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Proceedings ArticleDOI

3D trajectory tracking control of quadrotor UAV with on-line disturbance compensation

01 Aug 2017-pp 2082-2087

TL;DR: Using the proposed formulation, it is shown that the performance of the control and its robustness level can be significantly improved and an in-depth discussion with respect to the control performance is highlighted by considering several scenarios and using several metrics.

AbstractIn this paper, we propose a revisited form of the so-called Model-Free Control (MFC). Herein, the MFC principle is employed to deal with the unknown part of the plant only (i.e. unmodeled dynamics, disturbances, etc.) and occurs beside an Interconnection and Damping Assignment-Passivity Based Control (IDA-PBC) strategy that is used instead of the PID structure as done in the classical MFC form. Using the proposed formulation, it is shown that we can significantly improve the performance of the control and its robustness level. This problem is studied in the case of Multi-Inputs Multi-Outputs (MIMO) system with an application to a small Vertical Take-Off and Landing (VTOL) vehicle where a stability analysis is also provided. The numerical simulations have shown satisfactory results where an in-depth discussion with respect to the control performance is highlighted by considering several scenarios and using several metrics.

Summary (2 min read)

INTRODUCTION

  • The quadrotors are considered as a good case study to design, to analyze and to implement flight control strategies.
  • Thus, its use as the basis of control allows the compensation of the uncertainties as well as other disturbances.
  • Therefore, the authors propose a Revisited Model-Free Control (R-MFC) strategy to simultaneously accommodate the unmodeled and neglected dynamics and external disturbances.
  • Passivity-Based Control (PBC) is well known especially in mechanical applications for controlling nonlinear systems.

III. R-MFC FLIGHT CONTROLLER DESIGN

  • The classic MFC approach proceeds by considering an ultralocal model, valid in short time that approximates the nonlinear model via input-output behavior using the experimental available data without any modeling step.
  • This online numerical differentiator and estimation may fail with some highly nonlinear and/or time-varying dynamics that need to be treated carefully.
  • This class of systems is widely adopted in the robotics and mechanical fields.
  • Usually, model ( 6) is quite simplified with neglected and unmodeled dynamics.
  • An additional effort is requested to deal with this new term 𝛿ℱ.

Remark 1: For the existing MFC technique, 𝑣 is fixed by the user and may equal to 1 or 2.

  • This estimation is valid for a short period 𝑇 only and it should be continuously updated at every iteration of the closed loop controller.
  • Many significant advances on the numerical differentiation of noisy signals are elaborated in the literature [10] .
  • This updated term 𝛿ℱ ̂ captures the unknown dynamics of the system as well as the disturbances during each period 𝑇 and then brings the required changes in the control input by compensation.
  • Herein, the authors proceed with a different way by employing a sophisticated tool rather than the PID structure where the main goal is to ensure the asymptotic convergence, towards the origin, of the tracking errors of closed-loop of model (10) .
  • To achieve the desired specifications, by using another control procedure, is more challenging.

IV. IDA-PBC BASED AUXILIARY INPUT

  • In the following, trajectory tracking control is achieved using the IDA-PBC approach.
  • The authors modify the total energy function of (10) to assign the desired equilibrium and damping injection matrix to meet the asymptotic stability.
  • To preserve the energy interpretation, the closed-loop system is presented in a Port-Controlled Hamiltonian (PCH) representation.

A. System energy and PCH model

  • This system has a natural stable equilibrium configuration.
  • From (12), the dynamic of the quadrotor can be written as We take the reference trajectories as desired equilibrium configuration.the authors.the authors.

C. Energy shaping & damping injection

  • The controller is obtained by substituting (23) in (15) and making the resulting equations equal to (20).
  • 𝐶 deals with the unknown parts and allows to maintain a certain level of robustness, 𝑢 𝐸𝑆 allows to meet the desired specification through the target model components and finally the damping injection term 𝑢 𝐷𝐼 in order to guarantee a damped response.

D. Control design for quadrotor and stability analysis

  • Closed-loop of system ( 12) written under PCH form, using control law ( 31) is asymptotically stable, also known as EQUATION Theorem 1.
  • Following the IDA-PBC approach described above, closed loop system ( 12 So, closed loop of system (12) is asymptotically stable, also known as Proof.

