=Paper=
{{Paper
|id=Vol-2387/20190178
|storemode=property
|title=Formation Control of Multiple Autonomous Fixed-Wing Unmanned Aerial Vehicles in Dynamic Environment
|pdfUrl=https://ceur-ws.org/Vol-2387/20190178.pdf
|volume=Vol-2387
|authors=Ihor Skyrda,Valeriy Chepizhenko,Tetiana Davydenko
|dblpUrl=https://dblp.org/rec/conf/icteri/SkyrdaCD19
}}
==Formation Control of Multiple Autonomous Fixed-Wing Unmanned Aerial Vehicles in Dynamic Environment==
https://ceur-ws.org/Vol-2387/20190178.pdf
Formation Control of Multiple Autonomous Fixed-Wing
Unmanned Aerial Vehicles in Dynamic Environment
Ihor Skyrda1[0000-0002-9363-8921], Valeriy Chepizhenko2 and Tetiana Davydenko3
1 Ukrainian State Air Traffic Services Enterprise, Boryspil, Ukraine
2 National Aviation University, Kyiv, Ukraine
3 National Aviation University, Kyiv, Ukraine
skyrda2@gmail.com
Abstract. This paper presents Modified Artificial Potential Field (MAPF) ap-
proach application for decentralized formation control of multiple Unmanned
Aerial Vehicles (UAVs) flying through dynamic environment. MAPF is based
on Formation Potential Field (FPF) and it allows preventing mid-air collisions
within defined security zone around multiple UAVs. This technique combines
issue resolution connected with oscillation effects produced by potential fields,
UAV fixed-wing type specification with the respect to application in the dynamic
environment. Based on measured ranges between Remotely Piloted Aircraft
(RPA) and obstacles (buildings, restricted areas), attraction and repulsion forces
are formulated and are converted to aircraft flight control commands via rudder,
aileron trims and engine throttle. The simulation results are used to validate and
verify a given approach of real application, provision of optimal, collision-free,
and safety flight path between initial UAVs positions and destination area.
Keywords: multiple unmanned aerial vehicles, remotely piloted aircraft, artifi-
cial potential field, formation control, mid-air collision, obstacle collision
avoidance, path planning, dynamic environment.
1 Introduction
Unmanned Aerial Vehicles (UAVs) are the remotely piloted aircraft (RPA), automation
levels of such vehicles vary from those that are fully piloted from a remote location to
fully automated. These ‘pilotless’ aircraft are developed for a big variety of applica-
tions, such as surveillance, rescue, border control, agricultural production support, etc.
UAVs’ world legal acceptance is connected with their integration into the existing avi-
ation system without negatively affecting manned aviation and infrastructure, such as
mid-air collisions (MACs) – that is the main challenge today [1]. The International Civil
Aviation Organization’ (ICAO) and current European Commission’ (EC) regulatory
documents will only permit the autonomous maneuvers to override operator command
in emergencies such as communication failure or collision risk. Multiple UAVs opera-
tions have both practical potential in different applications and theoretical challenges
arising in coordination and control of the vehicles group. One of the main problems
regarding to autonomous UAVs activities in a group is an ability to move between ob-
stacles and avoid collision with them effectively, which itself includes subproblems
such as obstacles detection, path planning, group formation and data exchange between
vehicles.
UAVs are usually used in remote and dangerous areas, especially fixed-wing that
have a high speed and heavy payload in comparison to rotary wing UAVs type. The
complexity appears because of the UAVs’ size is becoming smaller and as a result their
weight is becoming lighter. Therefore, taking into account these properties, UAVs have
not the ability of carrying heavy sensors such as Light Identification Detection and
Ranging (LIDAR) [2] or radar. Hence, the suitable solution is to use the on-board cam-
eras due to their advantage of lightweight and low power consumption.
In addition to camera’s lightweight and the lower power consumption, the cameras
are able to provide detailed environmental information Therefore, they are considered
as the important sensors mounted on the small UAVs. The following obstacle avoid-
ance sensors are being used in the RPAs, e.g.:
- Stereo Vision;
- Ultrasonic (Sonar);
- Time-of-Flight;
- Infrared;
- Monocular Vision.
