Filiberto Muñoz

Iván González-Hernández

Sergio Salazar
email: sergio.salazar.cruz@gmail.com

Eduardo S Espinoza

Rogelio Lozano

Second Order Sliding Mode Controllers for Altitude Control of a Quadrotor UAV: Real-Time Implementation in Outdoor Environments

This article deals with the design and real-time implementation of different second order sliding mode controllers for the altitude tracking of an aerial vehicle known as Quadrotor aircraft, a comparative study based in the error analysis is realized in order to know which controller has the best performance in a real-time application in outdoors environments. The strategies to compare are Classical First Order Sliding Mode Controller, Super Twisting Sliding Mode Controller, Modified Super Twisting Sliding Mode Controller and Nonsingular Terminal Super Twisting Sliding Mode Controller. The last three controllers mentioned previously are based on the second order sliding mode technique by the fact that ensure robustness with respect to modelling errors even under external disturbances while reducing the chattering phenomenon in comparison with first order sliding mode controllers. The Lyapunov stability theory is used to guarantee the convergence in finite time of the altitude tracking error in the different control laws proposed. To demonstrate the performance of the proposed solutions, an extensive set of simulation and real-time experiments results outdoor are presented. From the theoretical and experimental results it can prove the advantages and disadvantages of each of the techniques onto the aerial vehicle in external conditions.

I. INTRODUCTION

In recent years, Unmanned Aircraft Systems (UASs) have attracted significant attention because of their wide range of applications. For example, sports media is making use of different kind of multi-rotorcrafts equipped with imaging systems to obtain and record video feed that can not be obtained by conventional means. In the domain of agriculture, UASs are being used for monitoring crop fields in a more efficient way. Highway monitoring is another area where UASs are being implemented to collect important data about the situation in crowded streets to improve the flow of vehicles. Disaster relief is another area that gets a lot of support from the UAS community. Having a UAS providing a first status of the disaster situation reduces risks for humans and increases the efficiency of rescue crews. Therefore, both rescuers and victims can benefit from this technology.

It is expected that Unmanned Aircraft Systems (UASs) will displace manned aircraft in diverse activities, before that happens, UASs must be safely integrated into the airspace system along with other manned and unmanned aerial vehicles. At present, the required level of autonomy for safe UASs operations is yet to be fully developed. Whether the quadrotor is in Hover Flight Mode or in Trajectory Tracking Flight Mode, it is absolutely crucial maintain a desired altitude in order to have a satisfactory performance in autonomous mode for any of the applications previously mentioned. For this reason and because of their importance, the robust altitude control problem for an quadrotor UAS is studied in this research work.

In order to accomplish the autonomy necessary, robust flight control systems are required to track desired trajectories in the presence of wind or other disturbances. Robust Control strategies based on Sliding Mode Control (SMC) have shown to be an effective method for the control of dynamic systems with uncertainties. SMC strategies are appealing due to their ability to reject both disturbances and parameter variations, which is very useful for practical applications. Unfortunately, SMC induces signal chattering due to the discontinuous terms in the control law. These type of signals are undesirable because they can cause damage and accelerate tear and wear in electromechanical systems. Recently, SMC has been extended to incorporate novel techniques known as higher-order sliding mode control (HOSMC) [START_REF] Perruquetti | Sliding Mode Control in Engineering[END_REF], [START_REF] Edwards | Advances in Variable Structure and Sliding Mode Control[END_REF]. HOSMC preserves the main advantages of SMC, while at the same time yields improved performance with respect to (w.r.t) chattering effects as well as higher accuracy. To date, diverse systems have been controlled in real-time by means of HOSMC, see for instance [START_REF] Bartolini | Second-order sliding-mode control for container cranes[END_REF], [START_REF] Shtessel | A novel adaptivegain supertwisting sliding mode controller: Methodology and application[END_REF].

One of the most powerful HOSMC is the Second Order Super Twisting Sliding Mode Controller and their variations (Modified Super Twisting-SMC, Non-Singular Terminal-SMC) [START_REF] Levant | Higher-order sliding modes, differentiation and outputfeedback control[END_REF], [START_REF] Davila | Second-order sliding-mode observer for mechanical systems[END_REF], [START_REF] Moreno | A Lyapunov approach to secondorder sliding mode controllers and observers[END_REF]. This algorithm generates a continuous control function that drives the sliding variable and its derivative to zero in finite time. The Super Twisting algorithm ensure robustness with respect to modelling errors and external disturbance, also this controller contains a discontinuous function under the integral term, attenuating the chattering effect [START_REF] Shtessel | Lyapunov design of adaptive supertwisting controller applied to a pneumatic actuator[END_REF]. In practice the controller gains are not easy to adjust due the bounds of perturbations, non-modeling dynamics and their time derivatives are need to known [START_REF] Utkin | About second order sliding mode control, relative degree, finite-time convergence and disturbance rejection[END_REF]. In order to overcome this disadvantage adaptive gains versions of the Super Twisting SMC have been developed. In [START_REF] Utkin | Adaptive sliding mode control with application to super-twist algorithm: equivalent control method[END_REF], [START_REF] Shtessel | A novel adaptivegain supertwisting sliding mode controller: Methodology and application[END_REF] in these papers an adaptive sliding mode super-twisting algorith is proposed in order to reduce at minimum the chattering phenomena by using the adaptation law for the control gains.

Related Works

In the literature, a wide class of controllers based on SMC have been proposed for the quadrotor position and orientation control problem. Most of them controllers are validated only with simulation results, a set of these works are presented to continuation. For example, the authors in [START_REF] Besnard | Quadrotor vehicle control via sliding mode controller driven by sliding mode disturbances[END_REF] developed a SMC for a small quadrotor UAV, in this approach a First Order SMC using a Super twisting sliding mode disturbance observer for the estimation of perturbations. In [START_REF] Vega | Robust block second order sliding mode control for a quadrotor[END_REF], [START_REF] Vega | Block Linearization Control of a Quadrotor Via Sliding Mode[END_REF] the authors proposed a Robust Block Second Order SMC for a quadrotor, in this work an altitude control law based on Block Linearization Control technique is used and the Super Twisting control is employed for the longitudinal, latitudinal and heading motions control loops independently.

An Integral Backstepping control combined with adaptive terminal sliding mode to control the attitude of the quadrotor, and an adaptive robust PID controller is designed for the position control was developed in [START_REF] Modirrousta | Adaptive Second Order Terminal Backstepping Sliding Mode for Attitude Control of Quadrotor with External Disturbances[END_REF]. In [START_REF] Mokhtari | A new robust control for minirotorcraft unmanned aerial vehicles[END_REF] a backstepping method combined with sliding mode control for the position and orientation is applied for the subsystems of altitude, latitudinal and longitudinal, and heading control. A super twisting second order sliding mode control considering motor dynamics for position and orientation was designed in [START_REF] Jamali | Robust second order sliding mode control for a quadrotor considering motor dynamics[END_REF].

In [START_REF] Peng | Modeling and robust backstepping sliding mode control with Adaptive RBFNN for a novel coaxial eight-rotor UAV[END_REF] a robust backstepping sliding mode controller with adaptive radial basis function neural network is proposed to control the attitude of a eigh-rotor unmanned aerial vehicle. Furthermore, in [START_REF] Zheng | Second order sliding mode control for a quadrotor UAV[END_REF] a Second Order SMC is used in the controllers design for the actuated and underactuated systems of a small quadrotor UAV.

