Unmanned aerial vehicle for transmission line inspection using an extended Kalman filter with colored electromagnetic interference

Journal Pre-proof Unmanned aerial vehicle for transmission line inspection using an extended Kalman filter with colored electromagnetic interference Mathaus Ferreira da Silva, Leonardo M. Honório, Andre Luis M. Marcato, Vinicius F. Vidal, Murillo F. Santos

PII: DOI: Reference:

S0019-0578(19)30487-2 https://doi.org/10.1016/j.isatra.2019.11.007 ISATRA 3394

To appear in:

ISA Transactions

Received date : 11 April 2018 Revised date : 30 August 2019 Accepted date : 4 November 2019 Please cite this article as: M.F. da Silva, L.M. Honório, A.L.M. Marcato et al., Unmanned aerial vehicle for transmission line inspection using an extended Kalman filter with colored electromagnetic interference. ISA Transactions (2019), doi: https://doi.org/10.1016/j.isatra.2019.11.007. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

© 2019 Published by Elsevier Ltd on behalf of ISA.

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Unmanned Aerial Vehicle for Transmission Line Inspection Using an Extended Kalman Filter with Colored Electromagnetic Interference Mathaus Ferreira da Silva1 , Leonardo M. Hon´ orio1,∗, Andre Luis M. Marcato1 , 1 Vinicius F. Vidal , Murillo F. Santos1

Abstract

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Strong electromagnetic fields such as those generated by power stations and transmission lines cause disturbances that affect the on-board sensors of an autonomous unmanned aerial vehicles (AUAVs) and may lead to aircraft instability. To mitigate this effect, we use an extended Kalman filter with colored

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noise. In addition to the traditional aircraft dynamics, this approach considers the electromagnetic fields of transmission lines and their position, electrical current, and tower topology. In this way, the filter can predict and correct the interference in the aircraft sensors, thereby guaranteeing flight stability even

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when the AUAV is very close to the electromagnetic sources. This approach enables the AUAV to operate closer to the transformers and transmission lines, thereby paving the way for better autonomous inspection performed by electrical companies and further development of new technologies. To prove the effectiveness of this approach, theoretical and practical results involving a survey of transmission lines are demonstrated. Keywords: Transmission Lines Inspection; Extended Colored Kalman Filter;

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Unmanned Aerial Vehicle; Sensor Prediction; Electromagnetic Interference.

∗ Corresponding

author Email address: [email protected] (Leonardo M. Hon´ orio)

Preprint submitted to Journal of LATEX Templates

November 5, 2019

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1. INTRODUCTION

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The Autonomous Unmanned Aerial Vehicle unmanned aerial vehicles (UAVs) [1] field is one of the fastest growing areas in applied robotics. UAVs are used in military and civilian applications such as real-time reconnaissance [2], main5

tenance [3], surveillance [4], target acquisition [5], atmospheric sciences [6], and disaster relief [7]. One of the many concerns involving these vehicles is with regard to safe navigation and control [8, 9, 10] in several conditions including environmental disturbances [11].

Among all possible applications of autonomous unmanned aerial vehicles (AUAVs), visual and thermal inspections of transmission lines are considered the

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top priorities by electric companies. However, despite the enormous advances in the autonomous unmanned aerial vehicle (AUAV) field, most of them rely on manually operated AUAVs, manned helicopters, and airplanes to inspect

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thousands of kilometers of transmission lines. These inspections aim to obtain visual and multi-spectral related data from components such as insulators and splices, to identify possible nonconformities [12, 13]. Regarding the operational costs, inspections by manned helicopters are far more expensive than manually

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operated AUAVs[14].

As examples of transmission line inspections, in [15] a helicopter-type air20

craft called SmartCopter was applied to the monitoring of power transmission lines and components. However, the aircraft must operate at a safe distance of 50 m from the transmission line owing to electromagneticinterference, which, according to the authors, decreases the quality of the images captured by the camera. The authors concluded that the system can still be improved, but could be used as a good reference point for the power transmission industries.

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In [16],the authors approached the planning of trajectories for the inspection

of both towers and transmission lines. A genetic algorithm (GA) was used for both schedules, considering a safe distance of 10 m from the transmission line. The authors used a multi-rotor vehicle for tower monitoring and a fixed-wing

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aircraft to monitor the lines.

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There are several studies based on transmission line inspections by UAVs

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[17, 18, 19]; in all the presented approaches, a long safe distance is maintained between the UAVs and the electromagnetic source. This range increases when substations or power transformers are monitored [20]. It is possible to ac35

complish missions by maintaining a long safe distance; however, inspections from shorter distances, especially infrared inspections, can mitigate several measurement-based effects [21].

The reason for maintaining this distance is that transmission lines are significant electromagnetic disturbance sources [22]. Thus, the operation of autonomous vehicles guided by sensors that are susceptible to interference be-

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comes complex and dangerous for both the lines and the vehicle. A partial approach to solve this problem involves using computer vision techniques to acquire knowledge regarding the position of the vehicle, and mitigating electro-

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magnetic disturbances [23, 24]. However, one drawback of this methodology is that the AUAV can only approach transmission lines from areas where it has a direct view of the anchor points.

Therefore, reducing the effects of electromagnetic interference in AUAVs may improve the monitoring quality, thereby allowing the vehicle to reduce

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its distance from the transmission line and improve the monitoring quality; as a consequence, a higher identification accuracy can be achieved. To deal with nonlinear and colored interferences, the literature shows that minimum-variance [9, 25] and several Kalman filter variations [25, 26, 27, 28] are good alternatives. These variations are applied in several areas ranging from marketing [29] and robotics [30] to biomedicine [31] and several others. One interesting approach 55

is implemented when colored noises are considered. In this case, it is possible

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to augment the number of states of the original system by incorporating a mathematical model related to the noise [32]. Although the final system is a traditional extended Kalman filter (EKF), the formulation embeds a colored noise. Therefore, for simplicity, this augmented state type of EKF is called

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extended colored Kalman filter (ECKF) in this study. Under these amendments, the present study proposes a methodology that 3

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is capable of identifying and compensating for the electromagnetic interference

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generated by transmission lines and other disturbance sources, thereby allowing the use of AUAVs at a very close distance and improving the quality of monitor65

ing using visual and/or multi-spectral cameras. In this context, when an AUAV approaches an object, the alteration of the electromagnetic field is perceived by its sensors and then compensated for, thereby allowing the vehicle to operate normally. Therefore, this study presents a new application of EKFs applied to autonomous navigation in environments with a high level of electromagnetic

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disturbance. Moreover, this methodology allows the AUAV to safely approach

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transmission lines even in the presence of high currents.

