=Paper= {{Paper |id=Vol-3742/paper19 |storemode=property |title=Аircraft automation principles as a basis for the use of information technologies |pdfUrl=https://ceur-ws.org/Vol-3742/paper19.pdf |volume=Vol-3742 |authors=Leonid Romaniuk,Marcin Bernas,Vitalii Kartashov,Ihor Chykhira,Halyna Tulaidan |dblpUrl=https://dblp.org/rec/conf/citi2/RomaniukBKCT24 }} ==Аircraft automation principles as a basis for the use of information technologies== https://ceur-ws.org/Vol-3742/paper19.pdf

Аircraft automation principles as a basis for the use of
information technologies
Leonid Romaniuk 1,∗,†, Marcin Bernas2, †, Vitalii Kartashov1, †, Ihor Chykhira1, † and
Halyna Tulaidan 3,†

1 Ternopil Ivan Puluj National Technical University, 56, Ruska Street, Ternopil 46001, Ukraine

2 University of Bielsko-Biala, Willowa St. 2, Bielsko-Biala, 43-300, Poland

3 Ternopil Volodymyr Hnatiuk National Pedagogical University, 2, Maxyma Kryvonosa Street, Ternopil 46027,

Ukraine

Abstract
Small unmanned aircrafts frequently undergo short-term configuration changes due to their use
across a great variety of operational scenarios. For example, special payloads are attached,
batteries and screws or other components of modular system are changed. As a result, the
boundaries of the flight area are often unknown or uncertain. However, despite these
uncertainties, the autonomous unmanned aircraft should be able to follow the controlled
trajectory in the limited space. The adaptation of the kinematic motion model for automatic
trajectory planning of unmanned aircraft in response to the changing or previously unknown
boundaries of the flight area is investigated in this paper. Algorithms for the integration of
automatic UA route planning under different conditions, in the presence and absence of
obstacles, are proposed. The hypothesis of the investigation is that adequate reference
trajectories can be planned simply by determining certain parameters of the kinematic motion
model, without additional determination of the reasons of changes within the flight range limits
For this purpose, the parameters of the kinematic motion model used for trajectory planning
are automatically monitored and updated during the flight. This determination of the model
parameters should work without additional devices or additional stimuli from the unmanned
aircraft. If the parameter is changed, the reference trajectories are re-planned during flight in
accordance with the updated kinematic motion model, so that, on the one hand, the possible
sequence of the reference trajectory with limited preservation and restrictions of the available
flight area are still used. Subsystems for trajectory planning and for monitoring and
determining model parameters are evaluated using simulations and flight test data. The overall
system is evaluated by modeling Prometheus unmanned aircraft.

Keywords
Unmanned aircraft, operational scenarios, payload, flight area boundaries, kinematic motion
model, autonomous flight, reference trajectory1

CITI’2024: 2nd International Workshop on Computer Information Technologies in Industry 4.0, June 12–14, 2024,
Ternopil, Ukraine
∗ Corresponding author.
† These authors contributed equally.

leonidromanyuk@gmail.com (L. Romaniuk); mbernas@ath.bielsko.pl (M. Bernas); kartashov@tntu.edu.ua
(V. Kartashov); ig.vi.chi@gmail.com (I. Chykhira); tulaidan@tnpu.edu.ua (H. Tulaidan)
0000-0002-2538-4026 (L. Romaniuk); 0000-0002-0099-1647 (M. Bernas); 0000-0003-0530-3919 (V.
Kartashov); 0000-0002-8615-3635 (I. Chykhira); 0000-0003-2306-6435 (H. Tulaidan)
© 2024 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).

CEUR
ceur-ws.org
Workshop ISSN 1613-0073
Proceedings
1. Statement of the problem
The ability of autonomous aircrafts to follow trajectories with small spatial trajectory
displacements is the requirement for this type of aircraft that should be met in the vast
majority of applications, the fulfillment of which ensures that UA does not encounter
obstacles, does not violate the boundaries of designated airspace, maintain separation
from other air traffic participants, or provide good recordings due to the accurate
positioning of the carried sensors, such as cameras. The consequences of insufficient short
orbital distances can range from missing mission objectives to safety-critical events such
as invasion into undesignated airspace or, especially in the case of low-flying UAs, collision
with aircraft obstacles.

