IET Control Theory & Applications
Research Article
Switching formation strategy with the directed
dynamic topology for collision avoidance of a
multi-robot system in uncertain environments
ISSN 1751-8644
Received on 22nd April 2020
Revised 23rd July 2020
Accepted on 25th August 2020
E-First on 16th October 2020
doi: 10.1049/iet-cta.2020.0502
www.ietdl.org
Vu Phi Tran1 , Matthew A. Garratt1, Ian R. Petersen2
1School
of Engineering and Information Technology, University of New South Wales, Canberra, Australia
School of Electrical, Energy and Materials Engineering, The Australian National University, Canberra ACT 2601, Australia
E-mail: phivus2@gmail.com
2Research
Abstract: This paper tackles the distributed leader–follower cooperative control problem for networked heterogeneous
unmanned aerial vehicle–unmanned ground vehicle (UAV-UGV) systems in unknown environments requiring formation keeping,
obstacle avoidance, inter-robot collision avoidance, and reliable robot communications. To adopt various formations, we design
a novel negative imaginary (NI) switching formation protocol with a directed dynamic topology. To prevent an inter-mobile robot
collision, a new method to formulate the virtual propulsive force between robots is employed. To avoid unexpected obstacles, a
new obstacle avoidance technique that allows the UGVs' formation to change its shape and the UGVs' roles is developed. To
determine each UGV robot's order in obstacle avoidance formation, a quadrotor UAV, controlled by a strictly negative imaginary
controller involving good wind resistance characteristics, tracks the center of formation shape to guarantee the maintaining
visibility for multi-robot systems on the ground. The proposed control system's efficacy is investigated through a rigorously
comparative study with other control techniques, namely, the performance of artificial potential field and an NI obstacle
avoidance strategy using the switching formation control method without switching topology. Finally, we also conduct a stability
analysis of the closed-loop control system using the NI-systems theory.
1
Introduction
Cooperative control for multi-robot systems, including
synchronisation and consensus [1, 2], swarming and flocking [3,
4], region-following formation control [5, 6], has attracted
considerable research attention, with many works in science and
engineering. The research interest has mainly arisen from the fact
that networked systems under cooperative control can perform
complex tasks more effectively than a group of individually
operating robots, especially in surveillance, target tracking, selflocalisation and mapping, and disaster response. As a result, a large
number of cooperative control strategies have been presented and
analysed from various viewpoints and purposes [7, 8]. It is pointed
out in [9] that there are three fundamental approaches for formation
control of multi-vehicles: virtual leader, virtual structure and
behaviour, and leader–follower (L–F). Due to its simplicity and
effectiveness in practical applications, the L–F approach is
preferred by researchers [10–14].
Based on the L–F platform, a wide variety of formation control
strategies have also been developed for multi-agent systems. It is
widely admitted that the consensus-based formation control has
recently become a critical issue in the context of cooperative
control due to its potential engineering applications. A large body
of the control methods can be found in the literature, ranging from
scale-variant formation patterns [15–17] to time-varying dynamic
spatial shapes [7, 8, 18–20]. The main idea behind the shape
control strategies is to regulate a group of robots to form and
maintain a given formation throughout robot–robot interaction.
Although many formation strategies were proposed and
implemented successfully for multi-agent systems, almost all
previous studies [7, 18, 20–22] were mainly concentrated on agents
formulated by single or double integrator dynamics. Unfortunately,
the position and velocity tracking loops for unmanned vehicles
usually need to be represented by higher order transfer functions
[23, 24]. In addition, those approaches are all based on global
position measurements, making them impractical for situations
where only local state measurements may be accessed. For
example, GPS interference caused by urban canyon effects may
occur when larger groups of coordinating robots are requested to
IET Control Theory Appl., 2020, Vol. 14 Iss. 18, pp. 2948-2959
© The Institution of Engineering and Technology 2020
explore a small and tiny area. As a consequence, there is a strong
demand for a precise geometric formation of high-order systems
based on the relative positions among robots. However, until now,
only some previously published papers have reported solutions to
these existing formation control problems [16, 25, 26] by making
use of adaptive or negative imaginary (NI) consensus techniques.
Moreover, collision avoidance in unknown environments,
which is another important issue in the motion control and path
planning of multi-agent systems, has not been paid sufficient
attention. Obstacle and inter-robot collision avoidance has direct
impact on system safety, and therefore it should hold the highest
priority among all the objectives. In the obstacle avoidance
scenario, a common approach is to formulate the new desired
distances or bearing angles for the robots. As a result, it indirectly
formalises and switches a specified formation shape to a safe one.
In [27], the robots always produce a queuing formation for obstacle
avoidance. However, this strategy actually wastes energy and it is
overly time consuming while moving the robots into a line once a
potential collision is predicted. In [11, 12, 28], a collision-free waypoint is determined based on the geometric obstacle avoidance
control method (GOACM). Although the demonstrations on real
robots were conducted successfully, this approach would not work
with complex-shaped obstacles. Furthermore, the performance of
these obstacle avoidance techniques will be impossible if the space
between obstacles only fits one robot at a time. In this case, the
robots should be capable of switching into a column-line
formation, in which robots move one after another, while
simultaneously avoiding collision with other agents. As a
consequence, there is a strong demand for switching into a queuing
formation with collision avoidance for networked systems. Until
now, only formation control with collision avoidance as in [16] can
be developed further to partially solve this problem. Nevertheless,
if the centre point of this gap to one of the followers is closer to the
current leader, robot trajectories produced by this strategy through
a fixed-leader topology can be lengthened or may have more
oscillations than those made with an appropriate L–F role
switching.
For collision avoidance problem between vehicles, there is a
great number of suggested techniques. The work demonstrated in
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[29] is an example of inter-vehicle collision avoidance, where
collision avoidance is formalised as the problem of avoiding a bad
set of two-vehicle states using a brake and throttle velocity control
function. Although real-time experiments were conducted
successfully and it could be seen that a possible collision between
two vehicles is prevented, this method still needs to be extended to
crashes involving more than two vehicles. A potential field method
was used in [16, 30] to achieve inter-unmanned aerial vehicle
(UAV) collision avoidance using a virtual repulsive force derived
from the negative gradient of a potential function. The force
calculating method may cause oscillations in the trajectory or even
getting stuck due to local minima [31]. These observations have
inspired us to conduct the research work presented in this paper.
