PARALLEL IMPLEMENTATION AND COMPARISON OF

TWO UAV PATH PLANNING ALGORITHMS

Vincent Roberge, Mohammed Tarbouchi and Gilles Labonté

Department of Elec. and Comp. Eng., Royal Military College of Canada, Kingston, Canada

Keywords: UAV, Path planning, Genetic algorithm, Particle swarm optimization, Parallel implementation, T-test.

Abstract: The development of autonomous Unmanned Aerial Vehicles (UAVs) is of high interest to many

governmental and military organizations around the world. An essential aspect of UAV autonomy is the

ability for automatic path planning. In this paper, we use the genetic algorithm (GA) and the particle swarm

optimization algorithm (PSO) to cope with the complexity of the problem and compute feasible and quasi-

optimal trajectories for fixed wing UAVs in a complex 3D environment while considering the dynamic

properties of the vehicle. The characteristics of the optimal path are represented in the form of a multi-

objective cost function that we developed. The paths produced are composed of line segments, circular arcs

and vertical helices. We reduce the execution time of our solutions by using the “single-program, multiple-

data” parallel programming paradigm and we achieve real-time performance on standard COTS multi-core

CPUs. After achieving a quasi-linear speedup of 7.3 on 8 cores and an execution time of 10 s for both

algorithms, we conclude that by using a parallel implementation on standard multicore CPUs, real-time path

planning for UAVs is possible. Moreover, our rigorous comparison of the two algorithms shows, with

statistical significance, that the GA produces superior trajectories to the PSO.

1 INTRODUCTION

The path planner is an element of the UAV control

module (Chen et al., 2009). It allows the UAV to

autonomously compute the best path from a start

point to an end point. Whereas commercial airlines

fly constant prescribed trajectories, UAVs in

operational areas have to travel constantly changing

trajectories that depend on the particular terrain and

conditions prevailing at the time of their flight.

In the past, the best path has been associated with

the shortest path and deterministic search algorithms

were used to find the very shortest path. The

definition of the problem has since evolved and the

best path is now associated with the path that

minimizes the distance travelled, the average

altitude, the fuel consumption, the radar exposure,

etc. These are a few examples of the factors to be

considered and clearly show that the complexity of

the problem has grown. To cope with this

complexity, researchers have slowly moved from

using deterministic algorithms to using non-

deterministic algorithms (Masehian and

Sedighizadeh, 2007).

In this paper, we use two non-deterministic

algorithms to develop an operational path planning

module for fixed wing UAVs. Our research work

presents three important contributions. Firstly, we

propose a comprehensive cost function which

includes both the optimization and the feasibility

criteria. This allows us to use a generic optimization

algorithm (without modification) as the search

algorithm. In our case, we use the GA and the PSO,

but these could easily be replaced by other

algorithms. Secondly, we present a technique to

parallelize both the GA and the PSO while

minimizing the communication between the

processes in order to achieve a near linear speedup

and fully exploit the computing power of today’s

multicore CPUs. Finally, we offer a statistically

significant comparison between the quality of the

trajectories generated by our GA-based and PSO-

based path planners. Both algorithms have recently

been widely used for UAV path planning

(Pehlivanoglu, 2011), (Macharet et al., 2010), (Fu

and Gao, 2010), (Xia Li et al., 2010), (Bao et al.,

2010), (Yangguang Fu et al., 2009) and (Foo et al.,

2009). However, to our knowledge, there exists no

rigorous comparison between the two algorithms

162

Roberge V., Tarbouchi M. and Labonté G..

PARALLEL IMPLEMENTATION AND COMPARISON OF TWO UAV PATH PLANNING ALGORITHMS.

DOI: 10.5220/0003663501620167

In Proceedings of the International Conference on Evolutionary Computation Theory and Applications (ECTA-2011), pages 162-167

ISBN: 978-989-8425-83-6

 2011 SCITEPRESS (Science and Technology Publications, Lda.)

when applied to this particular problem. The results

we present in this paper provide clear insight as to

which of the two optimization algorithms is

preferable for UAV path planning in complex 3D

environments.

2 REPRESENTATION

The first step of path planning is to discretize the

world space into a representation that will be

meaningful to the path planning algorithm. This

representation is closely related to a search

algorithm and some algorithms will only perform

well when coupled with a specific environment

representation. An overview of the performance of

different representations used with different

algorithms is presented in (Sariff and Buniyamin

2006). In our implementation (see Figure 1), we use

an approximate cell decomposition of the terrain

using a 2D grid where each element of the matrix

represents the elevation of the terrain. This

representation allows us to use digital elevation

maps freely available from the GeoBase (Anon n.d.)

repository with no further processing. Our

representation of the environment also allows for the

definition of cylindrical danger zones (or no-fly

zones) to be kept in a separate matrix where each

row represents the coordinates and the diameter of

the cylinder. Complex no-fly zones can be built by

partially juxtaposing multiple cylinders. The

trajectories generated by the optimization algorithm

are composed of line segments and encoded in a

matrix where each row represents the (x, y, z)

coordinates of a waypoint. The trajectories are flown

at constant speed and can also be represented as a

function of time.