2. Analysis of the available investigation results
The idea of reducing complex relationships resulting in the aircraft motion, to a few
parameters of the kinematic motion model was formulated in paper [1]. In other words, it
was concluded that, in order to create reference trajectories, the parameters of the
kinematic motion model should not be derived from the detailed record of measurements
of all system and subsystem states or from detailed knowledge of the system. Probably,
the idea is that the direct determination of a certain parameters of the kinematic motion
model is sufficient for the reference trajectories creation.
In paper [2] the effect of wind speed and direction on UA flight states was investigated,
appropriate parameters and methods of their solution under the influence of wind
conditions and also the problem of UA logistics route planning, which simultaneously
takes into account the UA energy consumption limitations, customer time windows, and
the influence of wind conditions were solved. A large-scale neighborhood search (LNS)
algorithm was combined with genetic algorithm (GA) creating GA-LNS in order to solve
the static problem, while dynamic planning concepts of GA-LNS for solving the dynamic
trajectory optimization problem was used in the decoding process. The simulation results
show that the developed algorithms reduce the distribution expenses approximately by
9% compared to the ordinary GA.
An optimized route planning algorithm based on the artificial potential field (APF)
method was proposed in paper [3]. This method chooses preliminary planning of UA
trajectory on the basis of rapidly expanding random tree (RRT). The pre-planned route is
divided into continuous parts, and then intermediate route points are created. The route
point located nearby generates the gravitational force due to which the UA avoid the local
minimum while entering it. At the same time, taking into account the distance from UAV to
the obstacle and the radius of influence of the obstacle itself, the gravitational and
repulsive coefficients are dynamically adjusted, creating non-gravitational area around the
obstacle, which is beneficial for UA to avoid the obstacle.
Sensors are used in the development and operation of autonomous aircraft [4], [5]. An
important characteristic of various types of sensors is stability [6], [7]. The
implementation of artificial neural networks in the feedback loop in autonomous aircraft
improves coordination of movements, accuracy and speed. The article [8] presents the
results of a qualitative study of a neural network, including discrete and distributed time
delays. A method for calculating the exponential decay rate for a neural network model
based on differential equations with a discrete delay was developed and applied [9], [10].
Numerical modeling in cyber-physical sensor systems [11], [12] for automated control of
autonomous aircraft is important at the stage of their design.

3. Statement of the task

Accurate trajectory planning requires information about the kinematic or dynamic
model of unmanned aircraft motion for its proper trajectory planning. In this paper,
kinematic model of Dubins' aircraft motion is used for reference trajectory planning. The
reference trajectories that are planned using the Dubins motion model are described in
detail for the vast majority of mission scenarios, including obstacle settings, and the
application of this motion model is particularly suitable for efficient in-flight trajectory
planning.
For unmanned aircrafts, reference trajectories can be created by determining the
kinematic model parameters during nominal flight over rough terrain and adaptive
trajectory planning by means of the model of the Dubins aircraft motion with static wind,
even if the parameters of the kinematic model are known with errors only in advance.
Since aircraft movements similar to those of the Dubins automobile model occur in
three-dimensional space, the model was extended to three-dimensional configuration as
shown in Equation 1. The route velocity ⃑VK = (uk , vk , wk )T is parameterized according to
time t and is described as follows:

𝑢𝑘 (𝑡) = 𝑉𝑘 𝑐𝑜𝑠(𝜒̇ · 𝑡 + 𝜒0 ) 𝑐𝑜𝑠(𝛾) (1a)

𝑣𝑘 (𝑡) = 𝑉𝑘 𝑐𝑜𝑠(𝜒̇ · 𝑡 + 𝜒0 ) 𝑐𝑜𝑠(𝛾) (1b)

𝑤𝑘 (𝑡) = 𝑉𝑘 𝑠𝑖𝑛( 𝛾) (1c)

where vk is the value of route speed, χ̇ ˙ is the change of orbital azimuth, χ0 is the initial
orbital azimuth and γ is the trajectory angle. It is assumed that vk = m⁄s2 . Using this
model, the flight trajectory can be modeled in sections in straight and curved flight χ̇ ∈
{−χ̇ max, 0, χ̇ max}, as well as in horizontal flight, climb or descent γ ∈ {−γ max, 0, γ max}.
The model equations can be integrated analytically by closed segments in time. With the
t t
time parameter τ and x⃑g (t) = ∫ ⃑Vk (τ)dτ in forward flight τі x⃑g (t) = ∫ ⃑Vk (τ)dτ, the
0 0
following is applied

