Fast Path Planning for Firefighting UAV Based on A-Star algorithm

When the long distance oil-gas pipeline accident occurs, the fire UAV can give priority to the place where the accident occurs. Emergency investigation and fire rescue, greatly reduces the harm of the accident. However, due to the limitation of the UAV navigation system, the UAV will accumulate the positioning errors over time in the flight process. If the positioning errors can not be corrected in time, it will make the UAV unable to reach the intended destination, thus leading to the failure of the rescue mission. In view of this phenomenon, we propose a UAV path planning scheme considering positioning errors. Taking the UAV’s total flight path as short as possible and errors correction points as few as possible, a multi-objective programming model is established considering errors correction constraints and path constraints. The Euler distance with coefficient is selected as the estimated cost function of A-Star algorithm, and the optimal flight path of UAV is quickly planned through heuristic search. Taking the data of a certain flight area as an example, we have simulation results showing that the A-Star algorithm can quickly and effectively solve the problem of UAV flight path planning considering positioning errors.


Introduction
When carrying out rescue missions, firefighting UAV must be accurate and fast to reach the destination. This puts forward a certain requirement for the navigation accuracy of UAV. At present, the navigation technologies mainly used by UAV include inertial navigation, satellite navigation, geomagnetic navigation and terrain aided navigation [1]. However, in the complex terrain and bad weather, the UAV often can only use inertial navigation technology. There are some positioning errors when the UAV adopts the inertial navigation technology. They are the errors accumulated over time due to the inability of the UAV to accurately position itself during flight, including vertical errors and horizontal errors.
In recent years, the researches of UAV path planning mainly focus on the danger avoidance and mission requirements, and there are few researches on the path planning with positioning errors as the constraint conditions. Chen Chang applied the optimized A-Star algorithm to the global and local path planning of the UAV, which shortened the path length and pathfinding time, and improved the smoothness of the path. This method is suitable for the multi-obstacle avoidance of the UAV path planning [2]. Jianlin Xin used Dijkstra algorithm to initialize the flight path, and adopted multi-path selection strategy and simulated annealing mechanism to improve the global search ability, which improved the flight path planning ability of UAV in danger avoidance and complex environment [3]. Chengzhen Wu constructed the mathematical model of UAV under the constraint of positioning 2 errors, deduced the spatial arc trajectory equation by combining the path points and turning radius, and used the greedy algorithm to quickly plan the path of UAV. They provided ideas for the application of warehouse logistics path planning [4]. Xiaohui Li used the improved A-Star algorithm and combined with various types of no-fly zones to plan the optimal flight path for the UAV to avoid obstacles between two customer points. This method can effectively solve the obstacle avoidance path planning problem of UAV in the coexistence of multiple types of nofly zones [5]. To sum up, the research on UAV path planning with positioning errors as the constraint conditions is relatively shallow, so we designed a UAV path fast planning scheme based on A-Star algorithm under the positioning constraint conditions [6].

Problem description
It is known that the UAV needs to start from Station A to Station B to complete the rescue mission. There are several horizontal correction points and vertical correction points within the space range of AB, and the positions and types of each correction point are known. UAV's path planning is successful [7]. Our goal is to quickly planning out a path that would allow the UAV to reach Station B with the shortest possible distance and with the fewest possible correction points.

The establishment of the objective function
The path to be planned can be divided into three parts, as shown in Figure 1.  . Then, the first objective function with the shortest possible path is shown in Equation (1) .
The second objective function indicates that the number of correction points passed are as few as possible, so it can be expressed as min L S . According to the weighted coefficient method, a coefficient is assigned to each objective, and the multi-objective programming model is transformed into a single objective programming model. The model is shown in Equation (2) .
Due to the different units of measurement of each index in the model, it is necessary to standardize the index and map its value to a certain value interval through function transformation. The standardization processing formula is shown in Equation (3).

Algorithm design of A-Star
A-Star algorithm is a heuristic algorithm in artificial intelligence, which realizes optimization through regular expansion of the smallest points of the estimation function [8]. The estimation function set in this paper is shown in (10) .  precision of the algorithm. The classical A-Star algorithm uses Euclidean distance or Manhattan distance to represent the estimated cost. In this paper, some minor improvements are made to the estimation cost function, and the influence is adjusted by setting the coefficient, which makes the algorithm more flexible to solve the optimal flight path.

The simulation analysis
It is known that there are a total of 611 correction points in a certain flight area, among which the spatial coordinates and correction types of each correction point are known. We set MATLAB programming is used to realize the above algorithm, the errors correction information is shown in Table 2. The path length is solved as a result of 106350.06; the number of corrected points is 8. The results meet the restriction requirements of the constraint conditions [10]. The A-Star algorithm is compared with Dijkstra algorithm, and the comparison results are shown in Table 3.
It can be seen from the Table 3 that A-Star algorithm is superior to Dijkstra algorithm both in terms of algorithm accuracy and running time. This indicates that the UAV path planning method based on A-Star algorithm is more suitable for solving the problem of firefighting UAV path planning constrained by positioning errors.

Conclusion
In this paper, the path planning problem of firefighting UAV with positioning errors constraint is taken as the starting point, and the multi-constraint path planning problem of UAV based on A-Star algorithm is emphatically studied. The innovation point is that the positioning errors are combined with the flight path planning, and the A-Star algorithm is used to solve the fast flight path planning problem of the firefighting UAV. The performance of A-Star algorithm and Dijkstra algorithm is compared, and it is concluded that A-Star algorithm has certain advantages in solving this problem. The model and algorithm presented in this paper provide a theoretical basis for the rapid flight path planning of UAV.