Figure 1: Trajectory in a 3D environment.

3 COST FUNCTION

As previously stated, searching for the best path is

often associated with searching for the shortest path.

This is the case when solving the Traveling

Salesperson Problem (TSP), which consists of

finding the shortest path that visits all the given

cities only once. In the case of UAV path planning,

the optimal path is more complex and includes many

different characteristics. To take into account these

desired characteristics, a cost function is used and

the path planning algorithm becomes a search for a

path that will minimize the cost function. The cost of

a path decreases with the degree to which the desired

characteristics are being fulfilled. A path that fulfills

all the characteristics to a high degree would result

in a low cost. We define our cost function as

follows:





=



+



+

 

+



+



+



+



(1)

where C

length

penalizes longer paths, C

altitude

penalizes

paths with a higher average altitude, C

danger zones

penalizes paths going through danger zones, C

power

penalizes paths requiring more power than the

maximum available power of the UAV, C

collision

penalizes paths colliding with the ground, C

fuel

penalizes paths requiring more fuel than available in

the UAVs and finally, C

smoothing

penalizes paths that

cannot be smoothed using circular arcs. All terms

are normalized on the interval [0, 1]. C

length

, C

altitude

and C

danger zones

are optimization criteria and are used

to improve the quality of the trajectory whereas

power

, C

collision

, C

fuel

and C

smoothing

are feasibility

criteria that must be satisfied for the final trajectory

to be valid. In order to separate viable and non-

viable trajectories, we add a penalty constant to each

feasibility constraint not satisfied.

4 GENETIC ALGORITHM

The GA is a population based non-deterministic

optimization method that was developed by John

Holland in the 1960s and first published in 1975

(Holland, 1975). Based on the genetic theory of

Darwin evolution, the GA simulates the evolution of

a population of solutions to optimize a problem.

Similarly to living organisms adapting to their

environment over the generations, the solutions in

the GA adapt to a fitness function over an iterative

process using biology-like operators such as the

PARALLEL IMPLEMENTATION AND COMPARISON OF TWO UAV PATH PLANNING ALGORITHMS

163

crossovers of chromosomes, the mutations of genes

and the inversions of genes. In this work, the GA

simulates the evolution of a population of

trajectories adapting to the cost function defined in

the previous section. Our implementation uses

stochastic universal sampling as the selection

method, single point crossover as the reproduction

mechanism and addition, deletion and modification

as genetic operators (Yu and Gen, 2010). We also

used the concept of elitism when replacing the old

generation with the new one in order to improve

conversion. The flowchart of the GA is shown in

Figure 2 and the different genetic operators used, in

Figure 3.

Figure 2: Flow chart of the genetic algorithm.

Figure 3: GA operators.

5 PARTICLE SWA RM

OPTIMIZATION

The PSO is a population based non-deterministic

optimization method that was proposed by Kennedy

and Eberhart in 1995 (Kennedy & Eberhart 1995).

The algorithm simulates the movement of a swarm

of particles in a multidimensional search space

progressing towards an optimal solution. The

position of each particle represents a candidate

solution (a complete trajectory encoded in a single

vector) and is randomly initiated. At every step of

the iterative process, the velocity of each particle is

individually updated based on the previous velocity

of the particle, the best position ever occupied by the

particle (personal influence) and the best position

ever occupied by any particle of the swarm (social

influence). As outlined in (Clerc 2005), the

equations used to compute the velocity and position

of a single particle at iteration  are as follows:





=



+







.∗ (



−



)+







.∗ (



−



)

(2)





=



+



(3)

where variables in bold are vectors; v is the velocity

of the particle; x is its position; b is the best position

previously occupied by the particle; g is the best

position previously occupied by any particle of the

swarm; r

and r

are vectors of random values

between 0 and 1; and ω, c

and c

are the inertia, the

personal influence and the social influence

parameters. Still based on (Clerc, 2005), the flow

diagram of the PSO is displayed in Figure 4.

Figure 4: Flowchart of the particle swarm optimization.