Another issue is connected with the path planning, which consists of defining a set
of paths, parameterized by time in order to accomplish a mission determined by way-
points respecting flight specifications limits of both the UAV and the environment [3].
Also, path planning for multiple UAVs requires continues data exchange between for-
mation members, so it should take into account confounding factors such as network
latency, packet loss, and the unique UAV’s flight peculiarities.
The collision avoidance algorithms applied to UAVs operation can be divided into
5 main groups [4]:
1) Geometric Approach;
2) Evolutionary Algorithm Approach;
3) Grid-based Approach;
4) Mixed Integer Linear Programming Approach;
5) Artificial Potential Field Approach.
The artificial potential field method (APF) is an approach of generating trajectories
online. It enables UAVs to navigate in a real condition environment with static and
dynamic obstacles by avoiding them. It is widespread due to its mathematical, algorith-
mic simplicity and not computationally expensive [3]. This reduction in computational
complexity makes the APF approach tractable for large numbers of UAVs. Moreover,
because the force on each UAV is calculated independently, the problem could poten-
tially be distributed onto flight management systems aboard each of the UAVs, which
further reduces the computational burden on any single machine. Additionally, since
the UAVs operate independently, uncooperative aircraft in the airspace can be handled
without issues [5].
2 Related Work
The first approach proposed for collision avoidance based on artificial potential field
(APF) application was developed by Khatib [6]. The paper presented the process of
mobile robots movement to the goal position with one obstacle under the action attrac-
tion force produced by the destination point and artificial repulsion force created by the
obstacle surface. The main drawback of such classic approach connects with the calcu-
lation of local minima in case of the presence more than one obstacle. L. Wang, K.
Chen, and Y.S. Ong [4] proposed to eliminate such effect by decomposing a complex
problem into a set of simple one (subgoals) with grid-world environment dynamically
and automatically, but the resultant paths are not the optimal solutions. In [7] this work
the authors tried to apply APF for helicopter type UAVs formation flight control with
a virtual leader of the group and extended version of the potential field solution. The
reason for this was a swarm constellation instability during an obstacle and collision
avoidance. It is not applicable in case of fixed-wing UAVs operation because of flight
features (velocity limits, unable to hover). The main task of tradition APF is connected
with a centralized control scheme required to have either ground control station or vir-
tual leader, so it directly influences on a reliability level in case of failure, and does not
guarantee the effectiveness in a dynamic, unknown environment. The robust swarm
control strategy for multiple UAVs operation in uncertainties conditions and varying
mission environment have been proposed by K. Han, J. Lee, and Y. Kim [8]. The swarm
should perform highly coordinated movements when the UAVs meet the pop-up
threats. It is realized through assignment swarm geometry center and behavior set of
rules, e.g.: avoidance rule, velocity matching rule, flock center rule. The resultant vector
is used in the rules represented as a gradient vector, composed of attractive and repul-
sive potential functions. The UAVs must deal with a constant movement and limited
turning ability, which make a collision avoidance more complicated, especially in the
case of collision avoidance with dynamic obstacles in a limited airspace. The work done
in [5] using APF minimize the number of potential collisions and the amount of re-
quired maneuvers to avoid other UAVs in a way.
P. Vadakkepat, K. Chen Tan and W. Ming-Liang [9] proposed an evolutionary arti-
ficial potential field (EAPF) approach for a real time path planning composed of artifi-
cial potential field method and artificial intelligence combination. In comparison to tra-
ditional APF, where an obstacle is considered as a point of highest potential, and a goal
as a point of the lowest potential, vehicle moves from a high potential point to a low
potential one, EAPF method uses the multi-objective evolutionary algorithms to opti-
mize the potential field functions.
H. Yin, L. L. Cam, U. Roy [10] outlined two main drawbacks of APF approaches
for multiple UAVs formation control proposed earlier. First, the gradients at some spe-
cific points of field may not exist due to the presence of global attractive potential and
has a disrupting effect on the smoothness of the whole potential field. Second, the
method can still fail to achieve its goal when agents are not well distributed around the
formation area in other words UAVs can’t find the way to the target position since the
influence of a local attractive potential has been blocked by other vehicles. Modified
Artificial Potential Field (MAPF) [10] excludes these disadvantages by application For-
mation Potential Field (FPF) [11] and avoids situations where other repulsive potential
field neutralizes the attractions of the target attractive potential field when it should not,
simultaneously a potential function is divided into global and local.
