避障方法。The invention belongs to the field of UAV path planning and trajectory optimization, in particular to a method for trajectory planning and dynamic obstacle avoidance of a near-earth search UAV.
背景技术Background technique
最初,无人机由于其隐蔽性好、造价相对低廉、易操作、不惧伤亡等优点,受到了各国军事行业的重视。如今,无人机的运用由军事逐步扩散向教育、影视、农业以及服务行业之中。无人机也被称为飞行机器人或者无人驾驶飞行器。这些飞行器大多被用于观察、搜索和谨慎规划。近年来随着无人机技术的进步,使得无人机在城市及山区等复杂地形环境下的近地搜索和救援(SAR)成为可能。例如在俄勒冈州的一次救援任务中,无人机被用于确认狭槽峡谷中的死亡事件,并消除了搜救人员在夜间进行危险绳降的需要。该技术可以极大减少搜索时间,提高救援的效率,在人工巡逻困难且耗时的区域为团队提供引导帮助。目前而言,无人机在部分地区的空域活动依然十分有限。禁飞区的飞行任务更是需要相关部门的授权和许可。然而这将远远限制了无人机搜索和救援的范围,无法发挥出无人机的优势和工作水准。合理建立和规划基于无人机的搜索与救援体系框架,将无人机正确运用于城市和山区执行近地搜索任务,将会给救援提供巨大的帮助。Initially, due to its good concealment, relatively low cost, easy operation, and no fear of casualties, UAVs have been valued by the military industries of various countries. Today, the use of drones has gradually spread from the military to education, film and television, agriculture and service industries. Drones are also known as flying robots or unmanned aerial vehicles. Most of these craft are used for observation, search and careful planning. In recent years, with the advancement of drone technology, it has become possible for drones to perform near-ground search and rescue (SAR) in complex terrain environments such as cities and mountains. During a rescue mission in Oregon, for example, drones were used to confirm fatalities in slot canyons and eliminated the need for rescuers to make dangerous abseiling at night. This technology can greatly reduce search time, improve rescue efficiency, and provide guidance for teams in areas where manual patrols are difficult and time-consuming. For now, the airspace activities of drones in some areas are still very limited. Flight missions in no-fly zones require authorization and permission from relevant departments. However, this will far limit the scope of UAV search and rescue, and cannot give full play to the advantages and working standards of UAVs. Reasonable establishment and planning of a UAV-based search and rescue system framework, and the correct use of UAVs in cities and mountainous areas to perform near-ground search tasks will provide great help to rescue.
与其他商用飞机不同,无人机短距离在垂直方向上起飞和降落增加了无人机在复杂环境当中近地搜索的适配性。尽管如此,无人机在近地执行搜索和救援任务的过程中依然面临着巨大挑战。在目前,基于无人机的近地搜索和救援通常具有一组类似的限制条件。第一,搜索时间紧迫,无人机需要在尽可能快的情况下抵达任务地点,任何延误都可能导致出现不可逆转严重后果;第二、工作环境不友好,无人机在低空作业过程中,建筑物及森林等复杂场景较多,导致无人机生成路径总转折角数量过大。对于无人机而言这不仅消耗能量,而且增加了搜索时间;第三、执行任务过程中出现的动态威胁,无人机需要在工作环境和其他动态障碍物保持安全距离,防止出现航道冲突的现象。这些不利的限制因素使得无人机很难在城市以及山区的低空空域实现飞行任务。Unlike other commercial aircraft, UAVs take off and land vertically in short distances, which increases the adaptability of UAVs for near-ground search in complex environments. Nevertheless, unmanned aerial vehicles still face great challenges in the process of performing search and rescue missions near the ground. Currently, UAV-based near-terrestrial search and rescue typically has a similar set of constraints. First, the search time is tight, and the UAV needs to arrive at the mission location as quickly as possible, and any delay may lead to irreversible serious consequences; second, the working environment is not friendly, and the UAV is operating at low altitude. There are many complex scenes such as buildings and forests, resulting in an excessive number of turning angles in the path generated by the UAV. For unmanned aerial vehicles, this not only consumes energy, but also increases the search time; third, the dynamic threat that occurs during the execution of the mission, the unmanned aerial vehicle needs to keep a safe distance from the working environment and other dynamic obstacles to prevent the occurrence of channel conflicts Phenomenon. These unfavorable limiting factors make it difficult for UAVs to achieve flight tasks in low-altitude airspace in cities and mountainous areas.
发明内容Contents of the invention
为了解决上述问题,本发明提出了一种近地搜索无人机的轨迹规划及动态避障设计方法,通过基于八叉树离散化地图的三维JPS搜索算法所具有的高效快速的路径搜索能力来实现无人机在执行近地任务时的自主导航。In order to solve the above problems, the present invention proposes a trajectory planning and dynamic obstacle avoidance design method for near-earth search UAVs, through the efficient and fast path search ability of the three-dimensional JPS search algorithm based on the octree discretization map. Realize the autonomous navigation of UAVs when performing near-earth missions.
