Proceedings of the 2006 IEEEInternational Conference on Information AcquisitionAugust 20 - 23, 2006, Weihai, Shandong, China

Particle Swarm Optimization for RoutePlanning of Unmanned Aerial Vehicles

Shibo Li, Xiuxia Sun , Yuejian XuDepartment ofAutomatic Control

University ofAir Force Engineering

Shan xi Province, Xi'an, 710038,CHINAEmail: lsb97@l63.com

Abstract: Route planning for unmanned aerial vehicle (UAV) is aerial vehicles, we not only need to consider the obstacle

an extremely complex problem. Different means of optimization avoidance, but also need to evaluate the threat level of the

have been investigated for unmanned vehicles with various missile position, radar position, etc. when performing a urgent

algorithms like genetic algorithms, evolution computations, mission, we can intersect with the threat area that with a low

neutral networks etc. This paper presents the application of threat level to save the flight time.

Particle Swarm Optimization (PSO) for route planning problem. There are a wide variety of approaches that have been

The route planning area is represented by a mesh of equal square reported for solving the route-planning problem. Roughly,

cells. The objective function is constituted based on the factors of they can be listed as follows: dynamic programming

the flight time and safety. The threat level is evaluated with fuzzy Algorithm, A* Algorithm, probabilistic roadmap algorithm,

technique. The implementation of the PSO search strategy to the genetic algorithm, etc. Because of the intractable of the

route-planning problem is given. Simulation results indicate that route-planning problem and its importance in flight for

the PSO based algorithm is a feasible approach for route unmanned aerial vehicles, it is desirable to explore other

planning problem. avenues for developing good heuristic algorithms for this

problem. In this paper, we introduce an approach based on

I. INTRODUCTION particle swarm optimization for route planning.In recent years, great interest has focused on route-planning A recently developed new algorithm known as particle

problem for unmanned aerial vehicles. For unmanned aerial warm optimization (PSO) has proven to have great potentialvehicles, which perform missions such as reconnaissance, for optimization problems [2]. This technique combines the

succor, etc, it is very important to plan a path for the vehicles social psychology principles in socio-cognition human agents

to follow. Standard route planning algorithms usually generate and evolutionary computations. PSO has motivated by the

a minimum cost solution based on a predetermined cost behavior of organisms such as fish schools and bird flocks.

function (relating factors such as terrain features, threat Generally, PSO is characterized simple in concept, easy to

locations, mission requirements, etc.)[1]. Because aircraft implement, and computationally efficient. Unlike generallimitations and/or mission parameters must be taken in to algorithm, PSO has no evolution operators such as crossover

account, the path planning problem is considered to be and mutation and moreover, PSO has less parameter [3].NP-complete in nature. In this paper, a model of the route-planning problem is

Unlike the robots that performing their missions on the proposed. The route-planning problem is discussed and solvedground, there are some questions need to be solved for here by a novel P50 approach. The remainder of this paper is

unmanned air vehicles. When performing definite missions, organized as follows: Section II Provide the formulation ofthe obstacle-avoidance in the route planning area need to be the route planning problem. Section III describes the PSO

considered for the robot on the ground, but for unmanned algorithm for the route planning problem. section IV discuss

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the threat level assessment. Simulation results are reported in increase the probability of survive. According to the factors

section V. Finally, section VI concludes the paper. mentioned above, the objective function can be formulated as:

m-1

II. Problem Formulation J=LK + ZMhazadd (1)i=l

In this section, before studying the problem of route Where LK is the length of the route that the vehicleplanning, the question needs to be solved firstly is to deal with experience. Mhazad is the threat level of the node in the route.the searching space. Assuming the unmanned aerial vehicle The route distance experienced by the vehicle is defined asflies within a limited range of altitude in 3D space, the route the sum of the straight length between the nodes. The distanceplanning problem can be turned in to a 2D space route between the path node Li(xi,ykj) and the next path codeplanning problem in this case, The method used here is

described in the following paragraph. LI (x1,, Yk(j+,)) can be expressed as:

The hypothesis is given as follows: the start point is A, The

goal point is B, the straight distance between A and B is L, dab =1+ (Y(i+l)-Ykj , (i =1,2,...,m-1)m (2)The minimum yaw distance of the aircraft is C. the planning The length of the whole route isarea is within the quadrate space which take the line AB as the m-1LK (Ykl _-y)2 +yZ I+ (Yk(i1 Yki)midline, long distance is L, broad distance is 2C. LK = _(i+l)1+i) +

In order to simplify the problem, we set up the reference

frame, the nearside borderline and the underside borderline are 1+ (Yk(m_I) - y0 )2 (3)

taken as the X-axis and Y-axis, and the point of intersection is The enemy target such as missile and flack will cause sometaken as the origin. A mesh of equal square cells represents the damage to the UAV that flying in the planning area, we needplanning area; the whole planning area is divided in to m * n to avoid flying above them. The threat circle with determinatecells. The coordinate of the start point is A (XO, YO), the goal radius is used to express these threats. The size of the radiuspoint is B (Xm, Y0). The range of the X-coordinate is [0, m], represents the area that the threat covered, each threat isThe range of the Y-coordinate is [0, n].Thus in the planning distributed a value according to the kinds of threat and the killarea, there are (m+l)*(n+1) nodes for route planning, namely ability. We memorize the threat with a uniform form as (Xk, Yk,

LO(XI, YI), L0(X1, Y2), , LO(Xl, Ynl+±) Rk, Vk), where Xk, Yk represents the center coordinate of the

threat circle; Rkrepresents the size of the radius; Vkrepresentsthe threat level. Assuming the coordinate of a node is

Lm(Xm, Y1), Lm(Xm, Y2), , Lm(Xm, Yn+l) (Xi,1) in the searching space, then the distance from the

Where Li (x, yj ) represents the coordinate that the value node to the center of the circle is

of X-coordinate is x;, the value of Y-coordinate is yj. The d =V(XK -Xi)2 +(YK -Y)2 (4)

path from A to B can be expressed as follows: Now the threat level about the node to the threat circle isgiven here

Path= {A, LI(XIIYKI) I L2(X2,YK2), , Lm- (Xm-rnYk(rJ)) F(Id)*1Vh,d <=R (5)

B} (ki = ,2,.....I.,m

For the route-planning problem, the objective function if the number of the threat is q in the searching area, the

should be given in order to find an efficient path. Two factors total threat level isare considered here: (1) the length of the route should be made Mhdzu ZEm (6)minimum to reduce the oil consuming and the flight time. (2) =The vehicle should avoid flying through the threat area to III. Particle Swarm Optimization

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The Particle Swarm Optimization algorithm was initially while with a small one the particles is more intended to do

proposed by kennedy and Eberhart in 1995[4], it has been local exploration. A proper choice of the inertia weight w

applied successfully since then to a handful of problems. provides the balance between the global and local exploration.

Similar to the general algorithm and ant colony algorithms, Equation (7) is used to update the particle's new velocity

PSO algorithm is a computing technique based on swarm according to its velocity at previous time step and both the

intelligence. The PSO technique conducts searches using a distance between its current position from both its own best

population of particles, each particle represents a candidate historical position, and its neighbor's best position. Then the

solution to the problem at hand[5]. In a PSO system, particles particle flies toward a new position according to equation

change their positions by flying around in a multi-dimensional (8).The performance of each particle is measured according to

search space until a relatively unchanged position has been a pre-defined fitness function, which is usually proportional to

reached, or computation limitations are exceed. the cost function associated with the problem. The process is

In a PSO system, multiple candidates coexist and repeated until user-defined stopping criteria are satisfied.

collaborate simultaneously. Each potential solution, called a In the process of the optimization in route planning, a limit

particle, is evaluated by three factors: position, velocity and should be set to the particle's position and velocity. Vmax is

adaptability. Initially each particle is assigned a random the maximum allowable velocity for the particles, if the

position and velocity, and then each particle flies in a problem velocity of the particle exceeds Vmax, then it is limited to

space looking for the optimal position to land. The particles Vmax . Vmax is an important factor which affects the resolution

have memory and each particle keeps track of its previous best and fitness of search. If Vmax is too high, then particle will

position as well as the best position of its neighboring particles. move beyond a good solution, and if Vmax is too low,Tracking and memorizing the best position encountered build particles will be trapped in local minima. Also each particle's

the particle's experience. For this reason, the PSO algorithm position is limited to a fixed range [0, Ymax], Ymax represents

poses a huge memory requirement. PSO systems combine the the maximum value in the direction of y coordinate.