ECTA 2011 - International Conference on Evolutionary Computation Theory and Applications

164

6 PATH SMOOTHING

Consistent with solutions proposed in the literature

(Labonté, 2009), (Hasircioglu et al., 2008),

(Anderson et al., 2005), our solution generates a path

composed of line segments. This would be sufficient

for multi-directional ground robots, but inadequate

for a fixed-wing UAV. To remove all discontinuities

in the velocity, we smooth the final path by

connecting the line segments with simple circular

arcs (when the power available is sufficient) or

circles on a horizontal plateau (when the power

available is not sufficient to fly a simple circular arc)

based on (Labonté, 2009), (Anderson et al., 2005),

(Bottasso et al., 2008) and as shown on Figure 5.

Our final stage module also replaces any line

segment requiring more power than available with a

vertical helix as in (Labonté, 2009). Although

smoothing of the path is performed after the

optimization process, the feasibility of this operation

is verified in our cost function to ensure the

smoothing of the final trajectory is always possible.

Figure 5: Circular constructions used to smooth the final

trajectory and remove all discontinuity in the velocity (left

diagram shows a simple circular arc and the right diagram

shows a connection using 2 circular arcs and a circle on an

horizontal plane).

7 PARALLEL

IMPLEMENTATION

We have now discussed all the elements required to

build a complete path planning module for UAVs.

Although the generated trajectories are feasible and

nearly optimal, the computation time remains too

long for real-time applications. To address this

problem, we developed parallel versions of our GA

and PSO using the “Single-program, multiple-data”

parallel programming paradigm. Our

implementation was done in MATLAB. It minimises

the communication between the processes and

allows full use of today’s multicore CPUs. The

flowchart of our parallel GA is shown in Figure 10.

Although drawn for 2 processes, our implementation

allows any number of processes. Our parallel

version of the PSO is not shown in this paper but

follows the same principle. The execution time and

the speedup of our parallel GA were measured on a

system equipped with two Intel Xeon E5310 quad-

core processors using the parameters in Table 1 and

are plotted in Figure 6 and Figure 7. The execution

time and the speedup of our parallel PSO are not

presented here, but are almost identical.

Table 1: Algorithm parameter values.

Parameters Values

Terrain resolution 500 x 500

Number of waypoints per trajectories 8

Number of gen. (AG) or ite. (PSO) 100, 200 and 300

Number of chromo. (AG) or part (PSO) 128 and 256

Mutation rate (AG) 10 %

Elitism rate (AG) 10 %

ω (PSO) 0.7298

(PSO) 1.4960

Figure 6: Execution time of our parallel GA for different

work sizes.

Figure 7: Speedup achieved by our parallel GA for

different work sizes.

8 COMPARISON OF THE GA

AND THE PSO

Finally, we compare the performance of the GA and

the PSO using 40 different scenarios from two

PARALLEL IMPLEMENTATION AND COMPARISON OF TWO UAV PATH PLANNING ALGORITHMS

165

fictitious terrain elevation maps and six real terrain

elevation maps (see Figure 8 and Figure 9). The

digital elevation maps for the six real terrains were

taken from the GeoBase repository (Anon n.d.). The

average costs of 60 trajectories generated using our

parallel GA and parallel PSO are compared using

the T-test with 5% significance to conclude that:

 The GA produced trajectories significantly better

than those generated by the PSO for 25 of the 40

scenarios;

 the PSO produced trajectories significantly better

than those generated by the GA for 3 of the 40

scenarios; and

 the GA and the PSO produced trajectory of similar

quality for 12 of the 40 scenarios.

Based on these results, we conclude that the GA is

preferable to the PSO when solving the path

planning problem for UAVs in a fixed computation

time of 10 s on multicore COTS processors.

Figure 8: 3D visualisation of the computed path (fictitious

map, 25 km

, altitude ranging from 0 to 250 m ASL).

Figure 9: 3D visualisation of the computed path (Banff,

Alberta, CA, 1 360 km

, 1 290 to 3 079 m ASL).

9 CONCLUSIONS

This paper presents a path planning solution for

UAVs which considers the dynamic properties of the

UAV and the complexity of a real 3D environment.

We used two non-deterministic algorithms, the GA

and the PSO, to attack this complexity and produce

solutions in a relatively short computation time. We

further reduced the execution time by developing

parallel versions of our algorithms. After achieving a

quasi-linear speedup of 7.3 on 8 cores and an

execution time of 10 s for both algorithms, we

conclude that by using a parallel implementation on

standard multicore CPUs, real-time path planning

for UAVs is possible. Moreover, our rigorous

comparison of the two algorithms shows, with

statistical significance, that the GA produces

superior trajectories to the PSO.

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Figure 10: Flowchart of our parallel genetic algorithm.

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