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1
Online UAV Trajectory Planning for Covert Video
Surveillance of Mobile Targets
Hailong Huang, Andrey V. Savkin, and Wei Ni
Abstract—This paper considers the use of an unmanned aerial
vehicle (UAV) for covert video surveillance of a mobile target
on the ground, and presents a new online UAV trajectory
planning technique with a balanced consideration of the energy
efficiency, covertness, and aeronautic maneuverability of the UAV.
Specifically, a new metric is designed to quantify the covertness
of the UAV, based on which a multi-objective UAV trajectory
planning problem is formulated to maximize the disguising
performance and minimize the trajectory length of the UAV. A
forward dynamic programming method is put forth to solve the
problem online and plan the trajectory for the foreseeable future.
Additionally, the kinematic model of the UAV is considered in
the planning process so that it can be tracked without any later
adjustment. Extensive computer simulations are conducted to
demonstrate the effectiveness of the proposed technique.
Note to Practitioners—The “Follow Me” flight mode is available
in many UAV products, and this technique enables a UAV to
automatically follow a target. However, this flight mode may
make the UAV noticeable to the target, and compromise the
video surveillance missions of the UAV. Inspired by some security
surveillance applications where UAV surveillance is conducted so
that a target would not take actions to avoid being monitored,
we propose an efficient method to construct the trajectory for
the UAV. The proposed method takes into account the visual
covertness and the battery capacity limitation of the UAV, and
it can produce a trajectory online for the UAV. The proposed
method and scenario can potentially extend the “Follow Me”
flight mode and generate new applications and market for UAVs.
Index Terms—Unmanned Aerial Vehicles (UAVs), covert video
surveillance, trajectory planning, dynamic programming.
I. INTRODUCTION
THANKS to the excellent mobility and flexibility, un-
manned aerial vehicles (UAVs) have become an effective
and efficient tool for various applications, including but not
limited to, surveillance [1], [2], filming [3], parcel delivery
[4], [5]. wireless communication [6], [7], and agriculture [8].
Equipped with cameras, UAVs have been widely used to
monitor and track targets of interest [9]. They have also
been used to record targets’ misbehaviors as court evidence
in legal processes, which helps law enforcement to improve
countermeasures or quickly response to incidents [10], [11].
A prominent challenge in this application is that the target
This work was supported by the Australian Research Council. Also, this
work received funding from the Australian Government, via grant AUS-
MURIB000001 associated with ONR MURI grant N00014-19-1-2571.
H. Huang and A.V. Savkin are with School of Electrical Engineering and
Telecommunications, University of New South Wales, Sydney 2052, Australia.
(E-mail: {hailong.huang, a.savkin}@unsw.edu.au).
W. Ni is with Data61, The Commonwealth Scientific and Industrial Re-
search Organisation, Australia. (E-mail: Wei.Ni@data61.csiro.au).
can become aware of surveillance, when the UAV flies in
the currently available flying modes such as “Follow Me”
and “Orbit”. Once the surveillance is noticed, the target may
take actions leading to a potential failure of the surveillance
missions. Thus, it is important for the UAV to operate in a way
that can disguise visually its surveillance intention towards the
target.
This paper focuses on covert video surveillance by a UAV.
A target vehicle or a person moves based on its own objective
such as going to a destination. Executing a covert surveillance
task, the UAV needs to not only have a continuous view of
the target but also disguise itself. The UAV needs to avoid
being noticed visually by the target. For example, the police
may want to unnoticedly monitor a suspicious vehicle or a
criminal suspect, and record any of its misbehaviours. The
UAV flies along a carefully planned trajectory to maintain
a good and uninterrupted view of the target. The UAV also
needs to disguise itself by displaying random flying behaviours
towards the target. Despite some commercially available UAV
products can autonomously follow a target and shoot video,
they have not taken the covertness into consideration. To this
end, an important issue is how to quantify the disguising
performance. From a common sense, the UAV must be neither
too close to the target as would increase the likelihood of
being detected, nor too far away due to its limited sensing
range. Additionally, the UAV does not monitor the target from
a certain relative angle and distance, as may lead to a high
likelihood of being noticed.
A. Contributions
We propose a new online trajectory planning technique
for a UAV conducting covert video surveillance, under a
balanced consideration of energy efficiency, visual covertness,
and aeronautic maneuverability of the UAV. To achieve this,
we first design a new measure of the disguising performance,
which is a combination of the derivative of the UAV-target
angle and that of the UAV-target distance. A larger value of
the metric indicates a more significant change of the relative
UAV-target position and, in turn, a better performance of
disguising. Although the trajectory planning problem has been
investigated widely and various approaches are available, to
the best of our knowledge, this is the first attempt to take visual
covertness into account in the trajectory planning process.
With the new metric, we formulate a multi-objective op-
timization problem to minimize the trajectory length while
maximizing the disguising metric, subject to the aeronautics
of the UAV and the target’s presence in the sight of the UAV.
2
Target position
prediction
Trajectory planning using
forward dynamic
programming
Trajectory
tracking
Target monitoring,
Position measurement
Fig. 1: The predict-plan-calibrate working manner of the UAV.
We propose a dynamic programming (DP) based framework to
construct the trajectory online. At any time slot, the UAV pre-
dicts the target positions using the past observations, constructs
a feasible future flight zone, and optimizes the trajectory for
the foreseeable future. The UAV adjusts online if drifts occur,
as illustrated in Fig. 1. Moreover, we take into account the
UAV kinematic model when defining the state transfer cost
in the DP framework. Specifically, we consider the cost of
the feasible trajectory with aeronautic maneuverability. This
ensures that the constructed trajectory can be followed by the
considered UAV without any further adjustment.
As described, the key contributions of the paper are the con-
sideration of visual covertness and aeronautic maneuverability
when designing the UAV trajectory. To verify the effectiveness
of the proposed method, we conduct extensive computer sim-
ulations to show how the UAV moves guided by this method.
We also investigate the impact of the target’s movement on
the trajectory planning of the UAV via simulations.
B. Related work
We have seen some promising research results focusing
on two typical scenarios of video tracking by UAVs. In the
first scenario, a UAV monitors a target, and the movement
of the target is independent of the UAV. The references
[12], [13] develop vision-based control methods that enable
UAVs to track a moving ground target using video streaming.
