技术领域technical field
本发明涉及无人机航路规划技术领域，具体涉及一种基于改进混沌蚁群算法的无人机航路规划方法。The invention relates to the technical field of UAV route planning, in particular to an UAV route planning method based on an improved chaotic ant colony algorithm.
背景技术Background technique
无人机航路规划是指在给定的规划空间内，寻找无人机从起始位置到达目标位置且满足给定约束条件和性能指标的最优或可行航路。约束条件是指规划出的航路要满足无人机自身的机动性能约束、飞行空间的时空约束、飞行器携带油料的总量约束等约束条件。性能指标的选取取决于具体的研究对象和任务要求，或使其任务效能最高，或使其生存概率最大，或飞行时间最短，或按规定时间到达，或费用最小，或实时性高等。UAV route planning refers to finding the optimal or feasible route for UAVs from the starting position to the target position and satisfying given constraints and performance indicators within a given planning space. Constraint conditions mean that the planned route must meet constraints such as the UAV's own maneuverability constraints, the space-time constraints of the flight space, and the total amount of fuel carried by the aircraft. The selection of performance indicators depends on the specific research object and task requirements, or make it the highest task efficiency, or maximize the probability of survival, or the shortest flight time, or arrive at the specified time, or the least cost, or high real-time performance.
航迹规划算法对无人机的自主飞行、精确跟踪或打击起着决定性作用，关系着航路规划的效率甚至是无人机的生存概率。航迹规划中，无人机所执行的任务不同，所采取的航路规划算法亦不同。执行简单的侦查任务时，只需根据已经获得的信息规划出一条全局航路，无人机在起飞前只需加载该全局航路即可。而实施对敌打击时往往伴随着敌方动态威胁的出现，这时需要在全局参考航线的基础上适当做动态调整，以便躲避动态威胁。目前，国内外许多学者做了相当多的有建设性的工作并提出过多种方法，这些规划算法可以归纳概括为两种类别，一种是最优式算法，另一种是启发式搜索算法。最优式算法存在典型的缺点，随着搜索空间的增大该算法的计算量呈现指数增长趋势，算法的时间复杂度增加。因此，当问题规模不大时常采用该类型的算法。启发式搜索就是在状态空间中进行搜索，先利用启发函数对周围每一个待扩展位置评估，寻找能使启发函数值最小的点，然后从这个点开始继续搜索，依次重复该过程。这种思路明显降低了此类算法的时间复杂度。启发式搜索算法通常又分为随机搜索和确定搜索两大类。常用的确定型搜索算法有动态规划算法、Voronoi(维诺图)图法、A*(A-Start)算法以及Dijkstra(迪杰斯特拉)算法等；常用的随机型搜索算法有模拟退火算法、遗传算法、粒子群算法以及蚁群算法等。The trajectory planning algorithm plays a decisive role in the autonomous flight, precise tracking or strike of UAVs, and is related to the efficiency of route planning and even the survival probability of UAVs. In trajectory planning, the tasks performed by UAVs are different, and the route planning algorithms adopted are also different. When performing a simple reconnaissance mission, it is only necessary to plan a global route based on the obtained information, and the UAV only needs to load the global route before taking off. The implementation of strikes against the enemy is often accompanied by the emergence of dynamic threats from the enemy. At this time, it is necessary to make appropriate dynamic adjustments on the basis of the global reference route in order to avoid dynamic threats. At present, many scholars at home and abroad have done quite a lot of constructive work and proposed a variety of methods. These planning algorithms can be summarized into two categories, one is the optimal algorithm, and the other is the heuristic search algorithm. . The optimal algorithm has typical disadvantages. With the increase of the search space, the calculation amount of the algorithm shows an exponential growth trend, and the time complexity of the algorithm increases. Therefore, this type of algorithm is often used when the problem size is small. Heuristic search is to search in the state space. First use the heuristic function to evaluate each surrounding position to be expanded, find the point that can minimize the value of the heuristic function, and then continue to search from this point, and repeat the process in turn. This idea significantly reduces the time complexity of such algorithms. Heuristic search algorithms are usually divided into two categories: random search and deterministic search. Commonly used deterministic search algorithms include dynamic programming algorithm, Voronoi (Voronoi diagram) graph method, A* (A-Start) algorithm and Dijkstra (Dijkstra) algorithm, etc.; commonly used random search algorithms include simulated annealing algorithm , genetic algorithm, particle swarm algorithm, and ant colony algorithm.