V. RESULTS AND DISCUSSION

  • The authors test the effectiveness of the proposed controller not only in the ideal case but also in the presence of different disturbances.
  • For the sake of further comparison, the authors follow the same protocol and fit the same conditions.
  • The control parameters are tuned, using Genetic Algorithms (GA), in the ideal case then kept for the entire proposed scenarios and for which the objective is to reduce the steady state errors.

Target model Eq (20)

  • ℱ, ℬ promising results (for details one may refer to [5] ) whilst the second one is traditionally applied for quadrotors i.e.
  • The authors add the sensor noise on the states of the system.
  • These accelerations are considered as perturbations added to the equations related to the forces in the quadrotor model.
  • 3 , the three controllers exhibit an acceptable behavior with moderate consumed energy regardless the external effect.
  • The accuracy is almost the same using the MFC or R-MFC, which demonstrate the efficiency of the online estimation of the disturbance.

VI. CONCLUSION

  • It uses an auxiliary input and by bringing some changes (see Section III-IV), it operates in closed loop form.
  • It improves the performance with respect to structured and unstructured uncertainties.
  • Numerical simulations have been performed using the non-linear dynamic model of the quadrotor in order to test the effectiveness of the designed controller.
  • The good efficiency of their approach is demonstrated in multiple test scenarios.
  • The settling time is shown to be quite fast with good accuracy and a high level of robustness is ensured with respect to parameters uncertainties or external disturbances.

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3D trajectory tracking control of quadrotor UAV with
on-line disturbance compensation
Yasser Bouzid, Houria Siguerdidjane, Yasmina Bestaoui
To cite this version:
Yasser Bouzid, Houria Siguerdidjane, Yasmina Bestaoui. 3D trajectory tracking control of quadrotor
UAV with on-line disturbance compensation. 1st IEEE Conference on Control Technology and Ap-
plications (CCTA 2017), Aug 2017, Mauna Lani, HI, United States. �10.1109/CCTA.2017.8062760�.
�hal-01722001�

Abstract:1 In this paper, we propose a revisited form of
the so-called Model-Free Control (MFC). Herein, the
MFC principle is employed to deal with the unknown part
of the plant only (i.e. unmodeled dynamics, disturbances,
etc.) and occurs beside an Interconnection and Damping
Assignment-Passivity Based Control (IDA-PBC) strategy
that is used instead of the PID structure as done in the
classical MFC form. Using the proposed formulation, it is
shown that we can significantly improve the performance
of the control and its robustness level. This problem is
studied in the case of Multi-Inputs Multi-Outputs
(MIMO) system with an application to a small Vertical
Take-Off and Landing (VTOL) vehicle where a stability
analysis is also provided. The numerical simulations have
shown satisfactory results where an in-depth discussion
with respect to the control performance is highlighted by
considering several scenarios and using several metrics.
I. INTRODUCTION
The quadrotors are considered as a good case study to design,
to analyze and to implement flight control strategies.
Moreover, it is necessary to design a controller such that the
quadrotor will be able to efficiently follow a predefined
trajectory, particularly in the presence of disturbances. For this
reason, many studies have led to the development of
sophisticated and robust nonlinear control laws (as for instance
[1-3]). However, most of these proposed strategies require an
accurate model in order to perform a good control, which is
extremely difficult when the system is maneuvering in a harsh
environment.
In this regards, a strategy based on a Model-Free technique is
developed (MFC) (see as for instance [4]). The main
advantage of this control strategy is that it does not require the
knowledge of the system dynamics as it involves a continuous
updating of the input-output of a very local model. Thus, its
use as the basis of control allows the compensation of the
uncertainties as well as other disturbances. It is employed in
many real cases such as mobile robots [4] and quadrotors [5].
In a certain point of view, the control of a system with a model
free has already been used, since many decades, on the basis
of fuzzy logic control or the more popular one for linear
systems through Ziegler-Nichols method [6]. In addition,
assuming no available model is not totally a correct
assumption due to the fact that most of systems, at least, may
*
Y. Bouzid and Y. Bestaoui are with IBISC Laboratory, universitéd’Evry Val
d’Essonne, Université Paris-Saclay, Evry, France (e-mail:
yasseremp@gmil.com,Yasmina.Bestaoui@ufrst.univ-evry.fr).
H. Siguerdidjane iswith L2S, CentraleSupélec, Université Paris-Saclay, Gif
sur yvette, France (e-mails:
Houria.Siguerdidjane@centralesupelec.fr).
be approximated by mathematical models even with poorly
known dynamics.
Using the available information about the system will bring a
notable benefit and significantly improve the performance of
control. Therefore, we propose a Revisited Model-Free
Control (R-MFC) strategy to simultaneously accommodate the
unmodeled and neglected dynamics and external disturbances.
As in general, the tuning of PID parameters allows to meet the
desired specification of control, we use a reference model-
based control technique that achieves the control with the
required specifications, by means of Interconnection and
Damping Assignment-Passivity Based Control (IDA-PBC).
In the last two decades, the use of the so-called Port-Controlled
Hamiltonian (PCH) representation has attracted the attention
of researchers. Many control tools have been developed to deal
with this compact representation. Passivity-Based Control
(PBC) is well known especially in mechanical applications for
controlling nonlinear systems. An improvement was
developed through Interconnection and Damping Assignment
(IDA) where the use of energy shaping was originated in [7].
Recently, the IDA-PBC has become an efficient tool in
nonlinear control applications and has been illustrated in
several real experimentations including electrical motors [8],
magnetic suspension systems [9], etc.
Throughout this paper, a performance assessment is presented
via results of several illustrations, scenarios and numerical
simulations, with complementary comments of the proposed
revisited strategy of control with respect to other techniques.
The remainder of this paper is organized as follows: Section II
concerns the dynamics of the VTOL quadrotor and the control
architecture. Section III and Section IV introduce the design of
our nonlinear control approach. The simulation results are
illustrated in Section V. Finally, the paper is ended with
concluding remarks.
II. QUADROTOR MODELING & CONTROL
ARCHITECTURE
From the fundamental principle of dynamics, we model the
quadrotor as a rigid body for the validation of control
performance, neglecting some aerodynamic effects such as
the gyroscopic and ground effects. The system operates in two
coordinate frames: the Earth-fixed frame
󰇛󰇜 and
the body fixed frame
󰇛
󰇜
(see Figure 1). Let
󰇛
󰇜
describes the orientation of the aerial vehicle (Roll,
Pitch, Yaw) and χ
󰇛
󰇜
denotes its absolute position.
3D Trajectory Tracking Control of Quadrotor UAV with On-Line
Disturbance Compensation
Y. Bouzid*, H. Siguerdidjane, Y. Bestaoui

Figure 1. Frame representation.
In this study, we consider a simplified dynamic model of the
vehicle that is derived in our previous work [1] in order to
make the controller implementation simpler and easier and to
show the efficiency of our control strategy that can deal with
the unmodeled and neglected dynamics. The considered
mathematical model may be written under the general
mechanical equation, as follows
󰇛
󰇜
󰇘
󰇛
󰇗
󰇜
󰇗
󰇛
󰇜
(1)
where
󰇟
χ
󰇠
χ
is the generalized
coordinates,

󰇣
󰇤is composed
of the mass

and the inertia matrix,
󰇛
󰇗
󰇜




denotes the Coriolis term,
󰇟

󰇠
denotes the gravitational term,
󰇛
󰇜

denotes the input matrix, with



󰇗


󰇗
󰇛
󰇜
󰇗
󰇛
󰇜
󰇗


󰇗

󰇗
(2)
and










(3)
with the mass, the gravity acceleration,
the total thrust
of four rotors,
󰇛
󰇜
the control torque vector and
󰇛󰇜
and
󰇛󰇜
abbreviations for 󰇛󰇜 and 󰇛󰇜 respectively.
The parameters of the system UAV are displayed in Table 1.
Table 1. Quadrotor parameters.
󰇛󰇜
󰇛

󰇜

󰇛

󰇜
󰇛

󰇜

In order to simplify the design of the controller, two virtual
inputs
and
are given as




(4)
The reference angles,
and
are considered
as inputs for the rotation subsystem. From system (4), it
follows