本发明采用的技术方案是:近地搜索无人机的轨迹规划及动态避障设计方法,包括以下步骤:The technical scheme adopted in the present invention is: the trajectory planning and dynamic obstacle avoidance design method of near-earth search UAV, comprising the following steps:
S1,通过八叉树数据结构对无人机的三维工作空间进行离散,并针对跳点搜索算法(JPS)进行三维化扩展,使无人机基于三维静态环境生成无碰撞路径;S1, discretize the 3D working space of the UAV through the octree data structure, and perform 3D expansion for the jump point search algorithm (JPS), so that the UAV can generate a collision-free path based on the 3D static environment;
S2,基于Lazy-Theta*算法的多角度的寻路思想提出了一种路径长度优化法则,并以此实现JPS算法多角度寻路,进一步缩短了无人机的规划路径;S2, based on the multi-angle pathfinding idea of the Lazy-Theta* algorithm, a path length optimization rule is proposed, and the multi-angle pathfinding of the JPS algorithm is realized, which further shortens the planned path of the UAV;
S3,通过基于minimun snap的七阶多项式插值法对优化路径进行平滑性处理,保证路径节点处的连续性;S3, smoothing the optimized path through the seventh-order polynomial interpolation method based on minimun snap to ensure the continuity at the path nodes;
S4,通过虚拟引力场以及三维布雷森汉姆线算法对人工势场(APF)法进行改进,实现无人机在动态威胁冲突环境下的自主避障。S4, the artificial potential field (APF) method is improved through the virtual gravitational field and the three-dimensional Bresenham line algorithm to realize the autonomous obstacle avoidance of the UAV in the dynamic threat conflict environment.
进一步,所述步骤S1中基于无人机三维工作空间的八叉树地图建立以及JPS算法的三维化扩展方式,具体包括:Further, in the step S1, the establishment of an octree map based on the three-dimensional workspace of the drone and the three-dimensional expansion of the JPS algorithm specifically include:
S11,将无人机三维工作空间作为八叉树结构的根节点,依次将飞行空间进行8份或者0份的空间划分,并通过黑色、灰色以及白色色块对障碍物进行表达。S11, using the 3D working space of the UAV as the root node of the octree structure, divide the flight space into 8 or 0 parts in turn, and express obstacles through black, gray and white color blocks.
S12,使用7元结构体的方式对划分出来的子节点进行标记,并存储当前节点与邻居节点的位置关系,以及当前节点到达根节点的距离信息。S12. Use a 7-element structure to mark the divided child nodes, and store the positional relationship between the current node and neighbor nodes, and the distance information from the current node to the root node.
S13,基于三维离散八叉树地图模型对JPS算法的剪枝邻居法则做出了修正和扩充;S13, based on the three-dimensional discrete octree map model, the pruning neighbor rule of the JPS algorithm is corrected and expanded;
S14,基于三维离散八叉树地图模型对JPS算法的强迫邻居以及跳点选取方式进行了修正;S14, based on the three-dimensional discrete octree map model, the forced neighbors and jump point selection methods of the JPS algorithm were corrected;
S15,经过多次实验,对原始的JPS算法的扩展方向进行扩充和修改,使其从二维平面扩充到三维工作空间。S15, after several experiments, the expansion direction of the original JPS algorithm is expanded and modified, making it expand from a two-dimensional plane to a three-dimensional workspace.
进一步,八叉树结构的地图建立:Further, the map of the octree structure is established:
八叉树地图将三维工作空间看成一个整体并将其设置为八叉树结构的根节点,并依次将场景进行8份或者0份的划分。八叉树节点由三种颜色进行表达,分别为:黑色表示当前节点被障碍物占据,无人机无法通行;灰色表示当前节点具有多少障碍物并不明确;白色表示当前节点为可通行节点,无人机可以安全穿过此节点。在本发明中八叉树地图的层数取决于无人机体积的大小,即八叉树最小节点的体积应大于等于1.5倍的无人机体积。The octree map regards the 3D workspace as a whole and sets it as the root node of the octree structure, and divides the scene into 8 or 0 parts in turn. The octree nodes are represented by three colors, which are: black means that the current node is occupied by obstacles, and the drone cannot pass; gray means that the number of obstacles in the current node is not clear; white means that the current node is a passable node, Drones can safely pass through this node. In the present invention, the number of layers of the octree map depends on the volume of the drone, that is, the volume of the smallest node of the octree should be greater than or equal to 1.5 times the volume of the drone.
进一步,JPS算法的剪枝邻居法则的修正具体过程为:Further, the specific process of modifying the pruning neighbor rule of the JPS algorithm is as follows:
(1)当前节点x的父节点parent(x)与当前节点处于同平面直线扩展时,满足二维剪枝规则,且不涉及到其他平面。需要在同平面剪枝掉任何一个满足以下约束条件的邻居节点。(1) When the parent node parent(x) of the current node x is in the same plane as the current node, it satisfies the two-dimensional pruning rule and does not involve other planes. It is necessary to prune any neighbor node that meets the following constraints on the same plane.
len(<parent(x),....,n>\x)≤len(<parent(x),x,n>)len(<parent(x),....,n>\x)≤len(<parent(x),x,n>)
其中len函数表示节点之间的距离,<parent(x),....,n>\x表示不包含当前节点x的情况下从其父节点parent(x)到达任意邻居节点n的所有节点集合。The len function represents the distance between nodes, <parent(x),....,n>\x represents all nodes that reach any neighbor node n from its parent node parent(x) without including the current node x gather.
(2)若当前节点x的父节点parent(x)与当前节点处于同平面斜对角扩展时,同样满足二维剪枝规则,且不涉及到其他平面。即需要在同平面剪枝掉任何一个满足以下约束条件的邻居节点n:(2) If the parent node parent(x) of the current node x is in the same plane as the current node and extends diagonally, it also satisfies the two-dimensional pruning rule and does not involve other planes. That is, any neighbor node n that meets the following constraints needs to be pruned on the same plane:
len(<parent(x),....,n>\x)<len(<parent(x),x,n>)len(<parent(x),....,n>\x)<len(<parent(x),x,n>)
(3)若当前节点x的父节点parent(x)与当前节点为体对角线扩展时,需要沿对角线方向扩展至上层的同时满足以上两个公式。(3) If the parent node parent(x) of the current node x and the current node are expanded diagonally, it is necessary to expand to the upper layer along the diagonal direction and satisfy the above two formulas at the same time.