𝑥𝑔 (𝑡) = 𝑉𝑘 𝑐𝑜𝑠(𝜒0 ) 𝑐𝑜𝑠(𝛾) · 𝑡 + 𝑥0 (2a)

𝑦𝑔 (𝑡) = 𝑉𝑘 𝑠𝑖𝑛(𝜒0 ) 𝑐𝑜𝑠(𝛾) · 𝑡 + 𝑦0 (2b)

𝑧𝑔 (𝑡) = 𝑉𝑘 𝑠𝑖𝑛(𝛾) · 𝑡 + 𝑧0 (2c)
with the initial position x⃑0 = (x0 , y0 , z0 )T at the moment of time t 0 = 0 s and the
initial azimuthal angle of orbit χ0 . At turn χ ≠ 0, the result is as follows:

𝑉𝑘 𝑉𝑘 (3a)
𝑥𝑔 (𝑡) = sin(𝜒̇ · 𝑡 + 𝜒0 ) cos( 𝛾) + 𝑥0 − sin(𝜒0 ) cos(𝛾)
𝜒̇ 𝜒̇

𝑉𝑘 𝑉𝑘 (3b)
𝑦𝑔 (𝑡) = cos(𝜒̇ · 𝑡 + 𝜒0 ) cos( 𝛾) + 𝑦0 − cos(𝜒0 ) cos(𝛾)
𝜒̇ 𝜒̇

𝑧𝑔 (𝑡) = 𝑉𝑘 𝑠𝑖𝑛(𝛾) · 𝑡 + 𝑧0 (3c)

In case of γ = 0, the following applies to the resulting radius of the curve R:

𝑉𝑘 (4)
𝑅=
𝜒̇

Examples of trajectories according to equations (2) and (3) are shown in Figure 1. The
horizontal trajectory shown in Figure 1a consists of two straight segments and one
circular curve. Transitions between straight and turning flight are modeled by sudden
changes in the azimuth and angle χ of the trajectory. These sudden changes are the
approximation to the real UA motion. The boundaries of the segments are marked with
dashed lines.

Figure 1: Example of aircraft motion according to the Dubins’ aircraft motion model

The vertical trajectory shown in Figure 1b is the climb segment. The transitions
between horizontal flight and climb or descent are modeled by sudden changes in the
trajectory angle γ. This is also the approximation of UA motion model. Changes in the
trajectory speed Vk will be modeled as the approximation through sudden changes in Vk . as
well. While the Dubins aircraft motion model just roughly describes the motion of the real
aircraft at segment transitions, the simulated segment motion corresponds to the real
motion of the aircraft in the stationary flight.
Aircraft motion is modeled by the Dubins airplane motion model with the parameters
of the the angle of inclination of the flight wind γA and turn speed Ψ˙. Limitations of flight
characteristics are described by γA,max and Ψ̇max ., respectively. Another general
representation of the UA flight and technical characteristics under stationary flight
conditions is the description of the permissible values of the lift force coefficient CА ,
propulsion system power P, and multiple load n13 .
The following assumptions are used to consider stationary flight conditions. The
stationary flight is described by the balance of forces and moments and coordinated
turning flight is assumed, i.e., the sliding angle β = 0◦ and lateral force are zero. In
addition, it is supposed that there is no wind and the thrust vector is located along the UA
longitudinal axis. With centripetal force acting on the UA during turn Fzp = VA2 cos2 γ/R,
with curve radius R the balance of forces and moments along the fixed orbit coordinate
system (xk , yk , zk ) will be as follows:

∑ 𝐹𝑥𝑘 = 0 = 𝐷 − 𝑇𝑐𝑜𝑠 𝛼 + 𝐺𝑠𝑖𝑛 𝛾 (5a)

𝐺 𝑉𝐴2 𝑐𝑜𝑠 2 𝛾 (5b)
∑ 𝐹𝑦𝑘 = 0 = − 𝐴 𝑠𝑖𝑛 Ф + 𝑇𝑠𝑖𝑛 𝛼 sin Ф
8 𝑅

∑ 𝐹𝑧𝑘 = 0 = A cos Φ + T sin α cos Φ − Gcos 𝛾 (5c)