The objective is to keep a close UAV-target distance such
that the target state can be updated frequently or guide the
UAV to follow the motion of the target. The references [14],
[15] consider the problem of tracking a mobile target in
urban environments, where the line-of-sight (LoS) between
the UAV and the target is often blocked by buildings. The
authors focus on the design of the UAV trajectory such that
the probability of viewing the target is maximized. Paper
[16] proposes a coarse-to-fine UAV target tracking strategy
with deep reinforcement learning to tackle the frequently
changed aspect ratio of a target. These references all focus
on computer vision [17]. Some other publications, such as
[18], [19], account for the energy consumption in trajectory
planning to extend the UAV’s lifetime. When multiple targets
are monitored, the movements of UAVs are often required to
maximize the number of observable targets at any moment [2],
[9], and the duration of monitoring when energy limitation
is accounted [20]. Some companies have already released
commercial UAV products, which can autonomously follow
and monitor a target in the “Follow Me” mode, such as
DJI MAVIC-2 (https://www.dji.com/au/mavic-2). The other
popular scenario is that a UAV attempts to monitor a target
that is aware of the UAV and tries to avoid being monitored
[21]–[23]. Thus, a trajectory planning problem arises in an
adversarial setting and depends on the motions of both the
UAV and the target. This paper focuses on covert video
surveillance using a UAV, which is distinct from these two
scenarios.
In a different yet related context, trajectory planning and
tracking are important research topics. For trajectory planning,
the reference [24] derives two classes of flight trajectories for
tracking ground objects. The first class consists of switching
between clockwise and counter-clockwise orbits so that the
average moving direction of the UAV is the same as that of
the ground target. This class is suitable for tracking fast targets.
The second class consists of orbits and straight lines, which is
suitable for tracking slow targets. The reference [25] proposes
an acceleration-continuous path-constrained trajectory plan-
ning algorithm with a built-in tradeoff mechanism between the
cruise motion and time-optimal motion. Regarding trajectory
tracking, the paper [26] develops a control Lyapunov function
approach to addressing the problem of constrained nonlinear
trajectory tracking control for UAVs. The paper [27] presents
a non-uniform control vector parameterization approach with
time grid refinement for flight level tracking. One challenge
of these approaches is the complex computation of the control
inputs to the UAVs. Thus, some of the existing methods may
not be suitable for real-time planning and tracking. A simple
solution is to construct a trajectory for UAVs, which only
consists of arcs and straight lines [28]. The trajectory planning
algorithm proposed in the current paper follows this idea. The
generated trajectory can be tracked by the UAV easily by only
remembering some control inputs which are obtained in the
trajectory planning process.
C. Paper organization
The rest of this paper is organized as follows. We introduce
the system model in Section II. We specify the objective
function, formulate the problem of interest, and propose the
forward DP algorithm in Section III. In Section IV, we
present simulation results to evaluate and confirm the proposed
algorithm. Finally, we conclude the paper in Section V. The
notations used in the paper are summarized in TABLE I.
II. SY ST EM MO DE L
The considered system involves a UAV equipped with a
camera and a target moving on a road. Suppose that the UAV
flies at a fixed altitude h. Let p(t)=(x(t), y(t)) denote the
coordinates of the UAV on the horizontal plane at time t∈
[0, T ], where [0, T ]is the period of time during which the
UAV executes a video surveillance task. The following model
is considered for the UAV [29]–[31]:
˙x(t) = ν(t) cos θ(t),
˙y(t) = ν(t) sin θ(t),
˙
θ(t) = ω(t),
(1)
where θ(t)∈[0,2π)is the UAV heading measured in the
counter-clockwise direction from the x-axis, ν(t)∈(0, Vmax]
is the linear speed, ω(t)∈[−Wmax, Wmax ]is the angular
3
TABLE I: Main symbols and explanations.
Symbol Explanation
Used in formulating the problem
p(t)UAV position
θ(t)UAV heading
ν(t)UAV linear speed
ω(t)UAV angular speed
r(t)UAV turning radius
q(t)Target position
φ(t)Target moving direction
d(t)UAV-target distance
α(t)UAV-target angle
TMission time
TPrediction horizon
R1,R2,µParameters of feasible flight zone
Used in presenting the DP method
SkThe state space of stage k
ck
ij Cost from state iin stage kto state jin stage k+ 1
Jk(j)Minimum cost from initial state to state jin stage k+ 1
Used in local trajectory construction
σ[k]The angle from the x-axis to the vector −−−−−−−−→
p[k]p[k+ 1]
n[k]Unit vector perpendicular to the heading direction θ[k]
c[k]The centre of the turning circle
z[k]The tangent point
τ[k]The angle between vectors −−−−→
c[k]p[k]and −−−−→
c[k]z[k]
ρ[k]The angle between vectors −−−−−−−→
c[k]p[k+ 1] and −−−−→
c[k]z[k]
speed, and Vmax and Wmax are the maximum linear and
angular speeds, respectively. They depend on the mobility of
the UAV. When ω(t)6= 0, the UAV makes a turn, and the
turning radius is r(t) = ν(t)
ω(t). The kinematic model (1) has
been widely used to describe the motion of UAVs, see e.g.
[29]–[31]. Navigation algorithms developed on the basis of the
model or its minor variations have been successfully imple-
mented in experiments with UAVs, see e.g. [30], [32]–[34]. A
robust control framework could be utilized in coupling with the
proposed algorithm to suppress potential model uncertainties
and disturbance. At the first stage of the framework, the
proposed navigation/path planning algorithm is implemented.
At the second stage, a robust controller, e.g., robust sliding
mode controllers [32], [35], can be designed to reduce the
effect of uncertainties and disturbances and keep the actual
trajectory close to the one designed by the navigation/path
planning algorithm. The robust controller design problem is
beyond the scope of this paper, and will be part of our future
work.
Let q(t) = (xq(t), yq(t)) denote the position of the target
at time t. Since the target moves on a road, the movement of
the target is predictable for a certain period of time Tinto the
future. We first assume that the predictions are perfect. At any
time t0,q(t)is predicted for the time t∈(t0, t0+T].
We consider the task of covert video surveillance. The UAV
should not be too far away from the target, or the resolution
of video taken could degrade. The UAV should not be too
close to the target either, since being too close would increase
the possibility of being noticed by the target. We consider
that when the UAV flies in a feasible flight zone, it can have
the target in view with acceptable resolution. This region
is behind the target and characterized by three parameters:
R1, the distance that the UAV needs to keep to avoid being
noticed; R2, the maximum distance for the UAV to maintain an
-axis
(a)
(b)
Fig. 2: The feasible flight zone when the target movement
prediction is (a) accurate, (b) inaccurate.
acceptable resolution for its observation on the target, where
R1< R2; and an angle µ, see Fig. 2a. We explain how to
choose µbelow.
Given the predicted position of the target at a future instant
(t+δ), i.e., q(t+δ)(where δis a sampling interval), and
all the candidates of the UAV position at instant t, i.e., p(t),
we specify the feasible flight region of the UAV for instant
(t+δ), as follows. The feasible flight region collects the
intersections between the annulus specified by two concentric
circles centered at q(t+δ)with radii of R1and R2, and
the disc centered at each candidate of p(t)with radius equal
to the maximum distance that the UAV can travel within a
sampling interval δ. For ease of description, we define the
angle µin such a way that each feasible flight region at
instant tis entirely captured in the part of the corresponding
annulus specified by µ(referred to as the “feasible flight
zone” for the instant tin our paper), and µcannot be further
reduced. At instant (t+δ), part of the feasible flight zone
may not be reachable if the UAV is situated at a particular
position at instant t. An additional constraint is in place to
define an infinite cost for the UAV to fly from the particular
candidate position at instant tto any candidate position in the
unreachable part at instant (t+δ), as will be described in
Section III-B.