Based on the above arguments, we develop a novel NI
formation control with a dynamic L–F approach since the NI
cooperative framework has enormous potential for further
development. A distributed output feedback consensus law for a
network of strictly negative imaginary (SNI) systems has been
firstly presented in [17]. The objective of this theory is to achieve
the convergence of all SNI agent's outputs to a pre-defined constant
reference. We have adapted this approach to converge to a desired
formation pattern in our previous work [26, 32]. Real-time tests
with this theory show a strong consensus between networked robot
systems as well as a potential obstacle capability. However, the
obstacle avoidance based on the switching formation strategy with
a dynamic topology for a multi-robot system has not yet been
considered using the NI theory. It is assumed in [33] that
cooperative control problems with dynamic topologies for multirobot systems are much complicated and challenging than the fixed
cases. To the best of our knowledge, very little work has focused
on optimal L–F strategies for mobile robots. Despite these
shortcomings, the current NI technique can be improved to address
some problems of formation control with collision avoidance for
networked SNI systems interacting on directed network topologies.
For example, in order to switch into an obstacle avoidance
formation, the relative positions in a specified formation are
changed gradually based on the NI consensus-based formation
tracking controller and a novel geometric method, so that
oscillations/disturbances in the obstacle avoidance trajectories are
avoided, which is one of the main obstacles in [16, 30]. Next, the
NI formation control strategy can be easily connected to the other
NI control protocols while the internal stability and synchronous
characteristic of the fully distributed control structure are still
naturally guaranteed. Based on this characteristic of NI control
theory, an NI inter-robot collision avoidance approach can be
designed. Furthermore, the methods for dealing with the fixed
topology cases can be easily extended to the switching topology
cases without any constraints. Consequently, shorter and smoother
trajectories can be generated. Finally, using NI techniques also
opens up an excellent opportunity to control the consensus between
high-order systems.
Compared to the previous relevant results, the contributions of
this study are listed as follows:
• We are the first to present a novel NI robot–robot and robot–
obstacle collision avoidance strategy based on the NI formation
controller and a multi-robot order switching method for networked
NI L–F non-homogeneous complex multi-vehicles in a distributed
way while moving in hazardous environments through the dynamic
information exchange among agents. Using this new technique,
mobile robots are required not only to change their orders within
the L–F architecture but also to shift their positions to generate a
queuing pattern. Furthermore, the proposed control approach can
be perfectly combined with our previous works in [32] to generate
a comprehensive collision avoidance method in any circumstances
while maintaining the robots' given formation and reaching the
goal.
• We propose a new way of determining the magnitude and
direction of the repulsive force, using the region of intersection
between virtual circles surrounding the robots to escape local
minima and oscillation problems, which is a drawback of the
artificial potential field (APF) control theory [31, 34].
IET Control Theory Appl., 2020, Vol. 14 Iss. 18, pp. 2948-2959
© The Institution of Engineering and Technology 2020
• We conduct a stability analysis of the proposed control system
based on the internal stability of SNI agents and SNI consensus
controllers with their communication links.
• We evaluate the efficacy of the proposed NI control system, not
only in the form of numerical simulations but also in real robot
experiments in the absence or presence of exogenous disturbances
(e.g. wind gusts). Moreover, we also provide a rigorously
comparative study on the performance of our obstacle avoidance
theory with respect to that of the conventional APF controller and
the fixed-leader NI obstacle avoidance approach.
The remainder of this paper is organised as follows.
Preliminaries on NI formation architecture and graph theory are
given in Section 2. Dynamics for UAVs and unmanned ground
vehicles (UGVs) are proposed in Section 3. The obstacle and intercollision avoidance using NI theory is analysed and designed in
Section 4. The stability of the whole structure is verified in Section
5. The simulation results for the proposed approaches are
illustrated in Section 6, followed by the experiment results in
Section 7. Conclusions are drawn in Section 8.
2 Preliminaries on graph theory and negative
imaginary formation control theory
2.1 Graph theory
Graph theory can be used to mathematically describe the interagent interaction processes among the unmanned robots. Each
robot is represented as a vertex. Given a directed graph G = (ϑ, ε)
with N vertices and L edges (N × L matrix), such that ϑ = (ν1,
ν2, …, νN ) and ε ⊆ {(νi, ν j): νi, ν j ∈ ϑ, νi ≠ ν j} representing the finite
vertexes set and the ordered edges set, respectively, the robot
communication matrices are given as follows.
2.1.1 Incidence matrix: Suppose that each edge of G is assigned
an orientation, which is arbitrary but fixed. The vertex-edge
incidence matrix of G, denoted by Qin, is an N × L matrix defined
as follows:
Qini j = 1
if νi is the head of edge eνi, ν j,
Qin = Qini j = − 1 if νi is the tail of edge eνi, ν j,
Qini j = 0
if νi is not connected to eνi, ν j .
(1)
It is pointed out that the incidence matrix has a column sum
which equals to zero, which is assumed from the fact that every
edge must have exactly one head and one tail. Extending this graph
theory, given an arbitrary oriented set of the edge ε, the graph
Laplacian, ℒ(G), is defined as ℒ(G)=Qin(G)Qin(G)T.
For convenience in interpreting further the UAV–UGV/UGVs
cooperative theory, some mathematical communication graph
matrices are newly introduced.
2.1.2 Consensus matrix: Let the N×L matrix Qco represent a
consensus matrix which corresponds to a graph (ϑco, εco) that has N
vertexes and L edges is the number of communication orientations.
This N×L matrix indicates which robot at vertex vi in ϑco will send
its consensus information to the adjacent vertexes v j in εco.
Qcoi j = 0
if νi is the head of eνi, ν j for
consensus,
Qco = Qcoi j = − 1 if νi is the tail of eνi, ν j for
consensus,
Qcoi j = 0
otherwise.
(2)
2.1.3 Reference matrix: The reference matrix Qre ∈ ℝN × 1
introduces the node or the UAV/UGV in a collaborative group
which will directly follow the reference trajectories
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Qrei j = 1 if νi directly follows the reference
path,
Qre =
Qrei j = 0 if νi does not directly follow the
reference path.
y = diagi3N= 1P(s)u,
(3)
2.2 SNI systems theory
Let us first recall the definitions of SNI and NI systems.
Definition 1: In the single input/single output case, a transfer
function P(s) becomes SNI if all its poles have negative real parts
and its Nyquist plot is contained below the real axis. According to
[35], this definition can be mathematically defined as follows: P(s)
∈ SNI if j[P(jω) −P∗(jω)] > 0 for all ω > 0 [35].