∑ 𝑀𝑥𝑘 = 0 (5d)

∑ 𝑀𝑦𝑘 = 0 (5e)

∑ 𝑀𝑧𝑘 = 0 (5f)

In equations 5, A is the lifting force, D is the resistance force, g = m • g is the gravity
force, T is the traction force, α is the angle of attack, , g ≈ 9,81 m/s is the gravitational
acceleration, Φ is the overhang angle, and γ is the trajectory angle. For small angles of
attack α, it is further assumed that cos α ≈ 1 and sin α ≈ 0. The result of the force
balance is as follows:

∑ 𝐹𝑥𝑘 = 0 = 𝐷 − 𝑇 + 𝐺𝑠𝑖𝑛 𝛾 (6a)

𝐺 𝑉𝐴2 𝑐𝑜𝑠 2 𝛾 (6b)
∑ 𝐹𝑦𝑘 = 0 = − 𝐴 𝑠𝑖𝑛 Ф
8 𝑅
∑ 𝐹𝑧𝑘 = 0 = 𝐴 𝑐𝑜𝑠 𝛷 + 𝑊 𝑐𝑜𝑠 𝛾 (6c)

The ratio is valid at a constant flight speed and horizontal flight without sliding

𝑔 ∙ tan Ф (7)
𝛹̇ =
𝑉𝐴

between the angle of overhang Φ and turning speed Ψ̇ with the gravity acceleration g.
The UA environment is described by the state space s X and states x ∈ X. In this state
space, it is required for agent A to plan its motion from state xs ∈ X to state xz ∈ X or into
the state space xZ ⊂ X. Agent A can move within its action space U with actions u ∈ U in
the space states. For the motion in state space, the function of transition f from state x to
the new state x́ is given in the form of the state transition equation:

𝑥́ = 𝑓(𝑥, 𝑢) (8)

Similarly, the transition equation is given in time-discretized representation

𝑥𝑡+1 = 𝑓(𝑥𝑡 , 𝑢𝑡 ) (9)

For the actual planning, the state space is transferred to the configuration space C with
the configurations q ∈ C that are relevant for planning. The allowable configuration space
is limited by the interference region Cobs . Space Cobs is often artificially enlarged in order
to ensure the absence of obstacle between agent A and the actual obstacle. In the
remaining free space Cfree = C/Cobs , agent A is able to move according to its action space
U. Similar to equation (8), the transition equation in configuration space is q́ = f(q, u).
Thus, the planning algorithm should be able to create continuous route τ: [0,1] → for
agent A from the initial configuration qS ∈ Cfree to the target configuration qZ ∈ Cfree or
CZ ∈ Cfree з τ(0) = qS і τ(1) = qZ or report correctly that this route does not exist. If
these properties are true, the planning algorithm is considered to be complete. Very often
the cost function g is also defined in such a way that the planning algorithm returns the
optimal route regarding the cost function.
Automatic route planning calculates the reference trajectories for cruise flight by UA
motion model. By means of appropriate reference route, route deviation occurring during
the route sequence can be minimized. While selecting the appropriate algorithm for route
planning against the background of obstacles, it is recommended to use sampling-based
approaches, as the obstacle background can be effectively taken into account by
discretizing the planning space depending on the method complexity.
PRM trajectory planning approaches that use kinematic motion model have been
presented for UA trajectory planning. These approaches use local motion planning in
accordance with the Dubins model of aircraft motion with curve straight curve (CSC)
segments and the cyclic search graph with cyclic search graph with search on the graph in
order to find the optimal reference trajectory according to the cost functionality. The
calculation of SCS trajectory segments makes it possible to solve efficiently the problem of
motion planning and results in reference routes where straight and curved segments
always alternate. Compared to planing by CSC segments, direct transitions between two
curves in opposite directions, which in the case of the airplane mean maximum sudden
changes in the overhang angle, are avoided. However, while selecting SCS segments for the
solution of motion planning in space without obstacles, the methods of trajectory planning
in obstacle conditions should be adapted and cannot be adopted from existing approaches
without modification. Eventually, the choice of local planning problem ensures sequential
movement of complex calculation steps to the initialization phase and less complex
calculation steps to the time-critical planning phase. In addition to the initial and target
states (qS , qZ ), the division makes it possible to set up the planning parameters
(Ψṗ , γA,p , VW,p , χW,p , Sp ) for each planning request and simultaneously the time to achieve
effective planning.
Applying the transition functions or equations of the Dubins aircraft motion model and
trajectory planning parameters Ψṗ , γA,p , VW,p , χW,p , the segmental reference trajectories
for aircraft x⃑p (t) can be calculated with fixed wing in space without obstacles Cfree in the
fixed Earth coordinate system:
𝑡
(10)
𝑥𝑝 (𝑡) = ∫ 𝑥𝑝 (𝜏)𝑑𝜏 + 𝑥𝑝0
0