3 Problem Statement
The global purpose of this research is to create an algorithm that guarantees safe flight
generation and collisions avoidance for autonomous UAVs operation without human
controlling within a limited airspace.
The main requirement is to handle collisions with fixed-wing UAVs that move at a
constant speed (cruise speed, Vcruise) because of low energy consumption.
The effectiveness will be evaluated as a possibility to avoid potential collisions and
conflicts, at maximum turn rate with correspondent velocity value (Vturn), occurred on
the way and guarantee destination zone achievement. Potential collision is character-
ized by inner protection zone (rmin) intersection with an obstacle and conflict – outer
protection zone (rmax) (Fig. 1). The sizes will be represented in a timely manner, for
small UAV (with a weight that does not exceed 20 kg) it may be tmin=5 and tmax=10
seconds correspondently.
𝑟𝑚𝑖𝑛 = 𝑉𝑡𝑢𝑟𝑛 × 𝑡𝑚𝑖𝑛 ; (1)
𝑟𝑚𝑎𝑥 = 𝑉𝑐𝑟𝑢𝑖𝑠𝑒 × 𝑡𝑚𝑎𝑥 ; (2)
These values satisfy next conditions: minimum number of collisions and maneuvers,
UAV-to-UAV communication network latency, packet loss, obstacles detection range,
unique UAV flight specifications depending on size or payload.
Fig. 1. UAV protection zone, inner circle corresponds to maximum turn rate in few seconds and
outer circle characterized by cruise speed
The algorithm tests will be done using a simulator, which has such advantages: to allow
finding the maximum number of UAVs safely operates in limited airspace, to model
ideal conditions without unforeseen environmental factors and, in opposite side, with
weather or technical factors influences. The main issues are connected with wireless
communication between UAVs in a group. For this case, there is a lot of technologies
for short-range line-of-sight (LoS) links deployment, which are flexibly configured and
can be installed fast. The important criteria, which influence on communication link
type, are data exchange rate, physical size and energy consumption. In general, UAVs
supposed to be used in remote areas without a ground control station coverage, for ex-
ample, in cases of severe shadowing by urban or mountains terrain, or communication
infrastructure damages by natural disasters.
Artificial Potential Field method is more preferable for the solution of such issues as
collision avoidance and formation control, because it is relatively simple for implemen-
tation, more efficient, fast and accurate. It assumes destination area or waypoints signed
as positive charges and other dynamic objects (UAVs or obstacles) in the space as neg-
ative charges. An optimal flight path is found by calculating a total force from the at-
traction force of UAVs towards their destination and repulsion force away from other
obstacles presented in the area (Fig. 2).
Fig. 2. Two obstacles and destination zone formulate potential field in the optimal way
However, the traditional APF usually has problems connected with local minimums in
the potential field, which generate limitations such as (Fig. 3):
1. No flight path between closely spaced obstacles.
2. Oscillations in the presence of obstacles.
3. Oscillations in narrow flight paths.
4. Non-reachable destination area or waypoint.
Fig. 3. Two obstacles and destination zone with high potentials formulate potential field
4 Proposed Approach
In this paper, an online (global) path-planning algorithm based on a modified APF ap-
proach is proposed for the control of UAVs swarm in dynamic environment, which
causes constant collision avoidance with buildings, UAVs coordinates and position cal-
culation errors based on Global Navigation Satellite System (GNSS), Inertial Naviga-
tion System (INS) and visual/radio sensors. The modification of the APF is for gener-
ating the shortest and safest path for the UAVs. Simulations are used to verify the pro-
posed approach using MATLAB.
The Artificial Potential Field is one of the classical path planning approaches that is
used for global and local path planning in the dynamic or static environments. The con-
cept about APF is to find a mathematical function to represent attraction and repulsion
forces acting UAVs and destination area both forces are generated by mathematical
functions that are represented graphically by high and low areas in the simulated space.
