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The study of unmanned combat aerial vehicle (UCAV) path planning is increasingly important in military and civil field. This paper presents a new mathematical model and an improved heuristic algorithm based on Sparse

Nowadays, unmanned combat aerial vehicle (UCAV) has long been a challenging area for researchers in military and civil field. Path planning is defined as looking for the optimal path of moving objects from the start point to the target point under specific constraints (including environmental constraint and movement constraint) [

The path planning problem of UCAV can be modeled as a constrained optimization problem. Before searching track, flight condition and elements (like terrain, threats, climate, etc.) of relevant path planning are represented as symbol information.

Let

Network graph.

Supposing the nodes of network graph form a set

Define a set that includes all paths from the start point to the end point as

Let

As can be seen from the above content, the performance constraint of UCAV is not reflected in the planning. If the nodes in the network graph are feasible points which take performance constraint of UCAV into account, the path with the performance constraint of UCAV can be reflected from solving the above optimization problems. This is a new mathematical model. Compared with [

There are many factors that influence the result of path planning. These factors, which include terrain features, threat locations, and mission requirements, are basic constraints in mathematical modeling. Path planning should meet basic constraints, and they mainly include the following constraints [

On the premise that some constraints are met, the UCAV path planning aims to generate trajectory with the highest survival rate. Therefore, threat locations in battle field should be fully taken into account. Threat factors and fuel restriction are mainly taken into account when calculating trajectory cost.

In this paper, the cost calculation function relates to threat cost and fuel cost. Because fuel cost is proportional to the voyage, the cost calculation function can be given as

The calculation of the threat index on the

Heuristic search [

The primary problem to be solved is how to acquire the candidate node set in the search process. The expression of nodes in state space can be divided into two general types: nodes of graphic expression and nodes of grid expression. The former extends nodes out in the form of ray; the latter divides state space into grids with a certain size and then extends the adjacent grid points out. For example, basic

Nodes have been extended.

Nodes have been generated but has not been extended.

Nodes have not been generated.

The first kind of nodes is called closed nodes, and we can construct a table named

Szczerba et al. provided an advanced version of the basic

The basic extension of

SAS [

Let

SAS extension of nodes.

The constraint of route distance is the allowable maximum length of the route which represents the payload of fuel and arrival time constraint in a specific task. The route whose length is longer than maximum distance (

On the basis of the above discussion, the cost function of heuristic search can be represented as

The basic

In traditional search method, the path may prematurely tend to the predetermined target direction so that the resulting path may not be the shortest path. Only when the aircraft nears the target can the aircraft turn to the predetermined target direction in the long distance flight, it is not necessary to have been proceeding angle heuristic throughout the whole search process. In the proposed method, heuristic function

On the basis of the above discussion, it is very important to find a reasonable heuristic function for getting an approximate optimal solution without reducing search speed. It is also important to design corresponding appropriate heuristic function for different stages of track search.

From the above description, the ultimate goal of path planning system is to generate a set of track point data and then provide these data to flight task manager. Therefore, the initial route obtained by search algorithm needs to be processed so as to get the smaller number of track points. Track points located between start point and target point are stored in path table. Set start point as current point, and traverse other nodes in path table according to the order of the current point to next point. Check whether the connection line of current node and a certain visiting node will encounter threat. If the connection line of current node and a certain visiting node encounters threat, go back to the previous node, set the previous node as current node, delete all nodes between current node and the last current node, update information of current note, and retraverse from this current node until reaching the target node. Otherwise it continues to traverse and repeat above steps.

The following method is optimized in the search process. As shown in Figure

Track smooth straightening processing map.

The route obtained from the above methods can not only reduce route cost but also constrain the number of turns. Besides, valid information of track points can be generated which is in favor of the future navigation.

Define the range of path planning as

Supposing the coordinate of start point is

Supposing the coordinate of start point is

Supposing the coordinate of start point is

The first result.

The second result.

The third result.

The fourth result.

This paper presents an improved heuristic algorithm which is an improved version of SAS algorithm for UCAV path planning. Our algorithm considers not only traditional constraints of path planning but also various flight constrained conditions, like angle information, track smooth straightening processing, and so on. Compared with [

The authors declare no conflicts of interest.

This research was financially supported by National Natural Science Foundation of China (61401363), the Science and Technology on Avionics Integration Laboratory and Aeronautical Science Foundation (20155153034), and the Fundamental Research Funds for the Central Universities (3102016AXXX005, 3102015BJJGZ009).