Definition 2: A transfer function P(s) has NI property if its
Nyquist plot for ω ⩾ 0 is contained in the lower half of the
complex plane. This Nyquist plot can touch, but not cross the real
axis; i.e. P(s) ∈ NI if j(P(jω) −P∗(jω)) ⩾0 [35].
Lemma 1: A positive connection between an NI system and an
SNI system results in an SNI systems structure [35].
After an SNI/NI plant is found, Petersen and Lanzon [35] stated
that a necessary and sufficient condition for the internal stability of
a positive feedback interconnection between an SNI plant N(s) and
an SNI/NI controller M(s) is provided as follows:
λmax(M(0)N(0)) < 1,
(4)
where λmax( . ) denotes the maximum eigenvalue of transfer
functions.
Developed from the consensus approach of MIMO NI systems
[17], an NI-systems formation implementation was successfully
designed and tested for multi-UAV models in our previous work
[26]. In the paper, a new reference matrix Qre, consensus matrix
Qco, and the offset distance terms (X f , Y f ) between UAVs are added
into the original consensus structure to solve the existing formation
control problems as presented in Fig. 1. The major experimental
results verify that the formation pattern generated by UAVs is
maintained during their rectangular movements. The overall
equation of this architecture is given as
pr = 1N ⊗ r,
(5)
er = y + pr,
(6)
ȳ = (QT ⊗ Im)er = ([Qin Qre]T ⊗ Im)er,
(7)
e f = ȳ + p f ,
(8)
u = (Q ⊗ Im)diagi3N= 1K(s)e f
= ([Qco Qre] ⊗ Im)diagiN= 1K(s)e f ,
(9)
(10)
where N, m, and l represent the number of agents, the maximum
output number of each agents, and the number of edges in the
information graph. r ∈ ℝ2 × 1 denotes the reference position on the
plane of the master, pr ∈ ℝ2n × 1 is the reference, and p f corresponds
to the relative position between the slave UAVs and the master
UAV in the configured formation. u ∈ ℝm × 1 is the velocity set
point input of each UAV on the x and y axes while the output
y ∈ ℝm × 1 is the current position of each UAV. u ∈ ℝlm × 1 and
y ∈ ℝlm × 1 are the input and output of overall network plant. er is
the error between the desired position of the master and its current
position, while e f is the error between the desired relative position
and the current relative position of each UAV. K(s) ∈ ℝlm × lm is the
group of SNI consensus and tracking controllers for the group of
UAVs, and Q, Qin, Qco, and Qro are the general communication,
incidence, consensus, and reference matrix of agents, respectively.
Equation (7) is similar to a distributed consensus structure for
agent i
ui =
3N
∑ ai jdiagi N K(s)(yi − y j),
j=1
3
=1
(11)
where ai j is the element of the adjacent matrix, j is the index of
neighbouring vertex connecting to vertex i.
It also implies that [Ps, K s] is internally stable if and only if the
following condition in Lemma 2 is held.
Lemma 2: Given any SNI MIMO system P(s) and NI/SNI
MIMO controller K(s), a stability result for the whole structure is
obtained as follows [17]:
λmax(P(0))λmax(K(0)) <
1
1
=
,
λmax(ℒ) λmax(QQT)
(12)
1
.
(13)
λmax(QQT) × λmax(K(0)))
where λmax is the maximum eigenvalue.
As can be seen from experimental results in [26], the
performance of the two UAVs is satisfactory. The follower can
imitate the behaviour of the master when following the rectangular
trajectory. This result shows that our SNI consensus-based
formation controller is able to work effectively with high-order
systems such as UAV, which is in contrast to most existing
algorithms analysed for single or double integrator linear dynamics
[7, 18, 20]. To strengthen our argument, the convergence analysis
of consensus in our former NI consensus-based formation control
method [26] is validated through its direct application, called
rendezvous problem. In this test, the UAV plants discussed in
Section 3 are employed with the initial positions in the three axis
being [54;−80;0], [75;75;0], [−18; − 90;0], [8;−96;0],
λmax(P(0)) <
Fig. 1 NI formation control protocol for multi-UAVs
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IET Control Theory Appl., 2020, Vol. 14 Iss. 18, pp. 2948-2959
© The Institution of Engineering and Technology 2020
Fig. 2 Communication graph for four drones
system as presented in Definition 1. The AR Drone responds to
attitude commands sent from the ground station (GS) over WiFi.
Meanwhile, the UGV receives the yaw rate and speed commands
from the GS. During flight tests, to capture the overall dynamic
behaviour of the drone, a sinusoidal wave, in which the frequency
varies from 0 to 20 Hz and the maximum amplitude is at 0.5 m/s, is
used as the velocity setpoints for the quadcopter along three axes.
Moreover, we linearise the non-linear dynamics of our UGVs and
UAV along its x, y, and z axes, and represent its behaviours in the
form of transfer functions, valid within the normal operating points
of the system where the linear model is still sufficiently accurate.
Using the input and output data obtained from the Vicon MCS,
we derived the transfer functions for the AR Drone and the UGV
via parametric identification by means of several identification
methods available in the System Identification Toolbox of
MATLAB, e.g. autoregressive with extra input model which has
the standard form as follows [36, 37]:
A(z)y(k) = B(z)u(k − d) + e(k),
Fig. 3 (top) 3D robust rendezvous of four SNI UAV systems via the NI
consensus-based formation protocol, and (bottom) relative position errors
of four UAV
(14)
where (u(k),y(k)) are the system input and its output response, d is
the system delay, k is the present time, and e(k) is the disturbance
in the system.
The quality of the created model is then evaluated through the
fitting percentage formula between identified model output and
measured real one. The evaluating equation is given as
f it% = (1 −
∥ y − y~ ∥
)100% .
∥ y − mean(y) ∥
(15)
3.1 SNI closed-loop transfer function models for a UAV
Fig. 4 Nyquist plots of two velocity control loops for the UAV
respectively. The relative position of each agent p f = [0; 0; 0] and
the pre-defined rendezvous point pr is [−60;40;70]. All SNI
consensus controllers along three directions are indicated as
[(−(s + 300))/(s + 2); (−(s + 270))/(s + 2); (−(s + 11))/(s + 2)].
The communication graph is exactly the same as Fig. 2 and the
reference only sends information to the drone master, which gives
Qin = [1 1 1 1; − 1 0 0 0; 0 − 1 0 0; 0 0 − 1 0; 0 0 0 ,
− 1]T
and
Qre = [1; 0; 0; 0]T,
Qco = [0 0 0 0; − 1 0 0 0; 0 − 1 0 0; 0 0 − 1 0; 0 0 0 .