 󰇡




󰇢
(5)
III. R-MFC FLIGHT CONTROLLER DESIGN
The classic MFC approach proceeds by considering an ultra-
local model, valid in short time that approximates the
nonlinear model via input-output behavior using the
experimental available data without any modeling step.
However, this online numerical differentiator and estimation
may fail with some highly nonlinear and/or time-varying
dynamics that need to be treated carefully. In addition, most
systems have a mathematical model even if it is not accurate.
Note also that the MFC does not distinguish between model
mismatches and perturbations. Therefore, to be more realistic,
our approach employs the model-free principle to only deal
with the unknown part of the controlled system where the use
of the known part brings more benefit and makes the control
more efficient.
This proposed formulation that we can denote by the acronym
R-MFC is explained through a class of systems written under
the general mechanical equation. This class of systems is
widely adopted in the robotics and mechanical fields. For the
sake of clarity, equation (1) is written under a compact form
considering the general case
󰇘
󰇛
󰇗
󰇜
󰇛
󰇜
(6)
where
󰇛
󰇗
󰇜

󰇛
󰇜

󰇛
󰇛
󰇗
󰇜
󰇗
󰇜
and
󰇛
󰇜
󰇛
󰇜

󰇛
󰇜
is the output vector,

is
the inertia matrix,
󰇛
󰇗
󰇜

denotes the Coriolis term,
denotes the gravitational term,
󰇛
󰇜

denotes
the input matrix and
denotes the input vector.
Usually, model (6) is quite simplified with neglected and
unmodeled dynamics. Moreover, the execution of trajectories
can be easily affected by external disturbances, which
introduces some unknown terms. Therefore, a term could
be added to nominal model (6) gathering the neglected and
unmodeled dynamics and the external disturbances. An
additional effort is requested to deal with this new term.
Thus, the input-output relationship of the anticipated model
may be represented by the following system:
󰇛󰇜
󰇛
󰇗
󰇜

󰇛
󰇜
κ (7)
where

is a positive definite diagonal scale matrix
fixed by the user and  is an estimated term. In fact, the order
of model (7) is chosen according to the prior knowledge
of the system. It equals to the order of the mathematical model
(6).
Remark 1: For the existing MFC technique, is fixed by the
user and may equal to 1 or 2.
Therefore, the difference between model (6) and (7) lies in the
presence of the unknown modeled part that can be estimated
as

󰇘
󰇛
󰇗
󰇜
󰇛
󰇛
󰇜
κ
󰇜
(8)
As the past input vector in the previous time interval and
the actual

derivative of the measured output vector are
known, the value of
is computed. This estimation is valid
for a short period only and it should be continuously
updated at every iteration of the closed loop controller.

Obviously, the estimate of the second-order derivative
󰇘
yields an estimate of
. Many significant advances on the
numerical differentiation of noisy signals are elaborated in the
literature [10]. This updated term 
captures the unknown
dynamics of the system as well as the disturbances during
each period and then brings the required changes in the
control input by compensation. From (7), the control input for
our R-MFC proposed strategy can be split into two parts:
󰇛
󰇛
󰇜
󰇜

󰇛

󰇜
(9)
where the matrix
󰇛
󰇜
is non-singular in
.

plays the role of compensator of the unknown part
and
is considered as an auxiliary input that ensures the
asymptotic convergence of the tracking errors of the closed
loop into the origin. Injecting input (9) in (7), leads to a new
and fully known nonlinear model eliminating the unknown
part
󰇘
󰇛
󰇗
󰇜
(10)
The existing MFC technique employs, in the case of , a
PID controller as an auxiliary input :
󰇘
󰇛
󰇜

󰇗
(11)
that leads to the intelligent PID where
is the
tracking error vector and
is the reference trajectory
vector.
and
denote the usual tuning gains.
Herein, we proceed with a different way by employing a
sophisticated tool rather than the PID structure where the
main goal is to ensure the asymptotic convergence, towards
the origin, of the tracking errors of closed-loop of model (10).
In this stage, a broad range of strategy can be applied.
The use of PID, in the classic form of MFC, allows to ensure
a given performance of the system time response according to
the given specifications (overshoot, settling time, accuracy)
via the tuning of the control parameters. To achieve the
desired specifications, by using another control procedure, is
more challenging. Therefore, we employ a reference model
based control strategy where the control specifications are a
priori fixed. Then the control input pushes the system to
follow the same behavior as the target model.
IV. IDA-PBC BASED AUXILIARY INPUT
In the following, trajectory tracking control is achieved using
the IDA-PBC approach. In this technique, we modify the total
energy function of (10) to assign the desired equilibrium and
damping injection matrix to meet the asymptotic stability. To
preserve the energy interpretation, the closed-loop system is
presented in a Port-Controlled Hamiltonian (PCH)
representation.
A. System energy and PCH model
Explicitly, system (10) is written as
󰇛
󰇜
󰇘
󰇛
󰇗
󰇜
󰇗
󰇛
󰇜
(12)
The system’s Hamiltonian energy
󰇛
󰇜
, the sum of the
kinetic energy,
󰇛
󰇜
and the potential one, 󰇛󰇜 is written
as:
󰇛
󰇜
󰇛
󰇜
󰇛󰇜 (13)
So,
󰇛
󰇜