The feasible flight zone is a function of the target position
and heading angle. Let φ(t)denote the moving direction of
the target, which is measured from the x-axis in the counter-
clockwise direction; see Fig. 2a. This direction is tangent
to the road at the position q(t). Thus, given the road and
the current target position, φ(t)can be readily computed. To
further compute the feasible flight zone, we introduce two
more angles β1and β2, which are µ
2away from the opposite
direction of the target moving direction φ:β1=φ+π−µ
2
and β2=φ+π+µ
2; see Fig. 2a. Given q,µ,R1,R2,β1
and β2, the feasible flight zone can be obtained. Since µ,R1,
and R2are constants, β1and β2are two functions of φ, and
φdepends on the target position q(t), the feasible flight zone
is a function of q(t)given the road. Let Φ(q(t)) denote the
feasible flight zone when the target is at q(t). The UAV must
be within the feasible flight zone Φ(q(t)):
p(t)∈Φ(q(t)),∀t∈[0, T ].(2)
We assume that the onboard camera has a panoramic view, or
the capability of automatic tracking of targets. We also assume
that a gimbal is used on the UAV to stabilize the camera.
When the predictions of the future target positions are
not accurate, the inaccuracy can have impact on the feasible
4
Target
UAV
UAV
projection 𝑑
𝛼
Road
(𝑥𝑞, 𝑦𝑞)
(𝑥, 𝑦)
horizontal plane
X-axis
𝜙
ℎ
Fig. 3: The UAV-target angle and distance. As all the notations
in this figure are with the time index t,tis not shown.
flight zone of the UAV. The feasible flight zone can become
smaller when there is prediction uncertainty. In this paper,
we assume that the prediction uncertainty is bounded per
slot. This assumption is reasonable since the speed of the
target is bounded in practice. Thus, instead of an estimated
position, we have an estimated region, denoted by γ(q(t)), for
a certain time instant t. For any point of an estimated region
q0∈γ(q(t)) (see Fig. 2b), we can compute a feasible flight
zone that guarantees the view of q0, i.e., Φ(q0). Therefore, the
feasible flight zone to view any point inside the region γ(q(t))
is the intersection of the feasible flight zones corresponding to
all the interior points of γ(q(t)). Let Φ(γ(q(t))) denote this
zone. The potential UAV position is limited to be within it;
see Fig. 2b:
p(t)∈Φ(γ(q(t))) = ∩q0∈γ(q(t))Φ(q0),∀t∈[0, T ].(3)
Remark II.1. Given that the target vehicle moves continu-
ously with a smooth trajectory, the feasible flight zone of the
UAV changes continuously even when the target turns sharply
(including a U-turn). On the other hand, the construction
of the feasible flight zones does have to take more careful
consideration of the surrounding environment when the target
is turning. For example, the feasible flight zones may have to
extend vertically and reduce horizontally, so that the UAV can
still keep its distance to the target while avoiding crashing
into roadside buildings.
III. PROB LE M STATEM EN T AN D PROP OS ED SOLUTION
In this section, we propose the objective function and
formally state the problem of interest, and then propose a
forward DP based algorithm to address the problem online.
A. Problem Statement
An important issue to be addressed first is how to quantify
the disguising performance of the UAV carrying out covert
video surveillance. To avoid being noticed or detected by the
target, a possible way for the UAV to disguise its intention
is to change the UAV-target angle and distance as frequently
and drastically as possible. Given the altitude of the UAV, we
only consider the angle α(t)and the distance d(t)between the
UAV and the target on the horizontal plane. The UAV-target
distance is the Euclidean distance between the UAV projection
and the target on the horizontal plane; see Fig. 3:
d(t) := q(x(t)−xq(t))2+ (y(t)−yq(t))2.(4)
The UAV-target angle is defined as the angle between the
direction of the target-UAV connection and the heading angle
of the target (φ(t)) on the horizontal plane; see Fig. 3:
α(t) := arctan( y(t)−yq(t)
x(t)−xq(t))−φ(t),(5)
where the x-axis can be selected such that x(t)6=xq(t).
The considered model can be extended to the case where the
target moves along a road on an uneven terrain. The effect
of the changing altitude of the target can be compensated
by adjusting the altitude of the UAV. Such functionality is
available in many commercial UAV products, such as DJI
MAVIC-2 (https://www.dji.com/au/mavic2).
Let η > 0denote a given co-efficient. The proposed
disguising metric is given by a combination of the amplitudes
of the derivatives of the UAV-target angle and the UAV-target
distance:
κ(t) := η|˙α(t)|+|˙
d(t)|.(6)
The rationale of the (6) is that, if the target carries cameras
to monitor its surroundings, the UAV’s frequently changing
distance and angle with respect to the target also make it
difficult for the target to correctly focus its camera lens. As
a result, the target can hardly obtain a clear view of the
UAV. When the driver or passenger of a target vehicle tries
to visually detect possible trackers, e.g., the UAV, by naked
eyes, flying in the defined feasible flight zone, which keeps a
reasonable distance between the UAV and target, also makes
it difficult for the target to see the UAV or differentiate it from
the background.
The aim of disguising can be modelled as maximizing the
disguising metric (6) over the time period of [0, T ]:
max
p(t)ZT
t=0
κ(t)dt. (7)
Since the UAV is usually powered by a battery with limited
capacity, high energy consumption would result in a short life-
time. It is practically important to prevent the UAV consuming
too much energy. In this paper, we use the length of the UAV
trajectory to indicate the energy consumption. Then, the other
goal can be formulated as:
min
p(t)ZT
t=0
ν(t)dt. (8)
Given the locations of the target and parameters R1,R2,µ,
η,T,Wmax,Vmax ,p(0) and θ(0), the problem of interest is
formulated as follows:
min
p(t)ZT
t=0
ν(t)dt −λZT
t=0 η|˙α(t)|+|˙
d(t)|dt, (9)
s.t.
p(t)∈Φ(γ(q(t))),∀t∈[0, T ],(10)
where λin (9) is a given weighting factor. It is worth pointing
out that the integration in (9) is to evaluate the time average
of the proposed disguising performance metric. It can be
translated to maximize the metric at every time instant (or
in other words, keeping the metric high all the time).