In equation (10), ⃑⃑x p corresponds to the motion, t and τ to time, and x⃑ p0 to the initial
position at time t = 0.
Further, we consider the problem of planning the transition between two intersecting
lines and give the calculation rule for solving the planning problem. The transition
between the two intersecting lines is simulated by means of the curve, resulting in SCS
segment formation. The premise is that two linear flight segments [AB] and [BC] intersect
at point B, as shown in Figure 2. In this case.

⃑ 𝐾,𝐴 · 𝑡
𝑥𝐴𝐵 (𝑡) = 𝐴 + 𝑉 (11)

⃑ K,A at point
describes the initial segment [AB] with fixed relative to the Earth velocity V
A, while in

⃑ 𝐾,𝐶 · 𝑡
𝑥𝐵𝐶 (𝑡) = 𝐶 + 𝑉 (12)

the target segment [BC] with fixed relative to the Earth velocity V ⃑ K,C at point C is
described. In addition, condition ∆χ < 180◦ should be applied to the change of the azimuth
of the angle trajectory ∆χ := 180◦ − ∠ABC. The condition for intersection of segments [AB]
and [BC] isas follows:

⃑ 𝐾,𝐴 · 𝑡𝐴 = 𝐶 + 𝑉
𝐴+ 𝑉 ⃑ 𝐾,𝐶 · 𝑡𝐶 з 𝑡𝐴 , 𝑡𝐶 ≥ 0 (13)

Below, we describe The determination of the transition times t 1 , t 2 , t 3 between the
straight and curved segments shown in Figure 2 are described and calculation of the
reference trajectory with SCS segment, taking into account the Dubins aircraft motion
model is presented.

Figure 2: The straight-curve-straight planning problem in the obstacle-free space

First, the normalized air speed vector for two linear flight segments at points A and C is
calculated. The value of the flight speed VA , wind speed V ⃑ W and direction of the orbital
⃑ K,n are given:
velocity vector V

(14)
⃑ 𝐾,𝑛 · 𝑉
𝑉𝐾 = 𝑉 ⃑ 𝑊 + √(𝑉
⃑ 𝐾,𝑛 · 𝑉
⃑ 𝑊 )2 − 𝑉𝑤2 + 𝑉𝐴2

⃑ 𝐴,𝐴 =
1
⃑ 𝐾,𝑛 − 𝑉
⃑ 𝑊) (15)
𝑉 · (𝑉𝐾 · 𝑉
𝑉𝐴

With known air speed vectors, azimuth Ψ1 і Ψ3 for segments x⃑p,1 (t), x⃑p,2 (t) and the
change in azimuth ∆Ψ = |Ψ3 − Ψ1 | can be defined. For special case ∆Ψ = 0◦ the
reference route is the result of two linear segments [AB] and [BC].
Time ∆t 1,2 = t 2 − t 1 for curve segment x⃑p,2 (t) is defined now as:

∆𝛹 (16)
∆𝑡1,2 =
|𝛹𝑝̇ |

With known ∆t 1,2 , the endpoint for x⃑p,2 (∆t 1,2 ) can be determined by equations (3) and
initial values x0 = 0, y0 = 0, Ψ0 = Ψ1 . It is defined as the position vector Q ⃑⃑ ≔ x⃑(∆t 1,2 ).
Now the curve segment is known up to the actual starting point x⃑p,1 (t 1 ) = x⃑p,1 (∆t 0,1 )
since t 0 = 0 s. Points x⃑p,1 (t 1 ) і x⃑p,2 (t 2 ) can be found by the system of linear equations in
the horizontal plane, which can be expressed in the following way:

⃑ + ∆𝑥𝑝,3
𝐶 = 𝐴 + ∆𝑥𝑝,1 + 𝑄 (17a)

⃑ 𝐾,𝐴 · ∆𝑡0,1 + 𝑄
𝐶 −𝐴 = 𝑉 ⃑ +𝑉
⃑ 𝐾,𝐶 · ∆𝑡2,3 (17b)

⃑ =𝑉
𝐶 −𝐴−𝑄 ⃑ 𝐾,𝐴 · ∆𝑡0,1 + 𝑉
⃑ 𝐾,𝐶 · ∆𝑡2,3 (17c)
and can be solved for two unknown values ∆t 0,1 і ∆t 2,3 . Then the transition time results
in:

𝑡0 = 0, (18)

𝑡1 = ∆𝑡0,1 , (19)

∆𝑡1,2 (20)
𝑡21 = 𝑡1 + ,
2

∆𝑡1,2 (21)
𝑡22 = 𝑡21 + ,
2

𝑡3 = 𝑡22 + ∆𝑡2,3 (22)

In this case, the following condition should be applied: t 0 ≤ t 1 ≤ t 21 ≤ t 22 ≤ t 3.
Now the complete reference trajectory parameterized according to time t is known.
The second segment s2 is divided by the change of the inclination angle of the flight wind
into x⃑p,21 і x⃑ p,22. If points A,B,C are located on the straight line, then x⃑p,2 is descended,
since t 1 = t 21 = t 22 . In the general case, the SCS route segment x⃑p (t), t ∈ (0, t 3 ) results in:

⃑ 𝐾,𝐴 ,
𝑥𝑝,1 (𝑡) = 𝐴 + 𝑡 · 𝑉 𝑡 ∈ (0, 𝑡1 ], 𝛹𝑝̇ = 0, 𝛾𝐴,𝑝 = 𝛾1 (23a)

𝑥𝑝,21 (𝑡) = 𝑥𝑝,1 (𝑡) + 𝑥 (𝑡), 𝑡 ∈ (𝑡1 , 𝑡21 ], 𝛹𝑝̇ ≠ 0, 𝛾𝐴,𝑝 = 𝛾1 (23b)

𝑥𝑝,22 (𝑡) = 𝑥𝑝,21 (𝑡) + 𝑥 (𝑡), 𝑡 ∈ (𝑡21 , 𝑡22 ], 𝛹𝑝̇ ≠ 0, 𝛾𝐴,𝑝 = 𝛾3 (23c)

⃑ 𝐾,𝐶 ,
𝑥𝑝,3 (𝑡) = 𝑥𝑝,22 (𝑡) + 𝑡 · 𝑉 𝑡 ∈ (𝑡22 , 𝑡3 ], 𝛹𝑝̇ = 0, 𝛾𝐴,𝑝 = 𝛾3 (23d)

For cases γ1 > 0 ∧ γ3 > 0 ∧ Ψṗ ≠ 0 and γ1 < 0 ∧ γ3 < 0 ∧ Ψṗ ≠ 0 there is the
sudden change point in the vertical course. If this discontinuity is not desirable, the
transition can be smoothed, for example, by means of polynomial as stated in paper [19]
or the entire vertical profile can be smoothed using double integrator as in paper [20].

4. Main results
While planning motion only in obstacle-free space, in addition to the route segments by
specifying reference points A, B, C, complete reference routes can also be planned in
obstacle-free space. For this paper, the calculation rule was implemented in C++
programming language.
For clarifying reference points A1, B1, C1 for SCS segment are drawn in Figure 3a. The
complete reference route consists of four SCS segments. In order to illustrate the influence
m
of wind, the reference trajectory of the motion pattern for VA = 20 s , Ψ̇p = 0,85 rad/s
without and with wind VW,p = 6 m/s is shown. Transitions between separate straight
and curved route segments are shown by dotted lines. Comparing two reference
trajectories, one can clearly see the consideration of static wind during the trochoid-
shaped curve segments in Figure 3b.
z

Figure 3: Examples of trajectories according to the Dubins aircraft motion model with
static wind.

