3D Path Planning for Multi-UAV Base on Artificial Potential Field Method Zhong-tong GUO *, Hong-jie HU and Fei FENG

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1 07 International Conference on Electronic, Control, Automation and Mechanical Engineering (ECAME 07) ISBN: D Path Planning for Multi-UAV Base on Artificial Potential Field Method Zhong-tong GUO *, Hong-jie HU and Fei FENG School of Automation Science and Electrical Engineering, Beihang University, Beijng, China * Corresponding author Keywords: Artificial potential field, UAV, Path planning, Formation flying. Abstract. This paper puts forward the improved artificial potential for UAV path planning. The idea of segmentation planning is used to plan the cruise section and the end with different algorithms, and from a single UAV to multi UAV path planning. According to the angle of the UAV and the threat, the angle between the leader and the wingman and the threat calculated. The angle formula of the leader and the threat is taken as part of the angle of the wingman and the threat. By adjusting the leader and angle of threat and the follower aircraft coefficient. The angle formula of improved the wingman and threat is get. To solve the different starting point of multi UAV formation flying after confluence and reach the target point of the problem at the same time. Simulation results show the effectiveness of the algorithm. Introduction Path planning is based on the target point, obstacles and threat environment for the UAV planning to avoid the threats and reach the target point of the optimal path. We divide it into singular perturbation method [], nonlinear programing method [], dynamic programming [3], genetic algorithm [4], ant colony algorithm [5] and artificial potential field (APF) [6] etc. The APF converges quickly, but there are objects unreachable, easy to fall into the local optimal, and solve these problems through the improved artificial potential field method. Threat Analysis and Modeling Terrain Model In addition to its own constraints, UAVs also have to consider various threats during flight. It is divide into natural environment and enemy air defense threat [7]. Natural environmental threats mainly refer to peaks and terrain threats. Enemy air defense fire, including radar, anti-aircraft artillery and so on. For terrain, it is difficult to use accurate model to express. Therefore, this paper uses the literature [8] given the random terrain function:,=sin++ sin+ cos + +.cos+ sin + +.cos () In the above equation,, represent the coordinates in the horizontal plane, represents the corresponding height information.,,,,,, Stand for constant coefficients. Mountain Model After getting the random terrain, the model of the mountain topography is described next. The mountain terrain model can be approximated by the following function: z x,y= z exp () In the above equation, represents the total number of peaks,, represent the central coordinate of a mountain peak,, indicate the slope of a mountain. Radar Model In general, the radar threat is treated as a terrain with the same range as the radar in 3D path planning. Thus, elevation data of radar range and radar center can be obtained: 86

2 Z( x, y) = Ra ( R0 ( x x0) ( y y ) ) 0 (3) In upper model, is a parameter related to radar characteristics, represents the radar s radius of the threat.,, which is the coordinates of the threat center. Anti-aircraft Model According the number of anti-aircraft guns and the probability of threat, the equivalent elevation data can be obtained: zx,y= P z +R x x y y 0<<R 0 r>r (4) r=x x +y y (5) In the above equation, indicates the level of the UAV to the center of the artillery threat center,, which is the coordinates of the threat center. Path Planning Algorithm Subsection Planning Algorithm For the cruise section, due to the need to maintain low altitude flight to avoid radar detection, but also can t fly too low to prevent the collision accident. The APF combined with digital elevation map (DEM) is used to path planning. In the end, the UAV to quickly occupy a favorable position to perform combat missions, if continue to limit the flight altitude is not suitable, so the use of 3D case of improved artificial potential field (IAPF) for path planning. D IAPF Algorithm In the traditional APF, when the UAV is close to the target point, the gravitational tend to zero, if there is an obstacle near the target point, may make the repulsion greater than gravity led to UAV can t reach the target point. When the obstacle is located at the center of the UAV and the target point, if the gravitation force is equal to the size of the repulsive force, the UAV falls into the local optimum. Aiming at the above problems, the APF is improved by changing the repulsion field. The improved repulsion field is as follows: η ρp,p, ρ U = (6) 0 ρp,p >ρ The corresponding repulsive function is: F = U = η F + η F ρp,p ρ 0 ρp,p >ρ (7) F rep = ρ, ( p p ) obs a ρ ρ o ρ ( p, p ) g ( p, p ) obs F a rep ( p, pobs ), = ρ ρ ρo ( p p ) g 87 (8)