local search methods with the global search method, IV Threat Level Assessmentattempting to balance exploitation and exploitation. The

particles are manipulated according to the following In the route planning area, unmanned aerial vehicle can be

time-transition equations [6][7]: affected by many threat factors; the vehicle must avoid flyingthe threat area, so the threat level assessment for different

V, [k + 1] = w * V, [k] + Cl * Randl( * (Pbest j (k) - Pi (k)) kinds of the threat is essential in the route planning process.

+C2 * Rand2( * (Gbest(k) - Pi (k)) (7) The threat factors, such as the circumstance of the planningPi (K + 1) = P, (K) + V, (K) (8) area, the kill ability of the threat, are taken in to consideration,

The parameters used in the PSO are described as follows: threat level assessment system give a numeral value to the

Vi(k) represents the velocity of the ith particle at time k; Pi(k) threat such as missile, radar. The value can be used to make

presents the particle position; Pbesti[k] represents its "best" decision for the planning system and assure the safety of the

position in its past experience; and Gbest[k] is the best position unmanned aerial vehicle.

among all particles in the population. Randl and Rand2 are Many factors must be taken in to account in the threat level

two uniform random functions with a range [0, 1]. C1 and C2 assessment, it can be divided in to three aspects, namely the

are positive constants, called the cognitive and the social kill ability of the threat to the aircraft, the resistance ability of

parameter respectively. The inertia weight w is employed to the aircraft, and the weather condition of the planning area.

control the impact ofthe previous history of the velocities on When perform planning task, we need evaluate the three

the current velocity. In some sense, this inertia regulates the aspects synthetically in order to acquire a reasonable value

trade-off between the global and the local exploration abilities about the threat level. The detailed description of the three

of swarm. A large inertia weight facilitates global exploration, aspects is described below:

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1) The kill ability of the threat to the aircraft: the kill ability input linguistic variables are assigned an integral value in the

is comprised of a series of factors, including the kinds of the range of [0,10]. To make the input of the fuzzy system more

threat resources and the parameter of the threat. The kinds of objective, three or five expert given a value according to the

the threat resources mean the threat such as radar, missile and threat factors, and then the average value is computed and

artillery; the parameter of the threat includes the taken as the input value. Considering the number of the inputtarget-discover ability of the threat, the kill probability of the linguistic variables, the format of the input is [X, Y, Z] ,

target, the maneuverability of the threat and so on. where X, Y, Z represents the value that the expert given about

2) The resistance ability of the aircraft: it includes the he kill ability of the threat to the aircraft, the resistance ability

disturbing measure that the aircraft possessed, the of the aircraft, the weather condition of the planning area.

maneuverability of the aircraft, the flying velocity and the Gauss function is used as the membership function of the

flying velocity altitude. The more advanced the equipment input linguistic variables; Triangle function is used as the

that equipped by the aircraft, the better maneuverability the membership function of the output linguistic variables. Fuzzy

aircraft possessed, the more easily the aircraft can escape the if-then rules provide a good way to extract and formulate an

beating of the threat. expert's experience. The simple structure of the if-then rules

3) The weather condition of the planning area: Whether the allows the expert to formulate his experience using linguisticaircraft can arrive the destination successfully has much terms. Linguistic knowledge is easier to extract from an expert

relation to the weather condition of the planning area. The than crisp mathematical terms. For example, an expert would

weather condition (visibility, wind speed, air pressure) has say

much influence for the aircraft to escape the beating of the IF the weather condition is goodthreat. The weather condition is introduced to the threat level THEN the threat level is low.

assessment system to increase the objectivity of the threat Weight =R1.level assessment. The rule's weight assigns an important value in the range

The destination of the threat level assessment is to get a of [0,1] to reflect its importance with respect to the other rules.