Terminal Sliding Mode Controllers with nonlinear sliding mode surface have been developed for the control problem of a quadrotor also. In [START_REF] Xiong | Position and attitude tracking control for a quadrotor UAV[END_REF], [START_REF] Zheng | Quad-rotor unmanned helicopter control via novel robust terminal sliding mode controller and under-actuated system sliding mode controller[END_REF] a position and attitude tracking control is proposed, in this approach a robust terminal sliding mode control is develop for the altitude control, in this approach is not included the term corresponding to the Super Twisting control. A Fixed-time Terminal Sliding Mode Trajectory Tracking Control of a quadrotor is designed in [START_REF] Yun | Fixed-time Terminal Sliding Mode Trajectory Tracking Control of Quadrotor Helicopter[END_REF], the novelty of this approach is that the settling time of the system can be assigned ahead of time and does not depend on the system initial conditions. The authors in [START_REF] Modirrousta | A novel nonlinear hybrid controller design for an uncertain quadrotor with disturbances[END_REF] developed an adaptive second order terminal backstepping sliding mode for attitude control for a quadrotor. In [START_REF] Zhou Weidong | Position and Attitude Tracking Control for a Quadrotor UAV Based on Terminal Sliding Mode Control[END_REF] the dynamical model of a Quadrotor UAV is divided into actuaded and underactuated subsystem, and a terminal sliding mode control is used to ensure that the yaw angle and the altitude can reach their desired value.

Unlike the large number of simulation results, only a reduced number of works related with the Super Twisting implementations in quadrotors have been developed until now. The following works present results of Super Twisting Control implementation in different subsystems of the quadrotor, all these works have been implemented in indoor environments. In [START_REF] Derafa | Super Twisting Control Algorithm for the Four Rotors Helicopter Attitude Tracking Problem[END_REF], [START_REF] Derafa | Super twisting control algorithm for the attitude tracking of a four rotors UAV[END_REF] a real time implementation of the Super Twisting controller for the attitude tracking in a quadrotor where set of indoor experiments were performed. In a first set of experiments a stationary ball joint base is employed restricting the aircraft yaw movement around ±30 • and the movement in the three-dimensional space in a fixed point. Moreover, in [START_REF] Derafa | Super twisting control algorithm for the attitude tracking of a four rotors UAV[END_REF] was carried an experiment in free flight where the attitude is stabilized around zero with the altitude controller at around 1 m over the floor by an operator through a remote-control system. Another experiment results for attitude stabilization of a quadrotor UAS using Classical and Second Order SMCs was realized in [START_REF] Bouchoucha | Classical and second order sliding mode control solution to an attitude stabilization of a four rotors helicopter: From theory to experiment[END_REF], in this work the controller implemented was based on Super Twisting algorithm.

In [START_REF] Sumantri | Robust Tracking Control of a Quad-Rotor Helicopter Utilizing Sliding Mode Control with a Nonlinear Sliding[END_REF] a sliding mode controller using a nonlinear sliding surface for the rotational and traslational subsystem of a quadrotor is designed e implemented in a indoor experimental fixed test bed with displacements in three-dimensional space around of ±0.5 meters in axis X, Y and Z. In [START_REF] Muñoz | Super Twisting vs Modified Super Twisting algorithm for altitude control of an Unmanned Aircraft System[END_REF] a Super Twisting and a Modified Super Twisting are applied to the altitude control of a quadrotor system in a indoor environment using a Motion Capture System Optitrack, in this work the maximum altitude is about 1.1 meters over the floor.

Main Contributions

Since the Second Order Sliding Mode Controllers have been implemented only in a few works related to the robust altitude control of UAS, and the reported works present results only on indoor environments, in this work the implementation problem for altitude controller based on Super Twisting Sliding Mode Controller in outdoor environments is addressed. With the aim to verify in real time the higher performance of the Second Order SMC, a conventional First Order SMC is also implemented.

The rest of the paper is organized as follows. The altitude dynamic model of an underactuated UAS and the Second Order Sliding Mode Controllers: ST-SMC, MST-SMC are described in Section II. Numerical simulations results are presented in Section III. Furthermore, an extensive set of experimental results are presented in Section IV. Finally, the manuscript closes in Section V with some conclusions and future works.

II. SECOND ORDER SLIDING MODE CONTROLLERS DESIGN

The adopted mathematical model describing the altitude dynamics for a quadrotor UAS is given by [START_REF] Carrillo | Quad Rotorcraft Control[END_REF]

z = -g + 1 m (cos θ cos φ) u + ξ (t, z, ż) (1)
where z represent the altitude, ż is the altitude velocity and z is the altitude acceleration, φ and θ are the roll and pitch angles respectively (roll and pitch angles are measured in the experiments), m is the mass of the UAS, g is the gravitational force and ξ (t, z, ż) includes the perturbations and uncertainty in the process dynamics (ξ in the following). Defining a state variables z 1 and z 2 as z 1 = z y z 2 = ż, the system (1) is rewritten as

ż1 = z 2 ż2 = cos θ cos φ m u -g + ξ
The control objective is design and implement three robust controllers (ST-SMC, MST-SMC, NSTST-SMC) u such that the system output z 1 can track a given reference z 1d , even in the presence of uncertainty in the process dynamics, as well as external disturbances. In order to develop the Super Twisting-SMC and the Modified Super Twisting-SMC a linear sliding mode surface s is defined as

s = ė + β 1 e (2)
where e and ė represent the tracking error and the derivative of the tracking error and are defined as e = z 1 -z 1d and ė = z 2 -ż1d respectively, and β 1 > 0. The objective of the controllers is to enforce the sliding mode into the surface s = 0.

A. Super Twisting-SMC

The proposed Super Twisting-SMC strategy is given by the following equation

u ST = m cos θ cos φ g + zd 1 -β 1 ė -k 1 |s| 1/2 sign (s) -k 2 t 0 sign (s) dτ (3)
and with this controller the closed loop error dynamics are rewritten as

ṡ = -k 1 |s| 1/2 sign (s) -k 2 t 0 sign (s) dτ + ξ (4)
Defining new variables x 1 and x 2 as

x 1 =s x 2 = -k 2 t 0 sign (s) dτ + ξ
the sliding surface close loop dynamics (4) are given by

ẋ1 = -k 1 |x 1 | 1/2 sign (x 1 ) + x 2 ẋ2 = -k 2 sign (x 1 ) + ξ (5)
Theorem 1. Suppose that for system (1) the derivative of the perturbation is globally bounded by | ξ| < ξ 1 with ξ 1 > 0, and the gains k 1 and k 2 are selected according to

k 1 > 0 k 2 > k 1 6ξ 1 + 4 ξ1 k1 2 2k 1 (6)
Then, the Super-Twisting control law (3) yields finite-time convergence of the sliding surface s = 0 and the tracking errors e and ė will asymptotically converge to zero [START_REF] Moreno | A Lyapunov approach to secondorder sliding mode controllers and observers[END_REF], [START_REF] Moreno | Strict Lyapunov Functions for the Super-Twisting Algorithm[END_REF].

B. Modified Super Twisting-SMC

The proposed Modified Super Twisting-SMC strategy is given by the following equation

u M ST = m cos θ cos φ g + zd 1 -β 1 ė -k 1 |s| 1/2 sign (s) -k 2 s -k 3 t 0 sign (s) dτ -k 4 t 0 sdτ (7)
and the closed loop error dynamics ṡ are given by

ṡ = -k 1 |s| 1/2 sign (s) -k 2 s -k 3 t 0 sign (s) dτ -k 4 t 0 sdτ + ξ
Defining new variables x 1 and x 2 as

x 1 =s x 2 = -k 3 t 0 sign (s) dτ -k 4 t 0 sdτ + ξ
it can be obtained the following closed loop dynamic corresponding to the surface sliding

ẋ1 = -k 1 |x 1 | 1/2 sign (x 1 ) -k 2 x 1 + x 2 ẋ2 = -k 3 sign (x 1 ) -k 4 x 1 + ξ (8)
Theorem 2. Suppose that for system (1) the derivative of the perturbation is globally bounded by

| ξ| < ξ 1 + ξ 2 |x 1 | with ξ 1 > 0 and ξ 2 > 0, assuming that the gains k 1 , k 2 , k 3 , k 4 are selected according to k 1 > ξ 1 k 2 > 1 2 8ξ 2 k 3 > ξ 1 k 4 > k 1 1 2 k 3 1 (2k 2 -ξ 2 ) + 5 2 k 2 2 + ξ 2 p 1 k 1 p 1 -1 2 k 3 1
where

p 1 = k 1 1 4 k 2 1 -ξ 1 + 1 2 k 1 2k 3 + 1 2 k 2 1
Then, the Modified Super Twisting SMC (7) yields finite-time convergence of the sliding surface s = 0 and the tracking errors e and ė will asymptotically converge to zero [START_REF] Moreno | A Lyapunov approach to secondorder sliding mode controllers and observers[END_REF], [START_REF] Moreno | Strict Lyapunov Functions for the Super-Twisting Algorithm[END_REF].

