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Optimization of UAV Flight Control Algorithm and Flight Simulation in
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AMAE 2020
IOP Conf. Series: Materials Science and Engineering 887 (2020) 012046
IOP Publishing
doi:10.1088/1757-899X/887/1/012046
1
Optimization of UAV Flight Control Algorithm and Flight
Simulation in Two-dimension
Xiao Xu, Jie Li, Chengwei Yang*, Ziquan Wang, Jin Xiong and Chang Liu
School of Mechanical and Electrical Engineering, Beijing Institute of Technology,
Beijing 100081, China
*Corresponding author e-mail: yangchengwei@bit.edu.cn
Abstract. Large-scale Unmanned Aerial Vehicle (UAV) groups flight simulation in two-
dimensional planes is commonly applied to UAV cluster mission planning algorithm design. In
this paper, an UAV control algorithm optimized for two-dimensional planes is designed. The
tandem structure of closed loops, as well as the control laws of L1 and Total Energy Control
System (TECS), are transplanted to an UAV model that is simplified to a moving particle of a
two-dimensional space, and UAV flight simulation is performed based on the flight control
algorithm. Compared with the traditional 3D space flight simulation, it can save hardware
resources and improve the simulation efficiency. Compare with the flight simulation based on
the geometric method, on the premise of maintaining the dynamics basis, the trajectory and
dynamics curves are closer to the actual flight results in 3D space, and the dynamics data onto
the entire flight can be recorded. It has been verified that 50 UAVs need only 0.8s to perform
100 square-area snake-like search simulation experiments, and the fitting degree of the UAV's
flight curve to the three-dimensional space is greater than 80%. The two-dimensional plane
flight control algorithm and flight simulation proposed in this paper provide a new simulation
method for the design of UAV cluster mission planning algorithms, therefore can help promote
the development of the subject.
1. Introduction
In modern wars, UAVs, as an important reconnaissance force, have been increasingly used by various
countries. The UAV flight process is mainly divided into take-off, cruise and descent recovery (final
guidance) stages.[1] The main flight process is cruise at fixed altitude. Therefore, in the simulation
experiments of the UAV task planning algorithm, the planned waypoints are often set on a two-
dimensional plane. For many long-time flight simulations involving large number of UAVs, such as
machine learning-based UAV mission planning algorithms, traditional 3D dynamic simulation is
inefficient due to excessive computing power consumption, and the number of simulation nodes is
limited by hardware resources ; The path simulation based on geometric method lacks a dynamic basis,
which results in a large difference between the simulation result and the actual trajectory, low
reliability, and unable to perform dynamic data recording and analysis.[2] Therefore, it is necessary to
design UAV trajectory simulation method of a dynamic basis that can simulate the 3D space UAV
dynamic trajectory on a 2D plane, can track and record the dynamic data, and only consume small
amount of calculation and hardware resources.
This paper designs a fixed-wing UAV flight control algorithm optimized for 2D planes for flight
simulation in mission planning. The track points are input in a two-dimensional plane with a certain
AMAE 2020
IOP Conf. Series: Materials Science and Engineering 887 (2020) 012046
IOP Publishing
doi:10.1088/1757-899X/887/1/012046
2
height. Based on the UAV adaptive control algorithm in three-dimensional space, the UAV flight
control algorithm in two-dimensional space is designed to quickly and stably generating a flight
trajectory that simulates the real environment, and record the kinetic data in flight process.
The structure of this paper is as follows: Section 2 introduces the algorithm background, that is, the
problem of transplanting UAV flight control algorithm in three-dimensional space, normal L1 and
tangential TECS (Total Energy Control System) flight control algorithm to two-dimensional
environment.[3] The third section introduce the cascade closed-loop flight control algorithm of UAV
in two-dimensional plane separately from the outer and inner loops. Section 4 uses the personal PC as
the hardware foundation, and simulates the algorithm on the Pyhon3.5.2 platform, and compares it
with the geometric method and three-dimensional space flight dynamics simulation curves. Section 5
summarizes the advantages of the algorithm and its value of the development of UAV cluster task
planning algorithms.