5
B. Predictive DP based Trajectory Planning Algorithm
The problem under consideration is difficult to be solved
due to the second term of (9). This is because the operator | · |
makes (9) non-differentiable at point zero. Besides, |˙α(t)|and
|˙
d(t)|are non-convex with respect to p(t)=(x(t), y(t)). As
the objective function (9) is a continuous function of ν(t),α(t)
and d(t), finding the analytical solution is not straightforward.
Furthermore, it is difficult to accurately predict the movement
of the target for the whole surveillance period at the beginning
of the task. In this subsection, we propose a DP based method
to solve the problem and plan the trajectory of the UAV online.
Such a method periodically constructs the local UAV trajectory
based on the target movement prediction for a short period of
future time T.
We first discretize the system. Given the sampling interval δ,
the period [0,T]can be discretized into a number of slots with
equal length, and the movement of the target is predictable
for N(N=bT
δc) slots. At any slot, the UAV can only
construct a trajectory for the next Nslots. All the notations
defined in the continuous-time domain can be transferred to
the discrete-time domain. At the k-th slot (k= 0,1, . . . , N ),
the position, heading angle, linear speed, and the turning radius
of the UAV are p[k]=(x[k], y[k]),θ[k],ν[k], and r[k],
respectively. The position and heading angle of the target
are q[k] = (xq[k], yq[k]) and φ[k], respectively. The UAV-
target angle and distance are α[k]and d[k], respectively. The
objective function (9) can be discretized as follows:
min
N−1
X
k=0
(ν[k]δ−λη|α[k+ 1] −α[k]| − λ|d[k+ 1] −d[k]|).
(11)
When the UAV needs to construct the next local trajectory,
we regard current slot as the initial stage, i.e., stage 0. In this
stage, the UAV has a known initial position s=p[0]. We look
for Nbounded control inputs ν[k]and ω[k],k= 0, . . . , N −1
such that p[k+ 1] ∈Φ(γ(q[k+ 1])) and (11) is minimized,
where p[k+ 1] is computed by a discretized form of (1):
x[k+ 1] = x[k] + ν[k] cos θ[k]δ,
y[k+ 1] = y[k] + ν[k] sin θ[k]δ,
θ[k+ 1] = θ[k] + ω[k]δ.
(12)
Clearly, given the state of the UAV at stage k, i.e., x[k],y[k],
θ[k], we obtain the state in the next stage k+1 when applying
the control inputs ν[k]and ω[k].
Let Skdenote the state space of stage kfor the UAV. This
state space is the feasible flight zone, i.e., Sk= Φ(γ(q[k])),
see Fig. 2b. Let g(p[k], ν[k], ω [k]) denote the state transition
cost from state p[k]∈Skto state p[k+ 1] ∈Sk+1 by
applying the control inputs ν[k]and ω[k]. The expression for
g(p[k], ν[k], ω [k]) is given by:
g(p[k], ν[k], ω [k]) = ν[k]δ−
λη|α[k+ 1] −α[k]| − λ|d[k+ 1] −d[k]|,(13)
where d[k+1] and α[k+1] can be computed based on p[k+ 1]
and q[k+ 1] by replacing twith kin (4) and (5), respectively.
We grid each feasible flight zone, i.e., the state space, and
the position of the UAV at any slot is on a grid point of
the feasible flight zone. Thus, in each stage, the state space
is finite. Let pi[k]denote the i-th candidate for p[k]in Sk,
and pj[k+ 1] denote the j-th candidate for p[k+ 1] in Sk+1.
νij [k]and ωij [k]are the suitable values of the control inputs
ν[k]and ω[k], which allow the UAV to fly from pi[k]to
pj[k+ 1]. According to the definition of the function g(·,·,·),
the state transition cost from pi[k]to pj[k+ 1] is given by
g(pi[k], νij [k], ωij [k]). For illustration convenience, we define
ck
ij =g(pi[k], νij [k], ωij [k]). In the rest of this subsection,
we present the DP framework, and in the next subsection, we
detail how to compute νij[k]and ωij [k]for the transition from
pi[k]to pj[k+ 1].
As mentioned in Section II, not all states in a stage can
transit to any state in the next stage. Thus, if we cannot
find feasible values for ν[k]and ω[k], the corresponding state
transition cost is set as infinity, i.e., ck
ij =∞. For the cost
associated with the final stage N, we introduce a virtual final
state f. The final cost of a state in the final stage Nis cN
if = 0,
since we do not specify the final UAV position.
A local trajectory consists of N+ 1 states. Besides the
known initial state s, the rest of the Nstates are to be
selected from the predicted Nstate spaces. Let Jk(j)denote
the minimum cost of a segment of the local trajectory from
the initial state sto a state jin stage k+ 1. Then, the DP
algorithm takes the following form:
J0(j) = c0
sj , j ∈S1,(14)
Jk(j) = min
i∈Sk
{ck
ij +Jk−1(i)}, j ∈Sk+1,
∀k= 1, . . . , N −1.
(15)
Once JN−1has been addressed, the optimal cost is given by:
JN= min
i∈SN
{cN
if +JN−1(i)}.(16)
This is a forward DP algorithm. In stage 0, it records the
sub-trajectory cost from the initial state sto a state in stage
1. From stage k, the algorithm uses the already obtained
minimum sub-trajectory cost Jk−1to construct a new sub-
trajectory by adding a single state transition cost. This repeats
until all the states in stage N−1, i.e., JN−1(j), j ∈SN, are
evaluated. As the final cost is 0 for any state in the final stage,
(16) can be simplified by JN= mini∈SNJN−1(i). Now, we
can obtain the minimum cost of the optimal trajectory.
To construct the trajectory, we further need a standard back-
tracking algorithm [36]. Indeed, the predecessor position and
the linear speed of each minimum sub-trajectory cost Jk(j)
should be recorded accordingly. Given the initial heading angle
and the positions and linear speeds found by the backtracking
algorithm, the trajectory can be constructed for the UAV. An
illustrative example is provided in Fig. 4, where there are
three stages and each stage has two states. We calculate the
minimum cost from the initial state sto each state in a stage.
At each state in a stage, the state which is in the previous
stage and transits to the current state with the minimum cost
is recorded. For example, state 1 of stage 1 records state sof
stage 0, and state 1 of stage 2 records state 2 of stage 1. The
path incurring the minimum end-to-end cost is backtracked
by recursively selecting the preceding state associated with
6
Stage 0 Stage 1 Stage 2
Stored state s
Stored state s
Stored state 2
Stored state 1
Stored state 1
Stage 3
Fig. 4: An illustrative example of constructing the path.
the minimum cost from the final stage, i.e., f, till the initial
state s. In Fig. 4, the waypoints of the identified path are state
sof stage 0, state 2 of stage 1 and state 1 in stage 2.
