Odile Bourquardez
email: odile.bourquardez@voila.fr

Robert Mahony
email: robert.mahony@anu.edu.au

Franc ¸ois Nicolas Guenard
email: nicolas.guenard@cea.fr

Tarek Chaumette
email: francois.chaumette@irisa.fr

Laurent Hamel
email: laurent.eck@cea.fr

Eck

L Eck

T Hamel
email: thamel@i3s.unice.fr

Image-Based Visual Servo Control of the Translation Kinematics of a Quadrotor Aerial Vehicle

Keywords:

In this paper, we investigate a range of image-based visual servo control algorithms for regulation of the position of a quadrotor aerial vehicle. The most promising control algorithms have been successfully implemented on an autonomous aerial vehicle and demonstrate excellent performance.

I. INTRODUCTION

Visual servo algorithms have been extensively developed in the robotics field over the last ten years [7], [10], [19], [START_REF] Pissard-Gibollet | Applying visual servoing techniques to control of a mobile hand-eye system[END_REF]. Visual servo control techniques have also been applied recently to a large variety of reduced-scale aerial vehicles, such as quadrotors [START_REF] Altug | Control of a quadrotor helicopter using dual camera visual feedback[END_REF], [START_REF] Romero | Stabilization and location of a four rotor helicopter applying vision[END_REF], helicopters [START_REF] Amidi | A visual odometer for autonomous helicopter flight[END_REF], [START_REF] Nordberg | Vision for a UAV helicopter[END_REF], [START_REF] Saripalli | Visually-guided landing of an unmanned aerial vehicle[END_REF], [START_REF] Wu | Vision-aided inertial navigation for flight control[END_REF], airships [4], [START_REF] Zhang | Visual servoing with dynamics: Control of an unmanned blimp[END_REF], and airplanes [5], [START_REF] Rives | Visual auto-landing of an autonomous aircraft[END_REF]. In this paper, we consider visual servo control of a quadrotor aerial vehicle.

Much of the existing research in visual servo control of aerial robots (and particularly, autonomous helicopters) has used position-based visual servo techniques [START_REF] Altug | Control of a quadrotor helicopter using dual camera visual feedback[END_REF], [START_REF] Amidi | A visual odometer for autonomous helicopter flight[END_REF], [START_REF] Nordberg | Vision for a UAV helicopter[END_REF], [START_REF] Romero | Stabilization and location of a four rotor helicopter applying vision[END_REF]- [START_REF] Shakernia | Landing an unmanned air vehicle: Vision based motion estimation and nonlinear control[END_REF], [START_REF] Wu | Vision-aided inertial navigation for flight control[END_REF]. The estimated pose can be used directly in the control law [START_REF] Altug | Control of a quadrotor helicopter using dual camera visual feedback[END_REF], or as part of a scheme fusing visual data and inertial measurements [START_REF] Wu | Vision-aided inertial navigation for flight control[END_REF]. In this paper, we do not deal with pose estimation, but consider image-based visual servo (IBVS), similar to the approach considered in [4], [17], and [START_REF] Zhang | Visual servoing with dynamics: Control of an unmanned blimp[END_REF].

The system dynamics is sometimes explicitly taken into account in IBVS. This strategy has been applied for robotic manipulators [9], [12], [20] and for aerial vehicles [15], [START_REF] Zhang | Visual servoing with dynamics: Control of an unmanned blimp[END_REF]. Another popular approach (as usually done for most robotic systems such as robot arms, mobile robots, etc.) is based on separating the control problem into an inner loop and an outer position control loop. As for helicopters, the inner attitude loop is run at high gain using inputs from inertial sensors, rate gyrometers, and accelerometers acquired at high data rate, while the outer loop is run at low gain using video input from the camera [START_REF] Saripalli | Visually-guided landing of an unmanned aerial vehicle[END_REF], [START_REF] Shakernia | Landing an unmanned air vehicle: Vision based motion estimation and nonlinear control[END_REF]. The outer (visual servo) loop provides set points for the inner attitude loop and classical time-scale separation and high-gain arguments can be used to ensure stability of the closed-loop system [START_REF] Altug | Control of a quadrotor helicopter using dual camera visual feedback[END_REF], [11], [15], [START_REF] Shakernia | Landing an unmanned air vehicle: Vision based motion estimation and nonlinear control[END_REF].

In this paper, we take the inner/outer loop stability for granted (see [14] for details) and concentrate on the specific properties of the outer IBVS control design. It allows designing kinematic controllers, which give many advantages in practice. For example, using an embedded camera that sends the images to a ground station implies time delays and then a slow image-based control loop. It is thus interesting to have a lower level loop to ensure the stabilization of the system. Then, another advantage to consider kinematic control is to enable easier reuse of the IBVS scheme, since it is not close to the material equipment of the aerial vehicle. In this paper, several control schemes are proposed, compared, and the most promising ones are shown to be stable in practice and to provide satisfactory behavior.

Following earlier work [15], [17], [START_REF] Tahri | Point-based and region-based image moments for visual servoing of planar objects[END_REF], we have chosen to use zero and first-order image moments as primary visual features for the control design. Perspective projection moments with suitable scaling along with a classical IBVS control design lead to satisfactory transients and asymptotic stability of the closed-loop system when the image plane remains parallel to a planar target. However, the system response may lack robustness for aggressive maneuvers. In order to overcome this problem, several control schemes, based on spherical first-order image moments, are designed and their performance is analyzed. The most promising control algorithms have been successfully implemented on an autonomous aerial vehicle showing excellent performance.

The paper is organized as follows. Section II develops a classical IBVS control scheme using perspective image moments. Section III introduces the definition and properties of first-order spherical image moments and presents a range of control laws for the translational motion of the camera using this visual feature. Section IV provides an analysis and a comparison of the control laws proposed. Experimental results are presented in Section V.

II. PERSPECTIVE PROJECTION

In this section, an IBVS control for regulation of the translation kinematics of an aerial vehicle is presented.

In order to obtain a quasi-linear and decoupled link between the image space and the task space, the image features used are perspective projection image moments [START_REF] Tahri | Point-based and region-based image moments for visual servoing of planar objects[END_REF]. The visual feature vector s = (x n , y n , a n ) is defined such that [START_REF] Tahri | Point-based and region-based image moments for visual servoing of planar objects[END_REF]

a n = Z * a * a , x n = a n x g , y n = a n y g
where a is the area of the object in the image, x g , y g its centroid coordinates, a * the desired area, and Z * the desired depth between the camera and the target. The time derivative of s and the relative motion between the camera and the object can be related by the classical equation

ṡ = L υ υ + L ω ω (1)
where υ and ω are, respectively, the linear and angular velocity of the camera both expressed in the camera frame, and where L υ and L ω are, respectively, the parts of the interaction matrix related to the translational and rotational motions. The desired image feature is denoted by s * , and the visual error is defined by e = ss * . Classical IBVS control design aims to impose linear exponential stability on the image error kinematics [10], [21], [START_REF] Tahri | Point-based and region-based image moments for visual servoing of planar objects[END_REF] to ensure an exponential decoupled decrease for e ( ė = -λe, with λ a positive gain). Using e to control the translational degrees of freedom, the classical IBVS control input is

υ = -(L υ ) -1 (λe + L ω ω), λ > 0. (2)
Generally, the interaction terms L υ and L ω depend nonlinearly on the state of the system and cannot be reconstructed exactly from the observed visual data. The visual feature s = (x n , y n , a n ) is of particular interest since L υ = -I 3 in the case where the camera image plane is parallel to the target plane [START_REF] Tahri | Point-based and region-based image moments for visual servoing of planar objects[END_REF]. In that case, since the link between image space and task space is linear and decoupled, the control scheme (2) is known to lead to satisfactory closed-loop behavior for holonomic robot [START_REF] Tahri | Point-based and region-based image moments for visual servoing of planar objects[END_REF]. It is, in fact, equivalent to a position-based visual servo, but without any pose estimation required.

In the application considered, the camera is mounted to point directly downward in the quadrotor and the image and target plane are never more than a couple of degrees offset. As a consequence, the approximation L υ ≈ -I 3 is valid. Furthermore, the motion of the quadrotor is smooth and slow and the value of L ω ω is small compared with the error λe in [START_REF] Amidi | A visual odometer for autonomous helicopter flight[END_REF]. Thus, a reasonable approximation of (2) for the purposes of this paper is

υ = λe, λ > 0. (3)
Equation ( 3) does not require the estimation of any 3-D parameters and can be implemented based only on the observed image features s. This control was implemented on the experimental platform and the results are discussed in Section V-B. The limitation of this approach, however, lies in its dependence on the particular geometry of the application considered and the requirement to consider only smooth slow trajectories of the vehicle. If the vehicle undertakes aggressive manoeuvres, or the parallel target plane assumption is invalidated for a particular application, the approximation L υ ≈ -I 3 will fail, and more importantly, the approximation L ω ω ≈ 0 may also fail. This second issue introduces a significant dynamic disturbance in the system response that cannot be cancelled directly without the risk of introducing zero dynamic effects into the closed-loop response similar to those studied in recent research [11], [18]. The potential limitations of the classical IBVS control design based on perspective projection features motivate us to consider a class of spherical projection features and nonlinear control design techniques.