2. Background Description
The solution proposed in this paper is to design a two-dimensional plane UAV flight control algorithm.
The L1 and TECS flight control algorithms in three-dimensional space are transplanted to a two-
degree-of-freedom UAV model that is simplified to two-dimensional moving particles.
This section briefly analyses the UAV motions model in the two-dimensional space, then proposes
the main problems and solutions.
2.1. Two-dimensional plane UAV motion model
In order to improve the efficiency of the UAV control in the two-dimensional plane and reduce the
complexity of the control algorithm as much as possible, this paper first discusses the simplified model
of the UAV. The simplified UAV dynamics model is the basis of the two-dimensional planar UAV
control algorithm. It should meet the following three requirements[4]:
Able to do two-degree-of-freedom motion in a two-dimensional plane;
Able to transparent L1 and TECS adaptive control laws in a two-dimensional plane;
Under the first two conditions, the model dynamic parameters are minimized.
In a two-dimensional coordinate plane, simplifying an UAV into a moving particle of a velocity
direction is the limit of the simplification of a motion model that can be achieved. So the UAV body
model assumes the following:
The UAV is a particle, and its speed direction coincides with the direction of the UAV axis;
UAV propulsion controls the thrust by adjusting the throttle;
The resistance to the UAV is constant;
UAV cruise altitude and desired airspeed are constant.
This model involves coordinate systems including cruise plane coordinate system and
airflow coordinate system , which are defined as follows:
Cruise plane coordinate system : The origin is selected at the position of the center
of mass when the UAV starts cruising. In the horizontal plane,
ee
OY
points to the north
direction and
ee
OX
points to the east direction;
Airflow coordinates system : The origin is at the center of mass of the UAV, the
direction is consistent with the speed direction, and the direction and
direction are at an angle of 90 ° clockwise. The general diagram are shown as figure 1.
e e e e
S o x y
w w w w
S o x y
e e e e
S o x y
w w w w
S o x y
ww
ox
ww
oy
ww
ox
AMAE 2020
IOP Conf. Series: Materials Science and Engineering 887 (2020) 012046
IOP Publishing
doi:10.1088/1757-899X/887/1/012046
3
(1)
(2)
Figure 1. Schematic diagram of cruise plane coordinate system and airflow coordinate system
Among them, the angle between the -axis of the air current coordinates system and the -
axis of the cruise plane coordinate system is the azimuth of the track in a two-dimensional plane,
which is denoted as . The UAV motion model can be described by the following equation:
_
_
w w obs wl
w w obs wt
x x a dt
y y a dt
Where is the tangential and normal speed of the UAV at time ; is the
actual tangential and normal speed of the UAV at time ; is the tangential and normal
acceleration of the UAV at time ; is integral The step size, the minimum time interval, depends
on the frequency of the UAV status sensor.
By projecting the UAV speed in the air current coordinate system to the cruise plane coordinate
system, we get the speed of the UAV in the direction of cruise plane and :
cos sin
sin cos
e w w
e w w
x x y
y y y
2.2. Improvement plan
According to the definition of the UAV motion model in Section 2.2, the default UAV height will not
change in the two-dimensional plane, which is an environmental constraint and therefore cannot be
controlled. Think of the UAV as a moving mass, and it does not involve attitude angle and steering
gear control. Based on the establishment of a two-dimensional plane UAV motion model, the research
problem of this paper is transformed into a three-dimensional space UAV control algorithm being
transplanted to a two-dimensional space simplified motion model. The control objects are the normal
and tangential acceleration of the UAV, and the purpose is to achieve rapid tracking of the mission
planning trajectory and airspeed.[5]
Similar to the effect of the lateral acceleration of the UAV in three-dimensional space[1], the
normal acceleration of the UAV controls the yaw distance of the UAV so that the UAV approaches
the desired track and is controlled by the L1 algorithm; the tangential acceleration controls the UAV
Airspeed, controlled by TECS algorithm.