To achieve this objective, this study uses a nonlinear kinematics and dynamics model of a quadrotor-type AUAV along with nonlinear magnetic field interference generated by the respective model of the transmission line. All these models (kinematics, dynamics, and electromagnetic) are used to assemble

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an EKF with colored noise that can identify and compensate for the electromagnetic interference in the values read by the sensors of the vehicle. Thus, it is possible to reduce the effects of electromagnetic interference on the vehicle, thereby allowing autonomous flight as previously planned. To present this methodology, the paper is organized as follows: the AUAV

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and transmission line modeling are presented in Section 2, the ECKF formulation joining these two models is shown in Section 3, several results, both theoretical and practical, are demonstrated in Section 5, and, finally, the conclusion is drawn in Section 6.

2. AUAV AND TRANSMISSION LINE MODELING

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2.1. AUAV Modeling The AUAV used in this study is a quadrotor. This architecture was chosen

because of its flight characteristics [33]. The vehicle used in this study was designed and built to be simple, lightweight, and versatile as shown in Figure 1a.

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The design did not use mu-metal shields [34] because this would only reduce the

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(b) Quadrotor axes representation.

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(a) Real quadrotor.

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Figure 1: Designed and real AUAV.

electromagnetic field in one axis and the AUV must fly around the transmission

Autopilot board.

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line for the desired inspections. The vehicle is equipped with a Pixhawk Px4

The inertial coordinate system considered was the north-east-down (NED) 95

as shown in [1, 35]. The following state variables were adopted: the vector

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η1 = [pn , pe , h]T represents the inertial north, east, and altitude (facing down) positions along the (ˆii , ˆj i , −kˆi ) axes representing the inertial frame; the vector η2 = [φ, θ, ψ]T represents the roll, pitch, and yaw angles considering the vehicle

frame (ˆiv , ˆj v , −kˆv ); the vectors ν1 = [u, υ, ω]T and ν2 = [p, q, r]T represent the 100

three-dimensional speeds and angular velocities over the axes (ˆib , ˆj b , −kˆb ) of the

body frame [36, 37].

Summarizing, the quadrotor position is defined by η1 ∈ R3 in the inertial

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frame (F i ), whereas its angles are defined by η2 ∈ R3 in the vehicle frame (F v ),

and ν1 ∈ R3 and ν2 ∈ R3 are the linear and angular velocities in the vehicle

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body (F b ).

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The velocity can be represented by the following Equations 1 and 2: η˙ 1

=

J1 (φ, θ, ψ)ν1

(1)

η˙ 2

=

J2 (φ, θ)ν2

(2)

where

=

J2 (φ, θ)

=

cθcψ

sφsθcψ − cθsψ

   cθsψ sφsθsψ + cφcψ  −sθ sφcθ   1 sφtθ cφtθ      0 cφ −sφ    0 sφ/cθ cφ/cθ

cφsθcψ + sφsψ



  cφsθsψ − sφcψ   cφcθ

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J1 (φ, θ, ψ)



(3)

(4)

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with c(·) = c(·) and s(·) = s(·), and where J1 (φ, θ, ψ) ∈ R3×3 and J2 (φ, θ) ∈ R3×3 are the transformation matrices that map the body frame (F b ) into the

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inertial (F i ) and vehicle (F v ) frames, respectively. Considering the mass (m), the Coriolis–centripetal forces, both the inertia products and momentum over the body, the vehicle dynamics can be described

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by the Newton–Euler method as shown in Equations 5 and 6

ν˙ 1

=

ν˙ 2

=

1 · (F + Fg − mS(v2 ) · ν1 ) m    τφ      −1  ICG ·  τθ  − S(ICG · ν2 )    τψ

(5)

(6)

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where F ∈ R3 and Fg ∈ R3 represent the propulsion and gravitational forces

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acting over the vehicle in the body frame F b , respectively. The function S(·) :

R3 7→ SO(3) is a skew-symmetric operator; ICG ∈ R3×3 is the inertia mo-

mentum matrix [38]. The vector [τφ , τθ , τψ ]T represents the inertia momentum actions over the vehicle in the body frame F b . 6

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sum of each motor contribution (Fm∗ ):

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The propulsion force F = [0, 0, Fk ]T , where Fk ∈ R is composed of the

Fk = Fm1 + Fm2 + Fm3 + Fm4 and the gravitational force is given by

T

Fg = mJ1T (φ, θ, ψ) · [0, 0, g]

(7)

(8)

The motors also cause rolling, pitching, and yawing torques represented by τφ , τθ , and τψ , respectively, as shown in Equation 9: =

τθ

=

τψ

=

√ l( 2/2)(Fm2 + Fm3 − Fm1 − Fm4 ) √ l( 2/2)(Fm1 + Fm3 − Fm2 − Fm4 )

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τφ

(τm1 + τm2 − τm3 − τm4 )

(9)

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where m(1...4) represents each motor, and l is the quadrotor arm length, that is, the distance between the body frame origin and one of the motors once the vehicle is assumed to be symmetric.

Finally, it is possible to define the control vector as u ∈ R4 = [Fk τφ τθ τψ ]T .

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2.2. Magnetic field and transmission line model The transmission line electromagnetic field can be modeled using the Biot– 130

Savart and Amp`ere physical laws [39, 40]. The Biot–Savart law considers that the intensity of the total magnetic field vector can be calculated by integrating the contributions of the magnetic fields associated with stretches of a wire traveled by electrical current. The Amp`ere law considers that the integral of the

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magnetic field around any closed path is equal to the product of a constant and 135

the current flowing through that area [41]. These laws are evaluated by considering the transmission line frame (F L ) as

shown in Figure 2a, and Figure 2b shows the schematic to develop the module of the differential electromagnetic field element.

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(a)

Schematic

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(b) Magnetic field of an infinite wire.

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the line frame.

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Figure 2: Magnetic field over a transmission line.