Remark III.1. In general, N < bT
δc, i.e., the UAV can only
construct a trajectory based on the predictions of the target
locations for the next upcoming Nslots, instead of the whole
trajectory for the period of [0, T ]. When the predictions of the
target position are accurate, the UAV constructs the trajectory
every Nslots. However, when the measured target positions
are outside the predicted region, e.g., when the target turns
onto another road, the UAV reconstructs the trajectory using
the updated current position and the predictions based on the
current measurement.
C. Aeronautic Trajectory Refinement
In Section III-B, we propose the DP framework to construct
the UAV trajectory. In this subsection, we present a local
trajectory design method with the consideration of the UAV
kinematic model. In particular, we opt to determine ν[k]and
ω[k]such that the UAV can move from p[k]with the heading
angle θ[k]to p[k+ 1]. With ν[k]and ω[k],g(p[k], ν[k], ω[k])
in (13) can be computed.
There are various ways to design ν[k]and ω[k]. In this
paper, our design is that at p[k]the UAV starts to rotate at
the beginning of the slot (if necessary) with either Wmax or
−Wmax (we explain how to select it after Remark III.2) and
a linear speed ν[k]. When the UAV is at a position where its
heading is towards p[k+ 1], the UAV sets the angular speed
as zero. Such a position is a key point of the trajectory, and
as will be shown later it is a tangent point. Then, it moves
towards p[k+ 1] with the linear speed ν[k]along a straight
line. Thus, the UAV applies a constant linear speed ν[k]for the
whole slot and the maximum angular speed (either Wmax or
−Wmax) for part of the slot; see Fig. 5a. We will also explain
how to determine the linear speed ν[k]in the final part of this
subsection. This design simplifies not only the control of the
UAV but also the problem to find ν[k]and ω[k], because it
leads to a problem with only one variable, i.e., ν[k]. Under
such a design, the trajectory consists of an arc and a straight
line segment; see Fig. 5a. Note that if at p[k]the UAV is
heading towards p[k+ 1], there is no arc on the trajectory. It
is also worth pointing out that selecting the maximum angular
speed (either Wmax or −Wmax) leads to the shortest possible
trajectory. As shown in Fig. 5b, given p[k],θ[k]and p[k+ 1],
with the decreasing angular speed, the turning circle radius
𝑝[𝑘 + 1]
𝜃[𝑘]
𝑝[𝑘] X-axis
𝜎[𝑘]
(a)
𝜃[𝑘]
𝑝[𝑘]
𝑧[𝑘]
𝑝[𝑘 + 1]
𝑧[𝑘]
(b)
𝑝[𝑘 + 1]
𝜃[𝑘]
𝑧[𝑘]
𝑝[𝑘] 𝑐[𝑘]
𝑟[𝑘]
𝜌[k]
𝑛[𝑘]
X-axis
𝜏[𝑘]
(c)
Fig. 5: (a) UAV trajectories that can reach p[k+ 1] from p[k]
with heading angle θ[k]. (b) A larger angular speed results
in a shorter trajectory. (c) Notations to build up the relations
between ν[k]and the turning circle and the tangent line.
becomes larger and the trajectory becomes longer. For a UAV
modeled by (1), applying either Wmax or −Wmax results in
the minimum turning circle and the shortest trajectory.
Remark III.2. Despite its relevance to the popular Dubins car
model [37], this design is different in the sense that the linear
speed can be adjusted here, offering more flexibility than the
Dubins car model with a fixed linear speed. The adjustable
linear speed further leads to a variable turning radius, which
also differs from the fixed radius in the Dubins car model.
Now, we consider how to determine the turning direction,
i.e., the selection of Wmax or −Wmax. The UAV can either
turn right or left at p[k]. Then, there are two feasible turning
circles on both sides of the heading angle θ[k]; see Fig. 5a. As
there are two tangent lines from an outside point to the circle,
there exist four sets of trajectories to reach p[k+ 1]. Two of
them are not feasible since the headings at the end of the
arcs are not consistent with the corresponding tangent lines;
see Fig. 5a. Moreover, as one of our goals is to minimize
the length of the UAV trajectory, the UAV should choose a
direction such that the trajectory is shorter than that turning in
the other direction. Such a decision is easy to make: if p[k+1]
is on the left of the heading angle θ[k], the UAV makes a left
turn; otherwise, it makes a right turn. For example, in Fig.
5a, p[k+ 1] is on the right of the heading θ[k], thus the UAV
should turn right and follow the red trajectory.
To facilitate the description of this decision making, we
introduce some more symbols, and we demonstrate them in
Fig. 5. Let σ[k]∈[0,2π)denote the angle from the x-axis to
the vector −−−−−−−−→
p[k]p[k+ 1] in the counter-clockwise direction; see
Fig. 5a. Then, the angle from the heading θ[k]to the direction
of the vector −−−−−−−−→
p[k]p[k+ 1] in the counter-clockwise direction
is given by σ[k]−θ[k]∈(−2π, 2π). The UAV determines the
7
turning direction by the following rule:
no turn, if σ[k]−θ[k] = 0;
turn right, if σ[k]−θ[k]∈[−π, 0) ∪[π, 2π);
turn left, if σ[k]−θ[k]∈(−2π, −π)∪(0, π).
(17)
It is easy to show the correctness of (17). For a given
heading θ[k], if p[k+ 1] is on the left of θ[k], we can rotate
θ[k]by an angle σ[k]−θ[k]in the counter-clockwise direction
to get the direction σ[k]. Since we always wish to obtain a
shorter trajectory, the rotated angle should be smaller than π,
i.e., σ[k]−θ[k]∈(0, π). We can further subtract 2πon the
right to obtain σ[k]−θ[k]∈(−2π, −π). This is the last rule
in (17). The correctness of the second rule can be shown in
the similar way, where we need rotate θ[k]in the clockwise
direction. Note that when σ[k]−θ[k] = πor −π, turning left
results in the same trajectory length with turning right.