进一步,JPS算法的强迫邻居以及跳点选取方式,具体包括:Further, the JPS algorithm's forced neighbors and jump point selection methods include:
假设在一个以当前节点x为核心的最小集合当中,被剪枝的邻居集合为P=<x1,x2,x3...,xn>。存在障碍物xob∈P,如果存在任意一个xob的邻居节点xi∈P,xi≠xob满足如下条件,则xi被称之为当前节点x的强迫邻居。同时,x被称之为跳跃点。Assume that in a minimum set with the current node x as the core, the set of neighbors to be pruned is P=<x 1 , x 2 , x 3 . . . , x n >. There is an obstacle x ob ∈ P, if there is any neighbor node x i ∈ P of x ob , and xi ≠ x ob satisfies the following conditions, then xi is called the forced neighbor of the current node x. Meanwhile, x is called a jump point.
len(<parent(x),x,n>)<len(<parent(x),...,n>\x)len(<parent(x),x,n>)<len(<parent(x),...,n>\x)
进一步,三维JPS算法的扩展方向为:Further, the extension direction of the 3D JPS algorithm is:
在八叉树所组成的三维空间当中生成JPS路径,遵循从同平面直线到同平面对角线,再到体对角线的扩展方式。三维JPS在扩展的过程中,以当前节点为基准,首先针对平行于x轴、y轴以及z轴的三个直线搜索方向进行扩展。只有在直线方向上没有寻找到跳跃点时才进行同平面对角扩展且同平面扩展遵循二维JPS算法扩展规则。若仍未发现跳跃点,则最后进行体对角线扩展,即沿地图体对角线扩展一个栅格并继续进行直线和平面搜索。The JPS path is generated in the three-dimensional space formed by the octree, following the expansion method from the straight line of the same plane to the diagonal of the same plane, and then to the diagonal of the body. During the expansion process of the 3D JPS, based on the current node, it first expands for three straight line search directions parallel to the x-axis, y-axis and z-axis. Only when no jump point is found in the straight line direction, the same-plane diagonal expansion is performed, and the same-plane expansion follows the two-dimensional JPS algorithm expansion rule. If the jump point is still not found, then finally carry out the diagonal expansion of the volume, that is, expand a grid along the diagonal of the map volume and continue the straight line and plane search.
进一步,所述步骤S2中基于Lazy-Theta*算法的多角度的寻路思想提出的路径长度优化法则,具体包括:Further, the path length optimization rule proposed in the step S2 based on the multi-angle pathfinding idea of the Lazy-Theta* algorithm specifically includes:
S21,针对JPS算法的搜索节点进行全路径补全,使路径任意两个节点之间直接相连;S21, performing full path completion for the search nodes of the JPS algorithm, so that any two nodes on the path are directly connected;
S22,针对所有路径节点进行父节点预设,将所有节点的父节点进行统筹管理和设计;S22. Perform parent node preset for all path nodes, and conduct overall management and design of the parent nodes of all nodes;
S23,通过视线(LOS)可达性检测重新为路径节点选择合适的父节点,并删除冗余路径间断点实现路径长度优化。S23. Re-selecting a suitable parent node for the path node through line-of-sight (LOS) reachability detection, and deleting redundant path discontinuities to realize path length optimization.
进一步,所述步骤S3中基于minimun snap的七阶多项式插值法对优化路径进行平滑性处理,具体包括:Further, in the step S3, the seventh-order polynomial interpolation method based on minimun snap performs smoothness processing on the optimized path, specifically including:
S31,为保证优化曲线与原路径的拟合程度和安全飞行走廊的设置,本方法对于三维JPS算法的节点集合按照固定步长进行节点插值处理;S31, in order to ensure the degree of fitting between the optimized curve and the original path and the setting of the safe flight corridor, this method performs node interpolation processing on the node set of the three-dimensional JPS algorithm according to a fixed step size;
S32,按照三维JPS算法生成的路径节点集当中的节点个数进行路径分段;S32, performing path segmentation according to the number of nodes in the path node set generated by the three-dimensional JPS algorithm;
S33,将minimum snap设置为最优化目标,并根据路径节点和插值点的位置、速度、加速度以及加加速度的信息设置等式约束条件;S33, setting the minimum snap as the optimization target, and setting the equality constraint condition according to the information of the position, velocity, acceleration and jerk of the path node and the interpolation point;
S34,通过空间膨胀策略,将无人机飞行走廊的设置作为不等式约束加入约束矩阵,并利用二次规划进行求解优化结果。S34, using the space expansion strategy, adding the setting of the UAV flight corridor as an inequality constraint to the constraint matrix, and using quadratic programming to solve the optimization result.