III. SPHERICAL PROJECTION

A. Modeling

In this section, we use an unnormalized first-order spherical image moment along with an inertial goal vector to generate an image error [17]. Consider a point target consisting of n points P i corresponding to image points p i (i ∈ (1, . . . , n)) on the spherical image surface. The centroid of a target is defined to be q = n i = 1 p i . The centroid q is a 3-D vector. Thanks to the spherical camera geometry, the third entry of the centroid is nonlinearly related to the depth of the camera from the observed target constellation.

For a point target comprising a finite number of image points, the kinematics of the image centroid are easily verified to be [17]

q = -ω × q -Qυ, where Q = i = n i = 1 π p i |P i | and π p = (I 3 -pp ).
As long as there are at least two points p i in image space, the matrix Q is positive definite [17].

Let b denote the vector that defines the direction of the fixed desired set point for the visual feature q, expressed in a fixed inertial frame F A . The image-based error considered is

δ = q -q * (4)
where q * = R b, and the rotation matrix R between the camera frame F C and the fixed inertial frame F A (see Fig. 1) is assumed to be known, a common assumption when dealing with the control of under-actuated systems such as helicopters [17].

The reason for choosing the image error in this manner is that it ensures the passivity property. The image error kinematics are [17] δ = δ × ω -Qυ.

(

) 5
Authorized licensed use limited to: UR Rennes. Downloaded on June 16, 2009 at 05:06 from IEEE Xplore. Restrictions apply. It can be shown that |δ| and δ 0 = Rδ are a function of position only [6]. This property can be exploited to control the translational dynamics independently of the rotations.

B. Proportional Control

A pure proportional feedback of the unnormalized centroid [17] ensures global asymptotic stability (GAS) property, but in practice it has been shown in [6] that task space and image space behavior are not acceptable. This is due to the fact that the convergence rates are given by Q, and this matrix is not well-conditioned. The simple control law

υ = k δ δ, k δ > 0 (6)
is thus not suitable in practice.

C. Partitioned Control

A solution for compensating the poor sensitivity in the previous control design is to use a partitioned approach by singling out the problematic component for special treatment [8], [15].

The idea is to separate the visual error term into two criteria with different sensitivity. The new visual feature

δ A = δ 11 + λq * 0 δ 12 (7)
is defined by using the constant λ (chosen as shown in [6]), and the following two new error terms

δ 11 = q * 0 × q, δ 12 = q * 0 δ, with q * 0 = q * |q * | .
It can be shown that the control law

υ = k A A(q * 0 ) δ A , k A > 0 (8)
with A(q * 0 ) = sk(q * 0 ) + λq * 0 q * 0 ensures that the system is GAS [6]. Note that sk(q * 0 ) is the skew-symmetric matrix such that sk(q * 0 )w = q * 0 × w for any vector w. This partitioned control scheme has been used in [15] by designing and experimenting a dynamic control of a quadrotor. As shown in Section V-C1, although it enables to ensure the desirable GAS property in practice, the partitioned control scheme can lead to poor behavior of the system as soon as the distance between initial and desired position increases [6], [15]. In order to ensure good behavior in practice, we propose the following control laws.

D. Rescaled Image Feature

To improve the relationship between task space behavior and image space behavior, it is natural to try to determine an image feature that is as close to the 3-D translation between the camera and the target as possible [START_REF] Tahri | Point-based and region-based image moments for visual servoing of planar objects[END_REF]. Such a choice leads to an interaction matrix close to the identity, leading to a linear and decoupled link between the image features and the translational degrees of freedom. Furthermore, satisfactory behavior of the image features will automatically induce an acceptable behavior in the task space.

We propose to consider a new image feature

f = F (|q|)q 0 , with F (|q|) = R|q| n 2 -|q| 2 (9)
where q 0 = q |q | is the normalized first-order moment and F (|q|) represents a rough approximation of the actual depth Z from the geometric center of the target. n is the number of points observed and R is the approximate radius of the target.

The error δ f is defined as follows

δ f = f -f * = F (|q|)q 0 -F (|q * |)q * 0 . ( 10
)
It can be shown

that δf = -ω × δ f -MQυ where M(q) = ∂ F (|q |) ∂ |q | q 0 q 0 + F (|q |) |q | I 3 -q 0 q 0 [6].
It can be shown that f -ξ (where ξ represents the camera position with respect to the target, expressed in the camera frame) and MQM Q -1 [6]. Since f -ξ, an intuitive idea is to choose

υ = k f δ f , k f > 0. ( 11
)
Since MQ I 3 , we obtain approximately the same convergence rate for the components of the error [6]. As we will see in Section V-C2, the experimental results using this control law show excellent performance. Its advantage is also that it is easily implemented, since the control law is a direct function of the visual error δ f . Furthermore, since (10) has the additional passivity property, it is expected to be well-adapted for a wide range of aerial vehicles and experimental conditions.

However, similar to the perspective moments control design, the global asymptotic stability has not been demonstrated.

E. GAS Control Law With Modified Rescaled Image Feature

In this section, we attempt to define a new image feature and control law that combine the properties of good transient behavior, good local exponential stability, and global asymptotic stability. The approach taken is to define a new scaling function G(|q|) and scaled image feature

g = G(|q|)q 0 , with ġ = -ω × g -HQυ (12)
where G(|q|) can be chosen so that H induces good properties for asymptotic stability of the resulting control law. Similar to Section III-D for the derivation of M, we have the relationship between matrix H and function G(|q|) [6]:

H(q) = ∂ G (|q |) ∂ |q | q 0 q 0 + G (|q |)
|q | I 3q 0 q 0 . The error δ g is defined as follows

δ g = g -g * = G(|q|)q 0 -G(|q * |)q * 0 .
Recalling (12), the dynamics of this error function is given by δg = -ω × δ g -HQυ, and we can note that δ g ensures the passivity property, as expected from the choice of g.

Choosing the scale factor G(|q|) = α(|q|) |q|F (|q|), and control law

υ = k g H(q) α(|q|) 2 δ g , k g > 0 (13)
where α(|q|) is such that α(|q * |) = 1 [6], ensures GAS and good local exponential stability of the closed-loop system [6]. The new image feature g = G(|q|)q 0 , and the previous feature f = F (|q|)q 0 are designed in the same manner: the direction of the feature is given by q 0 , and the norm is given by the scaling factor G(|q|) and F (|q|), respectively. G(|q|) provides a less aggressive scaling correction than F (|q|) [6]. This improves the sensitivity of the image feature to pixel noise and improves robustness of the closed-loop system. A disadvantage of the new image feature g is that it is not as closely linked to the actual task space coordinates as the feature f (or the 2-D perspective moments used in Section II). Since F (|q|) is an approximation of the depth, the feature f = F (|q|)q 0 is directly related to the 3-D position. In case of the feature g, using the scale factor G(|q|) = α(|q|) |q|F (|q|), the relationship between image space and task space is nonlinear. This leads to some degradation of the global transient behavior for certain initial conditions. However, this issue has limited effect on the observed performance of the closed-loop system in practice. As shown in Section V-C3, the practical results are excellent.

IV. ANALYSIS

A range of IBVS schemes has been presented in Sections II and III. Table I gives summary of the properties for each control scheme in terms of stability, transient behavior, linearity, and passivity.

In practice, two of the most important properties are good transient conditioning (direct convergence of all elements of position in task space without any observed divergence or peaking transients), and balanced local exponential stability (equal asymptotic rate of convergence in all axes of the position in task space). Three control schemes present interesting properties: the perspective image moments (control scheme 1), the rescaled proportional feedback (control scheme 4), and the modified rescaled control (control scheme 5). Among these three best control laws, each one has advantages and drawbacks, and no one is globally better than the others. In the next section, these three control laws are validated and compared through experimental results.

V. EXPERIMENTAL RESULTS AND COMPARISON OF SOME CONTROL LAWS

In this section, we provide experimental verification of the performance of the proposed control schemes on an aerial robotic vehicle. The experiments were undertaken on a quadrotor aerial vehicle. The task considered is to stabilize the vehicle with respect to a specified target.

A. Experimental Conditions 1) Prototype Description:

The unmanned aerial vehicle used for the experimentation is a quadrotor, which is an omnidirectional vertical take off and landing (VTOL) vehicle ideally suited for stationary and quasi-stationary flight conditions. It consists of four fixed-pitch propellers linked to an electrical motor at each extremity of a cross frame (see Fig. 2). The vehicle is equipped with an avionics stack including an inertial measurement unit (IMU) supplying the vehicle attitude and a controller board [15]. The embedded loop allowing the attitude stabilization runs at 166 Hz and the time to reach an attitude order is about 300 ms. A numerical wireless link allows the transmission of the attitude command between the quadrotor and a ground station (Pentium 4) with a time transmission of 110 ms. A camera situated below the quadrotor is embedded and observes a target on the ground, consisting of four black marks on the vertices of a planar rectangle (30 cm×40 cm) (see Fig. 2). A wireless analog link transmits camera images to the ground station. All the visual servo controls tested are implemented on the ground station at the sample time of 60 ms. Consequently, considering the high sampling rate low level and the low sampling rate high level, we can assume that the low level and the high level control are entirely decoupled. A demonstration based on singular perturbations and similar arguments as in [13] can show the stability of the entire closed-loop system. A 3-D estimation of the vehicle position with respect to the target is also obtained by fusing the data of the embedded IMU and the visual data in a particle filter [3]. This estimate is used to provide an estimate of ground truth for the 3-D behavior of the vehicle and to provide an estimate of the linear velocity of the vehicle that is used by the inner loop controller of the airframe dynamics [14] (see Fig. 3). In this paper, only 2-D visual information is used in the outer IBVS control loop for position regulation.