− 1]T
It can be seen from Fig. 3 that robust rendezvous is then
guaranteed via the NI cooperative tracking controller. Four drones
with the control of our proposed strategy are driven from the initial
positions to the final rendezvous point within 7 s. However, it is
noted that a collision among four UAVs will really happen since all
aerial vehicles fly to one rendezvous point. Thus, p f should be
assigned the proper values based on a given formation.
Additionally, as can be seen in Fig. 3, the position output y
3×N
∈ ℝ12 × 1 achieves consensus (∑ j = 1 yi = y j) when y → 0 ∈ ℝ12 × 1.
This equation converts the output consensus problem to an
equivalent internal stability one as presented in Lemma 2, which
does not take into account that the communication topology is
fixed or switched. Moreover, the formation switch only takes place
two times, slowly changing from the current formation to the
queuing one and vice versa. Two significant assumptions yield the
ability to demonstrate the stability of our distributed NI consensusbased formation control approach subjected to switching
interaction using Lemma 2.
3
SNI UAV/UGV dynamic models
Proportional–integral–derivative controllers were applied with
properly tuned values via the Ziegler-Nichols method to help our
systems not only to stabilise the inner velocity control loops but
also to satisfy the necessary and sufficient conditions for an SNI
IET Control Theory Appl., 2020, Vol. 14 Iss. 18, pp. 2948-2959
© The Institution of Engineering and Technology 2020
The transfer function of the X-axis loop is given from the system
identification as follows:
−0.62s3 − 866.3s2 + 3156.3s + 39427.5
x(s)
= 4
,
3
2
ẋ(s) s + 31s + 53425.15s + 17296.3s + 1093.7
~
(16)
~
where ẋ and x highlight the actual position on the x-axis and its
desired velocity value. The vertical model in (16) has damping
factors of ζ1, 2 = [−1 1], τ1, 2 = [−119 0.443] s, and natural
frequencies of ω1, 2 = [0.00841 2.26] rad/s.
The transfer function of the Y -axis loop can be elaborated as
follows:
−1.71s3 + 249.1s2 − 66651.5s + 68465.9
y(s)
= 4
,
3
2
ẏ(s) s + 78.9s + 58525.8s + 50869.1s + 970.08
~
(17)
~
where ẏ and y denote the actual position on the y-axis and its
desired velocity value. The horizontal model in (17) gives ζ1, 2, 3, 4 =
[1 1 0.161 0.161], τ1, 2, 3, 4 = [51.3 1.18 0.0256 0.0256] s, and ω1, 2, 3, 4
= [0.0195 0.851 242 242] rad/s.
Overall, our transfer functions in (16) and (17) demonstrate a
reasonably good accuracy of around 99% between the modelling
and real-flight data, meaning that they can be used to entirely
describe the dynamic behaviours of our robot systems. On the other
hand, as seen in Fig. 4, all mathematical models found satisfy the
criteria of SNI systems.
3.2 SNI closed-loop transfer function models for a UGV
There are two control input signals for the UGV: yaw rate and
speed. While the translational velocities set-point on the x and y
axes drives the UGV towards target point, these inputs need to be
converted into yaw rate and speed command references. We first
achieve this using a yaw control loop based on an SNI controller.
The desired yaw angle ψ sp is determined from the desired
translational velocities as follows:
ψ sp = atan2(ẏ, ẋ) .
(18)
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k
ϵix =
∑i ϵix
,
k
k
ϵiy =
n
ϵx =
Fig. 5 Nyquist plot of the UGV velocity transfer function (left) - the
Nyquist plot of the UGV yaw transfer function (right)
∑i ϵix Ai
n
∑i Ai
∑i ϵiy
,
k
(22)
n
,
rx = ϵx + max (FOVx),
ϵy =
∑i ϵiy Ai
n
∑i Ai
,
(23)
ry = ϵy + max (FOVy),
(24)
Fig. 6 Obstacle detection algorithm within sensor FOV
where k is a specific number of simpler patterns within a
recognised obstacle area. ϵi and Ai indicate the centroid location
and area of each part. ri is the radius of obstacle's virtual circle.
In case the sensor's FOV (e.g. laser, RGB-D camera, stereo
camera etc.) is super-wide, the enormous obstacle's virtual circles
may be created by the obstacle detection algorithm running in each
robot. The size of vehicles occasionally cannot fit the narrow space
of free travelling formed by two obstacle circles. To handle this
issue, the radius of each obstacle's virtual circle should be limited.
If the actual radius is larger than the predefined maximum value,
another obstacle virtual circle is generated to cover the remaining
parts of the obstacles. In our tests, the maximum radius is 70 cm.
Based on the linear velocity on the x and y-axis, the scalar speed
command V is achieved as follows:
4.2 Distributed obstacle avoidance control scheme with
dynamic interactive topology switches
V = ẋ2 + ẏ2 .
(19)
From our systems identification, we obtain the following
transfer function for the translational speed and yaw angle:
−0.15s3 + 112.9s2 + 4320.5s + 1847912.3
Δp(s)
= 4
, (20)
~
s + 186.9s3 + 58740s2 + 1969445s + 39036.5
ṗ(s)
ψ(s)
17.25s2 − 1018.48s + 65838.57
= 3
,
~
2
ψ̇ (s) s + 1401.1s + 560049.64 s + 68857.54
(21)
~
where ψ and ψ̇ denote the actual yaw output and its yaw angular
rate reference signal. Δp represents the movement distance while a
~
translational velocity ṗ is provided.
Generally, the difference between mathematical modelling and
experimental data is only 1 % and the UGV transfer functions can
also be classified as SNI systems (see Fig. 5) via the definition of
an SNI system.
4 Distributed
obstacle
and
avoidance control protocol design
inter-collision
In the last section, we not only provide an fundamental review of
the NI theory and the communication graph, but also prove the
convergence of our proposed strategy through an identical example
and the feasibility of using the NI stability criteria for the multivehicle formation control problem under switching topology. In
this section, we propose three novel approaches: distributed
obstacle detection, distributed inter-robot collision, and distributed
obstacle avoidance, which means that algorithms are run in each
agent instead of a GS, to address the existing problems of collision
avoidance.
Although in our previous work [26], the NI formation architecture
was presented for only controlling an invariant formation, that
architecture can also be applied to modify the robot's formation
pattern over time. Therefore, we develop this theory for the
purpose of solving the multi-obstacle avoiding problem based on
the NI consensus-based formation control protocol.