C. Nonsingular Terminal Sliding Mode Control

In the development of the Nonsingular Terminal Super Twisting-SMC a nonlinear sliding mode surface s is defined as [START_REF] Tran | Nonsingular Terminal Sliding Mode Control of Uncertain Second-Order Nonlinear Systems[END_REF] s

= ė + β 1 e + β 2 exp -λt e -2α (9)
The proposed Nonsingular Terminal Super Twisting-SMC strategy is given as

u N ST ST = m cos θ cos φ g + zd 1 -β 1 ė -β 2 -exp -λt e -2α (λ + 2α ė) -k 1 |s| 1/2 sign (s) -k 2 t 0 sign (s) dτ (10)
with β 1 > 0, β 2 > 0, α > 0 and λ > 0. The closed loop error dynamics ṡ are given by

ṡ = -g + cos θ cos φ m u -z1d + β 1 ė + β 2 -exp -λt e -2α (λ + 2α ė) + ξ (11)
Replacing the control law [START_REF] Utkin | Adaptive sliding mode control with application to super-twist algorithm: equivalent control method[END_REF] in the dynamics [START_REF] Besnard | Quadrotor vehicle control via sliding mode controller driven by sliding mode disturbances[END_REF] we obtain

ṡ = -k 1 |s| 1/2 sign (s) -k 2 t 0 sign (s) dτ + ξ (12)
The closed loop error dynamics [START_REF] Vega | Robust block second order sliding mode control for a quadrotor[END_REF] correspond to the ones given in equation ( 4) for the Super Twisting-SMC. Therefore, the stability analysis corresponding to Nonsingular Terminal Super Twisting-SMC is the same given by the Theorem 1.

Remark 1. The Lyapunov stability proof of Theorems 1 and 2 has been presented in [START_REF] Moreno | A Lyapunov approach to secondorder sliding mode controllers and observers[END_REF] [4], [START_REF] Moreno | Strict Lyapunov Functions for the Super-Twisting Algorithm[END_REF]. Therefore, only a sketch of the stability analysis is presented in Appendix A.

III. SIMULATION RESULTS

In this section, the altitude dynamical model of the quadrotor UAS given by Equation ( 1) is used to test the validity and performance of the proposed Second Order SMCs (ST, MST, NSTST) when faced with external disturbances. The control laws employed in the simulation are given by Equations ( 3), [START_REF] Moreno | A Lyapunov approach to secondorder sliding mode controllers and observers[END_REF] and [START_REF] Utkin | Adaptive sliding mode control with application to super-twist algorithm: equivalent control method[END_REF]. The reference signal employed in all the simulations consists in a square waveform with magnitude equal to 1m, offset of 1m and frequency of 0.0333Hz. The disturbance signal used in the simulations is given by ξ = 1 2 cos (t). It is worth mentioning that the gains parameter used for the three SMCs are the same both in simulation and experimentation. A complete list of parameters employed is shown in Table I. In Figure 2 the altitude control performance of the first order sliding mode controller is shown. It can be appreciated that the UAS presents an tracking error in steady state. Moreover, the chattering effect is appreciated in the signal control and this phenomenon might excite unstable system dynamics and will degraded the overall controller performance in real-time implementation. The simulation results of the altitude control for the Second Order SMCs (ST, MST, NSTST) are presented in Figure 3. It can be seen that NSTST controller presents a faster response compared with ST and MST controllers. The ST-SMC and MST-SMC have a similar performance in terms of transient response and steady state. Should be noted that the three controllers follows efficiently the reference signal.

IV. EXPERIMENTAL RESULTS

In this section we present the results obtained when applying the different control techniques proposed in the main results section. For this objective, we use a small Quad-rotor aircraft with a laser sensor placed at the bottom (see Figure 9) in order to obtain the actual distance that the vehicle is flying to compare and observer the behaviour on the z-dynamic (altitude) for the aerial vehicle using different controls such as • Classical First Order Sliding Mode Control

• Super Twisting Sliding Mode Control

• Modified Super Twisting Sliding Mode Control

• Nonsingular Terminal Super Twisting Sliding Mode Control

We additionally use a Futaba 2.4GHz FASST radio system for transmitting the command signals to activate different corresponding altitude controls for the purpose of observe their performance. We implemented the control laws on a embedded high-performance autopilot-on-module system called pixhawk at 100 MHz, manufactured by 3D Robotics to test the efficiency of the proposed algorithms control for the altitude. The benefits of the Pixhawk system include integrated multithreading, a Unix/Linux-like programming environment for applications in real-time. The physical parameters of the used aerial vehicle are given in Table II. Furthermore, in order to obtain a better measurement of the height (z -position) of our aerial vehicle was used a compact high performance optical sensor by PulsedLight model LIDAR-Lite v2, this sensor is shown in Figure 8. The laser sensor can be interfaced via I2C or PWM to the Quad-rotor aircraft, in Figure 9 it can be observed the sensor mounted in the aerial vehicle. Finally, its operating range is up to 40 meters which is feasible for the development of our experiments outdoor. In Experiment IV-C, altitude control is placed at an initial height of 2 meters for about 40 seconds then the control is disabled until the aircraft increase or decrease its height as the case may, and afterwards the control is enabled to observe the behavior of the rate of response of different controls. Finally, in Experiment IV-D the altitude is externally disturbed to explore the disturbance rejection performance in stabilization around the desired altitude. For this application the gains picked for the controllers are described in the Table I.

We also carried out several real-time experiments to stabilize the altitude of aerial vehicle outdoor. The controllers parameters were tuned by simulations results, until obtaining a better responses performance of the system. Figures 10 to 22 presents all experimental results obtained by applying the different controllers previously described.

A. Hovering experiment

In this experiment, the Classical First Order SMC and the three Second Order SMC were implemented in hovering mode in order to observer the performance in outdoor environment. To start, Figure 10 illustrates the behavior of a typical sliding mode control with its corresponding control signal. The main disadvantage of this controller is that it has a poor performance due to the so-called chattering phenomenon (the effects of the discontinuous nature of the control). On the other hand, Figures 11 to 13 show the altitude response and the applied control signals. The desired reference changes from 1 meter to 2 meters in height and the signals corresponding to the control inputs applied at each instant. One can notice the effectiveness of the proposed second order sliding mode controllers compared with the typical sliding mode control above described. Fig. 10: Real-time altitude control response at a height of 1m using a typical sliding mode algorithm in outdoor environment.

B. Tracking experiment

Altitude tracking experiment has been carried out in outdoor environment. Figures 14 to 16 show the altitude response when the reference signal is a square wave with a period equal to T = 80s. The obtained results clearly show the effectiveness controllers. Moreover, we can notice that the applied control signal decrements in each case because the gains are bounded by the terms defined in the control laws (3), ( 6) and ( 9). On the other hand, we can see that the phenomenon of chattering persists in the control signal even when the integral action in each of the controls is added.