随机型搜索和确定型搜索虽然在航路规划中都有应用，但他们存在一些缺点。动态规划算法运用一种前向链驱动的方法，便于算法建模，然而当无人机航路规划空间复杂时，该算法会出现组合爆炸的情况，致使算法的时间复杂度上升，无法满足无人机航路规划对于算法实时性的要求；Voronoi图法算法具有较强的直观性，且能把复杂的空间规划问题转换成简单平面规划问题进行求解。求解无人机航路规划问题，需要先把已知的障碍和威胁考虑进去，在构造Voronoi图时，保证威胁点到Voronoi图边上的距离最远。但是，Voronoi图的缺点是只适用于单机航路规划，在存在动态威胁的战场环境中没有规划能力，不能满足现代战场的作战需要；A*算法是一种典型的确定型搜索算法，该算法需要构造启发函数，然而，所构造的启发函数直接决定了A*算法的运算效率，而由于规划空间中各种不确定因素的存在无法构造出精确体现飞行威胁的启发函数，因此在飞行约束复杂的环境下容易出现规划失败的情况；蚁群算法(Ant Colony Algorithm,ACO)也是一种典型的仿生算法，该算法模拟了昆虫王国中蚂蚁的觅食过程，每只蚂蚁在觅食过程中都会在经过的航路上留下信息素，后到的蚂蚁便会根据航路上残留的信息素为依据指导自己的出行，最终所有的蚂蚁都趋于选择同一条航路进行觅食。但是，当蚂蚁个数较多时，很难在短时间内在大量杂乱航路中找出最优航路，且算法收敛过程进行得较为缓慢；又由于算法正反馈特性的存在，可能会造成局部航路上的信息素堆积过量，这些浓度过高的信息素会对后到的蚂蚁在选择航路时造成影响，会使大量蚂蚁选择某一条航路，最终导致算法停滞现象的产生，为了提高算法收敛速度和全局寻优能力，可将改进的混沌机制加入到基本蚁群算法中。Although both random search and deterministic search are used in route planning, they have some disadvantages. The dynamic programming algorithm uses a forward chain drive method, which is convenient for algorithm modeling. However, when the UAV route planning space is complex, the algorithm will explode in combination, resulting in an increase in the time complexity of the algorithm, which cannot meet the requirements of unmanned vehicles. The real-time requirements of the algorithm for aircraft route planning; the Voronoi diagram algorithm has strong intuition, and can convert complex spatial planning problems into simple plane planning problems for solution. To solve the UAV route planning problem, it is necessary to take into account the known obstacles and threats first. When constructing the Voronoi diagram, ensure that the distance from the threat point to the edge of the Voronoi diagram is the farthest. However, the disadvantage of the Voronoi diagram is that it is only suitable for single aircraft route planning, and has no planning ability in the battlefield environment with dynamic threats, and cannot meet the operational needs of modern battlefields; the A* algorithm is a typical deterministic search algorithm, which requires Construct a heuristic function, however, the constructed heuristic function directly determines the operational efficiency of the A* algorithm, and due to the existence of various uncertain factors in the planning space, it is impossible to construct a heuristic function that accurately reflects the flight threat, so in complex flight constraints Planning failures are prone to occur in the environment; Ant Colony Algorithm (ACO) is also a typical bionic algorithm, which simulates the foraging process of ants in the insect kingdom. Pheromone is left on the passing route, and the ants that arrive later will guide their travel based on the pheromone remaining on the route. Eventually, all ants tend to choose the same route for foraging. However, when the number of ants is large, it is difficult to find the optimal route among a large number of chaotic routes in a short period of time, and the convergence process of the algorithm is relatively slow; and due to the existence of the positive feedback characteristics of the algorithm, it may cause local routes. Excessive accumulation of pheromones, these pheromones with too high concentration will affect the selection of routes by ants arriving later, and will cause a large number of ants to choose a certain route, which will eventually lead to the stagnation of the algorithm. In order to improve the convergence speed of the algorithm and global search Excellent ability, the improved chaos mechanism can be added to the basic ant colony algorithm.
发明内容Contents of the invention
为解决现有技术中的不足，本发明提供一种基于改进混沌蚁群算法的无人机航路规划方法，其特征在于，包括如下步骤：In order to solve the deficiencies in the prior art, the invention provides a kind of unmanned aerial vehicle route planning method based on the improved chaotic ant colony algorithm, it is characterized in that, comprises the following steps:
步骤S1，将混沌优化算法得到的优化解转化为蚁群算法的信息素初始值；Step S1, converting the optimal solution obtained by the chaos optimization algorithm into the initial value of pheromone of the ant colony algorithm;
步骤S2，通过蚁群算法再进行航路寻优，寻优结束后对符合条件的航路进行混沌映射，最终得到最优航路。In step S2, the route optimization is carried out through the ant colony algorithm, and after the optimization is completed, the chaotic mapping is performed on the qualified routes, and finally the optimal route is obtained.
前述的一种基于改进混沌蚁群算法的无人机航路规划方法，其特征在于，所述步骤S1，具体步骤包括：Aforesaid a kind of unmanned aerial vehicle route planning method based on improved chaotic ant colony algorithm, it is characterized in that, described step S1, concrete steps comprise:
步骤S11，对航路环境进行建模，确定每只蚂蚁当前规划点的候选规划点；Step S11, modeling the air route environment, and determining the candidate planning points of each ant's current planning point;
步骤S12，混沌优化算法初始化，得到初始混沌路径；Step S12, initializing the chaotic optimization algorithm to obtain the initial chaotic path;
步骤S13，设置航路代价函数和适应度函数，计算所有混沌路径的代价值和适应度值；Step S13, setting route cost function and fitness function, calculating the cost value and fitness value of all chaotic paths;
步骤S14，根据步骤S13计算得到的所有混沌路径的适应度值，从中选择前m个最大值，并把这m个值作为蚁群算法的信息素初始值。Step S14, according to the fitness values of all chaotic paths calculated in step S13, select the first m maximum values, and use these m values as the initial pheromone values of the ant colony algorithm.
前述的一种基于改进混沌蚁群算法的无人机航路规划方法，其特征在于，所述步骤S11对航路环境进行建模，选用二维栅格法表示规划空间，以任意段i→j为例，每只蚂蚁每个当前规划点i除边界外都有8个候选规划点j，无人机规划的航路由此类规划点组成。The aforementioned method of UAV route planning based on the improved chaotic ant colony algorithm is characterized in that the step S11 models the route environment, and uses a two-dimensional grid method to represent the planning space, with any segment i → j as For example, every current planning point i of each ant has 8 candidate planning points j except the boundary, and the route planned by the UAV is composed of such planning points.