Based on the Biot–Savart law and Figure 2b, the module of the differential 140

element of the magnetic field (dB) produced by a differential current element

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(i dx) can be calculated using Equation 10: dB =

µ0 sθ i dx 4π r2

(10)

where θ is the angle between the current direction and the radius, r ∈ R, towards the point of interest, µ0 = 4π × 10− 7 (H/m) is called the vacuum permeability 145

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constant given in units of Henry by meter, dx is the wire length differential element, and the orientation of dB is the same of the vector dx × rˆ (along ˆ). Considering an infinite wire and using Pythagoras theorem to substitute the

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r component, it is possible to obtain p r = x2 + z 2 z sθ = √ x2 + z 2 Z ∞ Bz = 2 dB 0 Z µ0 i ∞ z dx = 2 2π 0 (x + z 2 )3/2 µ0 i = 2πz

(11)

where i is the current flowing through the conductor, z is the orthogonal distance between the point of interest and the conductor, x is the distance between the 8

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differential element dx and the orthogonal projection of the point of interest

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ˆ over the conductor, and Bz ∈ R is the unidimensional projection over axis k. It is also possible to conclude by analyzing both Figure 2b and Equation (11) that the component Bx is null.

Considering a projection in point belonging to a plane orthogonal to the 155

ˆ > as shown in Figure 3, B ∈ R2 can be represented transmission line, i.e., < ˆ, k

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as a vector by Equation 12:

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ˆ >. Figure 3: Magnetic field projection over a point onto < ˆ, k

B=

µ0 i aϕ 2πr

(12)

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where aϕ ∈ R2 and can be written in Cartesian form as follows:   z − zn x − xn aϕ = − , r r p 2 r = (xn − x) + (zn − z)2

where (z − zn ) is the component in z of r and (x − xn ) is the x component of r.

2.2.1. Electromagnetic field of transmission lines As shown in Section 2.2, the magnetic field of a transmission line at any

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point can be calculated based on the Biot–Savart equation. Hence the magnetic field equation is µ0 (ir + jiim )(za − zn ) 2π((zn − za )2 + (yn − ya )2 ) µ0 (ir + jiim )(ya − yn ) =− 2π((zn − za )2 + (yn − ya )2 )

Bya = −

(13)

Bza

(14)

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where Bya and Bza are the components y and z of the magnetic field, respec-

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tively, ir and iim are the real and imaginary parts of the complex numbers, respectively. One can still write By(r)

= Bya(r) + Byb(r) + Byc(r) + ... + By∗(r)

By(i)

=

Bya(i) + Byb(i) + Byc(i) + ... + By∗(i)

Bz(r)

=

Bza(r) + Bzb(r) + Bzc(r) + ... + Bz∗(r)

Bz(i)

=

Bza(i) + Bzb(i) + Bzc(i) + ... + Bz∗(i)

where (i) and (r) represent the real and imaginary parts, respectively, and

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∗ represents any other electromagnetic source that contributes to the field in the environment. On transmission lines, the first three components that are the contribution of phases A, B, and C are used; however, to simulate other 170

equipment such as transformers, other components can be included. Thus, the

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components can be described by Equations 15 and 16. By = By(r) + jBy(i)

(15)

Bz = Bz(r) + jBz(i)

(16)

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Based on Equations 13 and 14 and considering phases A, B, and C of a three-phase transmission system, the resulting electromagnetic field at a given point can be written as

(17)

Bz = Bza + Bzb + Bzc

(18)

with module given by q

(Bya + Byb + Byc )2(r) + (Bya + Byb + Byc )2(i) q |Bz | = (Bza + Bzb + Bzc )2(r) + (Bza + Bzb + Bzc )2(i)

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By = Bya + Byb + Byc

|By | =

where, finally, we obtain q |B| = |By |2 + |Bz |2 ,

θ = arctan 10



|Bz | |By |



(19)

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2.2.2. Evaluating the Electromagnetic Field over the Vehicle Body Frame

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The electromagnetic field is given with respect to F L . It is possible to see

that F L is adopted as having the x (ˆ ı) axis along the wire; thus, the final axes 180

have orientation according to the angles (φL , θL , ψL ). Therefore, it is possible to rotate the magnetic field from F L to F b as shown in Equation 20: BF b

= J1T (φL , θL , ψL )BF L

(20)

where BF L ∈ R3 = [0, By , Bz ]T is the electromagnetic field in F L , and BF b ∈

R3 is the electromagnetic field in the body frame F b . 185

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Considering the magnetic field of the Earth, the magnetometer measurement is given by Equation 21:

BM AG

=

BF b + BE

(21)

where BE ∈ R3 is the earth’s magnetic field. Finally, it may be noted that

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BM AG can be represented by a function that depends on the position and angle of the aircraft as shown in the following Equation 22, considering that both position and orientation of the transmission lines are also known and treated as 190

constant:

(22)

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BM AG = q(pn , pe , h, φ, θ, ψ)

3. EXTENDED KALMAN FILTER WITH COLORED MEASUREMENT INTERFERENCE NOISE The EKF is an efficient method for incorporating noisy measurements to estimate the system states in nonlinear dynamics systems [42]. Because the 195

objective is the monitoring of a transmission power line, the presence of a non-

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Gaussian time-variant noise with nonzero mean value must be considered, an approach necessary to study this type of noise, better known as colored noise [43].

Although different references relating the Kalman filter (KF) to colored noise

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([44], [43])were found, there is no related work, as per our knowledge, that relates EKF to colored noise to mitigate electromagnetic disturbances. Thus, this 11

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study presents the necessary adaptations and the final mathematical formulation

model.

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applied to ECKF for considering the AUAV dynamics and the electromagnetic

Consider a nonlinear discrete time system with linear measurement given by

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xk = f (xk−1 , uk ) + k yk = Hk xk + υk k ∼ N (0, Qk ) υk ∼ N (0, Qυk )

(23)

where the system f (·) ∈ Rn is a nonlinear function. The variable xk ∈ Rn

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represents the system states, the matrix Hk ∈ Rm×n maps the state variables

to the measurements, yk ∈ Rm is the measurement vector, k ∈ Rn is the zero mean process noise with covariance Qk ∈ Rn×n , and υk ∈ Rm is a white

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measurement noise with covariance Qυk ∈ Rm×m (see [45]).