C. Disable/Enable control experiment

Altitude disable/enable switch control experiment has been carried out in outdoor environment. Figures 17 to 19 show the altitude response when the control is disabled and subsequently is taken up again the control (enabled) in order to see if this control is able to return the aerial vehicle to the given reference. From these Figures, it is clear that the Quad-rotor aircraft has a better behavior towards the reference when the control strategy considers the integral term, attenuating the chattering effect as in the previous cases. Notice that, in Figure 18 you can see the immediate response of the control input when the control is triggered in order to increase or decrease the energy depending on the case to carry the aircraft to the reference at 2 meters. Fig. 17: Altitude response test with disable/enable switch control using super twisting-SMC in outdoor environment. As a particular case of different control techniques used in this article, Figures 21 and22 show the behavior of the altitude using the super-twisting controller. The response is quite satisfactory because the disturbance is rejected almost immediately by the control so that the tracking altitude corresponds to the reference given demonstrating the effectiveness of real-time controller to external disturbances (in this case: the wind). Notice that, all previous experiments were performed autonomously, only one selector position of a radio was used to indicate the start of each test. these results it can be concluded that Modified Super Twisting-SMC has the best performance. In Figure 24 an error histogram for Hovering experiments is presented. It can be observed that the greater number of samples with near zero error are obtained with the Modified Super Twisting-SMC proving its best performance. A video of the experiments carried out can be seen at https://youtu.be/T5KAzwkH9Ig

V. CONCLUSIONS AND FUTURE WORKS

The altitude in a quadrotor helicopter is a great issue due to their dynamic include the mass and the roll and pitch angles. The disturbances in altitude could be provided from the many factors, the rotational dynamics, change of mass, wind gusts, etc. We presented a comparative study of three second-order sliding mode controllers in real-time application for the altitude of a quadrotor rotorcraft. In the practice we increase the performance in outdoors flight due to attenuation the chattering effects and the rejection of disturbances even of mass changes. We presented an error comparative study in order to show that the best performance is the modified super twisting algorithm in a hover outdoors flights. The future work could be included the X and Y positions in order to compensate the GPS noisy and perturbation like wind gusts.

T the system (5) is rewritten as follows

ν1 = 1 |v 1 | - 1 2 k 1 ν 1 + 1 2 ν 2 ν2 = 1 |v 1 | (-k 2 ν 1 ) + ξ (13)
The system ( 13) is written in matrix form as follow

ν1 ν2 = 1 |ν 1 | -1 2 k 1 1 2 -k 2 0 A(ν1) ν 1 ν 2 + 0 ξ G( ξ) (14)
Remark. If ν 1 , ν 2 → 0 in finite time, then x 1 , x 2 → 0 in finite time.

The following Lyapunov function candidate is introduced in order to prove the convergence of ν 1 , ν 2 in finite time [START_REF] Moreno | Strict Lyapunov Functions for the Super-Twisting Algorithm[END_REF]

V (ν) = 2k 2 ν 2 1 + 1 2 ν 2 2 + 1 2 (k 1 ν 1 -ν 2 )
2 which can be rewritten as

V (ν) = ν T P ν (15)
with P = P T defined by

P = P T = 2k 2 + 1 2 k 2 1 -1 2 k 1 -1 2 k 1 1
the matrix P is positive definite if k 2 > 0.

Remark 2. The function V is continuous but not locally Lipschitz, for this reason, the usual second method of Lyapunov is not valid. In [START_REF] Moreno | Strict Lyapunov Functions for the Super-Twisting Algorithm[END_REF] all the conditions required by the Zubov's theorem were obtained for the proposed Lyapunov candidate function. Therefore, we can continue the Lyapunov analysis following these ideas. For those points where the derivative does not exist the arguments presented in [START_REF] Poznyak | Advanced Mathematical Tools for Automatic Control Engineers[END_REF], [START_REF] Salgado | Proportional derivative fuzzy control supplied with second order sliding mode differentiation[END_REF] are employed.

The temporal derivative of ( 15) is given has

V (ν) = 1 |ν 1 | ν T A T (ν 1 ) P + P A (ν 1 ) ν + 2ν T P G ξ = - 1 |v 1 | ν T Qν + ξq 1 ν
with Q = Q T and q 1 defined as

Q = k1 2 k 2 1 + 2k 2 - k 2 1 2 - k 2 1 2 k1 2 , q 1 = [-k 1 2]
Assuming that the perturbation term of the system ( 5) is globally bounded by

| ξ| ≤ ξ 1
it can be shown that

V (ν) ≤ - 1 |v 1 | ν T Qν (16)
where

Q = k1 2 k 2 1 + 2k 2 -k 1 ξ 1 - k 2 1 2 -ξ 1 - k 2 1 2 -ξ 1 k1 2
From Equation( 16) it can be observed that V (ν) is negative definite if Q is definite positive, this fact is ensure if the gains k 1 and k 2 are chosen as in Equation [START_REF] Davila | Second-order sliding-mode observer for mechanical systems[END_REF].

Considering the inequalities

λ min {P } ν 2 ≤ V (ν) ≤ λ max {P } ν 2 ( 17
)
|ν 1 | ≤ ν ≤ V 1/2 (ν) λ 1/2 min {P } (18)
equation ( 16) can be rewritten as

V (ν) ≤ -γV 1/2 (ν) (19)
with γ defined as γ = λ

Fig. 1 :

 1 Fig. 1: Photo of the Quadrotor aircraft used with the embedded control system pixhawk.

Fig. 2 :

 2 Fig. 2: Altitude response tracking simulation test using First Order Sliding Mode control.

Fig. 3 :

 3 Fig. 3: Altitude response tracking simulation test using ST, MST, NSTST.

Figures 4 -

 4 Figures 4-6 show the control signal of Super Twisting, Modified Super Twisting and Nonsingular Terminal Super Twisting Sliding Mode Controllers, respectively. From the Figures the reduction of the chattering effected is noted in the

Fig. 4 :

 4 Fig. 4: Control signal of Super Twisting controller.

Fig. 5 :

 5 Fig. 5: Control signal of Modified Super Twisting controller.

Fig. 6 :Fig. 7 :

 67 Fig. 6: Control signal of Nonsingular Terminal Super Twisting controller.

Fig. 8 :

 8 Fig. 8: (LIDAR-Lite v2) laser sensor used to measure the altitude of the Quad-rotor aircraft outdoor.

Fig. 9 :

 9 Fig. 9: Photo of the Quad-rotor aircraft setup with the laser sensor mounted used for testing.

Fig. 11 :

 11 Fig. 11: Altitude response stabilization in hover-mode using super twisting-SMC in outdoor environment.

Fig. 12 :

 12 Fig. 12: Altitude response stabilization in hover-mode using modified super twisting-SMC in outdoor environment.

Fig. 13 :

 13 Fig.13: Altitude response stabilization in hover-mode using nonsingular terminal sliding mode control in outdoor environment.

Fig. 14 :

 14 Fig. 14: Altitude response tracking test using super twisting-SMC in outdoor environment.

Fig. 15 :

 15 Fig. 15: Altitude response tracking test using modified super twisting-SMC in outdoor environment.

Fig. 16 :

 16 Fig. 16: Altitude response tracking test using nonsingular terminal sliding mode control in outdoor environment.

Fig. 18 :

 18 Fig.18: Altitude response test with disable/enable switch control using modified super twisting-SMC in outdoor environment.

Fig. 19 :

 19 Fig.19: Altitude response test with disable/enable switch control using nonsingular terminal sliding mode control in outdoor environment.

Fig. 20 :Fig. 21 :Fig. 22 :Fig. 23 :

 20212223 Fig. 20: Altitude hover response test at 9m and 17m using super twisting-SMC under disturbances in outdoor environment.

Fig. 24 :

 24 Fig. 24: Performance of error histogram for Hovering experiments.

1 / 2 min

 12 {P }λ min{Q} 2λ max {P } From equation (19) is obtained that V (ν) and ν converge to zero in finite time at most after T = 2V 1/2 (ν(t0)) γ units of time. If the condition on the gains k 1 and k 2 are satisfied, s = 0 in finite time. Therefore, according to s = c 1 e + ė it can be concluded that lim t→∞ e = 0 and lim t→∞ ė = 0 providing asymptotic convergence of the tracking error.