󰇛
󰇜
(14)
where
is the generalized momentum.
This system has a natural stable equilibrium configuration.
This latter one is related to the minimum of energy. The PCH
model is needed in order to design a controller based on the
IDA-PBC methodology. From (12), the dynamic of the
quadrotor can be written as
󰇗
󰇗
󰇟
󰇛
󰇜
󰇛
󰇜
󰇠
󰇩
󰇛
󰇜
󰇛
󰇜
󰇪
󰇛
󰇜
(15)
with
󰇟
󰇛
󰇜
󰇛
󰇜
󰇠



󰇛󰇜
(16)
B. Target dynamics
Motivated by equation (13), we propose a desired energy
function as being:
󰇛
󰇜
󰇛
󰇜
󰇛󰇜 (17)
We modify the total internal energy function of the closed
loop system to assign the desired equilibrium configuration
and we require that
󰇛
󰇜
will have a minimum at
󰇛
󰇜
,
thus
󰇛
󰇜
󰇛
󰇜

󰇛
󰇜󰇛
󰇜
󰇛󰇜 (18)
where
󰇛
󰇜
and
represent the desired closed
loop potential energy function and inertia matrix, respectively
with


󰇛
󰇜
(19)
We take the reference trajectories as desired equilibrium
configuration. In another words,
󰇛
󰇜
󰇛
󰇜
.
To preserve the energy interpretation we also require that the
desired closed loop system be in PCH form
󰇗
󰇗
󰇟
󰇛
󰇜
󰇛
󰇜
󰇠
󰇩
󰇛
󰇜
󰇛
󰇜
󰇪 (20)
where
󰇛
󰇜

󰇛
󰇜



󰇛󰇜
(21)
󰇛
󰇜
󰇛
󰇜
󰇛
󰇜

󰇛
󰇜
(22)
󰇛
󰇜
is a skew symmetric matrix and


contains the control parameters. Obviously, the matrix
󰇟
󰇛
󰇜
󰇛
󰇜
󰇠
has the same form as the original
system.
C. Energy shaping & damping injection
Commonly, the control input of IDA-PBC is decomposed into
two terms [11].


(23)
where

acts on the damping and

is designed for the
energy shaping.
The controller is obtained by substituting (23) in (15) and
making the resulting equations equal to (20). Thus




󰇩
󰇛
󰇜
󰇛
󰇜
󰇪
󰇛
󰇜
󰇛


󰇜




󰇛
󰇜
󰇛
󰇜
󰇛
󰇜
󰇩
󰇛
󰇜
󰇛
󰇜
󰇪(24)
injects a damping into the system via negative feedback of
the passive output
. The damping injection term is
then:



󰇛
󰇜
󰇛
󰇜
(25)
Thus, the second row leads to the energy shaping

󰇛
󰇜

󰇡
󰇛
󰇜
󰇛
󰇜
󰇛
󰇜
󰇛
󰇜
󰇛
󰇜
󰇢 (26)
Finally, the R-MFC is split into three parts as
󰇛
󰇜

󰇛



󰇜
(27)
where
deals with the unknown parts and allows to maintain
a certain level of robustness,

allows to meet the desired
specification through the target model components and finally
the damping injection term

in order to guarantee a damped
response. Our approach is summarized by Figure 2.
Figure 2. R-MFC scheme.
D. Control design for quadrotor and stability analysis
For the sake of simplification, we keep the interconnection
matrix unchanged, namely
and  therefore

becomes

󰇛
󰇜

󰇡
󰇛

󰇜
󰇛
󰇜
󰇛

󰇜
󰇢 (28)
So,


󰇛
󰇜
(29)
is an arbitrary function of and  From equation (19), the
necessary condition,
󰇛
󰇜
0 and the sufficient
condition,
󰇛
󰇜
, will hold at
.
has its minimum
at
.
In our case we choose
󰇛
󰇜
to be a quadratic function, which
leads to
󰇛
󰇜
󰇛
󰇜
󰇛
󰇜
󰇛
󰇜