In summary, the design steps of the two-dimensional planar UAV control algorithm can be
summarized as:
Decompose the UAV control algorithm into outer and inner loop controllers, and decompose
the outer loop controller into L1 controller with normal acceleration control and TECS
controller with tangential acceleration control;
Design TECS and L1 control algorithms for two-dimensional planes;
Design the inner loop PID control algorithm;
Debug the outer loop and inner loop control parameters to optimize the control effect;
ww
ox
ee
ox
,
ww
xy
1t
__
,
w obs w obs
xy
t
,
wl wt
aa
t
dt
,
ww
xy
x
y
AMAE 2020
IOP Conf. Series: Materials Science and Engineering 887 (2020) 012046
IOP Publishing
doi:10.1088/1757-899X/887/1/012046
4
Simulate outer loop and inner loop control effects.
3. UAV flight control algorithm based on L1 and TECS
In UAV mission planning algorithms, UAVs are often reduced to two-degree-of-freedom aircraft on a
two-dimensional plane. For many long-time flight simulations involving a large number of UAVs,
such as machine learning-based UAV mission planning algorithms, traditional 3D dynamic simulation
is inefficient due to excessive computing power consumption, and the number of simulation nodes is
limited by hardware resources ; The path simulation based on geometric method lacks a dynamic basis,
which results in a large difference between the simulation result and the actual trajectory, low
reliability, and unable to perform dynamic data recording and analysis.
3.1. Cascade closed-loop control strategy
The structure of the UAV control system is shown as figure 2.
Figure 2. Schematic diagram of two-dimensional planar UAV cascade control
According to the function of the control loop, the inner loop is the acceleration control system of
the UAV, which is used to control the tracking of the UAV's acceleration to the expected acceleration.
The outer loop is a trajectory control loop that calculates the expected acceleration, controls the speed
and yaw distance of the UAV, and enables the UAV to fly along the predetermined route and airspeed
at the desired speed.
According to the control channel decomposition, the control system can be divided into tangential
control system and normal control system. The tangential control system controls the acceleration of
the UAV along the speed direction, using the TECS control algorithm; the normal control system
controls the acceleration of the UAV along the vertical speed direction, and uses the L1 control
algorithm.
3.2. Lateral acceleration algorithm based on L1 adaptive control
The L1 control algorithm of the UAV in the two-dimensional plane also makes the motion of the UAV
close to the desired trajectory in the two-dimensional plane. The application scenario is as follows:
In a two-dimensional plane, the position
,
pp
P x y
and speed
,
xy
V v v
of the UAV at a certain
moment are known;
The desired track segment
i
is a straight line segment from the initial waypoint
,
ii
i a a
A x y
to
the end waypoint
,
ii
i b b
B x y
. If the UAV reaches the ending waypoint at this time, and the
ending waypoint is not at the end of the waypoint list, then the ending waypoint is set as the
initial waypoint at the next time, and the next waypoint in the waypoint list is the ending
waypoint . If the end waypoint is not reached at that time, the initial waypoint and the end
waypoint at the next time are unchanged;
AMAE 2020
IOP Conf. Series: Materials Science and Engineering 887 (2020) 012046
IOP Publishing
doi:10.1088/1757-899X/887/1/012046
5
(3)
(4)
(5)
(6)
(7)
The L1 control law calculates the expected normal acceleration
exp
l
a
pointing to the desired
track perpendicular to the speed direction.
According to the position relationship between the position of the UAV and the desired track, the
angle
between the speed direction and the virtual waypoint is calculated in three cases, so that the
UAV can approach the endpoint of the desired track segment as soon as possible when it is away from
the desired track segment . In either case, the L1 length is always determined by the product of speed
and natural frequency:
11
ratio
L V L
Among them,
1
L
is the distance from the current position to the virtual waypoint, and
1ratio
L
is the
natural frequency, which represents the ratio of the expected airspeed to
1
L
.