前述的一种基于改进混沌蚁群算法的无人机航路规划方法，其特征在于，所述步骤S12，混沌优化算法初始化，得到初始混沌路径，具体步骤为：设蚁群规模为m，蚂蚁搜索的范围为[a,b]，随机设定一个初始值x(0)∈[0,1]，式(1)为Logistic映射表达式：The aforementioned a kind of UAV route planning method based on the improved chaotic ant colony algorithm is characterized in that, in the step S12, the chaotic optimization algorithm is initialized to obtain the initial chaotic path. The range of is [a,b], randomly set an initial value x(0)∈[0,1], formula (1) is the Logistic mapping expression:
x(n+1)＝4x(n)[1-x(n)] (1)x(n+1)=4x(n)[1-x(n)] (1)
其中，当x(0)＝0时，令x(0)＝0.1；当x(0)＝0.25时，令x(0)＝0.26；当x(0)＝0.5时，x(0)＝0.56；当x(0)＝0.75时，x(0)＝0.76；当x(0)＝1时，x(0)＝0.9，n为自然数，将式(1)迭代(m-1)次可以得到m个不同的混沌变量Xc：Wherein, when x(0)=0, let x(0)=0.1; when x(0)=0.25, let x(0)=0.26; when x(0)=0.5, make x(0)= 0.56; when x(0)=0.75, x(0)=0.76; when x(0)=1, x(0)=0.9, n is a natural number, the formula (1) is iterated (m-1) times m different chaotic variables Xc can be obtained:
Xc＝(x(0)，x(1)，x(2)，...x(m-1)) (2)Xc=(x(0), x(1), x(2), . . . x(m-1)) (2)
再进行线性变换，得到新的位于[a,b]区间的混沌序列Xd：Then perform linear transformation to obtain a new chaotic sequence Xd in the [a,b] interval:
Xd＝a+(b-a)Xc (3)Xd=a+(b-a)Xc (3)
Xd＝(x'(0)，x'(1)，x'(2)，...x'(m-1)) (4)Xd=(x'(0), x'(1), x'(2),...x'(m-1)) (4)
其中，参数a、b为蚁群搜索范围[a,b]的边界值；最后将序列Xd中的m个x新混沌变量利用全排列构造原理构造出m！个不同的初始混沌路径。Among them, the parameters a and b are the boundary values of the ant colony search range [a, b]; finally, the m x new chaotic variables in the sequence Xd are constructed using the principle of full permutation to construct m! different initial chaotic paths.
前述的一种基于改进混沌蚁群算法的无人机航路规划方法，其特征在于，所述步骤S13，设置航路代价函数和适应度函数，计算所有混沌路径的代价值和适应度值，具体步骤为：Aforesaid a kind of unmanned aerial vehicle route planning method based on improved chaotic ant colony algorithm, it is characterized in that, described step S13, set route cost function and fitness function, calculate the cost value and fitness value of all chaotic paths, specific steps for:
综合考虑雷达威胁和燃料威胁，采用加权方法可以得到代价函数F，计算公式如下：Considering the radar threat and the fuel threat comprehensively, the cost function F can be obtained by using the weighting method, and the calculation formula is as follows:
式中：ωtp表示无人机通过第p个航路段所受到的雷达威胁；p和q分别表示第p个航路段和第q个雷达；Lp表示第p个航路段的路径长度；d14,p,q，d24,p,q，d3/4,p,q分别表示第q个雷达距离第p个航路段的1/4处，2/4处，3/4处的距离；N表示雷达威胁的个数；In the formula: ωtp represents the radar threat received by the UAV through the p-th route segment; p and q represent the p-th route segment and the q-th radar respectively; Lp represents the path length of the p-th route segment; d14, p, q, d24, p, q , d3/4, p, q represent the distances from the qth radar to the 1/4, 2/4, and 3/4 of the p-th route segment respectively; N represents the radar the number of threats;
ωt表示无人机在所搜索到的从起始点到目标点的整个航路上所受的雷达威胁；M表示航路段的个数；ωt represents the radar threat encountered by the UAV on the entire route from the starting point to the target point; M represents the number of route segments;
ωf表示无人机燃油威胁；L表示从起始点到目标点的航路长度；两者之间成正比例关系，比例系数为kf；ωf represents the UAV fuel threat; L represents the route length from the starting point to the target point; there is a direct proportional relationship between the two, and the proportional coefficient is kf ;
F表示航路代价函数，kz∈[0,1]为动态加权因子，反映雷达威胁代价及燃油代价的权重；适应度函数Ffitness与航路代价函数之间满足Ffitness＝1/F。F represents the route cost function, and kz ∈ [0,1] is the dynamic weighting factor, which reflects the weight of radar threat cost and fuel cost; the relationship between the fitness function Ffitness and the route cost function satisfies Ffitness = 1/F.
前述的一种基于改进混沌蚁群算法的无人机航路规划方法，其特征在于，所述步骤S2，具体步骤包括：Aforesaid a kind of unmanned aerial vehicle route planning method based on improved chaotic ant colony algorithm, it is characterized in that, described step S2, concrete steps comprise:
步骤S21，迭代次数u初始化为0，最大值为Ncmax；Step S21, the number of iterations u is initialized to 0, and the maximum value is Ncmax;
步骤S22，将m只蚂蚁都放在无人机的起飞点，每只蚂蚁按照状态转移公式选择下一节点，直到到达目标点则输出m个航路，计算当前迭代次数u下的m个航路所对应的航路代价值，取m个航路代价值中最小值作为当前迭代次数的最优解，记作bgest(u)；bgest(0)为u＝0时的最优解，当迭代次数u≥1时，将当前迭代次数下的最优解与上一次迭代获得的最优解进行比较，取两者的最小值替换当前迭代次数下的最优解bgest(u)，蚂蚁的状态转移公式如下：Step S22, put m ants on the take-off point of the UAV, each ant selects the next node according to the state transition formula, and outputs m routes until reaching the target point, and calculates the number of m routes under the current iteration number u. For the corresponding route cost value, the minimum value among the m route cost values is taken as the optimal solution of the current iteration number, which is recorded as bgest(u); bgest(0) is the optimal solution when u=0, when the iteration number u≥ When 1, compare the optimal solution under the current number of iterations with the optimal solution obtained in the previous iteration, and take the minimum value of the two to replace the optimal solution bgest(u) under the current number of iterations. The state transition formula of the ant is as follows :