2) Experimental Protocol: In order to compare the proposed different kinematic visual servo controllers, the initial conditions of the experiments were chosen identically. For each experiment, the quadrotor was servo-controlled to a specific initial position using a standard state-space controller deriving information from the task space position estimate. When the vehicle is stabilized at this position, the visual control is initiated and the 3-D position, obtained from the particle filter, is recorded. This protocol ensures that the flight conditions are the same and allows the comparison between the different controllers. The velocity demand was also saturated at 20 cm/s to ensure the vehicle remains in quasi-stationary flight regime [16]. Considering times latency and the high sampling of the high-level controller, only low gains have been used. The technique used to tune these gains consists in increasing the gain to increase the bandwidth and stopping just before the UAV becomes unstable. Then, these gains have been reduced in order to have an exponential convergence in about 10 s.

The initial position of the vehicle is X 0.7 m, Y -0.65 m, Z 2 m, and its desired position is X 0 m, Y 0 m, Z 1.4 m (which is above the center of the target at 1.4 m height of the ground). The asymptotic value for the matrix Q is Q * = diag(2.35, 2.36, 0.057) and we have b (0, 0, 3.96).

In the following subsections, four kinematic image-based control schemes for the translational motion of the quadrotor are considered. For each experiment, the 3-D position of the camera in the task space reference frame is depicted, along with the velocity output of the visual servo control law. The evolution of the visual error considered is also depicted, as well as the trajectory of the four black marks in the image plane.

B. Perspective Image Moments

The classical perspective image moments controller (control law 1) provides a linear correspondence between the image space and task space as long as the relative rotation between image and target plane is small. The resulting closed-loop system response is expected to be satisfactory both in transient performance and asymptotic convergence and in both image and task space. The practical results using the quadrotor are very satisfactory (see Fig. 4) under the considered experimental conditions. However, as a consequence of the limiting assumptions on the rotation, the system is neither GAS nor passive. Moreover, it is expected that strong rotational motion will significantly disturb the performance of the system.

C. Spherical Image Moments 1) Partitioned Control:

With the partitioned control law using decomposition at the set point and spherical image moments (control law 3), the visual error components are quite perturbed but converge [see Fig. 5(c)]. The problem is that the control law is not adequately far from the desired position. Consequently, we can see that the convergence rate is not the same on the three components of the position, and Z component is not suitable [see Fig. 5(a)]. Moreover, the velocity output of the visual servo control is very disturbed, even after convergence [t > 25 s, see Fig. 5(b)].

2) Proportional Feedback: The rescaled proportional feedback using spherical image moments (control law 4) has the same desirable image feature properties as control law 1. The practical results are very satisfactory (see Fig. 6) and similar to the results obtained with control law 1. In fact, the rescaled visual feature f = F (|q|)q 0 is very close to the 3-D position, analogously to the visual features used in control law 1. The control laws are a simple proportional feedback in the two cases. The advantage of the spherical image moments is that they ensure the passivity property, and should be more robust to aggressive maneuvers of an aerial vehicle as well as leading more naturally to a full dynamic IBVS control design. A potential problem, however, is the requirement to estimate the camera attitude in order to reconstruct the image-based error term. There is no formal proof of GAS for control law 4; however, due to the natural structure of the image feature, we expect that the domain of stability for this control law will be sufficiently large so that unstable behavior will not be encountered in practice.

3) GAS Control Law: The last suitable control law ( 5) is based on a modified rescaled visual feature, in order to ensure GAS. This control law provides the guarantee of GAS that is missing in control law 4. Its only drawback is that the visual feature is no longer linearly related to the 3-D position and this may lead to slightly degraded transient response in task space.

As can be seen in Fig. 7, this control scheme leads to very satisfactory behavior: equal convergence rates of the visual error components, and equal convergence rates in the task space. Moreover, in the considered experiment, the transient behavior is acceptable.

D. Noise Sensitivity

At first glance, the results (see Figs. 4, 6, and7) for the three suitable control schemes are very similar.

A potential problem with the control laws 4 and 5 is that the rotation matrix R between the camera frame and the inertial frame has to be estimated. However, this estimation does not seem to introduce noise, delay, or any significant perturbations in practice (compare Fig. 4 with Figs. 6 and7).

To better understand the noise sensitivity of each control scheme, we have computed the root-mean-square error (RMSE) of the velocity demand over the period between 10 and 25 s, during which period all three closed-loop systems are stabilized in a neighborhood of the set point. Note that to get rid of the effect of the gains, we consider the velocity output without the gains λ, k f , and k g . We compute 2 , for K ∈ {X, Y, Z} and where ῡK is the average of υ K between 10 and 25 s.

σ υ = σ 2 υ X + σ 2 υ Y + σ 2 υ Z along with σ υ K = i (υ K i -ῡK )
As can be seen in Table II, the noise measured at the output of all control laws is very similar. The three control laws have very similar behavior with respect to noise.

VI. CONCLUSION

This paper has investigated a suite of image-based kinematic visual servo control schemes to control a quadrotor. Using the well-known perspective image moments to design a classical IBVS translational control law leads to good system behavior in the experimental studies undertaken. However, this control scheme does not ensure global asymptotic stability or passivity of the closed-loop system, both properties that we believe will be important for the development of fully dynamic IBVS control schemes in the future. First-order spherical image moments along with an inertial goal vector allow us to design translational control laws independent from the rotation motion. Global asymptotic stability is obtained by using these visual features and a simple proportional feedback, but the behavior on the Z-axis is not acceptable. A range of control laws has been proposed in order to improve the behavior of the system. The most promising approach investigated involves rescaling the spherical image moments to obtain an image feature that minimizes the sensitivity in the depth axis. The perspective image moments control design, as well as three of the control laws using spherical image moments were implemented on the quadrotor. In practice and as expected, three control algorithms lead to acceptable behavior of the system.

Qualitative Vision-Based Path Following

Zhichao Chen and Stanley T. Birchfield, Senior Member, IEEE Abstract-We present a simple approach for vision-based path following for a mobile robot. Based upon a novel concept called the funnel lane, the coordinates of feature points during the replay phase are compared with those obtained during the teaching phase in order to determine the turning direction. Increased robustness is achieved by coupling the feature coordinates with odometry information. The system requires a single off-the-shelf, forward-looking camera with no calibration (either external or internal, including lens distortion). Implicit calibration of the system is needed only in the form of a single controller gain. The algorithm is qualitative in nature, requiring no map of the environment, no image Jacobian, no homography, no fundamental matrix, and no assumption about a flat ground plane. Experimental results demonstrate the capability of real-time autonomous navigation in both indoor and outdoor environments and on flat, slanted, and rough terrain with dynamic occluding objects for distances of hundreds of meters. We also demonstrate that the same approach works with wide-angle and omnidirectional cameras with only slight modification. Index Terms-Control, feature tracking, mobile robot navigation, visionbased navigation.

I. INTRODUCTION

Route-based knowledge, in which the spatial layout of an environment is recorded from the perspective of a ground-level observer, is an important component of human and animal navigation systems [31]. In this representation, navigating from one location to another involves comparing current visual inputs with a sequence of views captured along the path in a previous instance. Applications that would benefit from such a path-following capability include courier and delivery robots [4], robotic tour guides [32], or reconnaissance robots following a scout [7].

One approach to path following is visual servoing, in which the robot is controlled to align the current image with a reference image, both taken by an onboard camera [14]. Such an approach generally employs a Jacobian to relate the coordinates of world points to their projected image coordinates [5], a homography or fundamental matrix to relate the coordinates between images [20], [START_REF] Shakernia | Landing an unmanned air vehicle: Vision based motion estimation and nonlinear control[END_REF], [START_REF] Wu | Vision-aided inertial navigation for flight control[END_REF], [36], or bundle adjustment to minimize the reprojection error over multiple image frames [START_REF] Tahri | Point-based and region-based image moments for visual servoing of planar objects[END_REF]. As a result, the camera usually must be calibrated [5], [START_REF] Shakernia | Landing an unmanned air vehicle: Vision based motion estimation and nonlinear control[END_REF], [START_REF] Tahri | Point-based and region-based image moments for visual servoing of planar objects[END_REF], [36], and even uncalibrated systems require lens This paper has supplementary downloadable multimedia material available at http://ieeexplore.ieee.org, provided by the author. The material includes the video ("ramp.avi") that shows the mobile robot following a predetermined path.