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Now assume that the variable υk in Equation (23) is no longer a white noise. Instead, it has a nonzero mean with a nonlinear variation: υk = g(υk−1 ) + ζk

(24)

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where g(·) ∈ Rm is a nonzero mean, a well-known nonlinear function representing the interference. It can be seen that υk is a colored noise because it is 215

dependent on itself at a previous time, where ζk ∈ Rm is white noise with zero mean correlated to the function interference g(·). Thus, combining Equations (23) and (24), we have

xk = f (xk−1 , uk ) + k υk = g(xk−1 , υk−1 ) + ζk

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yk = Hk xk + υk

(25)

k ∼ N (0, Qk ) ζk ∼ N (0, Qζk )

This set of equations represents the nonlinear system with the presence of a

moving average noise (colored) where Qζk ∈ Rm×m is the covariance matrix of

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ζk . 12

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Performing a first-order Taylor series expansion around x ˆ+ ˆ+ k−1 , where x k−1

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is the a posteriori estimation of x ˆk−1 , it is possible to deduct the equations of the following steps. Prediction Step.

x ˆ− x+ k = f (ˆ k−1 , uk )

+ Pk− = Fk Pk−1 FkT + Qk

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where

∂f Fk = ∂x xˆ+

(26) (27) (28)

(29)

k−1

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and Pk ∈ Rn×n is the covariance of the estimation error with Pk− , and Pk+ is a

z˜k = yk − Hk x ˆ− x− k − g(ˆ k , υk−1 ) − ζk

(30)

+ Sk = Ωk Pk−1 ΩTk + Qζk

(31)

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Update Step.

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priori and a posteriori estimations.

Kk = Pk− ΩTk Sk−1

(32)

x ˆ+ ˆ− ˜k k =x k + Kk z

(33)

+ Pk+ = (I − Kk )Pk−1

(34)

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where

Ωk = Hk +

∂g ∂x xˆ−

(35)

k

Integrating the AUAV dynamics with the electromagnetic model from Sec-

tions 2.1 and 2.2 results in

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=

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xk

[pn , pe , h, u, υ, ω, u, ˙ υ, ˙ ω, ˙ p, q, r, p, ˙ q, ˙ r, ˙ φ, θ, ψ]

yk

= xk  T g(·) = 017 | − q(pn , pe , h, φ, θ, ψ)

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(36) (37) (38)

where 017 ∈ R17 is a vector of zeros, and q(·) represents BM AG demonstrated in Equation (22), which embeds the electromagnetic model. Therefore, the final yaw (ψ) variable is a function of the current yaw reading, attitude angles, and the north, east, and altitude positions. Thus, any control looping would use

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this filtered variable directly without any further manipulation.

4. ATTITUDE AND POSITION CONTROL LOOPS

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The successive loop closure technique is defined as an indirect approach to the multi-rate synthesis of the control loop series [1, 46]. Following that concept, faster loops are placed internally, and they are responsible for the angular attitude stability. External loops are slower and control 240

the global position. Figure 4 is a summarized diagram representing the control

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loops.

Figure 4: Block diagram of the implemented successive loop closure technique.

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Figure 4 shows that the altitude (hd ), north position (Pnd ), east position

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(Ped ), and yaw angle (ψ d ) are the inputs to the controller. Moreover, the outputs are the propulsion force (Fk ), roll (τφ ), pitch (τθ ), and yaw torques (τψ ). The 245

outputs feed the control allocation algorithm presented in [47] and summarized by Equations (7) and (9). This yields four pulse-width modulated (PWM) signals (δ1 , δ2 , δ3 , and δ4 ) that control the AUAV.

The altitude, roll, pitch, and yaw proportional–integral–derivative (PID) controllers share the same topology. For simplicity, just the altitude loop control 250

is exemplified. The topology is shown in Figure 5 where the variables (kph , kih , kdh )

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represent the proportional, integral, and derivative gains, respectively. It is also possible to note that the derivative control action is obtained directly through

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the vertical velocity (ω), and abrupt responses due to noise are avoided.

Figure 5: PID topology implemented in the AUAV altitude control loop.

Figure 6 shows the position control loop topology that forces the error through a feedforward PD structure to become zero [47].

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Figure 6: Position controller topology implemented in the AUAV Px control loop.

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Table 1 lists the adopted controller gains tuned according to [1, 48, 49, 50]. Table 1: PD and PID controller gains used in the tests.

Gain

Value

Gain

Value

Gain

Value

kpPx

2.081

kiPx

0

kdPx

1.076

P ki y

0

P kd y

1.076

30

kih

2

kdh

10

7

kiφ

4.26

kdφ

4

7

kiθ

4.26

kdθ

4

5

kiψ

0

kdψ

0

kph kpφ kpθ

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kpψ

2.081

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P kp y

5. RESULTS

The results are divided into two parts: the first part contains the theoretical evaluation of the proposed approach, and the second part is a worst-case real scenario.

5.1. Simulated Results

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For the first part, the theoretical evaluation of the magnetic field was mod-

eled based on the data of a real 345 kV transmission line 1 . Because the magnetic 1 data

provided by TBE (Transmissoras Brasileiras de Energia)

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field produced by any line depends directly on the current, the measurements were acquired during a 24 h period. These measurements were obtained on July

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31, 2017, and they can be observed in Figure 7.

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100

80

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Electrical Current(A)

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60

40

0

5

10

15

20

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Time (H)

Figure 7: Electrical current of the transmission line in a 24 h period.

Within 5 m of sampling, it can be noticed that there are cases with a vari-

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ation of 60 A. To prevent this kind of oscillation from abruptly changing the electromagnetic field, it is necessary to maintain communication between a con270

trol center and the vehicle so that, regardless of the electrical current, the model is updated with the appropriate correction in real time. In addition to the current, the layout is also important to model the system. The adopted layout was the real one used for the same 345 kV transmission line. Figure 8 illustrates its layout and dimensions. Moreover, the evaluated magnetic field considering a 151 A current level (used in all simulations) can be

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observed. Hotter colors represent higher intensities of the electromagnetic field.

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Figure 8: Possible configuration of tower dimensions and conductors of a 345kV power trans-

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mission system.

Nonintrusive performance indices (NIPIs), integrated absolute error (IAE), and integrated squared error (ISE) indices, which consider the integral of the error [51], are used for system auditing. The IAE, shown in Equation 39,

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IAE =

Z

∞

0

|ε(t)|dt

(39)

integrates the absolute error over time without adding a penalty to any other characteristic of the system response [52]. This causes any error in the system response to have the same weight. In this way, a system with a low IAE tends to minimize its average error. The ISE index,

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ISE =

Z

∞

ε(t)2 dt

(40)

0

integrates the squared error over time. Thus, an optimized system considering this index tends to minimize large-amplitude errors more intensely but may present small-amplitude steady-state errors [53]. Owing to the disadvantage of quantifying on a larger scale the initial errors that may occur in oscillatory

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systems, this index is more suitable for control loops with less oscillatory char-

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acteristics.

The experimental results are presented considering two scenarios: (i) a traditional EKF with the AUAV dynamics but without the state augmentation; and (ii) the proposed ECKF approach, considering both the AUAV dynamics 295

and the electromagnetic (EM) disturbances.

Both results were compared with regards the IAE and ISE performance indices described previously.