式中：Pk(i,j)表示蚂蚁状态转移的概率；NearAllowk，k＝1,2…m，为步骤S11中第k只蚂蚁当前规划点的候选规划点的集合；τ(i,j)表示节点i与节点j之间航路上的信息素浓度，τ0为信息素初始值；α和β分别为信息素重要程度因子和能见度重要程度因子；η(i,j)为启发函数，表示蚂蚁从节点i转移到节点j的期望程度，计算公式如下：In the formula: Pk (i, j) represents the probability of ant state transition; NearAllowk , k=1, 2...m, is the set of candidate planning points of the kth ant’s current planning point in step S11; τ(i, j) represents the pheromone concentration on the route between node i and node j, τ0 is the initial value of pheromone; α and β are the pheromone importance factor and visibility importance factor respectively; η(i,j) is the heuristic function , which represents the expected degree of ant transferring from node i to node j, the calculation formula is as follows:
η(i,j)＝1/Fij (7)η(i,j)=1/Fij (7)
Fij表示节点i与节点j之间航路段的代价函数值；Fij represents the cost function value of the route segment between node i and node j;
步骤S23，引入混沌映射，以由步骤S22产生的当前迭代次数下的最优解bgest(u)为基础，通过式(8)产生ε个在对应于最优解bgest(u)的搜索点附近的具有混沌特性的搜索点，计算ε个搜索点的航路代价值，并将它们与bgest(u)进行比较，取两者的最小值替换bgest(u)，这些搜索点的计算公式如下：Step S23, introduce the chaotic map, based on the optimal solution bgest(u) under the current number of iterations generated by step S22, generate ε near the search points corresponding to the optimal solution bgest(u) through formula (8) The search points with chaotic characteristics, calculate the route cost value of ε search points, and compare them with bgest(u), take the minimum value of the two to replace bgest(u), the calculation formula of these search points is as follows:
X＝bgest(u)+ar×yn+1*random3 (8)X＝bgest(u)+ar×yn+1 *random3 (8)
Ulam_von Neumann映射的计算公式如下：The calculation formula of Ulam_von Neumann mapping is as follows:
yn+1＝1-2yn2 (9)yn+1 = 1-2yn2 (9)
其中，yn+1为当初始值y0∈[-1,1]时迭代ε次产生的序列；Among them, yn+1 is the sequence generated by iterating ε times when the initial value y0∈[-1,1];
ar为调节系数，计算公式如下：ar is the adjustment coefficient, the calculation formula is as follows:
ar＝ar*γu (10)ar=ar*γu (10)
γ为衰减系数，u为迭代次数；random为伪随机数；γ is the attenuation coefficient, u is the number of iterations; random is a pseudo-random number;
步骤S24，引入混沌扰动的信息素更新策略，对上述寻优过程获得到的航路按如下公式进行全局信息素更新；Step S24, introduce the pheromone update strategy of chaotic disturbance, and update the global pheromone according to the following formula for the route obtained in the above optimization process;
式中：Fk为第k只蚂蚁在本次循环中搜索到的可行航路的代价值；Q表示蚂蚁从起始点到目标点所释放的信息素总量；Δτk(i,j)为第k只蚂蚁从节点i转移到节点j释放的信息素增量，Δτ(i,j)表示m只蚂蚁在节点i和j的连接航路上释放的信息素之和；ρ为信息素挥发因素；Z(n+1)是通过序列ω(n+1)线性变换得到的，ω(n+1)为初始值ω(0)∈[0,1]时通过Logistic映射迭代产生的混沌序列；In the formula: Fk is the cost value of the feasible route searched by the kth ant in this cycle; Q represents the total amount of pheromone released by the ant from the starting point to the target point; Δτk(i, j) is the value of the kth ant The pheromone increment released by ants moving from node i to node j, Δτ(i,j) represents the sum of pheromone released by m ants on the connecting route between node i and j; ρ is the pheromone volatilization factor; Z( n+1) is obtained through the linear transformation of the sequence ω(n+1), and ω(n+1) is the chaotic sequence generated by Logistic map iteration when ω(n+1) is the initial value ω(0)∈[0,1];
步骤S25，令循环次数u＝u+1；将蚂蚁重新放回起始点，转步骤S22进行下一轮迭代；若迭代次数u>Ncmax，则寻优结束，输出最优航路。Step S25, set the number of cycles u=u+1; put the ant back to the starting point, go to step S22 for the next iteration; if the number of iterations u>Ncmax, then the optimization ends, and the optimal route is output.
前述的一种基于改进混沌蚁群算法的无人机航路规划方法，其特征在于，所述混沌序列ω(n+1)为初始值ω(0)∈[0,1]时通过Logistic映射迭代产生的混沌序列，ω(n+1)＝4ω(n)[1-ω(n)]，The aforementioned method of UAV route planning based on the improved chaotic ant colony algorithm is characterized in that, when the chaotic sequence ω(n+1) is the initial value ω(0)∈[0,1], iterates through Logistic mapping The generated chaotic sequence, ω(n+1)=4ω(n)[1-ω(n)],
其中：当ω(0)＝0时，令ω(0)＝0.1；当ω(0)＝0.25时，令ω(0)＝0.26；当ω(0)＝0.5时，ω(0)＝0.56；当ω(0)＝0.75时，ω(0)＝0.76；当ω(0)＝1时，ω(0)＝0.9。Among them: when ω(0)=0, let ω(0)=0.1; when ω(0)=0.25, make ω(0)=0.26; when ω(0)=0.5, make ω(0)= 0.56; when ω(0)=0.75, ω(0)=0.76; when ω(0)=1, ω(0)=0.9.