Fig. 1 .

 1 Fig. 1. Camera frame F C , fixed frame F A , and visual features q and q * .

Fig. 2 .

 2 Fig. 2. Experimental system.

Fig. 3 .

 3 Fig. 3. Low-and high-level control loops.

Fig. 4 .

 4 Fig. 4. Results obtained for υ = 0.4e: time evolution (in seconds) of the real position in the task space (in meters), (a) of them velocity output of the visual servo control υ (in meters per seconds) (b). The evolution of the visual error is plotted on (c), and the trajectory of the four black marks in the image plane are plotted in (d).

Fig. 5 .

 5 Fig. 5. Results obtained for υ = k A A(q * 0 ) δ A , configured as Fig. 4.

Fig. 6 .

 6 Fig. 6. Results obtained for υ = 0.47δ f , configured as Fig. 4.

Fig. 7 .

 7 Fig. 7. Results obtained for υ = 0.3 H (q ) α (|q |) 2 δ g , configured as Fig. 4.

  Manuscript received January 14, 2008; revised September 20, 2008. First published April 14, 2009; current version published June 5, 2009. This paper was recommended for publication by Associate Editor J. D. Tardos and Editor L. Parker upon evaluation of the reviewers' comments. This work was supported in part by a Ph.D. Fellowship from the National Institute for Medical Informatics.The authors are with the Department of Electrical and Computer Engineering, Clemson University, Clemson, SC 29634 USA (e-mail: zhichac@clemson.edu; stb@clemson.edu).

  The four quadrants are as follows: (Top left): Live video from the onboard camera during the replay phase. Red squares indicate features, with green outlines indicating features that guide the robot to the right, and yellow outlines indicating features that guide the robot to the left. (Top right): The milestone image captured during the teaching phase. (Bottom left): The robot as captured by an offboard video camera. (Bottom right): Top-down view of the path traveled by the robot (white: teaching, red: replay).The video is an AVI file that plays under Windows Media Player 11 (2006), as well as earlier versions such as Windows Media Player 6.4 (1999), on Windows XP. The size is 8.35 MB. Additional videos may be found at http://www.ces.clemson.edu/∼stb/research/mobile robot. Contact stb@clemson.edu for further questions about this work. Digital Object Identifier 10.1109/TRO.2009.2017140 1552-3098/$25.00 © 2009 IEEE Authorized licensed use limited to: UR Rennes. Downloaded on June 16, 2009 at 05:06 from IEEE Xplore. Restrictions apply.

TABLE I PROPERTIES

 I OF THE DIFFERENT CONTROL SCHEMES CONSIDERED

TABLE II RMSE

 II OF THE VELOCITIES FOR EACH CONTROL LAW

Authorized licensed use limited to: UR Rennes. Downloaded on June 16, 2009 at 05:06 from IEEE Xplore. Restrictions apply.

upon evaluation of the reviewers' comments. This work was supported by the Centre National de la Recherche Scientifique (CNRS) under the Project Robotique et Entités Artificielles (ROBEA)-Robvolint and the International Programs for Scientific Cooperation (PICS) between France and Australia on visual servo-control of unmanned aerial vehicles. O. Bourquardez and F. Chaumette are with the Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA)-Centre National


Lia Schlippe-Justicia

Jérémy Lemaire

Carolin Dittrich

Martin Mayer

Paco Bustamante

Bibiana Rojas
email: bibiana.rojas@vetmeduni.ac.at

Poison in the nursery: mercury contamination in the tadpole-rearing sites of an Amazonian frog

Keywords: contaminants, phytotelmata, parental care, French Guiana, poison frog

Artisanal and small-scale gold mining (ASGM) has become a major threat for Neotropical forests. This technique for obtaining gold is a substantial driver of small-scale deforestation and the largest contributor of Hg emissions to both the atmosphere and freshwater systems globally. Previous studies have demonstrated the impacts of Hg accumulation on various aquatic ecosystems and organisms. However, its consequences in other, more discrete systems such as phytotelmata (water-holding plant structures), and the organisms therein, have so far gone unnoticed. Here, we show high concentrations of Hg (mean ± SD: 1.43 ± 2.19 ppm) in phytotelmata and other small pools, the aquatic microenvironments used by the Neotropical poison frog Dendrobates tinctorius as tadpole rearing sites. In 17 % of the cases, we detected Hg concentrations above the severe effect level (SEL = 2 ppm) for the freshwater sediments. Hg concentrations varied depending on pool characteristics and tended to increase in proximity to known ASGM sites. We did not find an effect of Hg concentration on the number of D. tinctorius tadpoles in a given pool. Tadpoles were found in pools with concentrations of up to 8.68 ppm, suggesting that D. tinctorius fathers do not avoid pools with high Hg levels for tadpole deposition. While further research is needed to determine the potential effects of Hg on tadpole development, we found an intriguing tendency for tadpoles in later development al stages to have lower body condition when occurring in pools with higher Hg concentrations.

Our findings provide evidence of relevant Hg concentrations in the terrestrial water systems used by phytotelm-breeding anurans, and highlight the need of further field and experimental studies investigating the implications of Hg contamination for tadpole development and behaviour and the overall conservation of Amazonian biodiversity.

Introduction

Tropical rainforests such as Amazonia are among the most biodiverse terrestrial ecosystems in the world (e.g., [START_REF] Grenyer | Global distribution and conservation of rare and threatened vertebrates[END_REF]), but also among the most threatened [START_REF] Laurance | Forest loss and fragmentation in the Amazon: implications for wildlife conservation[END_REF]. Many regions of the Amazon basin are characterised by naturally high levels of environmental mercury (Hg), mostly due to the geochemical characteristics of the soils and biological decay [START_REF] Roulet | The geochemistry of mercury in central Amazonian soils developed on the Alter-do-Chao formation of the lower Tapajos River Valley, Para state, Brazil[END_REF][START_REF] Fadini | Is the Negro River Basin (Amazon) impacted by naturally occurring mercury?[END_REF]. However, anthropogenic activities such as artisanal and small-scale gold mining (ASGM; Peterson et al. 2001;Grau and Aide 2008;Hugo 2008;Kalamandeen et al. 2018) have led to dramatic increases in Hg levels in the environment over the last century [START_REF] Kumar | Presence of artisanal gold mining predicts mercury bioaccumulation in five genera of bats (Chiroptera)[END_REF]. ASGM is commonly illegal and, because it tends to occur in remote places, it is often in -or next to-protected areas and biodiversity hotspots [START_REF] Durán | Global spatial coincidence between protected areas and metal mining activities[END_REF][START_REF] Cuellar-Valencia | Bioaccumulation of mercury in direct-developing frogs: the aftermath of illegal gold mining in a National Park[END_REF][START_REF] Palacios-Torres | Mercury pollution by gold mining in a global biodiversity hotspot, the Choco biogeographic region, Colombia[END_REF]Alvarez-Berrios and Mitchell 2019;[START_REF] Bax | Land-use conflicts between biodiversity conservation and extractive industries in the Peruvian Andes[END_REF]), making it difficult to assess timely and directly the impacts on local wildlife. Nowadays, gold mining is the single largest contributor of Hg emissions to both the atmosphere and freshwater globally (UN Environment 2019).

However, other factors, such as industrial emissions, the historic application of mercurycontaining pesticides and fertilisers in agriculture, and sewage irrigation, also contribute to Hg pollution [START_REF] Mirlean | Mercury contamination of soil as the result of long-term phosphate fertilizer production[END_REF][START_REF] Chen | Characteristics and risk assessment of heavy metals pollution of farmland soils relative to type of land use[END_REF][START_REF] Bavec | Urban sediment contamination in a former Hg mining district, Idrija, Slovenia[END_REF][START_REF] Schneider | When toxic chemicals refuse to die-an examination of the prolonged mercury pesticide use in Australia[END_REF][START_REF] Fisher | A synthesis of mercury research in the Southern Hemisphere, part 2: Anthropogenic perturbations[END_REF].

Hg is an environmental contaminant of global concern due to its toxicity and the risks it poses to wildlife and human health [START_REF] Ashe | Elevated mercury concentrations in humans of Madre de Dios, Peru[END_REF][START_REF] Gibb | Mercury exposure and health impacts among individuals in the artisanal and small-scale gold mining community: a comprehensive review[END_REF][START_REF] Alvarez-Berríos | Impacts of small-scale gold mining on birds and anurans near the Tambopata Natural Reserve, Peru, assessed using passive acoustic monitoring[END_REF]WHO 2017;[START_REF] Markham | Evaluating wildlife vulnerability to mercury pollution from artisanal and small-scale gold mining in Madre de Dios, Peru[END_REF]. After being released to the air, land or water, and transformed by microorganisms into methylmercury (MeHg), its most toxic form, Hg can bioaccumulate in both aquatic and terrestrial organisms and biomagnify across the food webs (Kidd et al. 2011). Furthermore, gaseous Hg released in the atmosphere (for example, due to ASGM activities) can travel long distances before being deposited on surfaces and plants, or returned to the terrestrial landscape through dry or wet deposition (Meliéres et al. 2003;[START_REF] Zhou | Vegetation uptake of mercury and impacts on global cycling[END_REF][START_REF] Gerson | Amazon forests capture high levels of atmospheric mercury pollution from artisanal gold mining[END_REF].