We model the UAVs as negatively charged particles and destination area as a posi-
tively charged (Fig. 4). A repulsion force often dominates over the attraction force in
scenarios containing multiple UAVs causing the vehicles to never reach their destina-
tion area. Mathematical formulation of approach assumes a numerical value in each
point in space and time, and whose gradient represents forces (3).
𝐹𝑡𝑜𝑡𝑎𝑙 = 𝜉 × 𝐹 + + (1 − 𝜉) × 𝐹 − ; (3)
where Ftotal is a total force acting on one UAV, F+ – is an attraction force, F- – is a
repulsion force, ξ is an attraction force weighting coefficient (0 < ξ < 2) which ensures
attraction force domination under repulsion in order to guarantee UAV flight towards
destination area (Fig. 5).
Fig. 4. Dynamic objects’ interaction with different potentials
Fig. 5. Attraction force weighting coefficient dependence on distance to the destination
Oscillation effect referred to traditional effect is eliminated by changing circle to ellip-
tical artificial potential field around UAV with the same area. It increases in a size
toward the heading of UAV, indicating a flight direction (Fig. 1).
Additionally, the deadlock problem solution is presented, where at least two UAVs
are approaching each other head-on with destinations directly behind each other, since
UAVs cannot turn sharply or come to a complete stop to resolve this issue one UAV
turn to the left or right due to the action of artificial vortex repulsion field (Fig 6). In
some cases this principle is applied for collision avoidance with static obstacles [5].
Fig. 6. Artificial vortex repulsion field is formulated around obstacle
Path planning using MAPF is based on a design of a standard attraction force function
for the goal point, and repulsion force function with tunable parameters depending on
shape, size and location of obstacles. At each point the resulting potential field angle is
lying along the angle of the resultant attraction and repulsion forces formulated by
UAVs, potential field functions considered as function of distance (Fig. 7).
Fig. 7. Two obstacles and destination zone formulate potential field (red – obstacles, black –
destination)
5 Formation Control of Multiple Autonomous Fixed-Wing
Unmanned Aerial Vehicles Simulation
It is assumed that there are six UAVs, two obstacles and one destination zone for a
group. The aim is to plan an optimal collision-free path for the group, in case of multiple
UAVs application in a dynamic environment, where due to signal delay, multipath and
close obstacle location present an error of UAV coordinates definition and cooperation
in a group. The protection zone radius is equal to minimum value and remains a con-
stant during flight. The main peculiarity of such approach in comparison to others [1,
5, 7, 8] is that a group is operated without any leader.
UAV movement can be described by kinematic equation system:
𝑑𝑥𝑖
= 𝑓(𝑥𝑖 (𝑡), 𝑉𝑖 (𝑡), 𝜑𝑖 (𝑡)); (4)
𝑑𝑡
𝑑𝑦𝑖
= 𝑓(𝑦𝑖 (𝑡), 𝑉𝑖 (𝑡), 𝜑𝑖 (𝑡)); (5)
𝑑𝑡
where, i=1, 2, …, n is the index of multiple UAV, xi, yi – coordinates of the i-th UAV,
Vi – is a flight-path velocity vector of the i-th UAV, φi – is the course angle character-
izing the direction of the velocity vector to the destination zone.
The UAV coordinates can be calculated as a resultant force acting on i-th UAV pro-
vided by destination zone, obstacles and other UAVs:
1
𝑥̈ 𝑖 = ∑𝑛𝑖≠𝑗 𝐹𝑥𝑖𝑗
+ −
− 𝐹𝑥𝑖𝑗 ; (6)
𝑚𝑖
1
𝑦̈ 𝑖 = ∑𝑛𝑖≠𝑗 𝐹𝑦𝑖𝑗
+ −
− 𝐹𝑦𝑖𝑗 ; (7)
𝑚𝑖
where, mi – is a mass of the i-th UAV
Attraction F+ and repulsion F- forces can be calculated as:
𝐺𝑚𝑖 𝑚𝑗
𝐹𝑖𝑗+ = 𝛼 ; α ϵ {2, 3, …}; (8)
𝑟𝑖𝑗
𝐺𝑚𝑖 𝑚𝑗 𝑟кр
𝐹𝑖𝑗− = 𝛽 ; β ϵ {3, 4, …}; (9)
𝑟𝑖𝑗
rij = √(xi − xj )2 + (yi − yj )2 ; (10)
where, G – is a gravitational constant and rij – is a distance between UAV,
In order to provide the UAV movement to the destination zone, it is necessary that
its attraction force should be greater than total attraction force formulated by obstacles
and other UAVs [12].