TABLE I :

 I Simulation and Experimental Parameters.

	Parameters	ST	MST	NTSMC
	Mass of the quadrotor, (m) [kg]	1.4	1.4	1.4
	Gravitational acceleration, (g) [m s 2 ]	9.81	9.81	9.81
	k1	3.5	3	3
	k2	6	4.5	4.5
	k3	-	0.18	-
	k4	-	0.18	-
	β1	0.25	0.25	0.25
	β2	-	-	0.5
	λ	-	-	0.35
	α	-	-	0.5

TABLE II :

 II Quad-rotor aircraft physical parameters

	Parameters	Value
	Mass of the Quad-rotor aircraft, (m) [kg]	1.00
	Gravitational acceleration, (g) [m s 2 ]	9.81
	Distance, (d) [cm]	30
	Ixx, (kg • m 2 )	0.00029
	Iyy, (kg • m 2 )	0.00038
	Izz, (kg • m 2 )	0.00079

TABLE III :

 III Performance index for Hovering experiments.

	Performance Index	ST	MST	NTSMC
	IAE	559.8688	500.8595	611.1740
	ITAE	4.9569 × 10 3	3.7224 × 10 3	5.3738 × 10 3
	ISE	2.9768 × 10 4	2.7308 × 10 4	3.1499 × 10 4
	ITSE	7.0600 × 10 4	6.1070 × 10 4	8.5957 × 10 4

ACKNOWLEDGEMENTS

This work was partially supported by the Mexican Secretariat of Public Education (SEP) grant PRODEP UPPACH-004 and by the Project Red Temática de Sistemas Autónomos y Ciber-Físicos.

APPENDIX A STABILITY PROOF

A sketch of the proof of Theorem 1 is presented below, the complete proof of the theorem can be found on [START_REF] Moreno | A Lyapunov approach to secondorder sliding mode controllers and observers[END_REF], [START_REF] Moreno | Strict Lyapunov Functions for the Super-Twisting Algorithm[END_REF]. Introducing a new state vector ν defined as


Romaric Larcher
email: r-larcher@outlook.fr

Camille Maury

Guillaume Faivre

Geoffrey Dagod

Yann Dumont

Vincent Le-Moing

Maxime Villiet

Xavier Capdevila

Jonathan Charbit

Vincent Le Moing

Acquisition of extended-spectrum cephalosporin-resistant Gramnegative bacteria: epidemiology and risk factors in a 6-year cohort of 507 severe trauma patients

Keywords: Trauma ICU Antimicrobial resistance Extended-spectrum cephalosporin-resistant Gram-negative bacteria Extended-spectrum beta-lactamase AmpC beta-lactamase AIS, Abbreviated Injury Scale, AmpC-E, AmpC beta-lactamase producing Enterobacterales, AMR, antimicrobial resistance, CRAB, carbapenem resistant A. baumannii, ESBL-E, extended spectrum betalactamase producing Enterobacterales, ESCR-E, extended-spectrum cephalosporin-resistant Enterobacterales, ESCR-GNB, extended-spectrum cephalosporin-resistant Gram-negative bacteria, HR, hazard ratio, ICU, intensive care unit, ISS, Injury Severity Score, IQR, interquartile range, MDR, multidrug resistant, MRSA, methicillin-resistant Staphylococcus aureus, MSSA, methicillin-susceptible Staphylococcus aureus, NF-GNB, Non-fermenting Gram-negative bacteria, SAPS, Simplified Acute Physiology Score, SOFA, Sequential Organ Failure Assessment, 95% CI, confidence interval at 95%

Introduction

Antimicrobial resistance (AMR) is a major concern for health care professionals, especially in intensive care unit (ICU) set-tings [START_REF] Murray | Global burden of bacterial antimicrobial resistance in 2019: a systematic analysis[END_REF][START_REF] Brusselaers | The rising problem of antimicrobial resistance in the intensive care unit[END_REF]. Indeed, up to two-thirds of ICU-acquired infections are caused by drug-resistant bacteria [START_REF] Brusselaers | The rising problem of antimicrobial resistance in the intensive care unit[END_REF]. Therefore, the blended choice of broad-spectrum antibiotics is widely used in the most severely ill patients or in those who previously had an antimicrobial therapy or drug-resistant bacteria carriage [START_REF] Rhodes | Surviving Sepsis Campaign: International Guidelines for Management of Sepsis and Septic Shock: 2016[END_REF][START_REF] Evans | Surviving Sepsis Campaign: international guidelines for management of severe sepsis and septic shock: 2008[END_REF]. To limit the acquisition of drug-resistant bacteria, microbiological surveillance and antimicrobial stewardship were reported as efficient strategies [START_REF] Ramsamy | Microbiological surveillance and antimicrobial stewardship minimise the need for ultrabroad-spectrum combination therapy for treatment of nosocomial infections in a trauma intensive care unit: an audit of an evidence-based empiric antimicrobial policy[END_REF][START_REF] Timsit | Rationalizing antimicrobial therapy in the ICU: a narrative review[END_REF]. A better knowledge of the bacterial ecology of patients and units in association with the implementation of early antibiotic de-escalation allows minimization of broad-spectrum antibiotic consumption and reduces selection and colonization pressure [START_REF] Ramsamy | Microbiological surveillance and antimicrobial stewardship minimise the need for ultrabroad-spectrum combination therapy for treatment of nosocomial infections in a trauma intensive care unit: an audit of an evidence-based empiric antimicrobial policy[END_REF][START_REF] Timsit | Rationalizing antimicrobial therapy in the ICU: a narrative review[END_REF]. This kind of intervention could also reduce care costs and antimicrobial-associated harms [START_REF] Timsit | Rationalizing antimicrobial therapy in the ICU: a narrative review[END_REF][START_REF] Umscheid | Estimating the proportion of healthcare-associated infections that are reasonably preventable and the related mortality and costs[END_REF][START_REF] Arulkumaran | Antimicrobial-associated harm in critical care: a narrative review[END_REF]. Thus, in France, restriction of fluoroquinolone use has favoured a decrease in the rate of methicillin-resistant Staphylococcus aureus (MRSA) isolation [START_REF] Charbonneau | Fluoroquinolone use and methicillin-resistant Staphylococcus aureus isolation rates in hospitalized patients: a quasi-experimental study[END_REF]. However, at the same time, extended-spectrum cephalosporin-resistant Gramnegative bacteria (ESCR-GNB) have become the leading pathogens contributing to the burden of AMR, as in most ICUs worldwide [START_REF] Boutrot | Antibiotics with activity against intestinal anaerobes and the hazard of acquired colonization with ceftriaxoneresistant Gram-negative pathogens in ICU patients: a propensity score-based analysis[END_REF][START_REF] Kollef | Nosocomial Infection[END_REF].

In the context of severe trauma, antibiotics may be required for many reasons, such as penetrating trauma, open fractures, or aspiration pneumonia [ 12 , 13 ]. Moreover, immunoparalysis related to trauma (the first hit ) [START_REF] Lord | The systemic immune response to trauma: an overview of pathophysiology and treatment[END_REF] , as well as surgical aggression (the second hit ) [START_REF] Marik | The immune response to surgery and trauma: Implications for treatment[END_REF] , significantly increases infection risk and encourages use of an antimicrobial therapy [ 12 , 13 ]. Severe trauma is thereby a situation at risk of acquisition of drug-resistant bacteria, favored by antimicrobial therapy selection pressure [ 16 , 17 ]. However, surveil-lance data from large cohorts of severe trauma patients are scarce. Consequently, large observational cohort studies could advance our understanding of this issue in this specific population. The present study was therefore conducted to describe the bacterial ecology in a population of severe trauma patients and to assess the prevalence and acquisition rate of ESCR-GNB and the factors associated with acquisition of ESCR-GNB.