Below, we present how to compute the linear speed ν[k]
and the tangent point. ν[k]determines the turning radius
given the angular speed, and the tangent point determines
where the UAV stops turning. Let n[k]be a unit vector that
is perpendicular to the heading direction θ[k].n[k]can be
obtained by rotating θ[k]by π
2either clockwisely or counter-
clockwisely (depending on the UAV turning direction). Let
c[k]be the centre of the turning circle, and z[k]denote the
tangent point; see Fig. 5c. We further denote τ[k]as the angle
between the vectors −−−−→
c[k]p[k]and −−−−→
c[k]z[k]; see Fig. 5c. As the
turning circle centre c[k]is r[k](r[k] = ν[k]
Wmax ) away from
p[k]along the direction n[k],c[k]can be computed by:
c[k] = p[k] + ν[k]
Wmax
n[k].(18)
Since the tangent line −−−−−−−−→
z[k]p[k+ 1] is perpendicular to the
vector −−−−→
c[k]z[k], we have:
−−−−→
c[k]z[k]·−−−−−−−−→
z[k]p[k+ 1] = 0.(19)
With −−−−−−−−→
z[k]p[k+ 1] = −−−−−−−→
c[k]p[k+ 1] −−−−−→
c[k]z[k],r[k] = |−−−−→
c[k]z[k]|,
r[k] = ν[k]
Wmax and (18), we can obtain the following equations:
−−−−→
c[k]z[k]·(−−−−−−−→
c[k]p[k+ 1] −−−−−→
c[k]z[k]) = 0
⇒−−−−→
c[k]z[k]·−−−−−−−→
c[k]p[k+ 1] = |−−−−→
c[k]z[k]|2
⇒ |−−−−→
c[k]z[k]||−−−−−−−→
c[k]p[k+ 1]|cos ρ[k] = |−−−−→
c[k]z[k]|2
⇒cos ρ[k] = |−−−−→
c[k]z[k]|
|−−−−−−−→
c[k]p[k+ 1]|
=r[k]
|−−−−−−−→
c[k]p[k+ 1]|
⇒ρ[k] = arccos ν[k]
Wmax
|p[k+ 1] −c[k]|!
(20)
where |−→
· | is the length of a vector, and ρ[k]is the angle
between the vectors −−−−→
c[k]z[k]and −−−−−−−→
c[k]p[k+ 1]; see Fig. 5c.
Furthermore, we can rotate the unit vector of −−−−−−−→
c[k]p[k+ 1] by
the angle of ρ[k]in the counter-clockwise direction to obtain
the unit vector of −−−−→
c[k]z[k]:
−−−−→
c[k]z[k]
|−−−−→
c[k]z[k]|
=cos ρ[k]−sin ρ[k]
sin ρ[k] cos ρ[k]−−−−−−−→
c[k]p[k+ 1]
|−−−−−−−→
c[k]p[k+ 1]|
.(21)
With −−−−→
c[k]z[k] = z[k]−c[k],r[k] = |−−−−→
c[k]z[k]|,r[k] = ν[k]
Wmax
and (18), we obtain the expression for z[k]as follows:
z[k] = c[k] + ν[k]
Wmax cos ρ[k]−sin ρ[k]
sin ρ[k] cos ρ[k]×
p[k+ 1] −c[k]
|p[k+ 1] −c[k]|.
(22)
So far, we have derived the coordinates of the tangent point
z[k]as a function of ν[k](ρ[k]is already a function of ν[k]in
(20)). To find ν[k], we consider the following equation, which
requires the UAV to reach the point p[k+ 1] by the end of the
k-th slot at a constant speed ν[k]:
|
>
p[k]z[k]|+|−−−−−−−−→
z[k]p[k+ 1]|=δν[k],(23)
where |
>
p[k]z[k]|is the length of the arc
>
p[k]z[k]. Since τ[k]
is the angle between the vectors −n[k]and −−−−→
c[k]z[k], we have:
τ[k] = arccos −n[k]·−−−−→
c[k]z[k]
|−−−−→
c[k]z[k]|!(24)
With τ[k]in (24) and z[k]in (22), (23) can be re-written by:
τ[k]ν[k]
Wmax
+|p[k+ 1] −z[k]|=δν[k].(25)
As all the other notations can be presented as functions of
ν[k], (25) has only a single variable ν[k]. By solving (25), we
obtain the linear speed ν[k].
As mentioned, there are two tangent lines between a circle
and an outside point. However, the above method cannot
distinguish which one is feasible. Thus, we need to check
once z[k]is obtained by comparing the direction from z[k]
to p[k+ 1] and the direction when the UAV leaves the circle
at z[k]. If these two directions are the same, z[k]is feasible.
Otherwise, we need to replace ρ[k]in (21) with −ρ[k], which
gives another tangent point. This tangent point is feasible for
the UAV if the former is not.
For a brief summary, we have presented how to compute
ν[k]given p[k],θ[k]and p[k+ 1]. Once ν[k]is obtained, the
tangent point z[k]can be computed. The UAV follows the
following procedures to move:
1) applies the maximum angular speed of either −Wmax
or Wmax decided by (17) at p[k];
2) keeps turning until meeting z[k];
3) sets the angular speed as zero and then moves in a
straight line towards p[k+ 1].
With ν[k],g(p[k], ν[k], ω[k]) in (13) can be calculated, so
as the state transition cost. Then, the DP method presented
in Section III-B can be realized to construct trajectory for the
UAV. Since both the linear speed and the angular speed are
within their respective bounds, the constructed trajectory is
trackable by the UAV.
IV. SIMULATION RESULTS
We study the performance of the proposed method via
computer simulations using MATLAB. In this section, we
first demonstrate the performance of the proposed method
under different values of λ. Then, we investigate the impacts
8
-100 -50 0 50 100 150 200 250 300
X axis
-30
0
30
60
Y axis
(a) λ= 5.
-100 -50 0 50 100 150 200 250 300
X axis
-30
0
30
60
Y axis
(b) λ= 10.
-100 -50 0 50 100 150 200 250 300
X axis
-30
0
30
60
Y axis
(c) λ= 15.
Fig. 6: The UAV trajectories (red solid line) to monitor a target (blue dash line) for different values of λ(results of one off
simulations).
of several important factors, including target speed and road
conditions, on the proposed method. The system parameters
are set as follows: δ= 1 second, N= 5,η= 50,R1= 50
m, R2= 80 m, Vmax = 20 m/s, h= 40 m, Wmax = 1 rad/s,
µ=π
4,p[0] = [−60,0] and θ[0] = −π.
Following a given road, a target moves from left to right in
totally 90 slots (seconds), as shown in Fig. 6. We demonstrate
in Fig. 6 some trajectories for different weighting factors λ
ranging from 5 to 15. When λ= 5, the UAV moves slightly in
each slot; see Fig. 6a; while when λincreases, the movement
of the UAV becomes more significant; see Figs. 6b and 6c. TA-
BLE II summarizes the the average values of the linear speed,
the derivative of the UAV-target angle, and the derivative of the
UAV-target distance in these movements, which are consistent
with the trend shown in Fig. 6. The UAV-target distance
and angle are calculated based on (4) and (5), respectively.
The derivatives of the UAV-target distance and angle are the
differences between their respective values of two consecutive
slots, given the sampling time δ= 1. With the improvement
of the disguising performance by increasing λ, the cost is the
increased trajectory length (i.e., energy consumption). Since
the on-board battery is limited in capacity, it requires a careful
selection of λto balance these factors.
TABLE II: The average values of the linear speed ν(t), the
derivative of the UAV-target angle |˙α(t)|, and the derivative of
the UAV-target distance |˙
d(t)|, for the UAV movements under
different values of λ.