The heading angle φ can be estimated as a relation of attraction and repulsion force
influence on the UAV movement with correspondent coordinates.
𝑦̇ 𝑦 (𝑘)−𝑦 (𝑘−1)
𝜑𝑖 (𝑘) = 𝑎𝑟𝑐𝑡𝑔 ( 𝑖) = 𝑎𝑟𝑐𝑡𝑔 ( 𝑖 (𝑘)−𝑥 𝑖(𝑘−1)); (11)
𝑥̇ 𝑖 𝑥𝑖 𝑖
where, k – is the integration step of the equation system.
Fig. 8. Experiment 1. Flight trajectory of 6-th UAVs in a group with constant radius of protection
zone
The formation control problem of UAVs group in static and dynamic environment con-
sists of three main problems: plan, control and form a UAVs formation in a group at
their initial positions; group motion from initial position to destination; collisions
avoidance during the flight (Fig. 8).
Fig. 9. Experiment 2. Flight trajectory of 6-th UAVs in a group with varying radius of protection
zone
The zone around obstacles has double radius value and in case of its penetration, the
UAV security zone will be increased in accordance to Fig. 1, where radius is inversely
proportional to the distance between UAV and the nearest obstacle edge point of con-
tour, because obstacles can have rather different shapes.
The results of simulation depict applicability of MAPF regarding UAVs operation
in the real world with static obstacles. Experiment 2 (Fig. 9) has expensed less time to
reach the destination area in comparison to Experiment 1, where UAVs trajectories, in
some cases, drawing obstacle shapes. In Experiment 2 (Fig. 10) UAVs start collision
avoidance maneuvers earlier and characterized by potential collisions absence.
Fig. 10. Experiment 2. Destination zone is reached by 6-th UAVs in a group in 2400 seconds
The UAV motion in a dynamic environment is connected with potential conflicts pres-
ence with dynamic objects like UAV that has another speed value, shape, onboard
equipment, so they can’t be compatible for position data interchange performance. In
this case, UAV should be able detect any dynamic obstacles operatively, calculate
ranges and motion parameters. The traditional APF is characterized by dead lock prob-
lem and the solution provided by artificial vortex fields (Fig. 6) that act only around
obstacles and do not make an impact on a global potential function. In order to check
this Experiment 3 (Fig. 11) and Experiment 4 (Fig. 12) have been done. The main dif-
ference between them is an application of varying security zone radius. Experiment 3
shows a flight performance of two vehicles and their destination zones. In Fig. 11(b)
the flight path is optimal with less time consumption and slight maneuvers.
a) b)
Fig. 11. Experiment 3. Collision avoidance with dynamic obstacle, like UAV with constant (a)
and varying (b) radiuses of protection zone
Proposed MAPF has showed the best result in case of UAVs group motion in dynamic
environment based on time consumption and number of flight maneuvers correspond-
ing to lower energy consumption, it is the main issue characterized UAV operation
(Fig. 12).
Fig. 12. Experiment 4. Collision avoidance with dynamic obstacle, like UAV with constant ra-
dius of protection zone around UAVs in a group and varying around standalone
6 Conclusions
In this paper, the Modified Artificial Potential Field has been proposed to control a
group of autonomous UAVs to achieve the destination zone and maintain a given for-
mation while avoiding collisions with static and dynamic obstacles. Unlike other cen-
tralized UAV formation control methods, the MAPF method does not require a high
computational capability and the flying trajectory can be modified in real time when an
unexpected obstacle has been detected.
The MAPF approach is based on application of artificial vortex fields around obsta-
cles and varying protection zone radius of UAVs. It allows for significant scalability to
hundreds or thousands of autonomous UAVs provide enough airspace for a safe oper-
ation in a dynamic environment with non homogeneous vehicles types.
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