本发明所达到的有益效果：The beneficial effect that the present invention reaches:
1、通过混沌映射产生各个蚂蚁差异的初始信息素值替代原有蚂蚁相等的信息素初值，从而生成蚁群算法新的初始航路来提高算法搜索效率；1. The initial pheromone value of different ants is replaced by the initial value of pheromone equal to the original ants through chaotic mapping, so as to generate a new initial route of the ant colony algorithm to improve the search efficiency of the algorithm;
2、引入混沌扰动的信息素更新策略，动态更新已获得有效航路上的信息素，有效克服局部最优的缺陷，提高了收敛速度；2. Introduce the pheromone update strategy of chaotic disturbance, dynamically update the pheromone on the effective route, effectively overcome the defect of local optimum, and improve the convergence speed;
3、以当前迭代次数下的蚁群搜索到的最优解为基础，采用改进的混沌优化机制：通过变尺度地调整调节系数，使调节系数随着循环次数的增加有所衰减，改变以当前最优解为中心的搜索空间的大小；在该机制的最优搜索环节中，引入Ulam_von Neumann(乌兰·冯·诺依曼)混沌映射和伪随机数，进一步缩短搜索空间，加速收敛，提高寻优精度。3. Based on the optimal solution searched by the ant colony under the current number of iterations, an improved chaotic optimization mechanism is adopted: by adjusting the adjustment coefficient in variable scales, the adjustment coefficient is attenuated with the increase of the number of cycles, and the change is based on the current The size of the search space centered on the optimal solution; in the optimal search link of this mechanism, Ulam_von Neumann (Ulan von Neumann) chaotic maps and pseudo-random numbers are introduced to further shorten the search space, accelerate convergence, and improve Optimal precision.
附图说明Description of drawings
图1是本发明的航路规划方法的算法流程图；Fig. 1 is the algorithm flowchart of route planning method of the present invention;
图2是本发明的航路规划方法仿真图。Fig. 2 is a simulation diagram of the route planning method of the present invention.
具体实施方式Detailed ways
下面结合附图对本发明作进一步描述。以下实施例仅用于更加清楚地说明本发明的技术方案，而不能以此来限制本发明的保护范围。The present invention will be further described below in conjunction with the accompanying drawings. The following examples are only used to illustrate the technical solution of the present invention more clearly, but not to limit the protection scope of the present invention.
如图1所示，一种基于改进混沌蚁群算法的无人机航路规划方法，包括如下步骤：As shown in Figure 1, a UAV route planning method based on the improved chaotic ant colony algorithm includes the following steps:
步骤S1，将混沌优化算法得到的优化解转化为蚁群算法的信息素初始值；Step S1, converting the optimal solution obtained by the chaos optimization algorithm into the initial value of pheromone of the ant colony algorithm;
步骤S2，通过蚁群算法再进行航路寻优，寻优结束后对符合条件的航路进行混沌映射，最终得到最优航路。In step S2, the route optimization is carried out through the ant colony algorithm, and after the optimization is completed, the chaotic mapping is performed on the qualified routes, and finally the optimal route is obtained.
步骤S1中将混沌优化算法得到的优化解转化为蚁群算法的信息素初始值，包括以下步骤：In step S1, the optimal solution obtained by the chaos optimization algorithm is converted into the initial value of the pheromone of the ant colony algorithm, including the following steps:
步骤S11，对航路环境进行建模；即选用二维栅格法的方式表示规划空间，每个栅格的大小为5km，以任意段i→j为例，每只蚂蚁每个当前规划点i除边界外都有8个候选规划点j，且所规划的航路就是由这些规划点组成的。无人机航路规划以起飞点作为起始点，以目标点作为终止点，途径栅格网点，使航路代价值最小的航路规划；Step S11, modeling the air route environment; that is, choose the two-dimensional grid method to represent the planning space, the size of each grid is 5km, taking any segment i→j as an example, each ant and each current planning point i There are 8 candidate planning points j except the boundary, and the planned route is composed of these planning points. UAV route planning takes the take-off point as the starting point, takes the target point as the end point, passes through the grid points, and minimizes the route cost;
步骤S12，算法初始化，得到初始混沌路径；Step S12, the algorithm is initialized to obtain the initial chaotic path;
设蚁群规模为m，蚂蚁搜索的范围为[a,b]，在这里，设置a＝0，b＝50，随机设定一个初始值x(0)∈[0,1]，式(1)为Logistic(逻辑)映射表达式：Let the size of the ant colony be m, and the search range of ants is [a,b]. Here, set a=0, b=50, and randomly set an initial value x(0)∈[0,1], formula (1 ) is the Logistic (logic) mapping expression:
x(n+1)＝4x(n)[1-x(n)] (1)x(n+1)=4x(n)[1-x(n)] (1)
特殊的：当x(0)＝0时，令x(0)＝0.1；当x(0)＝0.25时，令x(0)＝0.26；当x(0)＝0.5时，x(0)＝0.56；当x(0)＝0.75时，x(0)＝0.76；当x(0)＝1时，x(0)＝0.9，Special: when x(0)=0, set x(0)=0.1; when x(0)=0.25, set x(0)=0.26; when x(0)=0.5, set x(0) =0.56; when x(0)=0.75, x(0)=0.76; when x(0)=1, x(0)=0.9,
n为自然数，将式(1)迭代(m-1)次可以得到m个不同的混沌变量Xc：n is a natural number, and m different chaotic variables Xc can be obtained by iterating formula (1) (m-1) times:
Xc＝(x(0)，x(1)，x(2)，...x(m-1)) (2)Xc=(x(0), x(1), x(2), . . . x(m-1)) (2)
再进行线性变换，得到新的位于[a,b]区间的混沌序列Xd：Then perform linear transformation to obtain a new chaotic sequence Xd in the [a,b] interval:
Xd＝a+(b-a)Xc (3)Xd=a+(b-a)Xc (3)
Xd＝(x'(0)，x'(1)，x'(2)，...x'(m-1)) (4)Xd=(x'(0), x'(1), x'(2),...x'(m-1)) (4)
其中，参数a、b为蚁群搜索范围[a,b]的边界值；Among them, the parameters a and b are the boundary values of the ant colony search range [a, b];
最后将序列Xd中的m个新混沌变量利用全排列构造原理构造出m！个不同的初始混沌路径；Finally, the m new chaotic variables in the sequence Xd are constructed using the principle of full permutation to construct m! different initial chaotic paths;
步骤S13，设置航路代价函数和适应度函数，计算所有混沌路径的代价值和适应度值；Step S13, setting route cost function and fitness function, calculating the cost value and fitness value of all chaotic paths;
综合考虑雷达威胁和燃料威胁，采用加权方法可以得到代价函数F，计算公式如下：Considering the radar threat and the fuel threat comprehensively, the cost function F can be obtained by using the weighting method, and the calculation formula is as follows:
式中：ωtp表示无人机通过第p个航路段所受到的雷达威胁；p和q分别表示第p个航路段和第q个雷达；Lp表示第p个航路段的路径长度；d14,p,q，d24,p,q，d3/4,p,q分别表示第q个雷达距离第p个航路段的1/4处，2/4处，3/4处的距离；N表示雷达威胁的个数；In the formula: ωtp represents the radar threat received by the UAV through the p-th route segment; p and q represent the p-th route segment and the q-th radar respectively; Lp represents the path length of the p-th route segment; d14,p,q ，d24,p,q ，d3/4,p,q represent the distances from the qth radar to the 1/4, 2/4, and 3/4 of the p-th route segment respectively ; N represents the number of radar threats;
ωt表示无人机在所搜索到的从起始点到目标点的整个航路上所受的雷达威胁；M表示航路段的个数；ωt represents the radar threat encountered by the UAV on the entire route from the starting point to the target point; M represents the number of route segments;
ωf表示无人机燃油威胁；L表示从起始点到目标点的航路长度；两者之间成正比例关系，比例系数为kf；ωf represents the UAV fuel threat; L represents the route length from the starting point to the target point; there is a direct proportional relationship between the two, and the proportional coefficient is kf ;
F表示航路代价函数，kz∈[0,1]为动态加权因子，反映雷达威胁代价及燃油代价的权重，可根据实际任务需要选择加权因子。F represents the route cost function, and kz ∈ [0,1] is the dynamic weighting factor, which reflects the weight of radar threat cost and fuel cost, and the weighting factor can be selected according to the actual task needs.