进一步,所述步骤S4中通过虚拟引力场以及三维布雷森汉姆线算法对人工势场(APF)法进行改进,实现无人机在动态威胁冲突环境下的自主避障,具体包括:Further, in the step S4, the artificial potential field (APF) method is improved through the virtual gravitational field and the three-dimensional Bresenham line algorithm to realize the autonomous obstacle avoidance of the UAV in a dynamic threat conflict environment, specifically including:
S41,本发明将布雷森汉姆线算法进一步在三维空间当中进行了扩充,并使用步长采样的方式完成两点之间是否直接可达的检测;S41, the present invention further expands the Bresenham line algorithm in the three-dimensional space, and uses step size sampling to complete the detection of whether two points are directly reachable;
S42,采用在产生局部最优点的障碍物周围增设虚拟目标点的方式促使无人机进行逃逸;S42, using the method of adding a virtual target point around the obstacle that generates the local optimum to prompt the UAV to escape;
S43,将无人机动态避障过程中出现陷入局部最优而无法到达路径目标点的情况进行分类,并使用三维布雷森汉姆线算法以及虚拟目标点进行优化。S43, classify the situation that the UAV falls into a local optimum and cannot reach the path target point during the dynamic obstacle avoidance process, and use the three-dimensional Bresenham line algorithm and the virtual target point for optimization.
本发明的优点及有益效果如下:Advantage of the present invention and beneficial effect are as follows:
对于执行近地搜索和救援的无人机来说,环境复杂、障碍物数量较多以及动态威胁的存在,都对于无人机的路径规划造成了很大的挑战。基于以上问题,本发明的主要有点总结如下:For UAVs performing near-ground search and rescue, the complex environment, the large number of obstacles, and the existence of dynamic threats all pose great challenges to UAV path planning. Based on the above problems, the main points of the present invention are summarized as follows:
(1)针对无人机工作环境当中的静态障碍物,本发明通过八叉树结构地图对于JPS算法进行三维化扩展,以引导无人机在三维空间当中执行飞行任务。通过算法对比实验可以发现,三维JPS算法在时间复杂度和空间复杂度的表现性良好。其中三维JPS算法相比于三维A*算法而言计算时间降低了88.45%到30.18%,相较于RRT算法计算时间降低了34.83%到4.75%。三维JPS算法满足无人机搜索以及救援任务当中对于工作效率高的需求。(1) For the static obstacles in the working environment of the UAV, the present invention expands the JPS algorithm in three dimensions through the octree structure map, so as to guide the UAV to perform flight tasks in the three-dimensional space. Through algorithm comparison experiments, it can be found that the three-dimensional JPS algorithm has good performance in time complexity and space complexity. Among them, the three-dimensional JPS algorithm reduces the calculation time by 88.45% to 30.18% compared with the three-dimensional A* algorithm, and reduces the calculation time by 34.83% to 4.75% compared to the RRT algorithm. The 3D JPS algorithm meets the requirements for high work efficiency in UAV search and rescue missions.
(2)本发明针对三维JPS算法的生成路径,采用了基于Lazy-Theta*算法的任意角度寻路策略对JPS算法的生成路径进行优化。通过改变路径节点当中的父子节点关系链来消除冗余转折点,以此实现三维JPS算法的多角度寻路。其次,本发明引入基于minimumsnap的七阶多项式插值优化,进一步平滑三维JPS算法生成路径的平滑性与连续性。通过实验可知,基于父节点传递法则优化后的路径比三维JPS算法所得到的路径,长度减少了4.8%到8.1%,路径总转折角降低了51.6%到93.2%,路径整体优化效果明显。同时父节点传递法则以及多项式插值优化所导致的算法时间复杂度以及空间复杂度都有所增加,运算时间上比三维JPS算法增加了2.5%到5.4%,内存占用率增加了0.0014%到0.0018%。(2) For the generation path of the three-dimensional JPS algorithm, the present invention adopts an arbitrary-angle pathfinding strategy based on the Lazy-Theta* algorithm to optimize the generation path of the JPS algorithm. By changing the parent-child node relationship chain among the path nodes to eliminate redundant turning points, the multi-angle pathfinding of the 3D JPS algorithm is realized. Secondly, the present invention introduces the seventh-order polynomial interpolation optimization based on minimumsnap to further smooth the smoothness and continuity of the path generated by the three-dimensional JPS algorithm. Experiments show that the path optimized based on the parent node transfer rule is 4.8% to 8.1% shorter than the path obtained by the 3D JPS algorithm, and the total turning angle of the path is reduced by 51.6% to 93.2%. The overall optimization effect of the path is obvious. At the same time, the time complexity and space complexity of the algorithm caused by the parent node transfer rule and polynomial interpolation optimization have increased, and the operation time has increased by 2.5% to 5.4% compared with the three-dimensional JPS algorithm, and the memory usage has increased by 0.0014% to 0.0018%. .
(3)最后,通过基于改进型的人工势场法避障策略来避开无人机在低空飞行作业当中所可能出现的动态威胁。首先本发明针对人工势场法所出现的陷入局部最优的问题进行改进,通过增设虚拟目标引力场和三维布雷森汉姆线算法促使无人机实现局部最优的逃逸。其次通过三维JPS算法结合改进型人工势场法的方式,针对进入警戒范围之内的动态威胁进行避障。通过实验可知,基于改进型的人工势场法的动态避障策略在单入侵者,同轨迹逆向入侵者以及多入侵者的情况下成功的完成避障任务。(3) Finally, through the improved artificial potential field method based on the obstacle avoidance strategy, the dynamic threat that may appear in the low-altitude flight operation of the UAV is avoided. Firstly, the present invention improves the problem of falling into the local optimum in the artificial potential field method, and promotes the UAV to realize local optimum escape by adding a virtual target gravitational field and a three-dimensional Bresenham line algorithm. Secondly, through the combination of the three-dimensional JPS algorithm and the improved artificial potential field method, obstacle avoidance is carried out for dynamic threats entering the warning range. The experiments show that the dynamic obstacle avoidance strategy based on the improved artificial potential field method successfully completes the obstacle avoidance task in the case of a single intruder, a reverse intruder on the same trajectory and multiple intruders.