All simulations considered a 10 Hz frequency for the position loop and 100

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Hz for the attitude loop. In addition, three paths are considered: the planned, the real (considering the states from simulation), and the filtered trajectories. Thone latter path will consider the two scenarios described previously, that is, with and without electromagnetic compensation.

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5.1.1. Flight situation 1

The purpose of situation 1 is to use the AUAV on a route where it is required 305

to cross over a transmission line. This is a common operation when spacers and insulators require inspection. In this case, the vehicle operates 5 m above the

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transmission line, and the setpoints (SP) are described in Table 2. This path is shown in Figure 9 by the green line (planned), and it is the same for both simulations.

Table 2: SP required for the flight situation 1.

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Control Loop

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Time 0s

10 s

70 s

North Position (m)

0

0

70

East Position (m)

0

0

0

Altitude (m)

0

23.8

23.8

◦

0

0

0

Yaw ( )

Figure 9a shows the trajectories without electromagnetic compensation. In

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this scenario, the vehicle was not able to reach the final location. The inter-

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ference made the controller act as though expecting one behavior that was not operational. It is possible to see that by analyzing the blue path (the real one), as the AUAV moves closer to the first transmission line, the readings of the yaw 315

angle change drastically, thereby making the vehicle diverge from the desired route. Figure 9b shows the result from the same planned path, when applying the electromagnetic modeling in the ECKF. It can be observed that the vehicle has followed the path as desired, obtaining a more reliable trajectory. Table 3 corroborates this conclusion by showing the performance indexes for both methodologies.

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Real Planned EKF

30

30

20

H(m)

20

10

0 100 80

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H(m)

Real Planned ECKF

10

0 100

100

80

60

120

80 100

60

80

60

40

40

20

Pn(m)

20

0

0 -20

Pe(m)

(a) EKF without electromagnetic compensa-

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tion.

40

60 40

20

Pn(m)

20 0

0

Pe(m)

(b) ECKF compensation.

Figure 9: Flight situation 1.

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Table 3: Flight situation 1: NIPI.

NIPI

EKF

ECKF

IAE

245.46

2.02

ISE

10067.09

1.16

5.1.2. Flight situation 2 Situation 2 shows a trajectory used to inspect transmission line conductors

where the AUAV must follow the line horizontally. The SPs for this mission are

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described in Table 4. Again, this path is shown in Figure 10 as a green line and is the same for both simulations.

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Table 4: SP for flight situation 2.

Control Loop

Time

0s

10 s

50 s

100 s

150 s

North Position (m)

0

0

40

40

0

East Position (m)

0

0

10

50

50

Altitude (m)

0

18.8

18.8

18.8

18.8

◦

0

0

0

0

0

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Yaw ( )

Figure 10a shows the result without the electromagnetic modeling. As expected, as soon as the vehicle approaches the conductor, the electromagnetic

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interference makes the AUAV diverge from the desired path. It can be seen that the vehicle correctly navigates towards the first SP, but soon after it loses 330

its heading reference, causing position instability. Figure 10b shows the same path simulation, using the proposed approach.

H(m)

20

10

0 100

Real Planned EKF

Real Planned ECKF

30

20

H(m)

30

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It is possible to see that the vehicle has followed the path correctly.

0 100

80

60

40

100

60

80 40

40

20

60 40

20

20

0

0

Pn(m)

Pe(m)

(a) EKF without compensation.

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120

80 100 80

60

Pn(m)

10

20 0

0

Pe(m)

(b) ECKF compensation.

Figure 10: Flight situation 2.

Table 5 analyzes the simulations by using the NIPIs. It can be concluded

once again that the technique has achieved better results.

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Table 5: Flight situation 2: NIPI.

NIPI

EKF

ECKF

IAE

379.44

ISE

20551.0

5.1.3. Flight situation 3

3.47

2.65

In this simulation, the vehicle must fly around a transmission tower to inspect its components. For that, the flight path was chosen to make a 360◦ circle around

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the tower at a 12 meter radius from its center. Figure 11 shows the planned path as a green line.

Figure 11a shows that the executed path has diverged from the desired one.

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Figure 11b presents the path used by the ECKF technique. Although a rota-

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tional movement around the tower demands a more precise measurement correction, the proposed technique has allowed the vehicle to follow the path as planned. The results comparing both methodologies for this scenario are listed 345

in Table 6 where, again, the numerical indexes have shown the effectiveness of

H(m)

20

10

0 40

30

Real Planned EKF

30 20 10

20

40

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-30

Pn(m)

10

-20

30 10

-20

0 -30

0 -10 -20

20

-10

30

20

-10

40

0

10

Pn(m)

10 0 40

30

0

Real Planned ECKF

20

H(m)

30

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the proposed approach.

-10 -20

Pe(m)

Pe(m)

(a) Trajectory without compensation.

(b) ECKF compensation.

Figure 11: Flight situation 3.

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Table 6: Flight situation 3: NIPI.

NIPI

EKF

IAE

276.9019

4.8090

ISE

8642.1

2.2402

5.2. Practical Results

ECKF

Practical tests were made at the Barra Grande power plant. Situated in the state of Santa Catarina, this plant has an installed power of 690 MW. Its location can be seen in Figure 12, and its georeferenced latitude and longitude

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position are -27◦ 46’ and 51◦ 13’, respectively [54].

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Figure 12: Barra Grande Hydroelectric plant in Google Maps.

As a short description, this plant has three, three-phase systems of 230 kV

and is responsible for 7800 A. The scenario has also some peculiarities owing to local geography. There are three transformers near to the transmission lines

355

feeding a minor tower, which is responsible for pointing the lines to a nearby

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slope. Each tower holds three conductors, generating a total of nine cables

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placed side by side. From the towers, the conductors are anchored at a nearby slope, then routed back over the power station to a major transmission line, and finally directed to the local substation. This layout creates a unique situation 360

where each conductor generates “two” transmission lines, vertically placed, with different current direction. Moreover, nearby transformers generate significant electromagnetic disturbances, configuring a possible worst-case scenario considering inspections of nearby EM sources and making traditional autonomous flight impracticable. The schematics and the real scenario can be seen in Figures 13 and 14, respectively.