Firstly, we now select the general form of the first-order SNI
consensus controllers K(s) given by
Ki(s) =
(25)
where a > 0 is the viscous damping constant relative to ω > 0. δi
points out the gain values of our controller. The transfer function in
(25) gives the time constant τ = (a/ω2) and the DC gain k = (δ/ω2).
Proof: Let ω > 0, δ > 0 and τ > 0, note that
Ki(s) − KiT (s) =
δ
δ
2δs
−
=
as + ω2 −as + ω2 a2s2 − ω4
(26)
has no zeros on the imaginary axis except at possibly s = 0. It then
follows from Definition 1 that the outer-loop model in (25) is an
SNI controller.□
It should be noted that the higher the assigned value δ is, the
faster response the system will give. If the gain increases to a
sufficiently high threshold, the system can become unstable. τ and
k must be adapted accordingly to drive the system back to
equilibrium.
Secondly, we recall the concept of the NI consensus-based
formation control algorithm, employed in each robot. Considering
the input–output model P(s), the recursive procedure for our
method can be mathematically described as follows:
4.1 Obstacle detection approach
~ (t)
It is evident that the real shape of an obstacle is often irregular in
an uncertain environment. Therefore, it is challenging to compute
the escape angle by using the obstacles' actual boundary as per
what the traditional GOACM method does [11, 12]. To solve this
issue, a virtual circle that surrounds the recognised obstruction
range within the sensor's FOV (see Fig. 6) is generated. Its centroid
is formulated by the geometric decomposition method (dividing the
whole detected obstacle into a finite number of simpler figures). Its
radius is determined by the distance from the centre point to the
sensor's max view point
~ (t)
2952
δ
δ/ω2
k
=
,
2 =
as + ω
a/ω2 s + 1 τs + 1
ẋL
Krx(prx + xL)
ẏL
Kry(pry + yL)
~ (t)
Kcx1(p f x1 + ΔxLF1)
ẋF1
u=
~ (t)
ẏF1
=
Kcy1(p f y1 + ΔyLF1)
~ (t)
⋮
KcxN − 1(p f xN − 1 + ΔxLFN − 1)
~ (t)
KcyN − 1(p f yN − 1 + ΔyLFN − 1)
⋮
ẋFN − 1
ẏFN − 1
,
(27)
IET Control Theory Appl., 2020, Vol. 14 Iss. 18, pp. 2948-2959
© The Institution of Engineering and Technology 2020
xL(t)
yL(t)
xF(t1)
yF(t1)
y=
= P(s)u,
(28)
⋮
(t )
FN − 1
x
yF(t)N − 1
where (prx, pry), (xL, yL) are the desired and actual position on the x
and y directions while ( p f xi, p f yi), (ΔxLFi, ΔyLFi) is the desired and
actual distance between L and F. (Krx,Kry), (Kcx, Kcy) are the
SNI/NI consensus controllers of L and F as illustrated in Section 5.
A time-varying formation can be achieved in a shorter time
interval if (Krx, Kry), (Kcx, Kcy) are assigned with higher values.
prx
Δt(prx + xL)
pry
Δt(pry + yL)
Krx
Kry
p f xi
Kcxi
K=
Kcyi
=
⋮
Kcxn − 1
Δt(p f xi + ΔxLFi
p f yi
,
(29)
Δt(p f yi + ΔyLFi
p f xN − 1
Kcyn − 1
Δt(p f xN − 1 + ΔxLFN − 1
p f yN − 1
Fig. 7 Formation variation for three UGVs from a triangular pattern to a
line-column one to avoid multiple obstacles using NI obstacle avoidance
strategy
Δt(p f yN − 1 + ΔyLFN − 1
where Δt is the desired time interval to transform a former
formation pattern to the new one.
When the spacing between two obstacles is less than that of two
robots and larger than that of one robot, the only way for the robots
to pass through the obstacles is to change their formation shape.
Thus, we outline a novel network topology switching strategy,
which guides all robots to autonomously re-arrange into a line
formation before passing through tightly spaced obstacles.
This strategy can be regarded as a process of automatically
redefining the robots' role via the relative distance between the
robots location and its destination as well as between L and F, and
then moving to the corresponding position in a known formation.
These role computations take place inside the UAV's built-in
computer once a potential collision with obstacles is detected.
When this task is accomplished, identification (ID) numbers that
stipulate the title of each UGV in their formation are published to
corresponding followers within UAV's sensor FOV. To do so, the
UAV is controlled by an SNI position controller to follow the
geometrical centre-point of the UGVs formation pattern. We
formulate the centre-point coordinate as follows:
ci =
n
∑ j = 1 posi j
∀i ∈ {1..2},
n
(30)
where i illustrates the horizontal or vertical axis, n denotes the
number of UGVs on the ground, and posi j presents the UGVs
location on the x and y axes.
For our application, the virtual midpoint of the connecting line
m, which is linking the obstacle's centre points, is adopted to
redetermine the role of each mobile robots in their formation by
seeking out the smallest distance between m and robots, and to
guide each robot to reach its proper position. This mode is
activated while the distance from L or F to m measured in each
ground vehicle is less than 1 m in front of m, and is disabled while
IET Control Theory Appl., 2020, Vol. 14 Iss. 18, pp. 2948-2959
© The Institution of Engineering and Technology 2020
the distance from L or F to m (Δim) is larger than 1 m behind m as
illustrated in Fig. 7. Considering a multi-robot system with N
agents, the queuing mode of agent i (i ∈ 1, 2, …, N) is described by
quei =
1 if Δim < 1∀i ∈ {1..n},
0 if Δim > 1∀i ∈ {1..n} .
(31)
When the value of que in each robot becomes 1, ID numbers are
recomputed based on the distance from m to its location
IDi =
k
if Δim < Δ jm∀i, j ∈ {1..n}&i ≠ j
&k = k + 1,
0 otherwise.
(32)
This updated information is also known as the order reference
number among followers UGV. The desired position of the rear
follower UGV is always referred to the robot position in front of it
with an offset distance while that of the leader on the horizontal
axis is m.