附图说明Description of drawings
图1为本发明的流程图;Fig. 1 is a flowchart of the present invention;
图2为基于八叉树数据结构的地图建立方式;Fig. 2 is the map building method based on octree data structure;
图3为轨迹优化流程框架;Figure 3 is the trajectory optimization process framework;
图4为无人机陷入局部最优的情况分类;Figure 4 is the classification of the situation where the UAV falls into a local optimum;
图5为第一实验仿真结果图;Fig. 5 is the first experimental simulation result figure;
图6为第二实验结果展示图;Fig. 6 is the second experimental result display figure;
图7为第三实验结果展示图。Fig. 7 is a diagram showing the results of the third experiment.
具体实施方式detailed description
下面将结合本发明实施例中的附图,对本发明实施例中的技术方案进行清楚、详细地描述。所描述的实施例仅仅是本发明的一部分实施例。The technical solutions in the embodiments of the present invention will be described clearly and in detail below with reference to the drawings in the embodiments of the present invention. The described embodiments are only some of the embodiments of the invention.
参见图1,本发明采用的具体方案是:Referring to Fig. 1, the concrete scheme that the present invention adopts is:
S1,通过八叉树数据结构对无人机的三维工作空间进行离散,并针对跳点搜索算法(JPS)进行三维化扩展,使无人机基于三维静态环境生成无碰撞路径:S1, discretize the 3D working space of the UAV through the octree data structure, and perform 3D expansion for the jump point search algorithm (JPS), so that the UAV can generate a collision-free path based on the 3D static environment:
S11,八叉树地图将三维工作空间看成一个整体并将其设置为八叉树结构的根节点,并依次将场景进行8份或者0份的划分。八叉树节点由三种颜色进行表达,分别为:黑色表示当前节点被障碍物占据,无人机无法通行;灰色表示当前节点具有多少障碍物并不明确;白色表示当前节点为可通行节点,无人机可以安全穿过此节点。在本发明中八叉树地图的层数取决于无人机体积的大小,即八叉树最小节点的体积应大于等于1.5倍的无人机体积。S11, the octree map regards the three-dimensional workspace as a whole and sets it as the root node of the octree structure, and divides the scene into 8 or 0 shares in turn. The octree nodes are represented by three colors, which are: black means that the current node is occupied by obstacles, and the drone cannot pass; gray means that the number of obstacles in the current node is not clear; white means that the current node is a passable node, Drones can safely pass through this node. In the present invention, the number of layers of the octree map depends on the volume of the drone, that is, the volume of the smallest node of the octree should be greater than or equal to 1.5 times the volume of the drone.
S13,本发明对于三维JPS算法的剪枝邻居法则做出了进一步的修正,具体修正如下:S13, the present invention makes further amendments to the pruning neighbor rule of the three-dimensional JPS algorithm, and the specific amendments are as follows:
(1)当前节点x的父节点parent(x)与当前节点处于同平面直线扩展时,满足二维剪枝规则,且不涉及到其他平面。需要在同平面剪枝掉任何一个满足以下约束条件的邻居节点。(1) When the parent node parent(x) of the current node x is in the same plane as the current node, it satisfies the two-dimensional pruning rule and does not involve other planes. It is necessary to prune any neighbor node that meets the following constraints on the same plane.
len(<parent(x),....,n>\x)≤len(<parent(x),x,n>)len(<parent(x),....,n>\x)≤len(<parent(x),x,n>)
其中len函数表示节点之间的距离,<parent(x),....,n>\x表示不包含当前节点x的情况下从其父节点parent(x)到达任意邻居节点n的所有节点集合。The len function represents the distance between nodes, <parent(x),....,n>\x represents all nodes that reach any neighbor node n from its parent node parent(x) without including the current node x gather.
(2)若当前节点x的父节点parent(x)与当前节点处于同平面斜对角扩展时,同样满足二维剪枝规则,且不涉及到其他平面。即需要在同平面剪枝掉任何一个满足以下约束条件的邻居节点n:(2) If the parent node parent(x) of the current node x is in the same plane as the current node and extends diagonally, it also satisfies the two-dimensional pruning rule and does not involve other planes. That is, any neighbor node n that meets the following constraints needs to be pruned on the same plane:
len(<parent(x),....,n>\x)<len(<parent(x),x,n>)len(<parent(x),....,n>\x)<len(<parent(x),x,n>)
(3)若当前节点x的父节点parent(x)与当前节点为体对角线扩展时,需要沿对角线方向扩展至上层的同时满足以上两个公式。(3) If the parent node parent(x) of the current node x and the current node are expanded diagonally, it is necessary to expand to the upper layer along the diagonal direction and satisfy the above two formulas at the same time.