To date, assessments of Hg interactions with tropical ecosystems and biodiversity lag behind those conducted in temperate and polar areas (but see Cuellar et al. 2016;[START_REF] De Oliveira Drummond | Trophic position, altitudinal distribution, and water dependence as determining factors for mercury concentrations in tropical montane anurans[END_REF][START_REF] Palacios-Torres | Mercury pollution by gold mining in a global biodiversity hotspot, the Choco biogeographic region, Colombia[END_REF][START_REF] Soe | Mercury pollution from artisanal and small-scale gold mining in Myanmar and other southeast asian countries[END_REF]; as examples of studies done in the tropics). Moreover, most studies carried out to date have focused on Hg dynamics and impacts in freshwater (rivers: [START_REF] Webb | Mercury contamination in an indicator fish species from Andean Amazonian rivers affected by petroleum extraction[END_REF][START_REF] Vieira | Distribution and availability of mercury and methylmercury in different waters from the Rio Madeira Basin, Amazon[END_REF]lakes: Brito et al. 2017;[START_REF] Gomes | Dynamics of (total and methyl) mercury in sediment, fish, and crocodiles in an Amazonian Lake and risk assessment of fish consumption to the local population[END_REF]) and estuarine systems [START_REF] Mol | Mercury contamination in freshwater, estuarine, and marine fishes in relation to small-scale gold mining in Suriname, South America[END_REF][START_REF] Vezzone | Mercury contamination in sediments and fish from an urban tropical estuary: ecological and human health risks[END_REF], while implications in other more discrete, inland aquatic systems remain unexplored. Phytotelmata, for example, are small bodies of water contained in vegetation structures (e.g. leaf axils, fallen bracts, holes in trunks and roots), which provide essential habitat for the breeding, feeding, refuge and development of a wide range of species [START_REF] Varga | Ein interessanter Biotop der Biocönose von Wasserorganismen[END_REF][START_REF] Fincke | Organization of predator assemblages in Neotropical tree holes: effects of abiotic factors and priority[END_REF][START_REF] Kitching | Food webs and container habitats: the natural history and ecology of phytotelmata[END_REF][START_REF] Lehtinen | Phytotelm-breeding anurans: past, present and future research[END_REF]), including many insects [START_REF] Orr | Life histories and ecology of Odonata breeding in phytotelmata in Bornean rainforest[END_REF][START_REF] Kitching | Food webs and container habitats: the natural history and ecology of phytotelmata[END_REF][START_REF] Campos | Coleopterans associated with plants that form phytotelmata in subtropical and temperate Argentina, South America[END_REF], and amphibians (e.g., [START_REF] Kam | Reproduction, oviposition-site selection, and tadpole oophagy of an arboreal nester, Chirixalus eiffingeri (Rhacophoridae), from Taiwan[END_REF][START_REF] Schiesari | Treeholes as calling, breeding, and developmental sites for the Amazonian canopy frog, Phrynohyas resinifictrix (Hylidae)[END_REF][START_REF] Lehtinen | Tests for competition, cannibalism, and priority effects in two phytotelm-dwelling tadpoles from Madagascar[END_REF][START_REF] Heying | Reproductive limitation by oviposition site in a treehole breeding Madagascan poison frog (Mantella laevigata)[END_REF]. Because these small pools are directly formed by rainwater and accumulate decomposing leaf litter from the surrounding canopy [START_REF] Kitching | Food webs and container habitats: the natural history and ecology of phytotelmata[END_REF], it could be expected that they accumulate high concentrations of Hg over time, particularly in the context of ASGM [START_REF] Malm | Use of epiphyte plants as biomonitors to map atmospheric mercury in a gold trade center city, Amazon, Brazil[END_REF]Meliéres et al. 2003;[START_REF] Gerson | Amazon forests capture high levels of atmospheric mercury pollution from artisanal gold mining[END_REF]. Furthermore, differences in the physico-chemical properties among phytotelmata, as well as in their morphology and durability, could influence the amount of Hg, its chemical form and, ultimately, its toxicity and absorption. For example, acidic pH conditions, warmer water temperatures, high dissolved organic carbon, and low dissolved oxygen and electrical conductivity, have been shown to increase Hg methylation (i.e. MeHg) in water and sediments in some environments [START_REF] Mauro | Mercury methylation in a tropical macrophyte: influence of abiotic parameters[END_REF][START_REF] Bank | Mercury bioaccumulation in green frog (Rana clamitans) and bullfrog (Rana catesbeiana) tadpoles from Acadia National Park, Maine, USA[END_REF][START_REF] Jardine | Food web analysis reveals effects of pH on mercury bioaccumulation at multiple trophic levels in streams[END_REF][START_REF] Brito | The influence of inundation and lake morphometry on the dynamics of mercury in the water and plankton in an Amazon floodplain lake[END_REF].

Neotropical poison frogs of the family Dendrobatidae are, in most part, dependent on phytotelmata as tadpole-rearing sites [START_REF] Summers | The evolutionary ecology of phytotelmata use in Neotropical poison frogs[END_REF][START_REF] Carvajal-Castro | Aposematism facilitates the diversification of parental care strategies in poison frogs[END_REF]) due to their elaborate parental care behaviour. Generally, one of the parents takes care of the terrestrial clutches and, upon hatching, transports tadpoles on its back to the bodies of water, such as phytotelmata, where offspring will remain confined until metamorphosis [START_REF] Weygoldt | Evolution of parental care in dart poison frogs (Amphibia: Anura: Dendrobatidae)[END_REF][START_REF] Summers | The evolutionary ecology of phytotelmata use in Neotropical poison frogs[END_REF]. Selecting a good tadpole-rearing site is determinant for tadpole survival, and some poison frog species are known to base such decisions on chemical cues, either for detecting (and avoiding) potentially cannibalistic conspecifics or predators [START_REF] Schulte | The smell of success: choice of larval rearing sites by means of chemical cues in a Peruvian poison frog[END_REF][START_REF] Rojas | Strange parental decisions: fathers of the dyeing poison frog deposit their tadpoles in pools occupied by large cannibals[END_REF] or for finding new deposition sites in the forest (Serrano- Rojas and Pašukonis 2021;[START_REF] Peignier | Odor cues rather than personality affect tadpole deposition in a neotropical poison frog[END_REF]. Because tadpoles are omnivores, largely feeding on detritus and larvae of insects and frogs [START_REF] Summers | The evolutionary ecology of phytotelmata use in Neotropical poison frogs[END_REF][START_REF] Grant | Phylogenetic systematics of dart-poison frogs and their relatives (Amphibia: Athesphatanura: Dendrobatidae)[END_REF][START_REF] Rojas | Strange parental decisions: fathers of the dyeing poison frog deposit their tadpoles in pools occupied by large cannibals[END_REF], have a thin and highly permeable skin [START_REF] Rowe | Physiological ecology of amphibians in relation to susceptibility to natural and anthropogenic factors[END_REF][START_REF] Quaranta | Why amphibians are more sensitive than mammals to xenobiotics[END_REF], and need to process water for respiration, they can be particularly exposed to, and affected by, both waterborne and dietary contaminants [START_REF] Burger | Metal levels in Southern leopard frogs from the Savannah River Site: location and body compartment effects[END_REF][START_REF] Unrine | Bioaccumulation of trace elements in omnivorous amphibian larvae: implications for amphibian health and contaminant transport[END_REF][START_REF] Rissoli | Effects of glyphosate and the glyphosate based herbicides Roundup Original® and Roundup Transorb® on respiratory morphophysiology of bullfrog tadpoles[END_REF]). Thus, Hg may pose a considerable threat to tadpoles of this and other species developing in phytotelmata if adults cannot detect and avoid Hg contaminated water bodies (e.g., via chemical cues) for oviposition or tadpole deposition. Previous studies in subtropical and temperate zones have reported high concentrations of Hg bioaccumulated in amphibian larvae through environmental exposure and diet [START_REF] Byrne | The occurrence of mercury in amphibia[END_REF][START_REF] Unrine | Bioaccumulation of trace elements in omnivorous amphibian larvae: implications for amphibian health and contaminant transport[END_REF][START_REF] Bank | Mercury bioaccumulation in green frog (Rana clamitans) and bullfrog (Rana catesbeiana) tadpoles from Acadia National Park, Maine, USA[END_REF], and negative effects of Hg on development (i.e. smaller body size, delayed metamorphosis, higher prevalence of malformations) and survival (Unrine et al. 2009;[START_REF] Shi | Chronic effects of mercury on Bufo gargarizans larvae: thyroid disruption, liver damage, oxidative stress and lipid metabolism disorder[END_REF].