For example, Fig. 7 shows that there are two arrays of multiple
obstacles blocking the moving path of three UGVs. Once (31) is
satisfied, the UGV order adopted in the ID matrix is recomputed by
comparing the distance from each robot to point m (32). In this
example, they are changed from (2)-(1)-(3) into (2)-(3)-(1). As a
result, all UGVs will immediately generate a new line-column
formation within the desired time interval based on the NI variant
formation control algorithm and the dynamic ID interaction
topology. After passing obstacles' midpoint m for a distance of
approximately 1 m, each UGV in this collaborative group will go
back to its former position with mutual collision avoidance in their
prototype formation with the original interaction topology
(2)-(1)-(3).
2953
Fig. 8 Control method for distributed NI inter-vehicle collision avoidance
Definition 3 [17]: The free body dynamics whose poles are at
the origin and A(∞) = 0 are NI plants.
The main results of Definition 3 then implies that the transfer
function of the mutual collision avoidance velocity given in (40) is
an NI plant containing a single integrator (having a pole at the
origin).
Now, an appropriate strategy must be designed to connect the
three fundamental tasks: maintaining a given formation,
approaching the destination, and guaranteeing collision avoidance.
Based on Lemma 1, NI mutual-collision avoidance transfer
functions A(s) and SNI vehicle dynamics P(s) can work and
interact well together by positive connections, namely, priority
weights for each task [ax; ay]. The incorporation of the two transfer
functions is exactly described as
4.3 Distributed mutual collision avoidance control scheme
For multi-robot formation applications, the capabilities of
localisation, obstacle avoidance, inter-vehicle collision avoidance,
and move-to-target action are essentially needed. Such abilities
ensure that the UGVs navigate a safe path and avoid collisions with
obstacles while trying to reach their goal. These fundamental
functions are independently operated and not intimately connected
to one another. Considering this aspect, we introduce a distributed
mutual collision avoidance method between robots.
In our approach, each vehicle is surrounded by a safe virtual
circle, which is similar to the obstacle circle. It is assumed that a
mutual collision may occur only in case one of them are executing
the obstacle avoidance behaviour or in case they are generating a
desired formation. While the safety margin of two robots is
violated, a repulsive force Fr is created to push the robot which has
a free-collision path away. This force's magnitude and direction are
expressed as in Fig. 8.
B1B2 = C2B1 − C2B2,
(33)
B1B2 = r2 − (C1C2 − C1B2),
(34)
B1B2 = r2 − (C1C2 − C1B2),
(35)
B1B2 = r2 − (C1C2 − r1),
(36)
Fr = krB1B2,
(37)
where C1 and C2 represent the two robots' virtual circles. B1, B2, C1,
C2 turn out four circle intersection points between two circles
centres.
It is clear that the Fr decreases gradually and linearly over time
when the distance B1, B2 between robots increases. Our controller
for inter-robot collision avoidance can generate smooth avoiding
paths without unexpected oscillations or getting stuck at some
points, which was a drawback of traditional APF methods [16, 30]
using the negative gradient of the repulsive potentials.
According to the Newton's second law of motion, the
acceleration set point for inter-vehicle collision avoidance is
obtained as follows:
→
Fr
ar = ,
m
→
~
→
~
ar =
A(s) =
(38)
→
kr × B1B2
,
m
→
~
vr
→
B1B2
=
kr
,
ms
→ →
(39)
(40)
where m is the mass of UGV and a~ r, v~ r are the desired avoiding
acceleration and velocity on the x–y planar plane. r1 and r2 are radii
of robot virtual circles. kr represents the stiffness of a virtual spring
used to generate the repulsive force.
2954
~ (t)
ẋL
Krx[ax0, 1(prx + xL) + ax0, 2 ẋr0]
~ (t)
ẏL
Kry[ay0, 1(pry + yL) + ay0, 2ẏr0]
~ (t)
ẋF1
~ (t)
ẏF1
Kcx1[ax1, 1ΔxLF1 + ax1, 2 ẋr1]
=
Kcy1[ay1, 1ΔyLF1 + ay1, 2ẏr1]
~ (t)
⋮
KcxN − 1[axN − 1, 1ΔxLFN − 1 + axN − 1, 2 ẋrN − 1]
~ (t)
KcyN − 1[ayN − 1, 1ΔyLFN − 1 + ayN − 1, 2ẏrN − 1]
⋮
ẋFN − 1
ẏFN − 1
,
(41)
where ax0, 1, ay0, 1, …, axN − 1, 1, ayN − 1, 1 are the task priority weights,
respectively.
It should be pointed out that in the aforementioned works [11,
12, 16, 28, 30], only complete formation control and collision
avoidance problems were considered, whereas their homogeneity
and synchronisation have not fully been taken into account. By
using (41), a homogeneous and synchronous consensus control
protocol for all problems and an internal stability of
[K(s), P(s), A(s)] are guaranteed via the NI framework.
5 Stability proof of the distributed formation
control switches and inter-vehicle collision
avoidance
As mentioned in Sections 3 and 4.3, the stability of the distributed
formation control switches and collision avoidance subjected to the
communication topology can be verified through the NI internal
stability criteria of [K(s), P(s), A(s)].
Since QQT and DC gain at zero frequency of P(0) have fixed
values which are greater than 0, only DC gain of SNI/NI
controllers K(0) at zero frequency can be tuned to achieve the
stability for formation switching control. For this reason, we select
the negative gain values for K(s) so that the required stability is
always guaranteed.
For example, regarding the UGV's velocity transfer function,
their real DC gains at the zero frequency are equal to
(1847912.3/39036.5) = 47.34 [1]. In addition, ℒ > 0 [2]. All SNI
controllers are chosen as (−1)/(s + 1); therefore, its DC gain at the
zero frequency is -1 [3]. Based on [1]–[3], the stability criteria in
Lemma 2 is naturally satisfied.
Additionally, a Nyquist diagram of a follower UGV along the xaxis is sketched in every sample time of our real tests. It is clear
from Fig. 9 that its contour does not encircle the critical point at
1+0j, meaning that our output consensus feedback control system
is globally stable via Nyquist stability criterion. The same approach
can be applied to prove system stability of the other robots.
6
Computer simulations
Three cases are given to illustrate the main results of our theories.
The first case examines the proposed approaches in Section 6 on
six boids that represent the mathematical models of six UGVs.
While the second case is to present the advantages of the NI
obstacle and inter-robot collision avoidance strategy based on the
IET Control Theory Appl., 2020, Vol. 14 Iss. 18, pp. 2948-2959
© The Institution of Engineering and Technology 2020
Fig. 9 Nyquist plots of a closed-loop UGV system showing stability under
the dynamic changes in communication topology
Fig. 10 Queuing behaviour of six boids via the distributed NI formation
switch and inter-vehicle avoidance control with L–F switching topology
formation switches with respect to APF method, the third case
compares the formation tracking and obstacle avoidance
performance of the proposed method with the robot switch and that
with the fixed L–F structure as in [32].