󰇛
󰇜
(30)
where
and
denote positive definite matrices of the
control parameters.
Now, the auxiliary input for the quadrotor is given by


(31)
where

󰇧
󰇛
󰇜
󰇛
󰇜
󰇗
󰇨 and


󰇛
󰇜
Proposition 1: if
and with
󰇛
󰇜
having a
quadratic form (30), the auxiliary input
for the quadrotor,
using IDA-PBC approach, can be given by (31).
The stability of the closed-loop dynamics of the quadrotor
system in form (12) is introduced by the following theorem.
Theorem 1: Closed-loop of system (12) written under PCH
form, using control law (31) is asymptotically stable.
Proof: Following the IDA-PBC approach described above,
closed loop system (12) written under PCH model (15) is
equivalent to the desired PCH model (20) using control law
(31).
󰇛
󰇜
is a positive definite function chosen herein as
Lyapunov candidate function where the first time derivative
is
󰇗
󰇛
󰇜
󰇗
󰇛
󰇜
󰇗
󰇛
󰇜
(32)
Using (29), we get
󰇗
󰇛
󰇜
󰇛
󰇜
󰇛
󰇜

󰇛
󰇜
󰇛
󰇜


󰇛
󰇜
(33)
Then
󰇗
󰇛
󰇜

󰇛
󰇜


󰇛
󰇜


󰇛

󰇜󰇛
󰇜
󰇛
󰇜
(34)
So, closed loop of system (12) is asymptotically stable.
V. RESULTS AND DISCUSSION
In this section, we test the effectiveness of the proposed
controller not only in the ideal case but also in the presence of
different disturbances. For the sake of further comparison, we
follow the same protocol and fit the same conditions. The
control parameters are tuned, using Genetic Algorithms (GA),
in the ideal case then kept for the entire proposed scenarios and
for which the objective is to reduce the steady state errors.
Thus, the fitness function is given by


󰇡
󰇢
󰇡
󰇢
(35)
where
and
denote the initial and the final instants of
optimization respectively. The obtained control parameters
are depicted in Table 2.
Table 2: R-MFC control parameters.

23.33

22.19

21.77

5.05

4.86

4.99

18.77

20.672
19.16

4.51

5.00

4.58
For a significant analysis of the features of the proposed
controller, two additional nonlinear controllers are considered.
The first one is the classic model-free technique that exhibits
System
IDA-PBC
Controller
Eq (23)
R-MFC (9)
Uncertainties
estimator
Eq (8)

Nominal
model
Eq (6)
Target model
Eq (20)

Citations
More filters

Proceedings ArticleDOI
12 Jun 2018
TL;DR: A generic and accurate dynamic model, based on Newton-Euler formalism, for multirotor vehicles taking into consideration aerodynamic effects is introduced and the MFC principle is employed to deal with the unknown part of the plant only.
Abstract: This paper introduces a generic and accurate dynamic model, based on Newton-Euler formalism, for multirotor vehicles taking into consideration aerodynamic effects. Besides, the paper considers a reformulation of the well-known Model-Free Control (MFC), which is applied for a low-cost quadrotor even in the presence of various type disturbances, including unmodeled or neglected dynamics, parametric uncertainties, external disturbances, etc. This reformulation takes into consideration the limitation of the estimator used by the classical MFC by using a Sliding Mode auxiliary Controller (SMC) leading to SMC-MFC controller. In addition, instead of using a pure data-driven based control, we introduce the available mathematical dynamics of the system even if they are poorly known. Herein, the MFC principle is employed to deal with the unknown part of the plant only (i.e., unmodeled dynamics, disturbances, etc.). The stability of the closed-loop system is guaranteed and for which a theoretical analysis is provided. The numerical simulations have shown satisfactory results. An in-depth discussion, with respect to the control performance and consumed energy, is highlighted by considering several scenarios and using several metrics.