Material and methods

Study design and setting

This observational retrospective cohort study aimed to assess the acquisition of ESCR-GNB and the factors associated with acquisition of ESCR-GNB in severe trauma patients. It was carried out from 01 January 2010to 31 December 2015 in a 20-bed trauma ICU in a French University Hospital (Level-I Regional Trauma Centre). The charts of patients admitted to our Trauma Centre during the study period were retrospectively screened. All consecutive patients with an Injury Severity Score (ISS) > 15 who had been hospitalized in the trauma ICU for at least 7 days were included [START_REF] Baker | The injury severity score: a method for describing patients with multiple injuries and evaluating emergency care[END_REF]. Patients previously admitted to another hospital and those with minor trauma or without microbiological sample were excluded.

Data collection

Demographical data, morbidities, and mechanism of injuries were retrospectively collected. Illnesses severity was assessed 24 h after admission using the Simplified Acute Physiology Score (SAPS) II, the Sequential Organ Failure Assessment (SOFA) score, and the ISS and Abbreviated Injury Scale (AIS) by anatomical area [START_REF] Baker | The injury severity score: a method for describing patients with multiple injuries and evaluating emergency care[END_REF][START_REF] Vincent | The SOFA (Sepsis-related Organ Failure Assessment) score to describe organ dysfunction/failure. On behalf of the Working Group on Sepsis-Related Problems of the European Society of Intensive Care Medicine[END_REF][START_REF] Gall | A new Simplified Acute Physiology Score (SAPS II) based on a European/North American multicenter study[END_REF][START_REF] Gennarelli | AIS 2005: a contemporary injury scale[END_REF]. ICU management, including the need for mechanical ventilation, vasopressor, renal replacement therapy, transfusion, and antimicrobial therapy (drug, treatment start date, and duration) were recorded, as well as global outcome and survival at ICU and hospital discharge. In addition, a specific bacteriological analysis was performed for the present study. All bacteriological samples drawn during ICU stay were retrospectively analyzed (by C.M. and G.F.) to col-ligate bacterial identification and antimicrobial susceptibility. Bacterial samples' drawing dates were also recorded specifically.

Bacteriological management

In our trauma ICU, patients had their own single room. A nasal and rectal swab were systematically performed upon admission and weekly for each patient for microbiological surveillance purpose of ESCR-GNB carriage [START_REF] Tacconelli | ESCMID guidelines for the management of the infection control measures to reduce transmission of multidrug-resistant Gram-negative bacteria in hospitalized patients[END_REF]. In case of fever or sepsis, additional bacteriological samples such as blood cultures, urine analysis, bronchoalveolar lavage or tracheal aspirate, peritoneal fluid analysis, or bone biopsies were drawn based on clinical orientation [START_REF] Rhodes | Surviving Sepsis Campaign: International Guidelines for Management of Sepsis and Septic Shock: 2016[END_REF][START_REF] Evans | Surviving Sepsis Campaign: international guidelines for management of severe sepsis and septic shock: 2008[END_REF]. Cultures and antimicrobial susceptibility testing were performed using standard laboratory techniques according to the European Committee on Antimicrobial Susceptibility Testing guidelines [START_REF] Matuschek | Development of the EUCAST disk diffusion antimicrobial susceptibility testing method and its implementation in routine microbiology laboratories[END_REF]. Extended-spectrum cephalosporin-resistance was phenotypically suspected on Mueller Hinton agar when the inhibition diameter zone from at least one of the cephalosporins tested (namely, cefoxitin, cefotaxime, ceftriaxone, ceftazidime, and cefepime) was inferior to the zone diameter breakpoints. Extended-spectrum beta-lactamase (ESBL) production was confirmed with the double-disk synergy method. To confirm high-level production of cephalosporinase (plasmid AmpC producers or chromosomal AmpC hyperproducers), the double-disk synergy test was per-formed using cloxacillin-supplemented medium (250 mg/L) [START_REF] Matuschek | Development of the EUCAST disk diffusion antimicrobial susceptibility testing method and its implementation in routine microbiology laboratories[END_REF]. When necessary, empirical or directed antimicrobial therapies based on institutional guidelines were used. Treatment of early-and late-onset pneumonia, open fractures, and penetrating trauma, or antibioprophylaxis for surgeries, were also protocolized in our unit. Selective decontamination of the digestive tract was not per-formed in our ICU or in our hospital and use of fluoroquinolones were discouraged by local guidelines. Antibiotic prescription and subsequent de-escalation or escalation were left to the physician's discretion based on microbiologic test results and clinical response to therapy. A multidisciplinary care meeting between ICU physicians, microbiologists, and infectious disease specialists dedicated to antimicrobial stewardship was scheduled once a week.

Study définitions

Traumatic injuries were qualified severe using an AIS ≥3. Initial antimicrobial therapy was defined as an antibiotic treatment started within the first 48 h following admission. Additional antimicrobial therapy was defined as antibiotic treatments pre-scribed after 48 h of ICU stay. Companion non-beta-lactam antibiotics were defined as: metronidazole, clindamycin, linezolid, and vancomycin.

ESCR-GNB were defined as follows: (i) Extended-spectrum cephalosporin-resistant Enterobacterales (ESCR-E), namely, AmpC beta-lactamase or ESBL producing Enterobacterales (AmpC-E or ESBL-E); (ii) Pseudomonas aeruginosa , including drugresistant (resistant to ≥1 antipseudomonal ß-lactam antibiotic) and multidrug-resistant (MDR) P. aeruginosa (resistant to at least one drug from at least three antimicrobial classes among penicillins, cephalosporins, carbapenems, fluoroquinolones, and aminoglycosides); (iii) Acinetobacter baumannii, including carbapenem resistant A. baumannii (resistant to imipenem and/or meropenem).

Prevalence of drug-resistant bacteria was defined as the proportion of patients having ESCR-GNB or MRSA during ICU stay. Acquisition of ESCR-GNB was defined as isolation, after day 5 following ICU admission, of ESCR-GNB that was not isolated before, from nasal or rectal swab or from an infected site sample. When ESCR-GNB emerged in a patient twice or more, only the first episode was considered.

Statistical Analysis

Categorical data were described as numbers and percentages, and continuous data as medians with 25 th and 75 th percentiles (interquartile range [IQR]). The population was divided in two groups according to the acquisition of ESCR-GNB. Categorical variables were compared by Chi-square or Fisher's exact test, and continuous variables were compared by Student's t test or Wilcoxon's rank-sum test as appropriate.

The analysis of factors associated with ESCR-GNB acquisition used a cause-specific Cox model. In this model, ICU death or ICU discharge were handled as competing risks. Analyses were right-censored at the time of the first ESCR-GNB acquisition and at day 30 of the ICU stay in patients without acquisition. Factors associated with ESCR-GNB acquisition in the univariate analysis (cutoff P ≤0.2) were included in the multivariate analysis. Results of Cox regression models were reported as hazard ratio (HR) with 95% confidence interval (95% CI).

All tests were two-sided, and P < 0.05 was considered statistically significant. Analyses were performed using R software version 4.0.3 (The R Foundation for Statistical Computing, Vienna, Austria).

3.Results

Study population

Among the 1873 patients suspected to be severely injured and admitted to our Level-1 trauma center during the study period, 507 were included in the present study (Fig. 1 ).