6.1 Distributed NI collision avoidance approaches
Two consensus scenarios are implemented to validate the NI
avoiding control response through a switching network topology
and its ability to achieve and maintain a new obstacle avoidance
formation, particularly a queuing one while approaching their goal
point. These numerical experiments are developed in the m-file
MATLAB environment containing the real UGV dynamic models
and our solutions. Moreover, we use the following numerical data
to implement our test: m = 1 kg, Kr = Kc = kr = −0.1, Fmaxr = 6 N,
~
V max = 2 cm/s, C1 = [−65, 50] cm, C2 = [50, −50] cm, r1 = r2 = 46
cm, rob = 35 cm, Goal = [300, 450] cm. The SNI consensus
controllers are chosen as (−1)/(s + 1). The initial position and
velocity of UGVs are defined by two functions: 160 (2 rand([N,2])
−1) and 0.002 (rand([N,2])−350), respectively.
In Fig. 10, the simulation results for the queue behaviour of six
UGVs can be seen. Throughout the first 1.98 s of the test, the
distributed NI inter-robot collision avoidance approach, coupling
with the NI distributed formation control protocol, is capable of
self-forming a V-shaped formation without any collisions. After
stabilising in 1.98 s, the obstacle avoidance strategy via the
formation and communication topology switch was turned on for
the remainder of the test when two arrays of obstacles ahead hinder
the robots' trajectories. The formation shape of six UGVs has
quickly re-arranged the robot orders. It was easily switched from a
V-shaped pattern to a straight line within 2.85 s before it was
successfully restored to the former shape and arrived at the
destination in 5.94 s.
Moreover, a hybrid method, combining the proposed NI
strategy with the dynamic L–F topology and the other NI obstacle
avoidance techniques, introduced in [32], is developed to generate
IET Control Theory Appl., 2020, Vol. 14 Iss. 18, pp. 2948-2959
© The Institution of Engineering and Technology 2020
a comprehensive and useful system for the obstacle avoidance
problem in an unknown environment. As shown in Fig. 11, under
the control of the hybrid method, a collaborative group of five
autonomous mobile robots can safely travel to the target point
[300, 450] cm within 21 s without any collisions with the eight
obstacles by regulating the appropriate relative positions between
mutual robots and robot-obstacle.
From these results, it is evident that a better formation to
overcome obstacles and evade other UGVs is achieved in a short
time. More particularly, the trajectories do not have any notable
oscillations, which was an unavoidable problem of some other
methods.
6.2 Negative imaginary versus artificial potential field
For the second case, we will demonstrate the ability of our control
law to achieve and maintain different formations. These results are
compared to the performance of a basic APF controller since APF
is the most common method used for formation keeping and
obstacle avoidance control. The values for potential functions,
gains, and control law of APF are chosen to be same as the ones
used in [38] while those of NI are repeated as in Simulation 1.
In APF, the potential function is defined as a scalar energy field
whose negative gradient is a vector field of forces. The goals are
surrounded by attractive potentials, and the obstacles are endowed
with repulsive potentials. The robot trajectory in the area is planned
by summing the effects of the attraction force of the target and the
repulsion forces of the obstacles, acting on the robot. The primary
purpose behind the potential functions is to find a complete and
safe path from the initial location of the robot to the final point at
the same time of avoiding obstacles. Besides, to form a desired
formation, some other forces were taken into account. The
followers must also have a potential field and a repulsive force that
keep them separated from others. Finally, friction forces are also
introduced to prevent the vehicles from swinging around their goal.
As can be seen in Fig. 12, although both methods are able to
pass through the narrow gap between obstacles by moving into a
line, the NI has considerably better performance over the APF. The
vehicles controlled by APF experienced trajectory oscillations once
the UGVs' formation is switched (Fig. 12a). Biswas and Kar [31]
state that swings in the trajectories associated with APF have not
yet been wholly cancelled out, especially in narrow passages
between a cluster of obstacles. Additionally, the vehicles with APF
slightly oscillate around their goal. However, the robot trajectories
are smoothed out if our proposed method is applied (Fig. 12b).
Furthermore, the SNI controller accomplished the formation
switch within a short reaction duration of only 1.45 s, which is
considerably shorter than the APF at 0.96 s. Last but not least, the
NI control system also easily maintains the queuing formation
whereas APF is unable to satisfactorily perform this due to its
complicated computation of net force. Consequently, four positive
results yield the robustness of the NI control methods and provide a
suitable dynamic switching solution between various formations.
6.3 negative imaginary with the dynamic topology versus
negative imaginary without the dynamic topology
The parameters of the third case, such as the obstacles' radius and
position, the UGV transfer functions, control gains, the goal point,
are repeated as in those of the second case.
Fig. 13 presents the actual trajectory outputs of the multiple
UGV system, controlled by the two NI controllers along the x and y
axes when crossing a thin area between the two significant
obstacles and then approaching the goal point. The NI control law
using the multi-robot order switches outperforms that using only
the fixed-order technique since it produces less sluggish
trajectories and fluctuations. This is because each robot's order is
pre-determined via its relative distance to the centre point m.
Consequently, the UGVs do not need to compete together to pass
through the obstacles.
2955
Fig. 11 Control responses of the hybrid NI formation and obstacle avoidance controller for three different tasks: goal-reaching, formation-following and
collision-avoiding implemented by five mobile robots
7
Real-time experimental tests
We have conducted two indoor experiments using an AR.Drone
UAV and three Pioneer UGVs to validate these results. Our indoor
flight test facility included 19 VICON Motion Capture Cameras
mounted on a rigid frame. Most significant parameters used in
simulation were kept the same. All videos relating to the
experimental tests can be viewed at the web links: https://
tinyurl.com/y7ygtwac.
7.1 Experimental apparatus
Fig. 12 Performance of two comparative controllers
(a) Oscillatory trajectory using APF, (b) Smoothness of the trajectory using the NI
strategy with the switching topology and the collision avoidance
2956
7.1.1 Hardware/software configuration: The hardware setup
used in this work consists of one UAV (AR Drone quadrotor
platform), three heterogeneous UGVs (Pioneer P3-AT and P3-DX),
one electrical fan and four plastic packing boxes used as obstacles.