10 citations


Cites background from "3D trajectory tracking control of q..."

  • ...Its anticipation property makes the control possible even with the presence of disturbances [10]....

    [...]


Dissertation
28 Jun 2018
TL;DR: This works is focused in the conception of a hybrid vehicle with the ability to fly or roll over the ground when necessary and some control algorithms have been developed for each operation mode: on ground or in air.
Abstract: This works is focused in the conception of a hybrid vehicle with the ability to fly or roll over the ground when necessary. A revision of the present prototypes is made and then a new prototype is proposed with enhanced characteristics. The prototype consists of a quadrotor with two additional passive wheels without any other additional servomechanism. The modeling of each operation mode is exposed and then a model for the hybrid form is proposed. In the next section, some control algorithms have been developed for each operation mode: on ground or in air. These algorithms are validated via numerical simulation in the first instance. The last section describes the MOCA room and the system used for capturing the position and attitude of the vehicle. Also, experimental tests were made in order to validate the developed control strategies. It was also validated that the vehicle can follows aerial and terrestrial trajectories. Finally, an observer is implemented in order to identify the moment when the vehicle touches the ground. This knowledge is used to switch from air mode to ground mode without the need of additional sensors.

1 citations


Journal ArticleDOI
TL;DR: This paper investigates and applies a revisited formulation of a reference model-based control strategy by introducing a boosting mechanism, inspired from the popular Active Disturbance Rejection Control technique, and shows promising results by improving the nominal control technique.
Abstract: It is relevant to develop an adequate control algorithm for quadrotors that guarantees a good compromise robustness/ performance. This compromise should be ensured with or without external disturbances. In this paper, we investigate and apply a revisited formulation of a reference model-based control strategy by introducing a boosting mechanism. This mechanism uses an Extended State-based Observer (ESO) to estimate the uncertainties and variety of disturbances. The estimation is continually updated and rejected from the main control loop. The reinforcement principle is inspired from the popular Active Disturbance Rejection Control (ADRC) technique in order to enhance the robustness ability of a nonlinear reference model-based control strategy (i.e. Interconnection and Damping Assignment-Passivity Based Control (IDA-PBC)). The obtained controller is augmented by an additional input, which is derived via sliding modes framework to handle the estimation errors and ensure asymptotic stability. This combination leads to promising results by improving the nominal control technique. The primary results are shown through numerical simulations and are confirmed, experimentally, with several scenarios.

1 citations


Journal ArticleDOI
TL;DR: This reformulation uses an Extended State based Observer (ESO) to estimate the uncertainties and the various disturbances and is used to boost the robustness ability of a reference model-based control strategy (Interconnection and Damping Assignment-Passivity Based Control).
Abstract: In this paper, we investigate and apply a revisited formulation of a reference model-based control strategy. This reformulation uses an Extended State based Observer (ESO) to estimate the uncertainties and the various disturbances. The estimation is continuously updated and rejected from the main feedback loop. This active disturbance rejection is used to boost the robustness ability of a reference model-based control strategy (Interconnection and Damping Assignment-Passivity Based Control). The primary results are shown through numerical simulations.

1 citations


Journal ArticleDOI
TL;DR: A nominal model-based control strategy doted by a robustness boosting mechanism is applied to develop a control algorithm for quadrotors that guarantees a good compromise robustness/performance in presence of external disturbances.
Abstract: The objective is to develop a control algorithm for quadrotors that guarantees a good compromise robustness/performance in presence of external disturbances. Thus, we investigate and apply a nominal model-based control strategy doted by a robustness boosting mechanism. This latter, uses an Extended State-based Observer (ESO) to estimate the uncertainties and the various disturbances. The obtained controller is augmented by an additional input, which is derived via a sliding modes framework to handle the estimation errors and ensure asymptotic stability. The primary results are shown through numerical simulations.