definite value. As a multi-attribute decision-making problem, The rule's weight is given according to the experiences of the

the different factors affecting the threat level can only be experts. In the inference process, Mamdani's Max-Min

described vaguely. For example the weather condition can implication and Center-of-Gravity defuzzification is used. The

only be described with good, middle and poor. Further more, structure of the fuzzy system for the threat level assessment is

the threat level has not a definite limitation, it possess a certain given as Fig. 1.

fuzzy character. So we can solve the problem with the fuzzytechnique.The factors which affect the threat level assessment are

taken as the input linguistic variable of the fuzzy logic systems, kill-ability (3 \

threat level is taken as the output linguistic variable. Fuzzy threat

representation supports linguistic modifiers like very,

somehow and kind of. Considering the input linguistic resistanceZability (3)

variable, the value of threat kill ability and the resistance 9 rulesthreatr-level (3)

ability is represented as low, med., high; the weather condition

is represented as poor, med., good; for the output linguisticweather-circumstance (3)

variable, the definition of the linguistic is low, med., high.

The input linguistic variable is a vague value, in order to System threat: 3inputs, 1 utputs,9 rules

increase thecnvenience of he input for te fuzzy logicFig. 1 the structure of the system for threat level assessmentsystem; we turn the fuzzy concept in to a definite value, the

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V. Particle Swarm Optimization for Route Planning Problem 5LD

In this section, we propose a PSO-based heuristic method 450

for solving the route planning problem. One of the key issues

in designing a successful PSO algorithm is the state 400

representation, i.e. finding a suitable mapping between350

problem solution and PSO particle's status. According to

section 2, for each value of X-coordinate, the corresponding 300

value of Y-coordinate must be found. In order to simplify the

problem, we allocate each X-coordinate a fixed value, which 250means the value of X1, X2, *-- Xr-i is given as 1, 2 m-1.m ~~~~~~~~~~~~~~~200

In order to demonstrate the feasibility of the algorithm, o 100 200 300 400 500 600 700 600 900 1Can example is given here. Assuming the start point and the

Fig.2 The best function with iteration numberdestination point was known, the route planning space was

constituted by means that described in the second section. The

planning area was divided in to a mesh of equal square cells,and the reference frame was set up [8]. The range of the

X-coordinate is [0, 50], The range of the Y-coordinate is [0,

50]. Assuming there are five threat zones in the planning area,

they are expressed as the threat circles and added to the

searching area.

Aimed at the planning area described in this example, Zw

each particle performs the route optimization in a *@ 2 i 9 t 1.-5E9i ti4s4 i9

49-dimensional search space. Each particle's position was

constrained to [0,50], the maximum allowable velocity for the

particles is 15. The other parameters of the PSO are: (1) the

size of the population: 20. (2) The inertia weight w: 0.75. (3)C l=C2=2. Fig. 3 The generated route with equal threat value 1.

The initial value of theparticle was randomly given. The

number of the evolution is 1000. In the first step, the value of

each threat circle is set to 1, after the evolution, the simulationresult is given. Fig.1 shows the relationship between the best

cost function with the iteration. Figure 2 shows the generatedroute. In the second step, the value of the fifth threat circle is k

set to 0.4, the other is set to 1. Figure 3 shows the generated

route in this case. . .

From the simulation results we can see that the generated l- I- I,a;aroute efficiently avoid the threat zones, the request for the

,

flyable path is satisfied. When the value of the threat circle , A;iE21a4gvEEBr 'I7B HSriBY&&hAgitiMriEsMWi M

becomes smaller, the generated route penetrates though the

threat zone. The reason can be explained from equation (1).Fig.4 The generated route with the different threat value 0.4

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As the threat value becomes smaller, the value of the

second part in the equation becomes smaller, the first part in

the equation becomes more important, so the penetration is

happened to shorten the route length.

VI. Conclusion

The route planning is of great importance for the efficient

utilization of the unmanned aerial vehicles. In this paper, the

PSO algorithm is adopted to solve the route planning problem.

The Simulations shows that the PSO algorithm is capable to

solve the problem. The studies indicated that the proposedPSO is an attractive alternative for solving the route panning

problem. The PSO algorithm is a new algorithm. There are

some questions need to be solved in the route planningproblem, For example the convergence time is long, it is not

suitable for real time planning at present. But because the PSO

algorithm has implicit parallelism, its application for route

planning problem has a good future.

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