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Figure 13: Scenario layout

Even with this chaotic scenario, there are several elements that must be inspected periodically from both above and below the transmission lines. For instance, in addition to the traditional electric power components, the slopes

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present a safety threat and must be inspected carefully. Therefore, the devel-

370

opment of AUAVs that are able to conduct these operations is crucial. To compensate for the real scenario layout, some components are added

to the electromagnetic model to provide a better signal estimation. In the presented formulation, the electromagnetic field evaluation is done considering a

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Figure 14: Real image showing the nearby slope and the first transmission towers

conductor from minus to plus infinity. This approach cancels some components of the electromagnetic field, and, because this scenario involves disturbances

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at the beginning of the transmission line, this simplification could not provide good results. To compensate for this situation, a punctual electromagnetic load is added at the beginning of the line representing components that will not be canceled. The resulting field displacement is shown in Figure 15. The load is

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defined empirically to approximate the measured signal to the estimated one.

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Figure 15: Magnetic field of a noninfinite wire.

Considering an inspection mission, the vehicle is set to follow a path under

the 9 conductors (18, considering they are routed back) and sideways to the power transformers with minimum head position deviation (yaw angle). Figure

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16 shows the schematic of the real triple three-phase systems and the executed path.

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H(m)

Real ECKF

10

0 120 100 80 60

60

40

40

20

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Pn (m)

20

0

0

-20

Pe (m)

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Figure 16: Real environment reproduced in the simulation.

Owing to the company’s safety policies, the vehicle was not allowed to be used in autonomous mode; thus, it was manually operated under the transmission lines. All the necessary information was acquired and processed, generating an autonomous heading output that was used by the operator to drive the UAV. This means that, although the mission was not fully autonomous, the final result

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was similar.

Figures 17 and 16 show the real magnetic field measured by the sensors and that estimated by the model, respectively. It is possible to see that the estimated electromagnetic interference (red line) 395

has presented an approximated result from the real measurement (blue line). Variations between the signals were caused by components, such as metallic

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structures and others, that were not considered in the mathematical model. Applying the proposed technique, the electromagnetic interference consid-

ered by the ECKF filter corrected the inertial measurement unit (IMU) readings,

400

compensating for any possible major error. Figures 18 and 19 present the vehicle position and heading, respectively. It

is possible to see that it moved forward without lateral deviation or considerable 26

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X Mag

Measured Simulated

0.5 0 -0.5 -1 0

5

10

15

25

0.5

0

-0.5 0

5

10

30

35

40

45

50

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0

-1

15

20

25

30

35

40

45

50

30

35

40

45

50

Time (s) Z Mag

0.5

-0.5

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Per-unit (PU)

20

Time (s) Y Mag

1

Per-unit (PU)

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Per-unit (PU)

1

0

5

10

15

20

25

Time (s)

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Figure 17: Magnetic field of each axis component.

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positioning or heading errors.

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Converted Longitude (m)

Relative Position

15

10

5

0 0

5

10

15

20

25

30

35

40

45

50

55

Converted Latitude (m)

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Figure 18: Real vehicle position.

1

0.5

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Degree

0

(ECKF Result)

-0.5

-1

-1.5

-2

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-2.5

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

Sample

Figure 19: Heading of the AUAV.

Figure 20 shows the final perceived interference angle by the sensor and that estimated by the model.

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Real Estimated

40 20

Degree

0 -20 -40 -60 -80 -100 0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

Sample

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Figure 20: Final angle interferences.

It is possible to see that the estimated interference angle was slightly different from the real one; however, they share the same behavior and characteristics.

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This was precise enough to allow a safe mission.

Finally, this scenario has demonstrated that the methodology was able to 410

predict and correct the sensor readings even in the presence of several sources of high-level electromagnetic disturbances. This makes it possible to safely con-

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duct autonomous flights around the facility.

6. CONCLUSIONS 415

In this study, we proposed a methodology to mitigate the effects of electromagnetic interference on AUAVs. This was achieved by incorporating the Biot-Savart physical equations as colored noise in a traditional EKF along with the flight dynamics of the vehicle.

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The resulting ECKF proved to be very efficient and accurate even when

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subjected to extremely noisy interferences. This approach allowed the mitigation of the electromagnetic interference in the IMU sensors of the UAV, thereby allowing the vehicles to fly closer to the transmission lines and other elements. Besides the direct result of providing better inspections, this correction allows

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that the control actions be more precise and stead, improving flying conditions, image acquisitions and battery life.

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By using computational simulations it was possible to verify the AUV operation by comparing the trajectories with and without the interference attenuation provided by the filter and it was possible to confirm a major impact over the flight stability. Moreover a real scenario in a hydroelectric power generation 430

facility was used to test the vehicle. As a result the AUV was able to correctly navigate near 230kV transmission lines, high power transformers, transmission towers and generators providing a 7800A current flow.

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Finally, as future work, this approach enables several other researches and development projects. For instance, it is possible to apply this technique on 435

UAVs, thereby making them land and dock autonomously on transmission lines. This can enable several new features such as fast sensor installation on hotlines

Acknowledges

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and UAV recharging, which can increase the mission range.

The work reported in this paper was performed as part of an interdisci440

plinary research and development project undertaken by Federal University of

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Juiz de Fora. The author acknowledge the financial funding and support of ´ the following companies: TBE, BAESA, ENERCAN and FOZ DO CHAPECO, under supervision of ANEEL - The Brazilian Regulatory Agency of Electricity, through Project numbers PD PD-04380-002/2015 and 03936-2607/2017.

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References

Jo

[1] R. W. Beard, T. W. McLain, Small unmanned aircraft: Theory and practice, Princeton University Press, Princeton, EUA, 2012.

[2] V. Roberge, M. Tarbouchi, G. Labont´e, Comparison of parallel genetic algorithm and particle swarm optimization for real-time UAV path planning,

450

in: IEEE Transactions on Industrial Informatics, Vol. 9, IEEE, 2013, pp. 132–141. 30

Journal Pre-proof

[3] D. Behnke, P.-B. Bok, C. Wietfeld, UAV-based connectivity maintenance

pro of

for borderline detection, in: 77th Vehicular Technology Conference (VTC Spring), IEEE, 2013, pp. 1–6. 455

[4] R. W. Beard, T. W. McLain, D. B. Nelson, D. Kingston, D. Johanson, Decentralized cooperative aerial surveillance using fixed-wing miniature UAVs, in: Proceedings of the IEEE, Vol. 94, IEEE, 2006, pp. 1306–1324. [5] M. Quigley, M. A. Goodrich, S. Griffiths, A. Eldredge, R. W. Beard, Target acquisition, localization, and surveillance using a fixed-wing mini-uav and gimbaled camera, in: Proceedings of the International Conference on

re-

460

Robotics and Automation (ICRA), IEEE, 2005, pp. 2600–2605. [6] G. L. Stephens, S. D. Miller, A. Benedetti, R. B. McCoy, R. F. McCoy Jr, R. G. Ellingson, J. Vitko Jr, W. Bolton, T. P. Tooman, F. P. J. Valero,

465

lP

The department of energy’s atmospheric radiation measurement (ARM) unmanned aerospace vehicle (UAV) program, Bulletin of the American Meteorological Society 81 (12) (2000) 2915–2938. [7] O. Arifianto, M. Farhood, Development and modeling of a low-cost un-

urn a

manned aerial vehicle research platform, Journal of Intelligent & Robotic Systems 80 (1) (2015) 139–164.