3 (9) a The IAPF increase the effect of the target point on the UAV ρ (p, p ). The repulsive force function corresponding to potential field function can be obtained. In the repulsive force function, the direction of Frep is directed by the obstacle to the UAV, the direction of Frep is directed by the target point to the UAV, a is the adjustment factor, and the different values determine the magnitude and direction of the repulsive force. In this paper, a is. 3D IAPF Algorithm The D path planning can be extended to 3D space can be the following formula: F rep Frep + Frep p ρ0 = 0 p > ρ 0 (0) g F =η,, (), F =η (), In the above formula,, represents the distance between the UAV and the threat center, and, represents the distance from the UAV to the target point. The direction of is directed to the UAV by the obstacle. The direction of is directed to the UAV by the target point. η is the coefficient of repulsion gain. The gravitational formula is: att att g ( ) F = K p p In the above formula K Multi-Uav Path Planning Multi-UAV Cooperative Planning att is the gravitational gain coefficient. Multi-UAV collaborative path planning refers to the planning of paths for multiple UAVs in consideration of synergistic constraints so that they can work together at the minimum cost. When multiple UAVs from different locations need to arrive at the same target point, coordination of multiple UAVs is required. Multi-UAV Formation Planning Compared with the independent planning to reach the target point of the path, through the confluence of the UAV to maintain a different height of the formation flight can be effective reduced by the radar detection cross-sectional area, generate a greater threat to the enemy target area and achieve combat mission. Take two UAVs as an example, assuming UAV is a long machine and UAV is a wingman. Getting the following formation flight diagram. (3) Figure. Schematic diagram of UAV formation flight. In the case of UAVs that require the formation to reach the target point, the gravitational 88

4 functions of the UAVs are the same as those of the single UAV. Gravitation and repulsion can be decomposed into force in the X and Y directions. The angle between the UAV, and the target point is θ, θ.the angle between UAV, and the obstacles is: [ ] ϕ = ϕ, ϕ ϕ n [ ] ϕ= ϕ, ϕ ϕn (5) Where is the number of obstacles. It possible to change the angle between the wingman and the obstacle by increasing the angle between the long machine and the obstacle in the formula of calculating the repulsion function of the wingman to achieve the intersection of the long machine and the wingman to reach the target point. The angle between the new UAV and the obstacle is obtained: (4) β β = φ = ω φ + ω φ (6) (7) ω +ω = (8) ω, ω for the weight coefficient, by adjusting the size of ω, ω can change the UAV on the UAV degree of influence. Assuming UAV, UAV by the target point and the obstacle forces are F att, F F att, rep F, rep.the following formula is thus obtained: F =F cos θ F =F sin θ (9) (0) F =F cos β () F =F sin β () Where i =,. Through the above formula, the force of each UAV in space can be calculated, and then the coordinates of the next position of the UAV can be determined. Simulation and Analysis In the 3D plane, the target point is set (70, 90, 0). In the cruise section, Katt = 5, η = 3.4.The coefficient of attraction =0. Single UAV Path Planning Figure. UAV flight path planning. 89

5 It can be seen from the figure that the IAPF can plan a way to avoid all threats to the UAV. Multi-UAV Independent Path Planning Multi-UAV independent path planning map is as follow: Figure 3. Multi-UAV independent path planning. Each UAV independent planning starting point to the target path, time coordination by adjusting [ ] the speed of the UAV flight V = v,v min max to meet the multi-uav at the same time to reach the target point, space collaboration by making the UAV flight height different guarantee. Multi-UAV Formation Path Planning The following chart can be obtained when Multi-UAV formation flying: Figure 4. Multi-UAV formation flight chart. Different starting points of the UAV arrive at the confluence point at the same time, and then form a formation to reach the target area. Conclusion Through the simulation results, IAPF can avoid the threat and plan an optimum path to the target point. In the Multi-UAV path planning through the control of the UAV speed, height and angle, to achieve a Multi-UAV after the formation flight. References [] Vascak J, Rutrich M, Path planning in dynamic environment using fuzzy cognitive maps, R. IEEE , 008:

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