Patients had a median ISS of 29 and a median ICU length of stay of 16 (IQR, 10-28) days, 396 of them (78%) were male. At ICU admission, median age was 42 (IQR, 26-59) years old, and median admission SAPS II and SOFA scores were 35 (IQR, 25-47) and 5 (IQR, 3-6), respectively. Severe injuries were frequent and mainly related to a vehicle crash or a fall (396; 78%): 266 patients (52%) had a severe head trauma, 232 (46%) a severe chest trauma, and 224 (44%) a severe trauma of extremities. The rates of mechanical ventilation and vasopressor needs were 91%, median duration 11 (IQR, 6-20) days, and 78% median duration 4 (IQR, 2-8) days, respectively. A total of 42 patients died during ICU stay, bringing the in-ICU mortality and hospital mortality rates to 8%. Patients' characteristics are summarized in Table 1 .

Antimicrobial therapies

More than three-quarter of patients (393/507; 78%) had an initial antimicrobial therapy, and more than a half (280/507; 55%) received an additional antimicrobial therapy for sepsis during ICU stay, bringing the total number of patients treated with antibiotics to 450 (89%). Antimicrobial therapies were mostly amoxicillin and clavulanic acid (amoxiclav: 343 patients, 68%), cephalosporins (cefotaxime, ceftriaxone or cefepime: 147 patients, 29%), and piperacillin-tazobactam (123 patients, 24%). Antibiotics were pre-scribed in association with an aminoglycoside in 194 cases (38%) and/or with another non-beta-lactam antibiotic (metronidazole, clindamycin, linezolid, or vancomycin) in 177 patients (35%). De-tails on antimicrobial treatments are reported in Table 2.

Bacterial isolates and ESCR-GNB acquisition

Epidemiology of bacterial isolates is summarized in Fig. 2 and Table 3 . Three hundred and ninety-five patients (78%) had at least one positive bacteriological sample. Before day 5, bacteria isolated from culture were mainly S. aureus (29%) and Enterobacterales (22%). Nonfermenting Gram-negative bacteria (NF-GNB) were found in only 7% of patients and were mainly P. aeruginosa (5%). After day 5, most isolated bacteria were Enterobacterales (42%), whereas prevalence of S. aureus decreased to 20%. P. aeruginosa was also found in 60 patients (12%) and A. baumannii in 25 (5%). Accordingly, prevalence of NF-GNB increased by more than two-fold to 17%.

Up to day 5, prevalence of ESCR-GNB was found in 13%, 95% confidence interval (CI; 10%-16%) of the cohort. Types of drug-resistant bacteria were mainly AmpC-E (6%) and ESBL-E (4%). After day 5, ESCR-GNB prevalence increased to 33%, 95% CI (29%-37%). Acquisition of ESCR-GNB was found in 29%, 95% CI (25%-34%) of patients (149/507), after a median of 10 days (IQR, 8-12) of ICU stay. Among Enterobacterales, resistance mechanisms were mainly related to AmpC beta-lactamases. Indeed, the acquisition rate for AmpC-E was 18%, whereas acquisition of ESBL-E were found in only 17 patients (3%), bringing the acquisition rate of ESCR-E to 21% . In the same line, prevalence of AmpC-E increased from 6% to 19% among ESCR-E, which increased from 10% to 23%. In contrast, prevalence of ESBL-E remained stable at around 4% between the two study periods. At the same time, acquisition of ESCR-GNB was also driven by acquisition of P. aeruginosa (10%) and A. baumanii (4%). Of note, MRSA prevalence and acquisition remained low at less than 1%.

Factors associated with ESCR-GNB acquisition

Acquisition of ESCR-GNB was significantly associated in univariate analysis with male sex ( P = 0.04), severe trauma of an extremity ( P = 0.01), higher admission SOFA score ( P < 0.001) and SAPS II ( P = 0.02), early need for massive transfusion ( P = 0.009), red blood cell ( P = 0.02), fresh frozen plasma ( P = 0.02) and platelet ( P = 0.02), early need for mechanical ventilation ( P = 0.003), vasopressor ( P = 0.02), and renal replacement therapy ( P < 0.001). Exposure to piperacillin-tazobactam ( P < 0.001), cephalosporins ( P = 0.002), carbapenems (P = 0.001), and an association with non-beta-lactam antibiotics ( P < 0.001) were also associated with acquisition of AMR. In the multivariate model, factors independently associated with ESCR-GNB acquisition were mechanical ventilation ( P = 0.01) and renal replacement therapy ( P = 0.01) needs, and exposure to extended-spectrum cephalosporin ( P = 0.02) and combination therapy with non-beta-lactam antibiotics such as metronidazole, clindamycin, linezolid, or vancomycin ( P = 0.01). Details of Cox regression analyses are presented in Table 4.

Discussion

This study reported a large and exhaustive cohort of 507 severely injured trauma patients hospitalized more than 7 days in a level one regional trauma center and described their bacterial epidemiology. At ICU admission, most of bacterial isolates were methicillinsusceptible Staphylococcus aureus (MSSA) and wild type Enterobacterales, and the prevalence of AMR remained low (13%). During ICU stay, acquisition rate of ESCR-GNB was 29%, increasing the prevalence up to 33%, and mainly because of the acquisition of AmpC-E (21%). Factors independently associated with ESCR-GNB acquisition were need for mechanical ventilation and renal replacement therapy, and longer treatment with extendedspectrum cephalosporin and combination therapy with non-beta-lactam antibiotics.

Few studies have described the bacterial ecology in such a large cohort of severe trauma patients [START_REF] Gilbert | Multidrug resistant gram-negative bacilli colonization risk factors among trauma patients[END_REF] . In non-traumatized critically ill patients, most were colonized or infected with Enterobacterales and Staphylococcus aureus isolates at ICU admission [START_REF] Trouillet | Ventilator-associated pneumonia caused by potentially drug-resistant bacteria[END_REF] . In these patients, during the first days following ICU admission, ESCR-E and MRSA prevalence were low, around 10-15% and less than 1%, respectively [ 25 , 26 ]. Our results in a trauma population were thus in agreement with those previously reported in medical or surgical ICU populations in France [ 25 , 26 ]. Despite the low prevalence of comorbidity in trauma patients, they appeared to have a similar initial bacterial ecology to that of non-trauma patients [START_REF] Trouillet | Ventilator-associated pneumonia caused by potentially drug-resistant bacteria[END_REF].

After 5 to 7 days of ICU stay, significant acquisition of ESCR-E was largely reported in literature in various ICU settings [START_REF] Kollef | Nosocomial Infection[END_REF][START_REF] Barbier | Infection related ventilator-associated complications in ICU patients colonised with extendedspectrum β-lactamase-producing Enterobacteriaceae[END_REF]; however, few studies have reported bacterial ecology in trauma patients [START_REF] Ramsamy | Microbiological surveillance and antimicrobial stewardship minimise the need for ultrabroad-spectrum combination therapy for treatment of nosocomial infections in a trauma intensive care unit: an audit of an evidence-based empiric antimicrobial policy[END_REF] . In line with our results, Ramsamy et al. [START_REF] Ramsamy | Microbiological surveillance and antimicrobial stewardship minimise the need for ultrabroad-spectrum combination therapy for treatment of nosocomial infections in a trauma intensive care unit: an audit of an evidence-based empiric antimicrobial policy[END_REF] have re-ported a 5% prevalence of ESCR-E, mainly related to ESBL-E, in 227 patients hospitalized in a level-1 trauma centre in South Africa. Nonetheless, the proportion of AmpC-E has not been documented in this cohort. In contrast, our findings highlighted that ESCR-E acquisition was more frequently related to AmpC-E (close to 20%) rather than ESBL-E ( < 5%). ESBL-E were also less frequently isolated in our cohort of severely injured patients than in the general ICU population in France [START_REF] Pilmis | Carriage of ESBL-producing Enterobacteriaceae in French hospitals: the PORTABLSE study[END_REF][START_REF] Barbier | Infection related ventilator-associated complications in ICU patients colonised with extendedspectrum β-lactamase-producing Enterobacteriaceae[END_REF], which could be explained by the limited use of fluoroquinolone in our hospital [START_REF] Pilmis | Carriage of ESBL-producing Enterobacteriaceae in French hospitals: the PORTABLSE study[END_REF]. The same was probably true for MRSA [ 6 , 9 , 24 ]. Furthermore, isolation of drug resistant NF-GNB were unsurprisingly higher in the cohort of Ramsamy et al. [START_REF] Ramsamy | Microbiological surveillance and antimicrobial stewardship minimise the need for ultrabroad-spectrum combination therapy for treatment of nosocomial infections in a trauma intensive care unit: an audit of an evidence-based empiric antimicrobial policy[END_REF] than in ours; A. baumannii is indeed known to be rarely isolated in the French ICUs compared to many other countries and particularly South Africa [ 11 , 27 , 28 ].