λ ν(t)|˙α(t)| | ˙
d(t)|
5 5.39 0.032 2.72
10 6.91 0.034 4.92
15 9.18 0.044 7.06
We have conducted other simulations to derive some in-
sights of the proposed method. Specifically, we have a look
at how the movement of the target influences the movement
of the UAV. Without loss of generality, we keep λ= 10.
Similar results can be obtained for other values of λ. We first
consider the speed of the target. On the same road as the above
simulations, the target now finishes the movement in totally
120 or 60 slots. The trajectories are shown in the first row of
Fig. 7. The trajectory when the UAV finishes the movement
in 90 slots is shown here again for comparison. The average
values of the disguising performance and the linear speed are
shown in Figs. 8a and 8b. From these trajectories and the
average values of the considered metrics, we can see that with
the increase of the target speed (i.e., decreasing the number
of slots to finish the movement), the UAV’s average linear
speed increases, since it needs to guarantee the view of the
target. Accordingly, the average derivatives of the UAV-target
angle and distance increase as well. Thus, a fast speed of the
target helps the UAV to disguise, because the UAV can adjust
its trajectory easily to change the relative angle and distance
between itself and the target. This is different from what we
typically think, i.e., the faster the target is, the less likely it
would be tracked.
Another interesting point influencing the method perfor-
mance is road condition. In addition to the road simulated
above, we create two other roads as shown in the second and
third rows of Fig. 7. They exhibit higher curvature than the
first road. We simulate them under different numbers of slots
to finish the movement. Correspondingly, the average values
of the considered metrics are shown in Figs. 8a and 8b. We
see that under the same target speed and the weighting factor
λ, the curvier the road is, the better disguising performance
and the larger speed the proposed scheme provides. For the
linear speed, as the target changes its heading angle more
significantly on a curvier road, the feasible flight zone moves
significantly as well. To make sure to have the target in its
view, the UAV needs to fly faster. Also, the target heading
(i.e., φ) relates to the UAV-target angle. Thus, a significant
change of the target heading (i.e., a larger derivative of the
target heading) can help increase the derivative of the UAV-
target angle; see (5).
For a brief summary, both a larger target speed and moving
on a curvier road help the UAV disguise its intention. If
the target moves slowly on a flat road, the weighting factor
λshould be carefully selected by taking into account the
expected disguising performance and the battery capacity.
To the best of our knowledge, the problem studied in this
paper is novel and has never been studied in the literature. To
demonstrate the effectiveness of the proposed approach, we
consider a random trajectory generation method as the bench-
mark for comparison purpose. Specifically, the benchmark
method randomly selects a way-point from each state space,
then the proposed trajectory refinement method is applied to
smoothly connect the way-points. We conduct 100 indepen-
dent simulations of the benchmark method under each of the
configurations considered in Fig. 7, and the average results of
different metrics are presented in Fig. 8. Fig. 7 plots the repre-
sentative trajectories produced by the proposed algorithm and
the random benchmark under different configurations. In Fig.
8, we see that the proposed method and the random method
achieve comparable disguising performances. The advantage
9
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X axis
-50
0
50
100
Y axis
Random
(a) Road 1, 120 slots
-100 -50 0 50 100 150 200 250 300
X axis
-50
0
50
100
Y axis
Random
(b) Road 1, 90 slots
-100 -50 0 50 100 150 200 250 300
X axis
-50
0
50
100
Y axis
Random
(c) Road 1, 60 slots
-100 -50 0 50 100 150 200 250 300
X axis
-50
0
50
100
Y axis
Random
(d) Road 2, 120 slots
-100 -50 0 50 100 150 200 250 300
X axis
-50
0
50
100
Y axis
Random
(e) Road 2, 90 slots
-100 -50 0 50 100 150 200 250 300
X axis
-50
0
50
100
Y axis
Random
(f) Road 2, 60 slots
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X axis
-50
0
50
100
Y axis
Random
(g) Road 3, 120 slots
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X axis
-50
0
50
100
Y axis
Random
(h) Road 3, 90 slots
-100 -50 0 50 100 150 200 250 300
X axis
-50
0
50
100
Y axis
Random
(i) Road 3, 60 slots
Fig. 7: UAV trajectories by the proposed approach (in red) and a random benchmark method (in green) when the target moves
on different roads in different speeds (results of one off simulations).
Road 1 Road 2 Road 3
6.5
7
7.5
8
8.5
Disguising performance
Proposed
Random
60 slots
90 slots
120 slots
(a)
Road 1 Road 2 Road 3
7
8
9
10
11
Average linear speed (m/s)
60 slots
90 slots
Proposed
Random
120 slots
(b)
Road 2 Road 3
-75
-70
-65
-60
-55
Objective function value
90 slots
60 slots
120 slots
Proposed
Random
(c)
Fig. 8: Comparison of the proposed method and the benchmark method (average results over 100 independent simulations).
of the proposed method to the random method is that the
average linear speed is lower in the proposed method than it is
in the random method; see Fig. 8a. As a result, the proposed
method leads to smaller values of the objective function; see
Fig. 8b. As the parameter λis selected to be relatively larger,
the disguising performance is given priority in the trajectory
generation process. To reflect realistic surveillance mission
considerations, we have also conducted simulations in which
the target moves on some other hand-crafted roads where the
target makes large turns. The trajectories of the UAV and
the results of linear speed and the derivatives of the UAV-
target distance and angle are presented in Figs. 9 and 10.
Moreover, we conduct simulations where the target moves on
real roads. In the case shown in Fig. 11, the target does not
follow a straight road. Instead, it moves onto another road at
an intersection. We can see that the UAV’s speed, angle and
distance change in the same way when the target is turning as
they do when the target is moving along a straight line. As a
result, the UAV can achieve consistent disguise performances
throughout a surveillance mission, even when the target turns
and changes roads.
Finally, the proposed algorithm is implemented and tested
on a UAV simulator, CoppeliaSim. The UAV in the Cop-
peliaSim simulation is controlled by MATLAB via an already
built API (see Fig. 12). A target moves along a road, part of
which is on a hill; see the black curve Fig. 13. The highest
elevation of the road on the hill is 5m. The UAV trajectory
is indicated by the pink curve in Fig. 13, where we consider
two cases. In the first case, the altitude of the UAV remains
unchanged with respect to the sea level; and in the second case,
the altitude (i.e., the z-coordinate of the UAV) is adjusted so
that the UAV can maintain its vertical distance to the target.
The movements of the UAV and the target in the simulation are
recorded in a video; see https://youtu.be/4zA8SPgE2Ec. We
present the results of |˙
d(t)|and |˙α(t)|of these two trajectories
in Fig. 14. As seen in Fig. 14a, the adjustment of the z-
coordinate of the UAV adapting to the hilly terrain has little
impact on the change of the relative UAV-target distance,
i.e., |˙
d(t)|. The impact is non-negligible on the change of
the relative UAV-target angle |˙α(t)|, see Fig. 14b. It is worth
10
0 50 100
X axis (m)
-100
-80
-60
-40
-20
0
Y axis (m)
Target
UAV
(a)
0 20 40 60 80 100 120
Time slot
2.5
3
3.5
4
4.5
(b)
0 20 40 60 80 100 120
Time slot
0
0.5
1
1.5
2
2.5
3
3.5
(c)
0 20 40 60 80 100 120
Time slot
0
0.01
0.02
0.03
0.04
0.05
0.06
(d)
Fig. 9: Simulation where the target moves along Road 4.