Here, we measured the concentrations of Hg found in different types of phytotelmata (hereafter referred to as "pools") over six different locations in French Guiana, a French Overseas Territory with high prevalence of ASGM [START_REF] Boudou | Les chercheurs d'or et la pollution par le mercure en Guyane française: conséquences environnementales et sanitaires[END_REF][START_REF] Grimaldi | Impact of gold mining on mercury contamination and soil degradation in Amazonian ecosystems of French Guiana[END_REF].

We covered a gradient from pristine/protected forest to disturbed, semi-urbanised areas, at variable distances from known ASGM sites, to assess whether pools potentially used as tadpole-rearing sites contained Hg and, if so, in what concentrations. We focused on pools that could be used by the dyeing poison frog, Dendrobates tinctorius, as males of this species use phytotelmata with a wide range of physical and chemical properties for tadpole deposition [START_REF] Fouilloux | Pool choice in a vertical landscape: tadpole-rearing site flexibility in phytotelm-breeding frogs[END_REF]. Dendrobates tinctorius parents can also use available water-filled plastic containers (e.g., [START_REF] Rojas | Mind the gap: treefalls as drivers of parental trade-offs[END_REF] to deposit their tadpoles. Thus, we also sampled artificial pools in this study. Because ASGM activities use Hg to facilitate gold extraction, we expected to find higher Hg concentrations in closer proximity to ASGM sites. Furthermore, because phytotelmata in tree holes, both in live and fallen trees, are generally more stable over time than other plant structures such as fallen palm bracts, they can accumulate higher amounts of rainwater and litterfall; thus, we predict this type of phytotelmata to have the highest Hg concentrations. Finally, we also recorded the presence/absence, number and size of D. tinctorius tadpoles in each of the pools sampled to investigate (1) potential parental avoidance of pools with high Hg concentrations, as seen in other anuran species which avoid herbicide polluted pools for oviposition (e.g. Takahasi 2007, Vonesh and[START_REF] Vonesh | Pesticide alters oviposition site selection in gray treefrogs[END_REF]; and (2) the potential impact of Hg on larval body condition. If parents are able to detect Hg in the water, we predict pools with higher Hg concentrations to hold fewer (or no) tadpoles than pools with low concentrations or no Hg. Moreover, if Hg negatively affects tadpole growth and development, as previously shown in some temperate species (e.g. Unrine et al. 2009), we predict pools with high Hg levels to harbour tadpoles with poorer body condition than those in pools with little or no Hg.

Material and methods

Study species

Dendrobates tinctorius (Figure 1a) is a rainforest dweller endemic to the Eastern Guiana Shield (French Guiana, Suriname and Northwestern Brazil), where it can be found on elevated ridges or plateaus up to 600 m above sea level [START_REF] Noonan | Refugial isolation and secondary contact in the dyeing poison frog Dendrobates tinctorius[END_REF]. They are diurnal, and characterised by a highly variable bright colouration coupled with the possession of skin toxins [START_REF] Rojas | Sexual dimorphism and intra-populational colour pattern variation in the aposematic frog Dendrobates tinctorius[END_REF][START_REF] Lawrence | Weak warning signals can persist in the absence of gene flow[END_REF]) and an elaborate male parental care. Their clutches are laid terrestrially, on the leaf litter or within hollow fallen logs or tree roots, and taken care of by the male until tadpoles hatch [START_REF] Rojas | From habitat use to social behavior: natural history of a voiceless poison frog, Dendrobates tinctorius[END_REF].

Upon hatching, males transport the tadpoles on their back to bodies of water contained in the vegetation (i.e., phytotelmata;[START_REF] Rojas | Strange parental decisions: fathers of the dyeing poison frog deposit their tadpoles in pools occupied by large cannibals[END_REF][START_REF] Rojas | Mind the gap: treefalls as drivers of parental trade-offs[END_REF][START_REF] Fouilloux | Pool choice in a vertical landscape: tadpole-rearing site flexibility in phytotelm-breeding frogs[END_REF]. Once deposited, tadpoles will remain in these pools (Figure 1b-d

Study areas and field sampling

From January to March 2023, we collected a mix of water and organic matter samples from pools in six different study sites in French Guiana. These sites are known to hold Dendrobates tinctorius populations, and are found under different degrees and types of disturbance, and at variable distances from the closest ASGM site (see Table 1). In each study site, we searched for pools along transects between 10 and 15 km in length, targeting suitable microhabitats such as fallen trees and trees with buttresses or hole structures. When a pool was found, we recorded its type according to the following three categories for phytotelmata: holes in fallen trees; holes in trunks and roots of living trees; and fallen palm bracts. In addition, we also included pools formed in rocky substrates and artificial plastic or metallic containers, as D. tinctorius tadpoles can be found in both types. Artificial pools were found in large numbers in Petit Matoury and Cacao, and only a small random subset was sampled. We obtained the distance to the closest ASGM site for each study area from the French 'Unité Spécialisée Nature', National Office for Forests (ONF).

Table 1. Overview of the study sites, the type of surrounding habitat, the distance to the closest ASGM site and the number of pools sampled. In addition, we noted each pool's morphological and physico-chemical characteristics, and its GPS position. Morphological parameters included height from the ground to the pool edge, largest width and length parallel to the water surface, and water depth. Based on these measurements, we calculated the surface area per water volume ratio (SA/V) of each pool using the formula for a semi-ellipsoid. Physico-chemical parameters included water pH, alkalinity (KH), and water temperature. Water temperature and pH were recorded with a pH metre (pH20, Apera Instruments®), and KH was measured using aquarium water testing strips (JBL EasyTest).

Location

For each pool, we collected a 4 ml mixture of water and sedimentary organic matter with a sterile syringe. Tadpoles use sedimentary organic matter for feeding and hiding, and may be therefore exposed to Hg concentrations from both water and organic matter. Further, we recorded the presence/absence of tadpoles and, when present, attempted to assess the total number of tadpoles and noted the species. If D. tinctorius tadpoles were found in the pool, we used a net or plastic spoons to catch five individuals representing the observed variation in developmental stage. Each captured tadpole was weighed to the nearest 0.01 g and photographed over graph paper to measure its length afterwards. We also noted each tadpole's developmental stage sensu [START_REF] Gosner | A simplified table for staging anuran embryos and larvae with notes on identification[END_REF]

Mercury analyses

Total Hg (THg) was quantified in 400 µL of water and sedimentary organic matter using a Direct Mercury Analyser (DMA-80, atomic absorption spectrometer, Milestone). The method was validated by the analysis of certified reference material (CRM) TORT -3 (Lobster hepatopancreas from the National Research Council of Canada (NRCC); certified Hg concentration 0.292 ± 0.022 ppm dw) at the beginning and the end of analytical cycle and after every 10 samples. Measured values for TORT-3 were 0.298 ± 0.007 ppm dw (n = 15). Blanks were included at the beginning of each analytical run and the limit of detection of the DMA-80 was 0.001 ng Hg. Mercury concentrations are presented in ppm.

Statistical analyses

We checked the normality of our data using a Shapiro-Wilks test, and log-transformed Hg concentration data to achieve normality of residuals. We used a linear mixed-effect model with a Gaussian distribution to assess the relationship between measured Hg concentration (response variable), distance to the closest known ASGM site, pool type, height, pH and SA/V (explanatory variables). We included study site as a random intercept to account for unmeasured differences between locations. We excluded KH and water temperature from our analysis since its variation between pools was very low and independent from the type of pool and the study site (see Table S1).

To investigate the effect of Hg concentration on the probability of presence of D. tinctorius tadpoles and tadpoles from all species recorded, we used generalised linear mixed-effects models (GLMM) with a binomial error distribution. In addition to Hg concentration, we included the pool type and pool traits (i.e. SA/V, height and pH) as fixed effects, and study site as random effect. For the analysis with only D. tinctorius, we also included the number of tadpoles present in the water body as a fixed effect, as it may influence parental care decisions [START_REF] Rojas | Strange parental decisions: fathers of the dyeing poison frog deposit their tadpoles in pools occupied by large cannibals[END_REF]. Further, we studied the effect of Hg on the total number of D. tinctorius tadpoles per pool using a GLMM with a Poisson distribution, including Hg concentration, pool type and pool traits as fixed effects, and study site as random effect. We repeated this last analysis for all tadpole species together.

We calculated the body condition of tadpoles using the scaled mass index (Peig andGreen 2009, 2010). For that, we used tadpole body length measured from the tip of the snout to the most posterior point of the body, excluding their tail to avoid errors due to tail injury. To analyse the effect of Hg concentration on tadpole body condition, we used a linear mixed-effects model with a Gaussian distribution. We included Hg concentration, number of tadpoles in the pool and pool traits as fixed effects, and pool ID nested in study site as a random effect to control for non-independence of the data. In addition, because body mass and SVL vary with Gosner stage as tadpoles approach metamorphic climax, we included stage categories and the interaction with Hg in our model to control for possible differences in body condition due to developmental stage rather than Hg levels.