Notably, the wheels of each UGV are equipped with optical
encoders to estimate the linear velocity, moving distance, and yaw
angular rate. For software settings, two systems were employed for
data collection and interaction protocol. All necessary data,
including posture and relative position of agents and obstacles, are
analysed and measured by a Vicon Motion Capture System (MCS).
Discrete commands or additional data exchanges among the robots
as well as those between the GS and the robots are achieved
utilising the robot operating system.
In order to conduct real-time experiments, it is assumed that
measurement of relative positions between the leader and follower
and between the robots and obstacles will be simulated using an
indoor MCS. Furthermore, we simulate the relative position
measuring capability of the UAV camera using our MCS to
calculate relative position between the UAV and each UGV.
IET Control Theory Appl., 2020, Vol. 14 Iss. 18, pp. 2948-2959
© The Institution of Engineering and Technology 2020
Fig. 13 Responses of the two NI control systems
(a) NI with the fixed robot orders, (b) NI with the switching topology
Fig. 15 Real-time performance of the multi-vehicles control system via
distributed NI time-varying formation control method and distributed L–F
strategy under two different scenarios
(a), (b) No wind gusts, (c) Added wind gusts
7.3 Multiple obstacles avoidance problem for multi-UGVs
with UAV's assistance
Fig. 14 Implementation of distributed NI inter-vehicle collision avoidance
approach in two various scenarios
(a) Slave 2 avoids the obstacle, Master avoid Slave2, and Slave 1 evades Master, (b)
Slave 2 and Master avoid the obstacles, and Slave 1 evades Master
A box fan with a maximum airflow of 5 m/s was used as a
disturbance generator for all of the experiments. It is placed at a
distance of 1.5 m blowing in the diagonal direction of the positive x
and y axes.
The fundamental parameters for these tests are as follows: m =
~
12 kg, kr = − 0.225, V max = 12 cm/s, r1 = r2 = 90 cm, rob = 35 cm,
target = [−100, 170] cm, ΔLF1 = [100,0], ΔLF2 = [−100,0]. The SNI
consensus controllers are (−0.4)/(s + 1.3).
7.2 Mutual collision avoidance problem between UGVs
From Fig. 14, it is apparent that our distributed solution in Section
4.3 can achieve good performance as all three UGVs can prevent
inter-robot collisions in any case and safely travel to their target.
IET Control Theory Appl., 2020, Vol. 14 Iss. 18, pp. 2948-2959
© The Institution of Engineering and Technology 2020
Following the previous tests' success, the remaining experiments
with the NI formation control method and dynamic robot network
interaction were conducted without any constraints. The UAV–
UGVs system is controlled to explore the two different scenarios
avoiding (i) one obstacle and (ii) two blocks of multiple obstacles.
As shown in Fig. 15a, there is only one obstacle obstructing the
robot Slave 2's path. Applying the first strategy for the formation
modification in our previous paper [32], the agents, including the
three ground vehicles and one air vehicle, were able to follow a
predefined trajectory and keep the desired shape of the formation
since only the relative positions between the robots and the
obstacles are modified.
As given in Figs. 15b and c, where autonomous mobile robots
must bypass a tiny space between obstacles that fit only one robot,
three UGVs automatically switched their role (L or F), changed
from (1) (2) (3) to (1) (2) (3) in the first figure and from (1) (2) (3)
to (1) (3) (2) in the second figure, based on the relative distance
from each robot to the centre point m when implementing the
obstacle avoidance behaviour. Next, they moved towards their own
position in a new horizontal-line formation shape before
overcoming the narrow space between two arrays of obstacles
and
‘The_Obstacle_2_Sphere’).
(‘The_Obstacle_1_Sphere’
Additionally, Fig. 15 also introduces the use of UAV as valuable
assistance for ground operators by tracking the centroid's three
2957
topology) in a pre-defined formation. As a result, UGVs are able to
cross through narrow spaces between two arrays of multiple
obstacles without any unexpected behaviours or physical
constraints as shown in [11, 12] or any oscillations [16, 31].
Also, since the robot's formation is maintained by the relative
distances between L and F as well as between robots and obstacles,
instead of being achieved by global robot positions as illustrated in
[7], our methods are also suitable to operate in a limited and
unreliable communication environment.
In future work, our SNI gains will be adapted to better cope
with multiple disturbances, including both severe external and
internal effects. Additionally, a leader-less control method for
networked vehicles will be considered to diminish the adverse
impacts of the leader loss situation.
9
[1]
[2]
[3]
[4]
Fig. 16 Trajectory tracking performance during one test in the presence of
wind gusts
(a) Desired and actual robot paths overtime, (b) Tracking errors
UGVs formation simultaneously in the presence of wind
disturbances. Although the UGVs' formation is transformed twice
and the real flight test is subject to wind gust disturbance, the
maximum position tracking error for all UGVs and the quadrotor
UAV is ∼15 cm on all vertical and horizontal axes (see Fig. 16).
This validates the robustness of NI control theory. Further, the
proposed avoidance technique with the switching directed topology
can perfectly combine with the strategies presented in our earlier
paper [32] to improve the robots' obstacle avoiding capability in
any circumstances.
Overall, the trajectory responses of the SNI controller meet the
goals of smoothly tracking the different formations while adapting
to unknown disturbances and maintaining minimal steady-state
error. Through these tests, it is noted that as long as the internal
stability of [K(s), P(s), A(s)] is ensured, the NI formation control
protocols using topology switches is capable of stabilising the
high-order systems such as UGV or UAV, opening up a great
opportunity to control the consensus of the complex dynamic
models. On the other hand, many different control approaches can
synchronously and effectively work together if they are designed
on an NI homogeneous control architecture, such as the NI
formation control and the NI collision-free solution. This strength
over others is a vital contribution to the formation control with
collision avoidance in future.
8
Conclusion
We have demonstrated two new improvements, including an NI
collision avoidance strategy and an L–F communication topology
switches, to facilitate the movement of a multi-vehicle system
which may face sensor constraints, obstacle and inter-robot
collision, and gust disturbances in uncertain environments.
Compared to the performance of conventional APF controller,
we have shown that the robot trajectories generated by our SNI
controller are much smoother than that of APF strategy in the same
scenario. The task completion time of our SNI controller is also
shorter than APF. Its superiority is achieved thanks to a quicker
response and an advanced obstacle and inter-robot collision
avoidance technique.
With respect to the existing approaches for multi-vehicle
formation control, our proposed methods help UGVs to selfarrange and self-decide their role (changing the ID interaction
2958
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
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