(a) Trajectories. (b) Linear speed. (c) Derivative of relative
distance. (d) Derivative of relative angle.
-50 0 50 100 150
X axis (m)
-150
-100
-50
0
Y axis (m)
Target
UAV
(a)
0 20 40 60 80 100 120
Time slot
1
2
3
4
5
6
7
(b)
0 20 40 60 80 100 120
Time slot
0
0.5
1
1.5
2
2.5
3
(c)
0 20 40 60 80 100 120
Time slot
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
(d)
Fig. 10: Simulation where the target moves along Road 5.
(a) Trajectories. (b) Linear speed. (c) Derivative of relative
distance. (d) Derivative of relative angle.
pointing out that in this simulation, the altitude of the target
on the path is relatively small. As the altitude of the target on
the path rises, the adjustment of the UAV’s z-coordinate (to
maintain the vertical distance to the target) can be increasingly
important to the disguising performance.
V. CONCLUSION
This paper considered the application of a UAV for covert
video surveillance of a mobile ground target. Different from
the widely studied target tracking, the UAV carrying out covert
video surveillance disguises its intention by changing the
100 200 300 400 500 600 700 800
X axis (m)
100
200
300
400
Y axis (m)
Target
UAV
(a)
0 20 40 60 80 100 120
Time slot
6
8
10
12
(b)
0 20 40 60 80 100 120
Time slot
0
2
4
6
8
10
(c)
0 20 40 60 80 100 120
Time slot
0
0.05
0.1
0.15
0.2
0.25
0.3
(d)
Fig. 11: Simulation where the target moves along real roads.
(a) Trajectories. (b) Linear speed. (c) Derivative of relative
distance. (d) Derivative of relative angle.
MATLAB
CoppeliaSim
Optimization
algorithm Target
UAV
Trajectory
Position
API
API
Fig. 12: The interaction between the optimization algorithm
in MATLAB and the simulation in CoppeliaSim.
relative UAV-target angle and distance as frequently and dras-
tically as possible. We proposed a new metric to quantify the
disguising performance, which involves both the derivatives
of the UAV-target angle and distance. We formulated a new
multi-objective UAV trajectory optimization problem, which
minimizes the energy consumption and maximizes the disguis-
ing performance, subject to the aeronautic maneuverability of
the UAV and the presence of the target in the UAV’s view.
A DP-based framework was presented to solve the problem
and construct the trajectory online for the UAV. Control rules
were specified to comply with the aeronautic maneuverability
of the UAV. Computer simulations demonstrate how the UAV
moves guided by our method. In the future, we plan conduct
11
Fig. 13: Simulation in CoppeliaSim. The movements of
the UAV and the target in the simulation are recorded in
https://youtu.be/4zA8SPgE2Ec.
0 30 60 90
Time slot
2
3
4
5
6
No hills
With hills
(a)
0 30 60 90
Time slot
0
0.01
0.02
0.03
0.04
0.05
No hills
With hills
(b)
Fig. 14: The absolute values of the derivative of UAV-target
distance and UAV-target angle.
field experiments to verify the effectiveness of the proposed
method. The current result will be extended to the more
complex UAV models. Target prediction inaccuracy will be
taken into account to make the method robust. We will also
extend our algorithm to the more complex system settings with
multiple UAVs and multiple targets.
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Hailong Huang was born in China in 1988. He
received the B.Sc. degree in automation, from China
University of Petroleum, Beijing, China, in 2012,
and received Ph.D degree in Systems and Control
from the University of New South Wales, Sydney,
Australia, in 2018. He is a research associate at
the School of Electrical Engineering and Telecom-
munications, University of New South Wales, Syd-
ney, Australia. His current research interests include
wireless sensor networks, networking protocols, and
guidance, navigation, and control of mobile robots.
Andrey V. Savkin was born in 1965 in Norilsk,
Russia. He received the M.S. and Ph.D. degrees in
mathematics from the Leningrad State University,
Saint Petersburg, Russia, in 1987 and 1991, respec-
tively. From 1987 to 1992, he was with the Tele-
vision Research Institute, Leningrad, Russia. From
1992 to 1994, he held a Postdoctoral position in
the Department of Electrical Engineering, Australian
Defence Force Academy, Canberra. From 1994 to
1996, he was a Research Fellow in the Department
of Electrical and Electronic Engineering and the
Cooperative Research Centre for Sensor Signal and Information Processing,
University of Melbourne, Australia. From 1996 to 2000, he was a Senior
Lecturer, and then an Associate Professor in the Department of Electrical
and Electronic Engineering, University of Western Australia, Perth. Since
2000, he has been a Professor in the School of Electrical Engineering
and Telecommunications, University of New South Wales, Sydney, NSW,
Australia. His current research interests include robust control and state esti-
mation, hybrid dynamical systems, guidance, navigation and control of mobile
robots, applications of control and signal processing in biomedical engineering
and medicine. He has authored/coauthored seven research monographs and
numerous journal and conference papers on these topics. Prof. Savkin has
served as an Associate Editor for several international journals.
Wei Ni M’09-SM’15) received the B.E. and Ph.D.
degrees in Electronic Engineering from Fudan Uni-
versity, Shanghai, China, in 2000 and 2005, respec-
tively. Currently, he is a Group Leader and Principal
Research Scientist at CSIRO, Sydney, Australia, and
an Adjunct Professor at the University of Technol-
ogy Sydney and Honorary Professor at Macquarie
University, Sydney. He was a Postdoctoral Research
Fellow at Shanghai Jiaotong University from 2005
– 2008; Deputy Project Manager at the Bell Labs,
Alcatel/Alcatel-Lucent from 2005 to 2008; and Se-
nior Researcher at Devices R&D, Nokia from 2008 to 2009. His research
interests include signal processing, stochastic optimization, learning, as well
as their applications to network efficiency and integrity.
Dr Ni is the Chair of IEEE Vehicular Technology Society (VTS) New South
Wales (NSW) Chapter since 2020 and an Editor of IEEE Transactions on
Wireless Communications since 2018. He served first the Secretary and then
Vice-Chair of IEEE NSW VTS Chapter from 2015 to 2019, Track Chair for
VTC-Spring 2017, Track Co-chair for IEEE VTC-Spring 2016, Publication
Chair for BodyNet 2015, and Student Travel Grant Chair for WPMC 2014.