S14,本发明对于三维JPS算法的强迫邻居判断标准和跳跃点选取则做出了进一步的修正。在三维JPS算法当中,强迫邻居和跳跃点是一组相对的概念。强迫邻居的数量和位置对于跳跃点而言有着直观的影响。我们假设在一个以当前节点x为核心的最小集合当中,被剪枝的邻居集合为P=<x1,x2,x3...,xn>。存在障碍物xob∈P如果存在任意一个xob的邻居节点xi∈P,xi≠xob满足如下条件,则xi被称之为当前节点x的强迫邻居。同时,x被称之为跳跃点。S14, the present invention makes further amendments to the forced neighbor judgment standard and jump point selection of the 3D JPS algorithm. In the 3D JPS algorithm, forced neighbors and jump points are a set of relative concepts. Forcing the number and location of neighbors has an intuitive effect on hop points. We assume that in a minimum set with the current node x as the core, the pruned neighbor set is P=<x 1 ,x 2 ,x 3 ...,x n >. There is an obstacle x ob ∈ P If there is any neighbor node x i ∈ P of x ob , and x i ≠ x ob satisfies the following conditions, then x i is called the forced neighbor of the current node x. Meanwhile, x is called a jump point.
len(<parent(x),x,n>)<len(<parent(x),...,n>\x)len(<parent(x),x,n>)<len(<parent(x),...,n>\x)
S15,在八叉树所组成的三维空间当中生成JPS路径,遵循从同平面直线到同平面对角线,再到体对角线的扩展方式。三维JPS在扩展的过程中,以当前节点为基准,首先针对平行于x轴、y轴以及z轴的三个直线搜索方向进行扩展。只有在直线方向上没有寻找到跳跃点时才进行同平面对角扩展且同平面扩展遵循二维JPS算法扩展规则。若仍未发现跳跃点,则最后进行体对角线扩展,即沿地图体对角线扩展一个栅格并继续进行直线和平面搜索。S15, generate a JPS path in the three-dimensional space formed by the octree, and follow the expansion method from the straight line on the same plane to the diagonal on the same plane, and then to the diagonal on the body. During the expansion process of the 3D JPS, based on the current node, it first expands for three straight line search directions parallel to the x-axis, y-axis and z-axis. Only when no jump point is found in the straight line direction, the same-plane diagonal expansion is performed, and the same-plane expansion follows the two-dimensional JPS algorithm expansion rule. If the jump point is still not found, then finally carry out the diagonal expansion of the volume, that is, expand a grid along the diagonal of the map volume and continue the straight line and plane search.
S16,基于八叉树地图的三维JPS算法的寻路步骤如下所示S16, the pathfinding steps of the three-dimensional JPS algorithm based on the octree map are as follows
(1)初始化静态空间环境并构建八叉树栅格地图模型,将无人机飞行区域离散化。(1) Initialize the static space environment and construct an octree grid map model to discretize the flight area of the UAV.
(2)设置无人机初始位置xstart和目标点xend。将添加到openlist列表当中。(2) Set the drone's initial position x start t and target point x end . Will Add it to the openlist list.
(3)按照当前节点与其父节点的位置信息选取邻居剪枝法则,计算当前节点的扩展方向。(3) Select the neighbor pruning rule according to the position information of the current node and its parent node, and calculate the expansion direction of the current node.
(4)通过强迫邻居的位置寻找跳跃点并将其加入openlist。(4) Find jumping points by forcing neighbors' positions and add them to openlist.
(5)通过启发式函数对openlist当中的每一个节点进行计算,并选取计算值最小的节点作为跳点和下一次搜索过程中的父节点。(5) Calculate each node in the openlist through a heuristic function, and select the node with the smallest calculation value as the jump point and the parent node in the next search process.
(6)将本次搜索过程中起到父节点作用的节点加入closelist列表当中,并检测closelist当中是否存在目标点。若存在目标点则退出搜索,并通过closelist列表形成搜索路径。若不存在目标点则重复执行步骤(3)到步骤(6)。(6) Add the node that acts as a parent node in the search process to the closelist list, and detect whether there is a target point in the closelist. If there is a target point, exit the search and form a search path through the closelist list. If there is no target point, repeat step (3) to step (6).
S2,如图3所示,本发明基于Lazy-Theta*算法的多角度的寻路思想提出了一种路径长度优化法则,并以此实现JPS算法多角度寻路,进一步缩短了无人机的规划路径。具体过程如下所示:S2, as shown in Figure 3, the present invention proposes a path length optimization rule based on the multi-angle pathfinding idea of the Lazy-Theta* algorithm, and realizes the multi-angle pathfinding of the JPS algorithm with this, further shortening the unmanned aerial vehicle. Plan your path. The specific process is as follows:
(1)首先,本发明针对三维JPS算法的路径节点进行补全,使三维JPS算法路径所经过的每个节点都被包含在节点集合内。设节点集合为pathlist=<xend,xn,xn-1,...,xi,...,x1,xstart>。(1) First, the present invention completes the path nodes of the 3D JPS algorithm, so that each node passed by the 3D JPS algorithm path is included in the node set. Let the set of nodes be pathlist=<x end , x n , x n-1 ,..., x i ,..., x 1 , x start >.
(2)将节点集合当中所有节点的父节点设置为初始节点,即默认所有节点与初始节点之间都具有直接可见性。(2) Set the parent node of all nodes in the node set as the initial node, that is, all nodes have direct visibility to the initial node by default.
(3)由于节点x1与xstart的父子关系没有被修改,因此只需要从x2节点到xend节点依次与xstart进行LOS可达性检测,以此来验证节点之间的可见性是否成立。(3) Since the parent-child relationship between node x 1 and x start has not been modified, it is only necessary to perform LOS reachability detection with x start from node x 2 to node x end in order to verify whether the visibility between nodes is established.
(4)若可见性成立,则无需改动当前节点的父节点关系,将当前节点与xstart之间的节点删除并加入deletelist列表当中。(4) If the visibility is established, there is no need to change the parent node relationship of the current node, and the node between the current node and x start is deleted and added to the deletelist list.