Scenario 1. From the UAV position to the desired flight path segment, foot
,
cc
C x y
is located
outside the desired flight path segment and is close to the initial waypoint
,
aa
A x y
, as shown in the
figure 3.
,
oo
O x y
is the virtual turning circle centre.
Figure 3. Schematic diagram of scenario 1
That is, when
cos 0PAB
, the virtual waypoint is set as the initial waypoint. The size of L1 is
independent of the relative initial waypoint position, and
is the angle from the UAV speed to
PA
.
The calculation formula for
and virtual turning radius
R
is as follows:
cos V PA
V PA
11
2
2sin 2 1 cos
LL
R
Therefore, the expected lateral acceleration
exp
l
a
is calculated as:
22
exp 2
1
2 1 cos
lVV
aRL
With equations 5 and 6, the expected lateral acceleration is expressed as:
2
exp
1
21
lratio
V V PA
aLV PA
Scenario 2. UAV positions to the desired track segment, foot
,
cc
C x y
is located outside the
desired track segment, and is close to the ending waypoint
,
bb
B x y
, as shown in the figure 4:
Figure 4. Schematic diagram of scenario 2 (left) and Schematic diagram of scenario 3 (right)
AMAE 2020
IOP Conf. Series: Materials Science and Engineering 887 (2020) 012046
IOP Publishing
doi:10.1088/1757-899X/887/1/012046
6
(8)
(9)
(10)
(11)
(12)
(13)
(14)
(15)
When
cos 0PBA
, set the ending waypoint as a virtual waypoint. As in the first case, although
the length of L1 is proportional to the speed of the UAV, the selection of the virtual waypoint has
nothing to do with the size of L1 until the end waypoint is reached.
cos V PB
V PB
2
exp
1
21
lratio
V V PB
aLV PB
Scenario 3. From UAV position to desired track segment, foot
,
cc
C x y
is located in the desired
track segment, as shown in the figure 4:
At this time,
cos 0PAB
and
cos 0PBA
are standard L1 algorithm scenarios, and the virtual
waypoint is located on track segment
AB
, and the distance to
i
P
is L1.
Let
1
be the angle between
V
and
AB
, and
2
be the angle between
PC
and
1
L
, then the angle
can be expressed as:
12
1
arccos , arcsin PC
V AB L
V AB
12
2
12
sin cos
Therefore, the virtual turning radius formula is:
1 1 1
12
2sin 2sin 2cos
ratio ratio
L V L V L
R
The formula of the normal acceleration of the UAV is:
22
exp 12
11
2
2sin cos
lratio
V V V
aR L L
The empirical parameter
1L
K
is introduced here to adjust the problem that the normal acceleration
of the UAV in the two-dimensional plane is too large and serious overshoot. Therefore, the expected
normal acceleration
exp
l
a
after optimization is:
exp exp 1l l L
a a K
The normal acceleration direction is perpendicular to the speed and points to the track segment. In
summary, the expected normal acceleration of the UAV in the two-dimensional plane can be obtained.
3.3. Algorithm for Tangential Acceleration of Outer Ring Based on TECS Control
TECS control the size of the UAV's throttle to change the output power of the UAV's engine, and
controls the UAV's elevator to change the power ratio of the UAV's potential energy and kinetic
energy to maintain or adjust the UAV's flying height[6]. In a two-dimensional plane, the height of the
UAV does not need to be adjusted, so the potential energy of the UAV is constant. Based on the most
simplified principle, the UAV altitude potential energy is set to zero. The TECS algorithm for a two-
dimensional plane can change the output power of the UAV by controlling the throttle valve without
changing the potential energy, so as to track the desired speed. The application scenario is described as
follows:
The UAV's flight speed is
state
V
at a certain moment, and the expected airspeed given by the
mission plan is
set
V
;
Limited by the performance of the UAV engine, the change rate of the total specific energy of
the UAV is constrained within the interval
min max
,STErate STErate
, where
min max
0STErate STErate
;
AMAE 2020
IOP Conf. Series: Materials Science and Engineering 887 (2020) 012046
IOP Publishing
doi:10.1088/1757-899X/887/1/012046
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(16)
(17)
(18)
(19)
(20)
(21)
Integrate UAV airspeed and desired airspeed, and calculate the expected throttle opening rate
p
throtle
of the UAV under the constraints of the total specific energy change rate and the
controllable change interval of the throttle valve.