References
More filters

Journal ArticleDOI
TL;DR: This work describes a class of systems for which IDA-PBC yields a smooth asymptotically stabilizing controller with a guaranteed domain of attraction, given in terms of solvability of certain partial differential equations.
Abstract: We consider the application of a formulation of passivity-based control (PBC), known as interconnection and damping assignment (IDA) to the problem of stabilization of underactuated mechanical systems, which requires the modification of both the potential and the kinetic energies. Our main contribution is the characterization of a class of systems for which IDA-PBC yields a smooth asymptotically stabilizing controller with a guaranteed domain of attraction. The class is given in terms of solvability of certain partial differential equations. One important feature of IDA-PBC, stemming from its Hamiltonian formulation, is that it provides new degrees of freedom for the solution of these equations. Using this additional freedom, we are able to show that the method of "controlled Lagrangians"-in its original formulation-may be viewed as a special case of our approach. As illustrations we design asymptotically stabilizing IDA-PBCs for the classical ball and beam system and a novel inertia wheel pendulum.

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"3D trajectory tracking control of q..." refers background in this paper

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    [...]


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TL;DR: This paper describes some features that may be included in the next generation of PID controllers, which seem technically feasible with the increased computing power that is now available in single-loop controllers.
Abstract: Autotuners for PID controllers have been commercially available since 1981. These controllers automate some tasks normally performed by an instrument engineer. The autotuners include methods for extracting process dynamics from experiments and control design methods. They may be able to decide when to use PI or PID control. To make systems with a higher degree of automation it is desirable to also automate tasks normally performed by process engineers. To do so, it is necessary to provide the controllers with reasoning capabilities. This seems technically feasible with the increased computing power that is now available in single-loop controllers. This paper describes some features that may be included in the next generation of PID controllers.

373 citations


"3D trajectory tracking control of q..." refers methods in this paper

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Journal ArticleDOI
TL;DR: It is shown that the introduction of delayed estimates affords significant improvement in numerical differentiation in noisy environment, and that the implementation in terms of a classical finite impulse response (FIR) digital filter is given.
Abstract: Numerical differentiation in noisy environment is revised through an algebraic approach. For each given order, an explicit formula yielding a pointwise derivative estimation is derived, using elementary differential algebraic operations. These expressions are composed of iterated integrals of the noisy observation signal. We show in particular that the introduction of delayed estimates affords significant improvement. An implementation in terms of a classical finite impulse response (FIR) digital filter is given. Several simulation results are presented.

346 citations


"3D trajectory tracking control of q..." refers background in this paper

  • ...Many significant advances on the numerical differentiation of noisy signals are elaborated in the literature [10]....

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Journal ArticleDOI
Abstract: In this paper, a nonlinear control scheme along with its simulation and experimental results for a quadrotor are presented. It is not easy to control the quadrotor because the dynamics of quadrotor, which is obtained via the Euler–Lagrangian approach, has the features of underactuated, strongly coupled terms, uncertainty, and multiinput/multioutput. We propose a new nonlinear controller by using a backstepping-like feedback linearization method to control and stabilize the quadrotor. The designed controller is divided into three subcontrollers which are called attitude controller, altitude controller, and position controller. Stability of the designed controller is verified by the Lyapunov stability theorem. Detailed hardware parameters and experimental setups to implement the proposed nonlinear control algorithms are presented. The validity of proposed control scheme is demonstrated by simulations under different simulation scenarios. Experimental results show that the proposed controller is able to carry out the tasks of taking off, hovering, and positioning.

180 citations


"3D trajectory tracking control of q..." refers background in this paper

  • ...For this reason, many studies have led to the development of sophisticated and robust nonlinear control laws (as for instance [1-3])....

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Journal ArticleDOI
Abstract: In this paper, a finite-time controller is proposed for the quadrotor aircraft to achieve hovering control in a finite time. The design of controller is mainly divided into two steps. Firstly, a saturated finite-time position controller is designed such that the position of quadrotor aircraft can reach any desired position in a finite time. Secondly, a finite-time attitude tracking controller is designed, which can guarantee that the attitude of quadrotor aircraft converges to the desired attitude in a finite time. By homogenous system theory and Lyapunov theory, the finite-time stability of the closed-loop systems is given through rigorous mathematical proofs. Finally, numerical simulations are given to show that the proposed algorithm has a faster convergence performance and a stronger disturbance rejection performance by comparing to the PD control algorithm.

38 citations


"3D trajectory tracking control of q..." refers background in this paper

  • ...For this reason, many studies have led to the development of sophisticated and robust nonlinear control laws (as for instance [1-3])....

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