470

[8] E.-H. Zheng, J.-J. Xiong, J.-L. Luo, Second order sliding mode control for a quadrotor uav, ISA transactions 53 (4) (2014) 1350–1356.

[9] M. Xiao, Y. Zhang, H. Fu, Z. Wang, Nonlinear unbiased minimum-variance filter for mars entry autonomous navigation under large uncertainties and

Jo

unknown measurement bias, ISA transactions (2018).

475

[10] Z. Song, K. Sun, Adaptive compensation control for attitude adjustment of quad-rotor unmanned aerial vehicle, ISA transactions 69 (2017) 242–255.

[11] E. Gauterin, P. Kammerer, M. K¨ uhn, H. Schulte, Effective wind speed estimation: Comparison between kalman filter and takagi–sugeno observer techniques, ISA transactions 62 (2016) 60–72. 31

Journal Pre-proof

480

[12] D. Balageas, X. Maldague, D. Burleigh, V. P. Vavilov, B. Oswald-Tranta,

pro of

J.-M. Roche, C. Pradere, G. M. Carlomagno, Thermal (IR) and other (NDT) techniques for improved material inspection, Journal of nondestructive evaluation 35 (1) (2016) 18.

[13] E. Spangenberg, G. Riquel, In service diagnostic of composite insulators 485

EDF’s test results, Electricite De France, 1997.

[14] L. F. Luque-Vega, B. Castillo-Toledo, A. Loukianov, L. E. GonzalezJimenez, Power line inspection via an unmanned aerial system based on

re-

the quadrotor helicopter, in: 17th Mediterranean Electrotechnical Conference (MELECON), IEEE, 2014, pp. 393–397. 490

[15] B. Wang, X. Chen, Q. Wang, H. Liu, Liang e Zhang, B. Li, Power line inspection with a flying robot, in: 1st International Conference on Applied

lP

Robotics for the Power Industry (CARPI), IEEE, 2010, pp. 1–6. [16] J. Cui, Y. Zhang, S. Ma, Y. Yi, J. Xin, D. Liu, Path planning algorithms for power transmission line inspection using unmanned aerial vehicles, in: 495

29th Chinese Control And Decision Conference (CCDC), IEEE, 2017, pp.

urn a

2304–2309.

[17] R. G. Austin, G. Earp, Power line inspection by UAV: A business case, in: 19th International UAV Systems Conference, Bristol, UK, 2004.

[18] Z. Li, S. Mu, J. Li, W. Wang, Y. Liu, Transmission line intelligent in500

spection central control and mass data processing system and application based on UAV, in: 4th International Conference on Applied Robotics for

Jo

the Power Industry (CARPI), IEEE, 2016, pp. 1–5.

[19] Y. Zhang, X. Yuan, Y. Fang, S. Chen, UAV low altitude photogrammetry for power line inspection, ISPRS International Journal of Geo-Information

505

6 (1) (2017) 14.

[20] A. Moore, M. Schubert, N. Rymer, Autonomous inspection of electrical transmission structures with airborne UV sensors and automated air traffic 32

Journal Pre-proof

management, in: The American Institute of Aeronautics and Astronautics

510

pro of

AIAA - Information Systems, Infotech@ Aerospace, 2018, p. 1628.

[21] E. C. Bortoni, L. Santos, G. S. Bastos, A model to extract wind influence from outdoor ir thermal inspections, IEEE Transactions on Power Delivery 28 (3) (2013) 1969–1970.

[22] M. Nafar, G. Solookinejad, M. Jabbari, Magnetic field calculation of 63KV transmission lines, Vol. 17, Academic Research Publishing 515

Agency:(arapapress), 2013, p. 218.

re-

[23] S. Jiang, W. Jiang, W. Huang, L. Yang, UAV-based oblique photogrammetry for outdoor data acquisition and offsite visual inspection of transmission line, Remote Sensing 9 (3) (2017) 278.

[24] X. Hui, J. Bian, X. Zhao, M. Tan, Vision-based autonomous navigation approach for unmanned aerial vehicle transmission-line inspec-

lP

520

tion, International Journal of Advanced Robotic Systems 15 (1) (2018) 1729881417752821.

[25] B. Cui, X. Chen, X. Tang, H. Huang, X. Liu, Robust cubature kalman filter

525

urn a

for gnss/ins with missing observations and colored measurement noise, ISA transactions 72 (2018) 138–146.

[26] Y.-g. Park, C. G. Park, Wind velocity estimation without an air speed sensor using kalman filter under the colored measurement noise, in: 30th Congress of the International Council of the Aeronautical Sciences in Daejeon, Korea, 2016.

[27] M. Ahmed, K. Subbarao, Target tracking in 3-d using estimation based

Jo

530

nonlinear control laws for uavs, Aerospace 3 (1) (2016) 5.

[28] M. Rakshit, D. Panigrahy, P. Sahu, Ekf with pso technique for delineation of p and t wave in electrocardiogram (ecg) signal, in: Signal Processing and Integrated Networks (SPIN), 2015 2nd International Conference on, IEEE,

535

2015, pp. 696–701. 33

Journal Pre-proof

[29] R. Bisoi, P. K. Dash, A hybrid evolutionary dynamic neural network for

pro of

stock market trend analysis and prediction using unscented kalman filter, Applied Soft Computing 19 (2014) 41–56.

[30] C. Luo, S. I. McClean, G. Parr, L. Teacy, R. De Nardi, Uav position es540

timation and collision avoidance using the extended kalman filter, IEEE Transactions on Vehicular Technology 62 (6) (2013) 2749–2762.

[31] M. Akhbari, M. B. Shamsollahi, C. Jutten, Fiducial points extraction and characteristicwaves detection in ecg signal using a model-based bayesian

545

re-

framework, in: Acoustics, Speech and Signal Processing (ICASSP), 2013 IEEE International Conference on, IEEE, 2013, pp. 1257–1261. [32] D. Simon, Optimal state estimation: Kalman, H infinity, and nonlinear approaches, John Wiley & Sons, 2006.

lP

[33] W. Hao, B. Xian, Nonlinear adaptive fault-tolerant control for a quadrotor UAV based on immersion and invariance methodology, Nonlinear Dynamics 550

90 (4) (2017) 2813–2826.