For all analyses, we used the variance inflation factor to identify multicollinearity between independent variables in the different models, and removed correlated variables when

Results and discussion

Total Hg levels found in the water and sediments of all pools in this study (including rock and artificial pools) were relatively high, ranging from 0.007 to 13.040 ppm (mean ± SD: 1.43 ± 2.19 ppm), being highest in Cacao and lowest in Mont Fortuné (Table 2). The concentrations found in this study are comparable to those reported in polluted water bodies near mining sites [START_REF] Jiang | Mercury pollution in China: an overview of the past and current sources of the toxic metal[END_REF][START_REF] Soe | Mercury pollution from artisanal and small-scale gold mining in Myanmar and other southeast asian countries[END_REF] or abandoned chlor-alkali plants [START_REF] Degetto | Santa Gilla lagoon (Italy): a mercury sediment pollution case study. Contamination assessment and restoration of the site[END_REF][START_REF] Song | Environmental mercury pollution by an abandoned chlor-alkali plant in Southwest China[END_REF] elsewhere. One sample was under the detection limit. An outlier value of 172.06 ppm belonging to an artificial pool (a rusty paint barrel) was removed from the main analysis, as we were unable to determine whether this high value could be attributed to a measurement error or to leftovers of the previous content therein. In 17% of our samples, Hg concentrations were above the severe effect level (SEL = 2 ppm) for freshwater sediments reported by the US National Oceanographic and Atmospheric Administration [START_REF] Buchman | NOAA screening quick reference tables[END_REF]. Above this level, sediments are considered heavily polluted and adverse effects are expected to occur in the majority of sediment-dwelling organisms. Pools in locations closer to known ASGM sites tended to accumulate higher Hg concentrations (Table 3, Figure 2a). Among the pools sampled, those in Cacao, which is only 1.6 km from the closest known ASGM site, had the highest concentrations of Hg. All other locations were ≥ 15 km from the nearest known ASGM. These findings suggest a potential link between ASGM activities and Hg pollution in pools. Another possible explanation for the high Hg concentrations found in Cacao could be the (historic) use of Hg-containing fungicides or phosphorus fertilisers with Hg impurities in the agricultural fields that dominate the landscape [START_REF] Mortvedt | Heavy metal contaminants in inorganic and organic fertilizers[END_REF][START_REF] Turull | Evaluation of mercury in a freshwater environment impacted by an organomercury fungicide using diffusive gradient in thin films[END_REF][START_REF] Tang | Mercury in rice (Oryza sativa L.) and rice-paddy soils under long-term fertilizer and organic amendment[END_REF]. Although Hg-containing fungicides have been banned in the EU since 2017 (https://minamataconvention.org), they were commonly used during the second half of the 20th century and can remain in the soil for long periods of time (Murphy and Aucott 1999;Horowitz et al. 2014;[START_REF] Ali | Environmental chemistry and ecotoxicology of hazardous heavy metals: environmental persistence, toxicity, and bioaccumulation[END_REF][START_REF] Schneider | When toxic chemicals refuse to die-an examination of the prolonged mercury pesticide use in Australia[END_REF]. Pools in Mont Fortuné, in contrast, had the lowest values of Hg. This could be explained by the fact that, despite being surrounded by urban areas, this location is not directly adjacent to agricultural fields or close to illegal ASGM activities, which often take place in remote locations [START_REF] Durán | Global spatial coincidence between protected areas and metal mining activities[END_REF][START_REF] Rahm | Monitoring the Impact of Gold Mining on the Forest Cover and Freshwater in the Guiana Shield. Reference year[END_REF].

Deeper pools in relation to their surface area, as well as pools closer to the ground, had higher concentrations of Hg (Table 3, Figure 2b-c). Pools in rock holes (mean ± SD: 3.38 ± 4.76 ppm) and artificial pools (2.32 ± 2.92 ppm) generally showed the highest levels of Hg, followed by fallen trees (1.59 ± 2.21 ppm) and tree holes (1.20 ± 1.83 ppm). Palm bracts had the lowest Hg concentrations (0.55 ± 0.50 ppm) (Figure 2d). After accounting for pool height and SA/V, pool type and pH were uninformative in explaining variation in Hg concentration (Table 3).

However, pool type and pool characteristics (SA/V and pool height) were interrelated (Figure S1, S2), and it is possible that other pool characteristics also influenced Hg concentrations (e.g., durability, material of artificial pools) [START_REF] Fouilloux | Pool choice in a vertical landscape: tadpole-rearing site flexibility in phytotelm-breeding frogs[END_REF]. For example, shallow pools in relation to their volume (i.e. high SA/V), which had the lowest Hg concentrations, were mostly represented by palm bracts (Figure S1). Palm bracts are typically ephemeral and may dry out and decompose rapidly [START_REF] Fouilloux | Pool choice in a vertical landscape: tadpole-rearing site flexibility in phytotelm-breeding frogs[END_REF], having relatively little time to accumulate Hg through rain and leaf litter. In contrast, water pools formed in rock holes may have naturally higher levels of Hg due to both, their permanent nature when compared to degrading plant structures, and their direct contact with Hg-rich soils [START_REF] Roulet | The geochemistry of mercury in central Amazonian soils developed on the Alter-do-Chao formation of the lower Tapajos River Valley, Para state, Brazil[END_REF][START_REF] Fadini | Is the Negro River Basin (Amazon) impacted by naturally occurring mercury?[END_REF]. S2). This is in line with previous findings indicating the surprisingly wide range of pool chemical properties that D. tinctorius tadpoles can withstand [START_REF] Fouilloux | Pool choice in a vertical landscape: tadpole-rearing site flexibility in phytotelm-breeding frogs[END_REF], which may even extend to potentially harmful substances, and suggests that phytotelm-breeding frogs might be unable to identify and/or avoid highly Hg-polluted pools for oviposition or tadpole deposition. Some Australian species, for instance, have been shown to struggle to develop in polluted wetlands, yet adults do not seem to discriminate between polluted and unpolluted pools [START_REF] Sievers | Frog occupancy of polluted wetlands in urban landscapes[END_REF]).

Alternatively, it could indicate that these frogs are selecting pools on the basis of other factors such as inter-/intraspecific competition and pool stability, as is the case in several other species [START_REF] Lehtinen | Tests for competition, cannibalism, and priority effects in two phytotelm-dwelling tadpoles from Madagascar[END_REF][START_REF] Summers | The evolutionary ecology of phytotelmata use in Neotropical poison frogs[END_REF][START_REF] Brown | Divergence in parental care, habitat selection and larval life history between two species of Peruvian poison frogs: an experimental analysis[END_REF][START_REF] Ryan | Competitive interactions in phytotelmata-breeding pools of two poison-dart frogs (Anura: Dendrobatidae) in Costa Rica[END_REF][START_REF] Schulte | The smell of success: choice of larval rearing sites by means of chemical cues in a Peruvian poison frog[END_REF][START_REF] Fouilloux | Pool choice in a vertical landscape: tadpole-rearing site flexibility in phytotelm-breeding frogs[END_REF]). However, understanding the influence of Hg contamination on pool selection requires further research on parental decision-making under controlled conditions. When accounting for all species recorded within the pools, which included Allobates femoralis, Rhinella spp., and Osteocephalus oophagus, we found a decrease in tadpole number (but not in presence probability) with increasing Hg concentrations (Table S3; Figure 3a). However, the number of tadpoles was significantly higher in palm bracts (Table S3), consistent with the restrictions of these species to lower pools for egg/tadpole deposition compared to D.

tinctorius [START_REF] Fouilloux | Pool choice in a vertical landscape: tadpole-rearing site flexibility in phytotelm-breeding frogs[END_REF]). Thus, the selection of low polluted pools may be due to a biological restriction to palm bracts, which showed lower Hg levels compared to other pool types, rather than an active avoidance of pools with higher Hg levels. In addition, the number of tadpoles also increased in pools closer to the ground, with smaller SA/V and higher pH (Table S3).

From all the tadpoles found, we sampled a total of 34 D. tinctorius tadpoles from developmental stages 25-29, 12 individuals from stages 30-35 and 8 from stages 36-43. This reduction in the number of tadpoles encountered with increasing developmental stages might be due to chance (as we sampled relatively few tadpoles per pool), detection bias due to increased flight behaviour [START_REF] Warkentin | The development of behavioral defenses: a mechanistic analysis of vulnerability in red-eyed tree frog hatchlings[END_REF], or mortality over time due to predation or mercury bioaccumulation. Further research should explore whether this pattern could also be explained by a lower survival of tadpoles to later stages as a consequence of longer exposure times to high mercury levels, with detrimental effects on their survival, or antipredatory behaviour. For example, [START_REF] Lefcort | Heavy metals alter the survival, growth, metamorphosis, and antipredatory behavior of Columbia spotted frog (Rana luteiventris) tadpoles[END_REF] reported reduced predator avoidance behaviour of tadpoles exposed to different heavy metals.