适应度函数Ffitness与航路代价函数之间满足Ffitness＝1/F关系，所以一旦确定航路代价值，对应的适应度函数值也随之确定。The relationship between the fitness function Ffitness and the route cost function satisfies Ffitness = 1/F, so once the route cost value is determined, the corresponding fitness function value is also determined.
步骤S14，根据步骤S13计算得到的所有混沌路径的适应度值，从中选择前m个最大值，并把这m个值作为蚁群算法的信息素初始值。Step S14, according to the fitness values of all chaotic paths calculated in step S13, select the first m maximum values, and use these m values as the initial pheromone values of the ant colony algorithm.
在此基础上，蚂蚁再进行路径的选择，通过步骤S1，有效解决了蚁群算法前期收敛速度慢的问题，结合两者的优势大大提高了搜索的效率及精度。On this basis, the ants select the path again. Through step S1, the problem of slow convergence speed of the ant colony algorithm in the early stage is effectively solved, and the combination of the advantages of the two greatly improves the efficiency and accuracy of the search.
步骤S2中通过蚁群算法再进行航路寻优，寻优结束后对符合条件的航路进行混沌局部搜索，最终得到最优航路的方法包括如下步骤：In step S2, the route optimization is carried out through the ant colony algorithm, and after the optimization is completed, the chaotic local search is performed on the qualified routes, and the method of finally obtaining the optimal route includes the following steps:
步骤S21，迭代次数u初始化为0，最大值为Ncmax；Step S21, the number of iterations u is initialized to 0, and the maximum value is Ncmax;
步骤S22，将m只蚂蚁都放在起始点位置，也就是无人机的起飞点，每只蚂蚁按照状态转移公式选择下一节点，直到到达目标点则输出m个航路，计算当前迭代次数u下的m个航路所对应的航路代价值，取m个航路代价值中最小值作为当前迭代次数的最优解，记作bgest(u)。一开始，bgest(0)为u＝0时的最优解，当迭代次数u≥1时，将当前迭代次数下的最优解与上一次迭代获得的最优解进行比较，取两者的最小值替换当前迭代次数下的最优解bgest(u)，蚂蚁的状态转移公式如下：Step S22, put m ants at the starting point, that is, the take-off point of the UAV, each ant selects the next node according to the state transition formula, and outputs m routes until reaching the target point, and calculates the current iteration number u For the route cost values corresponding to the m routes below, the minimum value among the m route cost values is taken as the optimal solution for the current iteration times, which is denoted as bgest(u). At the beginning, bgest(0) is the optimal solution when u=0. When the number of iterations u≥1, compare the optimal solution under the current iteration number with the optimal solution obtained in the previous iteration, and take the optimal solution of the two The minimum value replaces the optimal solution bgest(u) under the current number of iterations, and the state transition formula of the ant is as follows:
式中：Pk(i,j)表示蚂蚁状态转移的概率；NearAllowk(k＝1,2…m)为由步骤S11所示的第k只蚂蚁当前规划点的候选规划点的集合；In the formula: Pk (i, j) represents the probability of ant state transition; NearAllowk (k=1,2...m) is the set of candidate planning points of the kth ant's current planning point shown in step S11;
τ(i,j)表示节点i与节点j之间航路上的信息素浓度，τ0为信息素初值；α和β分别为信息素重要程度因子和能见度重要程度因子；τ(i, j) represents the pheromone concentration on the route between node i and node j,τ0 is the initial value of pheromone; α and β are the pheromone importance factor and visibility importance factor respectively;
η(i,j)为启发函数，表示蚂蚁从节点i转移到节点j的期望程度，计算公式如下：η(i,j) is a heuristic function, which indicates the degree of expectation of ant to transfer from node i to node j, and the calculation formula is as follows:
η(i,j)＝1/Fij (7)η(i,j)=1/Fij (7)
Fij表示节点i与节点j之间航路段的代价函数值；Fij represents the cost function value of the route segment between node i and node j;
步骤S23，引入混沌映射，以由步骤S22产生的当前迭代次数下的最优解bgest(u)为基础，通过式(8)产生ε个在对应于最优解bgest(u)的搜索点附近的具有混沌特性的搜索点，ε一般设置为8，计算这些搜索点的航路代价值，并将它们与bgest(u)进行比较，取两者的最小值替换bgest(u)，这些搜索点的计算公式如下：Step S23, introduce the chaotic map, based on the optimal solution bgest(u) under the current number of iterations generated by step S22, generate ε near the search points corresponding to the optimal solution bgest(u) through formula (8) The search points with chaotic characteristics, ε is generally set to 8, calculate the route cost values of these search points, and compare them with bgest(u), take the minimum value of the two to replace bgest(u), these search points Calculated as follows:
X＝bgest(u)+ar×yn+1*random3 (8)X＝bgest(u)+ar ×yn+1 *random3 (8)
式中，bgest(u)为步骤S22产生的当前迭代次数下的最优解；In the formula, bgest(u) is the optimal solution under the current number of iterations produced by step S22;
Ulam_von Neumann(乌兰·冯·诺依曼)映射的计算公式如下：The calculation formula of Ulam_von Neumann (Ulan von Neumann) mapping is as follows:
yn+1＝1-2yn2 (9)yn+1 = 1-2yn2 (9)
其中，yn+1为当初始值y0∈[-1,1]时迭代ε次产生的序列；Among them, yn+1 is the sequence generated by iterating ε times when the initial value y0 ∈ [-1,1];
ar为调节系数，随着循环次数的增加不断衰减，不断改变以当前最优解为中心的搜索空间的大小，从而加速收敛，计算公式如下：ar is the adjustment coefficient, which will decay continuously with the increase of the number of cycles, and constantly change the size of the search space centered on the current optimal solution, thus accelerating the convergence. The calculation formula is as follows:
ar＝ar*γu (10)ar=ar*γu (10)
γ为衰减系数，一般取0.96；u为迭代次数；γ is the attenuation coefficient, generally 0.96; u is the number of iterations;
random为伪随机数，引入random3可以进一步缩短搜索区间，加快收敛速度；random is a pseudo-random number, introducing random3 can further shorten the search interval and speed up the convergence speed;
步骤S24，引入混沌扰动的信息素更新策略，对上述寻优过程获得到的航路按如下公式进行全局信息素更新；Step S24, introduce the pheromone update strategy of chaotic disturbance, and update the global pheromone according to the following formula for the route obtained in the above optimization process;
式中：Fk为第k(k＝1,2…m)只蚂蚁在本次循环中搜索到的可行航路的代价值；Q表示蚂蚁从起始点到目标点所释放的信息素总量；Δτk(i,j)为第k只蚂蚁从节点i转移到节点j释放的信息素增量，当第k只蚂蚁从节点i访问节点j时，Δτk(i,j)＝Q/Fk，否则Δτk(i,j)＝0；In the formula: Fk is the cost value of the feasible route searched by the kth (k=1,2...m) ant in this cycle; Q represents the total amount of pheromone released by the ant from the starting point to the target point; Δτk (i,j) is the increment of pheromone released by the kth ant from node i to node j, when the kth ant visits node j from node i, Δτk (i,j)=Q/Fk , otherwise Δτk (i,j)=0;
Δτ(i,j)表示m只蚂蚁在节点i和j的连接航路上释放的信息素之和；ρ为信息素挥发因素；基本的蚁群算法的信息素更新策略为：Δτ(i,j) represents the sum of the pheromone released by m ants on the connecting route between nodes i and j; ρ is the pheromone volatilization factor; the pheromone update strategy of the basic ant colony algorithm is:
τ(i,j)＝(1-ρ)τ(i,j)+ρΔτ(i,j) (12)τ(i,j)=(1-ρ)τ(i,j)+ρΔτ(i,j) (12)
按照公式(12)进行信息素更新，虽然体现了信息素的正反馈特性，有利于加速收敛，但容易陷入局部最优解。这时可以利用混沌理论中的混沌扰动，在更新信息素时再加入混沌扰动量Z(n+1)，从而使算法跳出局部最优区间。因此，改进后的信息素更新公式为：The pheromone update according to formula (12) reflects the positive feedback characteristics of pheromone and is beneficial to accelerate the convergence, but it is easy to fall into the local optimal solution. At this time, the chaos disturbance in the chaos theory can be used, and the chaos disturbance Z(n+1) can be added when the pheromone is updated, so that the algorithm can jump out of the local optimal interval. Therefore, the improved pheromone update formula is:
τ(i,j)＝(1-ρ)τ(i,j)+ρΔτ(i,j)+Z(n+1) (13)τ(i,j)=(1-ρ)τ(i,j)+ρΔτ(i,j)+Z(n+1) (13)
式(13)中的Z(n+1)是通过式(11)中的序列ω(n+1)线性变换得到的。ω(n+1)为初始值ω(0)∈[0,1]时通过Logistic(逻辑)映射迭代产生的混沌序列ω(n+1)；其中：当ω(0)＝0时，令ω(0)＝0.1；当ω(0)＝0.25时，令ω(0)＝0.26；当ω(0)＝0.5时，ω(0)＝0.56；当ω(0)＝0.75时，ω(0)＝0.76；当ω(0)＝1时，ω(0)＝0.9。Z(n+1) in formula (13) is obtained by linear transformation of the sequence ω(n+1) in formula (11). ω(n+1) is the chaotic sequence ω(n+1) generated by Logistic (logic) mapping iteration when the initial value ω(0)∈[0,1]; where: when ω(0)=0, let ω(0)=0.1; when ω(0)=0.25, ω(0)=0.26; when ω(0)=0.5, ω(0)=0.56; when ω(0)=0.75, ω (0)=0.76; when ω(0)=1, ω(0)=0.9.
步骤S25，令循环次数u＝u+1；将蚂蚁重新放回起始点，转步骤S22进行下一轮迭代；若迭代次数u>Ncmax，则寻优结束，输出最优航路。Step S25, set the number of cycles u=u+1; put the ant back to the starting point, go to step S22 for the next iteration; if the number of iterations u>Ncmax, then the optimization ends, and the optimal route is output.