First, the expected airspeed change rate
set
TASrate
is the airspeed error at that moment, that is, the
ratio of the expected airspeed to the actual airspeed difference and the time interval
T
. Introduce the
empirical proportional parameter
V
K
to adjust the change rate to avoid the failure of the speed control
due to the expected change rate.
1
set set state V
TASrate TAS TAS T K
From the specific energy calculation formula, the actual total specific energy
state
STE
and the
expected total specific energy
set
STE
, and the total specific energy error
error
STE
can be obtained:
22
1
2
error set state set state
STE STE STE TAS TAS
The expected total specific energy change rate
set
STErate
is the expected change rate of the total
specific energy obtained by multiplying the specific energy magnitude and the desired speed change
rate at that moment.
set state set
STErate TAS TASrate
When the airspeed error rises, the expected airspeed change rate rises accordingly, which may
exceed the UAV's engine controls range. Therefore, according to the actual control ability of the UAV,
the calculation formula of
set
STErate
is as follows:
max min
max max
min min
,
,
,
set set
set set
set
STErate STErate STErate STErate
STErate STErate STErate STErate
STErate STErate STErate
From the principle of UAV dynamics, it is expected that the total specific energy change rate is
linearly related to the throttle opening rate, so the theoretical throttle opening rate
p
throtle
can be
calculated. The reference throttle value of the UAV is
const
throtle
. When the expected total specific
energy change rate is greater than 0, the total specific energy of the UAV increases, and the throttle
opening rate are directly proportional to the maximum opening rate
max
throtle
. In contrast, when the
expected total specific energy change When the rate is less than 0, the total specific energy of the
UAV decreases, and the throttle opening rate are proportional to the minimum opening rate
min
throtle
.
Calculate as follows:
max
max
min
min
, 0
, 0
set
const set
pset
const set
STErate
throtle throtle STErate
STErate
throtle STErate
throtle throtle STErate
STErate
In this case, the inner loop PID control algorithm for the tangential acceleration of the UAV can be
designed by the specific energy error
error
STE
, the throttle opening rate
p
throtle
, and the expected total
energy change rate
set
STErate
of the UAV.
3.4. Inner loop PID control algorithm
The UAV in the two-dimensional plane does not have the rudder surface control structure nor the
attitude angles control capability. Therefore, the desired acceleration command
exp
l
a
and throttle
opening rate
p
throtle
given by the outer ring controller of the inner ring controller are the control targets.
Tangent two parts, through the PID controller to simulate the operation process of the inner loop
controller in three-dimensional space.
The normal control law of the inner loop of the UAV is:
.
l
true P I D
l l l l l l
aa K K a dt K a
AMAE 2020
IOP Conf. Series: Materials Science and Engineering 887 (2020) 012046
IOP Publishing
doi:10.1088/1757-899X/887/1/012046
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(22)
(23)
Among them,
l
a
is the difference between the expected tangential acceleration and the actual
tangential acceleration of the UAV at this moment, and
p
l
K
,
I
l
K
, and
D
l
K
are the coefficients of the
proportional link, the integral link, and the differential link.
The tangential control law of the inner loop of the UAV is:
D P I
True P error error t t t error
throtle throtle STE STErate K K K STE dt
Among them,
error
TASrate
is the difference between the expected airspeed change rate and the actual
airspeed change rate at this moment, and
p
t
K
,
I
t
K
, and
D
t
K
are the coefficients of proportional link,
integral link, and differential link. Because the tangential acceleration of the UAV is proportional to
the throttle opening rate, the actual tangential acceleration of the UAV at this time is:
true
t acct True
a K throtle
acct
K
is the tangential acceleration proportionality factor.