Tadpole body condition was best explained by the intercept only model (Table S4). However, there was a visual tendency for a negative correlation between Hg concentration and body condition of tadpoles at later developmental stages (Figure 3b). In addition, when excluding from our model early stage tadpoles, which have been exposed to mercury for a few weeks only (Mean ± SD = 4.62 ± 0.99; C. Fouilloux and B. Rojas, unpublished), mercury was included in the second-highest ranking model within delta AIC <4 (Table S4). After model averaging, there was a negative correlation of Hg and tadpole body condition (estimate ± SE = -0.03 ± 0.01, Z = 3.47, p = <0.001; Table S5). More measurements from a wider range of Hg concentrations, especially of older tadpoles, would be needed to further investigate this pattern. One question that arises from this study is how much of the Hg detected in phytotelmata is ingested and accumulated in the tissues of developing tadpoles, as well as which are the potential repercussions on their development, ecology and behaviour. [START_REF] Bank | Mercury bioaccumulation in green frog (Rana clamitans) and bullfrog (Rana catesbeiana) tadpoles from Acadia National Park, Maine, USA[END_REF] found a significant correlation between Hg levels in ponds and Hg levels in tadpole tissue, with much lower concentrations than those found in our study (1.3e -6 -8.4e -6 ppm). In addition, they found that Hg concentrations increased with tadpole body length, pointing towards bioaccumulation of Hg as a function of age [START_REF] Bank | Mercury bioaccumulation in green frog (Rana clamitans) and bullfrog (Rana catesbeiana) tadpoles from Acadia National Park, Maine, USA[END_REF]). These results are in line with our findings, which point towards a detrimental effect of Hg on body condition in late developmental stages. Further, Unrine et al. (2009) found adverse effects on growth and development of Southern leopard frog larvae exposed to dietary Hg in concentrations similar to those reported here. The data from these studies suggest that the Hg concentrations detected in phytotelmata could also bioaccumulate in phytotelm-breeding frogs, negatively affecting the development at particularly sensitive developmental stages. Finally, given the neurotoxic and endocrine-disrupting nature of Hg [START_REF] Tan | The endocrine effects of mercury in humans and wildlife[END_REF][START_REF] Crump | Mercury-induced reproductive impairment in fish[END_REF], we urge to investigate the possible repercussions not only on the development of tadpoles, but also on their behaviour. To that end, experimental studies will be crucial to quantify the

Declaration of competing interest

The authors have no relevant financial or non-financial interests to disclose.

  ) selected by their father until metamorphosis, which is reached after 2-3 months (Rojas and Pašukonis 2019). D. tinctorius was declared a protected species in French Guiana in 2020 (Decree No. TREL2032100A from November 19th 2020).

Figure 1 .

 1 Figure 1. A male Dendrobates tinctorius carrying two tadpoles on his back (a) and the diversity of sampled pool

  required(VIF > 3; Zuur et al., 2010). We used model selection based on Akaike's Information Criterion for small sample sizes (AICc)(Burnham et al. 2011), using the R package 'MuMIn' (Barton 2020), selecting the model with the lowest AICc value. If two or more of the highest ranking models were within delta AIC < 4, we performed model averaging[START_REF] Symonds | A brief guide to model selection, multimodel inference and model averaging in behavioural ecology using Akaike's information criterion[END_REF]. Parameters that included zero within their 95% CI were considered uninformative (Arnold 2010). We accepted statistical significance at p < 0.05 and trends at p < 0.1. All statistical analyses were performed using the software R version 4.1.2 (R development Core Team 2022).

Figure 2 .

 2 Figure 2. The predicted (large symbols and lines) Hg concentration (ppm) for (a) the distance to the closest known

Figure 3 .

 3 Figure 3. (a) The predicted number (line) of tadpoles from all species in relation to Hg concentration (ppm) and (b)

  negative effects of various Hg concentrations on tadpole development, physiology, behaviour, and survival under standardised conditions, and to understand the mechanisms involved without the need to account for the myriad of confounding effects (such as predation, competition, pool type, water chemistry, etc.) that impede our ability to draw stronger conclusions from wild populations. Nevertheless, our results provide valuable baseline data of mercury concentrations in the wild and lay the foundation for future work on this important environmental issue.CRediT authorship contribution statementLiaSchlippe Justicia: Conceptualization, Methodology, Investigation, Data curation, Formal analysis, Visualization, Writingoriginal draft. Jérémy Lemaire: Conceptualization, Methodology, Formal analysis, Writingreview & editing. Carolin Dittrich: Investigation, Formal analysis, Writingreview & editing. Martin Mayer: Investigation, Formal analysis, Writingreview & editing. Paco Bustamante: Resources, Writingreview & editing. Bibiana Rojas: Conceptualization, Methodology, Supervision, Funding acquisition, Resources, Writing review & editing.

Surrounding habitat Distance to closest ASGM site (km) Number of sampled pools

	Petit Matoury	Urban	32	13
	Mont Fortuné	Urban	31	28
	Cacao	Agricultural	1.6	16
	Mataroni	Logging roads	16	14
	Mont Favard	Natural Reserve	27	13
	Camp Pararé	Natural Reserve	15	14

  Capture and sample collection were done under a permit from the Direction Régionale des Territoires et de la Mer de Guyane (R03-2022-12-28-00004) after assessment by the CSRPN, the regional scientific committee. Procedures employed at Nouragues Research Station were also approved by the Reserve's scientific committee.

					, and classified it into three categories
	(early	pre-metamorphosis:	25-29;	late	pre-metamorphosis:	30-35;	and	pro-

metamorphosis/metamorphic climax: 36-45) to account for its nonlinear nature. This means that larval development time to change from e.g. stage 26 to 27 is not equivalent to that from stage 42 to 43. Documenting tadpole developmental stages also allowed us to account for differences in exposure times to Hg in the pool. All tadpoles were returned to the same pool where they were caught immediately after.

Table 2 .

 2 Number of pool types sampled by study site, mean and standard deviation of Hg concentrations (ppm), total number of D. tinctorius tadpoles observed and number of D. tinctorius tadpoles sampled per study site.Columns coloured in green correspond to phytotelmata.

	Study	Type of pool				Mean ± SD	Number of	Number of
	site						Hg	D.	D.
		bract Palm	hole/ Tree	tree Fallen	hole Rock	Artificial	concentrati	tinctorius	tinctorius
			roots				on (ppm)	tadpoles	tadpoles
								observed	sampled
	Petit	2	4	0	0	6	1.38 ± 2.42	147	11
	Matoury
	Mt	0	25	3	0	0	0.77 ± 0.87	30	14
	Fortuné
	Cacao	0	6	5	5	2	2.72 ± 3.96	3	2
	Mataroni	0	7	6	0	0	1.70 ± 1.94	15	11
	Mt	7	4	0	1	0	1.30 ± 1.47	16	8
	Favard
	Camp	2	12	1	0	0	1.08 ± 0.87	16	9
	Pararé

Table 3 .

 3 Effect size, standard error (SE), lower (LCI) and upper (UCI) 95% confidence intervals, and P-values of explanatory variables for the analysis of Hg concentrations in pools. We performed model averaging of best models (ΔAICc < 4) to estimate the effect size of each variable. Informative parameters are presented in bold (95% confidence intervals do not overlap with zero).

	Variable	Estimate SE	LCI	UCI	P-value
	Intercept	-0.33	0.34	-1.00	0.35	0.34
	Pool height	-0.29	0.14	-0.57	-0.01	0.04
	SA/V	-0.40	0.16	-0.72	-0.09	0.01
	Distance from the closest ASGM	-0.37	0.21	-0.78	0.05	0.09
	Pool type Palm bract	-1.07	0.71	-2.48	0.33	0.13
	Pool type Tree hole	-0.27	0.40	-1.05	0.52	0.51
	Pool type Artificial	0.78	0.74	-0.68	2.24	0.30
	Pool type Rock hole	0.59	0.66	-0.72	1.89	0.38
	pH	-0.10	0.14	-0.37	0.18	0.49

Acknowledgements B.R., L.S.J., M.M. and C.D. received funding from the Research Council of Finland (Academy Research Fellowship, Decision 319949 to BR). LS and BR also received funds from the University of Veterinary Medicine Vienna via the International Relations Office (funds for research activities abroad; KUWI_MA) and startup funds, respectively. A huge thank you to Jennifer Stynoski, Chloé Fouilloux and Michael Roast for life-saving statistical advice. We are indebted to the 'Unité Spécialisée Nature' from the 'Office National des Forêts' for their assistance regarding information on illegal gold mining activities in French Guiana, and to the staff of CNRS Guyane, the Office National des Forêts, and the Nouragues Research Station (managed by CNRS), which benefits from "Investissement d'Avenir'' grants managed by Agence Nationale de la Recherche (AnaEE France ANR-11-INBS-0001; Labex CEBA ANR-10-LABX-25-01), for logistic support. BR is part of a multi-researcher partnership with the Nouragues Nature Reserve (Convention Cadre de Partenariat N°01-2019) aimed at improving and spreading knowledge about amphibians. We are grateful to Rosanna Mangione for insightful discussions, and to the Plateform Analyses Elémentaires of LIENSs for the access to the mercury analyser. Thanks are also due to the Région Nouvelle Aquitaine for co-funding the DMA of LIENSs laboratory. PB is an honorary member of the IUF (Institut Universitaire de France). Our manuscript greatly benefitted from the thoughtful feedback provided by Mar Comas and an anonymous reviewer.

Data availability

Data will be deposited in the Figshare repository upon acceptance.