(5)若可见性不成立,则需要在deletelist中为当前节点重新寻找父节点,并将剩余未进行LOS检测的节点的父节点更换成当前节点的父节点继续进行检测。(5) If the visibility is not established, it is necessary to re-find the parent node for the current node in the deletelist, and replace the parent node of the remaining nodes that have not undergone LOS detection with the parent node of the current node to continue detection.
(6)当xend的父节点传递完成则结束算法,输出最短路径。(6) When the transfer of the parent node of x end is completed, the algorithm ends and the shortest path is output.
S3,如图4所示,本发明基于minimun snap的七阶多项式插值法对优化路径进行了平滑性处理,具体过程如下所示:S3, as shown in Figure 4, the present invention is based on the seventh-order polynomial interpolation method of minimun snap and has carried out smoothness processing to optimized path, and specific process is as follows:
(1)为了保证优化曲线与原路径的拟合程度和飞行走廊设置,首先本发明对于三维JPS算法的节点集合按照固定步长进行节点插值处理。(1) In order to ensure the degree of fitting between the optimized curve and the original path and the setting of the flight corridor, firstly, the present invention performs node interpolation processing for the node set of the three-dimensional JPS algorithm according to a fixed step.
(2)按照三维JPS算法生成的路径节点集当中的节点个数进行分段。假设节点集当中具有n+1个节点,则整体路径被分为n段。对于n段路径的多项式表达式如下所示。(2) Segment according to the number of nodes in the path node set generated by the three-dimensional JPS algorithm. Assuming that there are n+1 nodes in the node set, the overall path is divided into n segments. The polynomial expression for n-segment paths is as follows.
其中pm,i表示第m段路径的第i个多项式系数,t表示无人机飞行时间,T0到Tn表示无人机经过每段路径端点的时刻。ti表示时间t的i次方,其中i∈[0,k]。k表示多项式的总阶数。Among them, p m,i represents the i-th polynomial coefficient of the m-th path, t represents the flight time of the UAV, and T 0 to T n represent the moment when the UAV passes through the endpoint of each path. t i represents the i power of time t, where i∈[0,k]. k represents the total order of the polynomial.
(3)通过对于f(t)执行多次求导计算,便可获得对应路径段的速度、加速度、jerk以及snap函数。本发明将minimum snap作为多项式的优化目标公式如下所示。(3) By performing multiple derivative calculations on f(t), the velocity, acceleration, jerk and snap functions of the corresponding path segment can be obtained. The present invention uses the minimum snap as the optimization objective formula of the polynomial as follows.
其中T表示无人机飞行总时间。对公式Jn进行扩展,即可得到PQ问题的二次规划求解方程,如下表达式所示。where T represents the total flight time of the UAV. By extending the formula J n , the quadratic programming solution equation of the PQ problem can be obtained, as shown in the following expression.
其中Jn径表示多项式优化目标函数,P表示路径节点的位置矩阵,Qn表示参数对角矩阵。Among them, J n path represents the polynomial optimization objective function, P represents the position matrix of path nodes, and Q n represents the parameter diagonal matrix.
(4)将路径过程中节点的位置(P=f(t))、速度(v=f'(t))、加速度(a=f”(t))、jerk函数(jerk=f(3)(t))以及snap函数(snap=f(4)(t))作为二次规划当中的等式约束。将每个节点的膨胀区间(膨胀半径为r)作为不等式约束进行求解,公式如下所示,即可得到平滑轨迹节点集合。(4) The position (P=f(t)), velocity (v=f'(t)), acceleration (a=f”(t)) and jerk function (jerk=f) of the node in the path process (3) (t)) and the snap function (snap=f (4) (t)) are used as the equality constraints in the quadratic programming. The expansion interval of each node (the expansion radius is r) is used as the inequality constraint to solve, the formula is as follows Shown, the set of smooth trajectory nodes can be obtained.
S4,本发明通过引入人工势场法,将无人机通过动态势场作用力的方式对路径碰撞区域的无人机飞行轨迹进行调整,以此避免动态威胁引发的碰撞现象。在无人机进行路径规划的过程中,目标点对于无人机所产生的引力与障碍物对于无人机所产生的斥力大小相等方向相反,即无人机处于非目标点处的受力平衡现象。当搜索陷入无人机受力平衡现象即无人机陷入局部最优时,将会导致无人机无法继续进行路径规划,最终无法到达目标点。本发明将人工势场会产生局部最优的情况划分为三种,S4, the present invention adjusts the flight trajectory of the UAV in the path collision area by introducing the artificial potential field method, so as to avoid the collision phenomenon caused by the dynamic threat. During the path planning process of the UAV, the gravitational force generated by the target point on the UAV is equal to the repulsion force generated by the obstacle on the UAV, and the direction is opposite, that is, the force balance of the UAV at a non-target point Phenomenon. When the search falls into the force balance phenomenon of the UAV, that is, the UAV falls into a local optimum, it will cause the UAV to be unable to continue path planning, and eventually cannot reach the target point. In the present invention, the situation that the artificial potential field will produce a local optimum is divided into three types,
(1)当障碍物处于目标点正前方与无人机处于同一航道,且当前无人机受到的引力与斥力大小相同方向相反,如图4(1)所示。(1) When the obstacle is directly in front of the target point and the UAV is on the same channel, and the current gravity and repulsion force on the UAV are the same in magnitude and opposite in direction, as shown in Figure 4(1).
(2)当障碍物处于无人机两侧,且斥力的合力方向与引力方向相反,大小相同。如图4(2)所示。(2) When the obstacles are on both sides of the UAV, and the resultant direction of the repulsive force is opposite to the direction of the gravitational force, the magnitude is the same. As shown in Figure 4(2).