[34] H. J. M. ter Brake, H. J. Wieringa, H. Rogalla, Improvement of the per-

urn a

formance of a mu-metal magnetically shielded room by means of active compensation (biomagnetic applications), Measurement Science and Technology 2 (7) (1991) 596.

555

[35] T. I. Fossen, Guidance and control of ocean vehicles, John Wiley & Sons Inc, 1994.

[36] J. Awrejcewicz, Modeling, Simulation and Control of Nonlinear Engineer-

Jo

ing Dynamical Systems, Springer, 2009.

[37] L. Dai, R. N. Jazar, Nonlinear Approaches in Engineering Applications 2,

560

Springer, 2012.

[38] G. J. Ducard, Fault-tolerant flight control and guidance systems: Practical methods for small unmanned aerial vehicles, Springer Science & Business Media, 2009. 34

Journal Pre-proof

[39] P. Pappas, The original ampere force and biot-savart and lorentz forces, Il Nuovo Cimento B (1971-1996) 76 (2) (1983) 189–197.

pro of

565

[40] G. B. Iyyuni, S. A. Sebo, Study of transmission line magnetic fields, in: Proceedings of the Twenty-Second Annual North American Power Symposium, IEEE, 1990, pp. 222–231.

[41] R. Resnick, D. Halliday, J. Walker, Fundamentals of physics, John Wiley 570

& Sons, New York, EUA, 1988.

[42] M. Shabani, A. Gholami, N. Davari, Asynchronous direct kalman filtering

ics 80 (1-2) (2015) 71–85.

re-

approach for underwater integrated navigation system, Nonlinear Dynam-

[43] M. Geist, O. Pietquin, et al., Kalman filtering & colored noises: the (autoregressive) moving-average case, in: Proceedings of International Conference

lP

575

On Machine Learning And Applications (ICMLA), no. 9, IEEE, 2011. [44] N. Ma, M. Bouchard, R. A. Goubran, Perceptual kalman filtering for speech enhancement in colored noise, in: International Conference on Acoustics,

580

urn a

Speech, and Signal Processing (ICASSP)., Vol. 1, IEEE, 2004, pp. I–717. ´ Naya, J. L. Blanco-Claraco, J. L. Torres-Moreno, [45] E. Sanjurjo, M. A. A. Gim´enez-Fern´andez, Accuracy and efficiency comparison of various nonlinear kalman filters applied to multibody models, Nonlinear Dynamics 88 (3) (2017) 1935–1951.

[46] M. C. Berg, The design of multirate digital control systems (1986). [47] R. W. Beard, Quadrotor dynamics and control, 2008.

Jo

585

[48] M. Santos, V. Pereira, A. Ribeiro, M. Silva, M. do Carmo, V. Vidal, L. Hon´orio, A. Cerqueira, E. Oliveira, Simulation and comparison between a linear and nonlinear technique applied to altitude control in quadcopters, in: 18th International Carpathian Control Conference (ICCC), IEEE, 2017,

590

pp. 234–239. 35

Journal Pre-proof

[49] M. F. Silva, A. C. Ribeiro, M. F. Santos, M. J. Carmo, L. M. Hon´ orio, E. J.

pro of

Oliveira, V. F. Vidal, Design of angular PID controllers for quadcopters built with low cost equipment, in: 20th International Conference on System Theory, Control and Computing (ICSTCC), IEEE, 2016, pp. 216–221. doi: 595

10.1109/ICSTCC.2016.7790668.

[50] M. F. Santos, L. M. Hon´ orio, E. B. Costa, E. J. Oliveira, J. P. P. G. Visconti, Active fault-tolerant control applied to a hexacopter under propulsion system failures, in: 19th International Conference on System Theory, Control and Computing (ICSTCC), IEEE, 2015, pp. 447–453. doi: 10.1109/ICSTCC.2015.7321334.

re-

600

[51] Y. L. Abdel-Magid, M. M. Dawoud, Optimal AGC tuning with genetic algorithms, Electric Power Systems Research 38 (3) (1996) 231–238.

lP

[52] Z. Kowalczuk, J. Kozlowski, Integrated squared error and integrated absolute error in recursive identification of continuous-time plants, in: UKACC 605

International Conference on Control’98.(Conf. Publ. No. 455), Vol. 1, IET, 1998, pp. 693–698.

urn a

[53] M. Jelali, Control performance management in industrial automation: assessment, diagnosis and improvement of control loop performance, Springer Science & Business Media, 2012.

610

[54] E. B. G. S. BAESA, Usina hidrel´etrica de barra grande, accessed: 05/02/2018 (2018).

URL http://www.baesa.com.br/baesa/categoria.php?&cod_modulo=

Jo

1&cod_categoria=1

[55] P. Corke, Robotics, vision and control:

615

fundamental algorithms in

R second, completely revised, Vol. 118, Springer, 2017. MATLAB

[56] Y. Ma, S. Soatto, J. Kosecka, S. S. Sastry, An invitation to 3-d vision: from images to geometric models, Vol. 26, Springer Science & Business Media, 2012. 36

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HIGHLIGHTS

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• A new approach that enables Unmanned Air Vehicle (UAV) to navigate very close to transmission lines • It incorporates the electromagnetic noise along with the UAV dynamics • An Extended Kalman Filter with state augmentation is used to filter the colored noise. • Can be used to obtain better visual and multispectral images from electrical components. • Tested in a real Hydroelectric power plant

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Conflict of Interest and Authorship Conformation Form Please check the following as appropriate: All authors have participated in (a) conception and design, or analysis and interpretation of the data; (b) drafting the article or revising it critically for important intellectual content; and (c) approval of the final version.

o

This manuscript has not been submitted to, nor is under review at, another journal or other publishing venue.

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The authors have no affiliation with any organization with a direct or indirect financial interest in the subject matter discussed in the manuscript

o

The following authors have affiliations with organizations with direct or indirect financial interest in the subject matter discussed in the manuscript:

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Leonardo de Mello Honório Mathaus Ferreira da Silva Andre Luis M. Marcato Vinicius F. Vidal Murillo F. Santos

Affiliation

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Author’s name

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All authors are affiliated to: FEDERAL UNIVERSITY OF JUIZ DE FORA