仿真分析：Simulation analysis:
如图2所示，对本发明的基于改进混沌蚁群算法的无人机航路规划方法(ACA)和基于基本蚁群算法的无人机航路规划算法(CACA)进行Matlab仿真分析，初始化相关参数：起飞点设为(4,40)，目标点设为(32,23)，雷达威胁半径统一为2，单位均为千米，蚁群数目m＝30,最大迭代次数Ncmax＝200,信息素重要程度因子α＝1，能见度重要程度因子β＝0.8，信息素挥发因素ρ＝0.5，蚂蚁循环一次所释放的信息素总量Q＝100，无人机燃油威胁与路径长度之间的比例系数kf＝1，雷达威胁占总代价函数的比重因子kz＝0.5，衰减系数γ＝0.96，调节系数ar初始化为0.1，迭代次数u初始化为0，雷达威胁个数N＝23。从图2(b)中可以看出，这两种算法均能规划出一条可行路径，其中CACA代表本发明方法规划出的可行路径，用实线表示，ACA代表基本算法规划出的可行路径，用虚线表示，横坐标为迭代次数，纵坐标为航迹代价也就是步骤S13得到的代价函数F；图2(a)中的横坐标为二维空间的X坐标，纵坐标为二维空间的Y坐标；采用本发明方法规划出来的路径在迭代次数趋近于13次，航迹代价值F趋于一个稳定值为37.0018，但采取基本算法规划出来的路径是在迭代次数趋于18次，航迹代价值F趋于一个稳定值为41.3227，所以在相同的迭代次数下，采用本发明方法规划出来的路径代价值比采用基本算法规划出的路径的代价值低，也就是说采用本发明方法规划出来的路径比采用基本算法规划出的路径更优，同时比较两者航迹代价值趋于稳定的迭代次数，可以得出，采用本发明方法规划出来的路径在获得稳定的航迹代价值所需的迭代次数比采用基本算法规划出的路径在获得稳定的航迹代价值所需的迭代次数小，也就说采用本发明方法规划出来的路径比采用基本算法规划出的路径收敛的更快。As shown in Figure 2, carry out Matlab simulation analysis to the unmanned aerial vehicle route planning method (ACA) based on improved chaotic ant colony algorithm of the present invention and the unmanned aerial vehicle route planning algorithm (CACA) based on basic ant colony algorithm, initialize relevant parameters: The take-off point is set to (4,40), the target point is set to (32,23), the radar threat radius is uniformly 2, the unit is kilometer, the number of ant colonies m=30, the maximum number of iterations Ncmax=200, pheromone is important Degree factor α = 1, visibility importance factor β = 0.8, pheromone volatilization factor ρ = 0.5, the total amount of pheromone released by ants in one cycle Q = 100, the proportional coefficient k between the UAV fuel threat and the path lengthf = 1, the proportion factor kz of radar threats in the total cost function = 0.5, the attenuation coefficient γ = 0.96, the adjustment coefficient ar is initialized to 0.1, the iteration number u is initialized to 0, and the number of radar threats N = 23. As can be seen from Fig. 2 (b), these two kinds of algorithms all can plan out a feasible route, and wherein CACA represents the feasible route that the present invention's method plans out, represents with solid line, and ACA represents the feasible route that basic algorithm plans out, Indicated by a dotted line, the abscissa is the number of iterations, and the ordinate is the track cost, which is the cost function F obtained in step S13; the abscissa in Fig. Y coordinate; the path planned by the method of the present invention approaches 13 times in the number of iterations, and the track cost value F tends to a stable value of 37.0018, but the path planned by the basic algorithm tends to 18 times in the number of iterations, The track cost value F tends to a stable value of 41.3227, so under the same number of iterations, the cost value of the path planned by the method of the present invention is lower than that of the path planned by the basic algorithm, that is to say, the cost value of the path planned by the method of the present invention is The path planned by the method is better than the path planned by the basic algorithm, and the number of iterations at which the cost of the two tracks tends to be stable is compared. The number of iterations required for the value is smaller than the number of iterations required for obtaining a stable track cost value than the path planned by the basic algorithm, which means that the path planned by the method of the present invention is more convergent than the path planned by the basic algorithm. faster.
本发明针对无人机航路规划过程中蚁群算法极易陷入局部最优解的问题，提出了一种基于改进混沌蚁群算法的无人机航路规划方法，它将混沌映射到标准蚁群算法的初始化环节中以此来设置初始信息素值，采用混沌扰动的局部再搜索机制和信息素更新策略，有效克服了局部最优的缺陷，提高了搜索效率。Aiming at the problem that the ant colony algorithm is very easy to fall into the local optimal solution in the process of UAV route planning, the present invention proposes a UAV route planning method based on the improved chaotic ant colony algorithm, which maps chaos to the standard ant colony algorithm The initial pheromone value is set in the initialization link of the algorithm, and the local re-search mechanism and pheromone update strategy of chaotic disturbance are used to effectively overcome the defect of local optimum and improve the search efficiency.
以上所述仅是本发明的优选实施方式，应当指出，对于本技术领域的普通技术人员来说，在不脱离本发明技术原理的前提下，还可以做出若干改进和变形，这些改进和变形也应视为本发明的保护范围。The above is only a preferred embodiment of the present invention, it should be pointed out that for those of ordinary skill in the art, without departing from the technical principle of the present invention, some improvements and modifications can also be made. It should also be regarded as the protection scope of the present invention.
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| CN201711330845.7ACN108413959A (en) | 2017-12-13 | 2017-12-13 | Based on the Path Planning for UAV for improving Chaos Ant Colony Optimization |
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| CN201711330845.7ACN108413959A (en) | 2017-12-13 | 2017-12-13 | Based on the Path Planning for UAV for improving Chaos Ant Colony Optimization |
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| CN201711330845.7APendingCN108413959A (en) | 2017-12-13 | 2017-12-13 | Based on the Path Planning for UAV for improving Chaos Ant Colony Optimization |
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