In severe trauma patients, many reasons prompt clinicians to widely prescribe antimicrobial therapy [START_REF] Cole | The burden of infection in severely injured trauma patients and the relationship with admission shock severity[END_REF][START_REF] Papia | Infection in hospitalized trauma patients: incidence, risk factors, and complications[END_REF], as illustrated by the large proportion of patients (89%) treated with antibiotics in our study. In the general population, acquisition of resistant bacteria under antibiotic exposure is not understood in detail [START_REF] Cantón | Emergence and spread of antibiotic resistance following exposure to antibiotics[END_REF]. It is reported as a complex phenomenon combining pharmacokinetic-pharmacodynamic concepts-such as mutant selection window, mutant prevention concentration-and the ecological effect of antibiotics on the human microbiota [START_REF] Cantón | Emergence and spread of antibiotic resistance following exposure to antibiotics[END_REF]. However, the correlation between antibiotic use and the frequency of AMR has been widely reported [START_REF] Ramsamy | The effect of prior antimicrobial therapy for community acquired infections on the aetiology of early and late onset ventilator-associated pneumonia in a level I trauma intensive care unit[END_REF][START_REF] Cantón | Emergence and spread of antibiotic resistance following exposure to antibiotics[END_REF][START_REF] Kollef | Inadequate antimicrobial treatment of infections[END_REF].

In the present study, we found an independent association between extended-spectrum cephalosporin use and development of resistance. This association was previously described in a 6-year cohort of surgical ICU patients including trauma patients [START_REF] Guidry | Whence resistance?[END_REF]. Noteworthy, ceftriaxone was the most prescribed extended-spectrum cephalosporin before 2015 in our ICU, which could have favored the high prevalence of AmpC-E in our cohort as previously reported [START_REF] Grohs | Fighting the spread of AmpC-hyperproducing Enterobacteriaceae: beneficial effect of replacing ceftriaxone with cefotaxime[END_REF]. The biliary excretion of this antibiotic increases its ecological effect on the intestinal microbiota [START_REF] Ruppé | Impact of antibiotics on the intestinal microbiota needs to be re-defined to optimize antibiotic usage[END_REF], and a benefit of replacing ceftriaxone with cefotaxime to limit the acquisition of ESCR-E has been suggested [START_REF] Grohs | Fighting the spread of AmpC-hyperproducing Enterobacteriaceae: beneficial effect of replacing ceftriaxone with cefotaxime[END_REF].

We also reported an independent association between ESCR-GNB acquisition and exposure to non-beta-lactam antibiotics such as metronidazole, clindamycin, linezolid, or vancomycin. The identification of these antibiotics as a risk factor for acquisition of drug-resistant Gramnegative bacteria might have seemed surprising, particularly regarding anti-Gram-positive antibiotics. Yet, these four antibiotics are known to be strong drivers of anaerobic microbiota disturbance [START_REF] Sullivan | Effect of antimicrobial agents on the ecological balance of human microflora[END_REF], which decreases intestinal colonization resistance to pathogens [START_REF] Woerther | Is the term "anti-anaerobic" still relevant?[END_REF] . Thus, as previously reported, "anti-anaerobic" antibiotics may have facilitated the colonization with drug-resistant bacteria [START_REF] Woerther | Is the term "anti-anaerobic" still relevant?[END_REF][START_REF] Harris | Risk factors for colonization with extended-spectrum beta-lactamase producing bacteria and intensive care unit admission[END_REF][START_REF] Harris | Risk factors for imipenem-resistant Pseudomonas aeruginosa among hospitalized patients[END_REF].

Among the main factors associated with acquisition of AMR, greater illnesses severity has been previously reported [START_REF] Campbell | Multi-drug-resistant Gram-negative infections in deployment-related trauma patients[END_REF]. In agreement with Campbell et al. [START_REF] Campbell | Multi-drug-resistant Gram-negative infections in deployment-related trauma patients[END_REF], we found that acquisition of ESCR-GNB was more frequent in severe trauma patients who need mechanical ventilation and/or renal replacement therapy. In this setting, acquisition of ESCR-GNB has multifactorial contributing factors, such as disrupted barrier function due to endotracheal tubes and catheters that increase risk for colonization and infection of lung, skin, and bloodstream, and dysbiosis that favors a shift towards Enterobacterales in intestinal, cutaneous, and respiratory microbiomes [START_REF] Kollef | Nosocomial Infection[END_REF][START_REF] Fromentin | Respiratory microbiome in mechanically ventilated patients: a narrative review[END_REF].

The present study has several limitations. First, its monocentric design, in a level-1 trauma center in a French teaching hospital, could limit the generalization of our results to ICUs worldwide since AMR epidemiology is widely variable around the world [START_REF] Kollef | Nosocomial Infection[END_REF].. Second, its retrospective design may have introduced bias in data collection and results interpretation. However, it is the largest re-cent analysis on acquisition of AMR in critically injured patients, and consecutive inclusions may have limited selection bias. Third, the acquisition of penicillinase enzymes among isolated bacteria was not recorded in our collection, leading to a possible under-estimation of the development of AMR related to the use of antibiotics, especially amoxiclav and piperacillin-tazobactam. Indeed, this study focused on AmpC-E, ESBL-E and NF-GNB, which are more relevant concerns for ICU and infectious disease physicians. Last, we did not demonstrate any association between mortality and acquisition of resistant bacteria, which may limit the importance of our results. Nonetheless, numerous studies have already reported a link between the acquisition of resistance and the worsening prognosis of ICU patients, underscoring the relevance of this issue [START_REF] Ramsamy | Microbiological surveillance and antimicrobial stewardship minimise the need for ultrabroad-spectrum combination therapy for treatment of nosocomial infections in a trauma intensive care unit: an audit of an evidence-based empiric antimicrobial policy[END_REF][START_REF] Arulkumaran | Antimicrobial-associated harm in critical care: a narrative review[END_REF]. Moreover, our surveillance data could help to limit AMR acquisition by contributing to antimicrobial stewardship in this specific population [START_REF] Ramsamy | Microbiological surveillance and antimicrobial stewardship minimise the need for ultrabroad-spectrum combination therapy for treatment of nosocomial infections in a trauma intensive care unit: an audit of an evidence-based empiric antimicrobial policy[END_REF][START_REF] Timsit | Rationalizing antimicrobial therapy in the ICU: a narrative review[END_REF].

In conclusion, acquisition of ESCR-GNB was a prevalent com-plication in severe trauma patients that was mainly related to AmpC-E acquisition. During ICU stay, the ESCR-GNB acquisition rate was 29%, and independent factors associated with ESCR-GNB acquisition were admission for severe trauma requiring mechanical ventilation or renal replacement therapy, and longer exposure to extended-spectrum cephalosporins or combination therapy with non-beta-lactam antibiotics. Further studies are mandatory to determine if a better choice of antimicrobial therapy or a decrease in antibiotic consumption may limit the acquisition of AMR in severe trauma patients and most importantly, improve outcomes.

Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Competing interests

The authors report there are no competing interests to declare.

Ethics approval

The Institutional Review Board of our Teaching Hospital ap-proved the study (No. IRB-MTP_2020_05_2020 0 0457) and waived the need for written consent.