VA = 25 m/s і Ψṗ = 0,167 rad/s are accepted for planning. The flight altitude is
constant and equals 100 m, and the reference trajectory describes the flight with planned
flight time of about 18 minutes.
Calculation times of separate motion planning segments for the implemented SCS
motion planning algorithm on the desktop and on-board computers are shown in Table 1.
Calculation time for CSC motion planning with the Dubins aircraft motion model with
static wind and calculation time for simple straight-straight–SS route planning are shown
for comparison,.

Table 1
Calculation results of separate motion planning segments for the implemented SCS motion
planning algorithm on the desktop and on-board computers
Individual motion Desktop PC results in ms On-board computer
planning results in ms
SCS(VW,p = 0m/s) 0.01 0.03
SCS(VW,p ≠ 0m/s) 0.07 0.22
SS (∆χ=0 )◦
◦ 0.00004 0.0002
CSC(VW,p ≠ 0m/s) 0.44 1.96

After the development of the UAV motion planning algorithm, it is requered to carry
out the experimental scenario, shown schematically in Figure 4. The UA should fly around
the right shaded obstacle, passing through the gap between the obstacles. Static obstacle
height Sstat = 10 m. is initially assumed for route planning. The expected route deviations
are initially taken as the expected dynamic route displacement of Sdyn = 15 m. Thus, the
initial baseline trajectory in Figure 4a is planned with the obstacles height of Sp = 25 m.
However, after the start of the mission, lateral deviations of the trajectory dy,max =
41,5 m occur on the first curve. These route deviations are taken into account in path
planning as Sdyn = 41,5 m (Sp = 51,5 m) at the moment of base route replanning. It
means that taking into account adaptive obstacle clearance, the route planning excludes
passage between obstacles and plans detours. The resulting reference trajectory does not
create the risk of breaking the static distance Sstat from obstacles or even collision.

Figure 4: Adaptation of obstacle clearance as the result of lateral route deviations

Automatic trajectory planning using the Dubins parametrized aircraft motion model
with static wind is effective due to the application of constant cyclic graphs. The local
problem of planning SCS motion in space without obstacles and representing the available
free space on the graph structure is proposed fo the approachThis devision makes it
possible to carry out intensive computations at one-time initialization stage and to
perform only efficient computations at the planning stage.
The presented approach for route planning solves the problem of route smoothing
after route planning, which is related to the question how the actual curve radii of the
aircraft can be taken into account during planning and not only during the trajectory
smoothing. In this investigation, The local motion planning during search on the graph is
solved and virtual dual graph is introduced in this investigation.
In case when we take into account the span of obstacles, information about maximum
spatial trajectory reached at the moment of flight is used. The assessment shows how
obstacles that have already been encountered can be taken into account when planning
their overcoming. Since the trajectory deviations resulting from incorrect
parameterization of flight characteristics can be accumulated, the obstacle clearance
adaptation is less suitable for consideration of incorrect parameterization of flight
characteristics. The resulting trajectory deviations are not affected by the obstacle
clearance adaptation.
The proposed method defines the trajectory planning parameterization due to which
unmanned aericraft can follow the planned reference trajectories close to the limits of
flight characteristics. If the increase of safety level is required, the distance from obstacles
can be adjusted by the static obstacle distance Sstat . Knowing the expected trajectory
positions due to uncertain wind estimate, the distance from obstacles can be regulated as
well.

Conclusions
The implementation of autonomous trajectory planning is a basic requirement for
various operational scenarios for unmanned aircrafts. Due to the Dubins motion model
combined with SCS trajectory planning algorithm, a reliable framework for efficient UA
navigation in complex environments was created.
The Dubins motion model offers a simplified approach to the fixation of motion
kinematics of UAV movement, making it possible to plan the trajectory accurately taking
into account the such limitations as minimum turning radius and maximum speed.
Integrating this model with SCS trajectory planning algorithm, which optimizes
trajectories based on spatial constraints and mission objectives, it is possible to obtain
synergistic interaction that increases the autonomy and adaptability of operations
involving direct UA participation. In general, the presented method of adaptive trajectory
planning represents the system that can relieve the workload of the ground station
operator by adapting automatically the trajectory planning parameters and contributes to
the increased autonomy of unmanned aircraft.

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