4. Generate trajectory and simulation calculation of dynamic parameters
In this paper, python3.5 is selected as the simulation platform. Using a two-dimensional plane flight
controls algorithm, given a serpentine search waypoint sequence, patrol at a constant speed of 30m / s
and a fixed height of 50m relative to the ground. The two-dimensional simulation trajectory,
traditional calculation path based on the Dobbins curve and the flight path of the UAV dynamics
simulation with the same waypoint in 3D space obtained is as figure 5:
Figure 5. Three-dimensional flight simulation trajectory of a fixed-wing UAV (previous page);
Trajectory simulation based on two-dimensional plane control algorithm (left) and Trajectory
Simulation Based on Geometric Algorithm (right)
It can be seen that the two-dimensional simulation trajectory can simulate the track characteristics
of the UAV slightly overshooting after reaching the waypoint, which is better than the Dubins curve
track. The clue-aware trajectory similarity (CATS) algorithm is used to calculate the similarity with
the 3D simulation trajectory[7]:
AMAE 2020
IOP Conf. Series: Materials Science and Engineering 887 (2020) 012046
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doi:10.1088/1757-899X/887/1/012046
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(24)
(25)
, , , , , , , ,
, max , | and ,
i l j i l j k j k j j k i l i l
score p T f p p p T t t t
,
, , ,
1
,,
i l i
i j i l j
pT
i
CATS T T score p T
T
The approximation of the two-dimensional trajectory simulation curve is 0.83. The similarity is
greater than 80%, indicating that the two-dimensional trajectory simulation is basically consistent with
the three-dimensional trajectory simulation.
The normal and tangential speed curves of the two-dimensional plane UAV flight control algorithm,
and the comparison diagram of the UAV speed curve in three-dimensional space are as figure 6 and
figure 7.
Figure 6. Three-dimensional space velocity curve
Figure 7. Two-dimensional space tangential velocity curve (left) and normal velocity curve (right)
The tangential velocity in 2D simulation is basically consistent with the tangential velocity curve in
3D space simulation. When changing the direction of flight speed, the UAV's normal speed changes
drastically, but it can converge to the 3D simulation value.
The tangential acceleration and normal acceleration curves of the two-dimensional simulation
UAV are as figure 8:
Figure 8. Two-dimensional space tangential acceleration curve (left)
and normal acceleration curve (right)
Fifty UAV serpentine formation searches flights took a total of 0.8ses to calculate on a personal
computer. The computing power of a three-dimensional dynamic simulation personal computer for the
same scenario cannot be supported. Compared with the simulation trajectory obtained by the Dubins
curve, it improves the approximation of the flight trajectory of a real UAV, and can output the
dynamic parameters of a single UAV at any time.
AMAE 2020
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IOP Publishing
doi:10.1088/1757-899X/887/1/012046
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5. Conclusion
This paper studies an UAV control algorithm optimized for two-dimensional planes. The core idea is
to borrow the mature outer-loop control algorithm in three-dimensional space, that is, the TECS
control law of the pitch channel and the L1 control law of the yaw and roll channels, and transplant it
to a dynamic model that is simplified to a two-degree-of-freedom particle in the two-dimensional
plane.
In this way, it can simulate similar motion trajectories and changes in dynamic parameters in three-
dimensional space, and greatly reduce the computing power requirements of three-dimensional space
dynamics simulation. Especially in the simulation of mission planning at the UAV cluster level, it can
greatly save hardware resources and time costs. For simulation experiments that require a large
number of UAVs for a long time and multiple flights, such as machine learning UAV mission
planning algorithm design a large amount of simulation training is required. This algorithm can solve
the problems of traditional path planning simulations such as the lack of dynamic basis in the Dubins
curve and the low credibility of the planned path, making dynamic simulation under this kind of
problem possible.
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