(3)当障碍物处于目标点后方,且斥力远远大于引力时,如图4(3)所示。(3) When the obstacle is behind the target point, and the repulsive force is much greater than the attractive force, as shown in Figure 4(3).
因此当无人机处于局部最优情况时,根据无人机与目标点之间是否存在直接可见性将情况分为两种。首先,当障碍物处于无人机和目标点之间,通过三维LOS可见性检测发现,无人机无法穿过障碍物直接到达,其必须受到不均等外力影响从而打破无人机受力平衡。因此本发明在无人机陷入局部最优解且无人机与目标点之间不存在直接可见性的情况下,采用在局部最优点周围增设虚拟目标引力场的方式促使无人机逃逸。其次,当无人机陷入局部最优解,但却存在直接可见性的情况时使用三维布雷森汉姆线算法即可测试无人机与目标之间的直线航道是否可以直达,若可直达则直接连接当前无人机与目标点位置即可。Therefore, when the UAV is in a local optimal situation, the situation is divided into two according to whether there is direct visibility between the UAV and the target point. First of all, when the obstacle is between the UAV and the target point, it is found through the 3D LOS visibility detection that the UAV cannot pass through the obstacle directly to reach it, and it must be affected by unequal external forces to break the force balance of the UAV. Therefore, when the UAV falls into a local optimal solution and there is no direct visibility between the UAV and the target point, the present invention promotes the UAV to escape by adding a virtual target gravitational field around the local optimal point. Secondly, when the UAV falls into the local optimal solution, but there is direct visibility, the three-dimensional Bresenham line algorithm can be used to test whether the straight-line channel between the UAV and the target can be reached directly. Just connect the current UAV and the target point directly.
S5,本发明在随机性地图的设计上分别采用8000栅格尺寸的地图,障碍物占比为20%、30%与40%。分别对三维JPS算法、三维A*算法、RRT算法以及Theta*算法的计算时间、空间占用率、路径节点个数、路径长度以及路径总转折角度进行总结分析。在仿真实验当中,本发明统一选取欧式距离公式当作启发式函数的距离计算。实验结果取自10次实验的平均值。仿真结果部分展示如下图5所示。其中图5(1)表示障碍物占比为20%的实验结果.图5(2)表示障碍物占比为30%的实验结果。图5(3)表示障碍物占比为40%的实验结果。S5, the present invention adopts maps with a grid size of 8000 in the design of the randomness map, and the proportion of obstacles is 20%, 30% and 40%. The calculation time, space occupancy rate, number of path nodes, path length and total turning angle of the 3D JPS algorithm, 3D A* algorithm, RRT algorithm and Theta* algorithm are summarized and analyzed respectively. In the simulation experiment, the present invention uniformly selects the Euclidean distance formula as the distance calculation of the heuristic function. The experimental results are the average of 10 experiments. The simulation results are partially shown in Figure 5 below. Figure 5(1) shows the experimental results when the obstacle ratio is 20%. Figure 5(2) shows the experimental results when the obstacle ratio is 30%. Figure 5(3) shows the experimental results when the obstacle ratio is 40%.
S6,本发明使用来自Moving AI Lab(https://movingai.com/)公开数据库当中的伦敦市、波士顿市、纽约市中心部分区域地图以及山脉区域地图,分别对于三维JPS算法、路径长度优化法则以及多项式插值优化后的结果路径进行对比实验。以此来验证基于三维JPS算法生成路径的轨迹优化的效果和真实性。本发明为方便展示,将路径长度优化法的路径简称为PNP-JPS,再经过多项式插值优化后的路径简称为OP-PNP-JPS。部分实验结果展示如图6所示。S6, the present invention uses London, Boston, New York city center partial area maps and mountain area maps from the public database of Moving AI Lab (https://movingai.com/), respectively for the three-dimensional JPS algorithm and the path length optimization rule And the result path optimized by polynomial interpolation is used for comparative experiments. In order to verify the effect and authenticity of trajectory optimization based on the path generated by the 3D JPS algorithm. For the convenience of display, the present invention abbreviates the path of the path length optimization method as PNP-JPS, and the path optimized by polynomial interpolation is abbreviated as OP-PNP-JPS. Some experimental results are shown in Figure 6.
S7,本发明基于公开数据集中的上海市中心部分区域地图,针对单动态威胁、同轨迹逆向威胁以及多动态威胁进行仿真测试。在本次实验的设计当中,无人机的警戒范围选取基于实验室无人机测试平台DJI Mavic 2的前视和侧视精确可探测范围的均值(20m)所组成的球状包围圈。当动态威胁进入警戒范围后即采取人工势场法进行动态避障。其中人工势场法当中障碍物所所产生的斥力场范围设置为5m,即无人机测试平台DJI Mavic 2前向和侧向红外传感器精确测量范围距离的平均值。当无人机与障碍物之间的距离小于等于5m时即对无人机产生斥力作用。现将实验结果展示如图7所示。其中Dynamic Threat表示动态威胁障碍物体,Obstacle avoidance path表示无人机避障路径。S7, the present invention conducts a simulation test for a single dynamic threat, a same-trajectory reverse threat, and multiple dynamic threats based on the map of a part of the central area of Shanghai in the public data set. In the design of this experiment, the warning range of the UAV is selected based on the spherical enclosing circle formed by the average value (20m) of the front-sight and side-sight precise detectable range of the laboratory UAV test
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