Part II: Advanced Approaches

Keywords:

T

his article is the second of a two-part tutorial on visual servo control. In Part I (IEEE Robotics and Automation Magazine, vol. 13, no. 4), we introduced fundamental concepts and descr ibed basic approaches. Here we discuss more advanced concepts, and present a number of recent approaches.

As described in Part I of the tutorial, visual servo schemes rely on the relationship ṡ = L s v c [START_REF] Ma | An Invitation to 3-D Vision: From Images to Geometric Models[END_REF] in which s is a set of geometrical features whose time derivative ṡ is linearly related to the spatial velocity v c of the camera through the interaction matrix L s . Using this relationship, control schemes are designed to minimize the error e between the current value of the visual feature s and its desired value s * : e = ss * . A classical proportional control scheme is given by:

v c = -λ L + e e, ( 2)
where L e is defined by

ė = L e v c , ( 3)
and L + e is an approximation of the pseudo-inverse of L e . An approximation must be used because visual servo schemes require the values of three-dimensional (3-D) parameters that are not available directly from the image measurements. Recall that for position-based visual servo (PBVS) schemes 3-D parameters appear both in the error e and in the interaction matrix, while for basic image-based visual servo (IBVS), the depth of each point considered appears in the coefficients of the interaction matrix related to the translational motions. This is the case even when L + e = L e * + is used in the control scheme, although in this case only the depth Z * of each point for the desired pose is needed, which is generally not difficult to obtain in practice. In all other cases, an estimation of the current depth must be made at each iteration of the control scheme. We begin Part II of the tutorial by describing two approaches to estimating the interaction matrix. First we describe how epipolar geometry can be used to estimate the 3-D parameters, which can then be used to construct the interaction matrix. We then describe how it is possible to estimate directly the numerical value of L + e . With these methods in hand, we then present more advanced techniques in visual servo control. These techniques aim to compensate for the relative shortcomings of the PBVS and IBVS methods. We then consider target tracking tasks, that is, tasks for which the target object is not stationary. Finally, we present a generalization of the modeling issues that allows one to consider both eye-in-hand systems and eye-to-hand systems.

Estimation of 3-D Parameters

If a calibrated stereo vision system is used, all 3-D parameters can be easily determined by triangulation, as evoked in Part I of the tutorial. Similarly, if a 3-D model of the object is known, all 3-D parameters can be computed from a pose estimation algorithm. However, such an estimation can be quite unstable due to image noise. It is also possible to estimate 3-D parameters by using the epipolar geometry that relates the images of the same scene observed from different viewpoints. Indeed, in visual servoing, two images are generally available:

MARCH 2007 110
the current one and the desired one. In contrast, we can estimate the interaction matrix directly as image measurements are made during the visual servoing task. Here, we discuss both approaches.

Epipolar Geometry

Given a set of matches between the image measurements in the current image and in the desired one, the fundamental matrix, or the esential matrix if the camera is calibrated, can be recovered [START_REF] Ma | An Invitation to 3-D Vision: From Images to Geometric Models[END_REF], and then used in visual servoing [START_REF] Basri | Visual homing: Surfing on the epipoles[END_REF]. Indeed, from the essential matrix, the rotation and the translation up to a scalar factor between the two views can be estimated. However, near the convergence of the visual servo, that is when the current and desired images are similar, the epipolar geometry becomes degenerate and it is not possible to estimate accurately the partial pose between the two views. For this reason, using homography is generally prefered.

Let x i and x * i denote the homogeneous image coordinates for a point in the current and desired images. Then x i is related to x * i by

x i = H i x * i ,
in which H i is a homography matrix. If all feature points lie on a 3-D plane, then there is a single homography matrix H such that x i = Hx * i for all i. This homography can be estimated using the position of four matched points in the desired and the current images. If all the features points do not belong to the same 3-D plane, then three points can be used to define such a plane and five supplementary points are needed to estimate H [START_REF] Malis | 2 1/2 D visual servoing with respect to unknown objects through a new estimation scheme of camera displacement[END_REF].

Once H is available, it can be decomposed as

H = R + t d * n * , ( 4
)
in which R is the rotation matrix relating the orientation of the current and desired camera frames, n * is the normal to the chosen 3-D plane expressed in the desired frame, d * is the distance to the 3-D plane from the desired frame, and t is the translation between current and desired frames. From H, it is thus posible to recover R, t/d * , and n. In fact, two solutions for these quantities exist [START_REF] Faugeras | Three-dimensional computer vision: a geometric viewpoint[END_REF], but it is quite easy to select the correct one using some knowledge about the desired pose. It is also possible to estimate the depth of any target point up to a common scale factor [START_REF] Mezouar | Path planning for robust image-based control[END_REF]. The unknown depth of each point that appears in classical IBVS can thus be expressed as a function of a single constant parameter. Similarly, the pose para-meters required by PBVS can be recovered up to a scalar factor as for the translation term. The PBVS schemes described in Part I of the tutorial can thus be revisited using this approach, with the new error defined as the translation up to a scalar factor and the angle/axis parameterization of the rotation. This approach has also been used for the hybrid visual servoing schemes described in the next section.

Direct Estimation

The approach described previously can be used to estimate the unknown 3-D parameters that appear in the analytical form of the interaction matrix. It is also possible to estimate directly its numerical value using either an off-line learning step, or an on-line estimation scheme. This idea is only useful for IBVS since, for PBVS, all the coefficients of the interaction matrix are directly obtained from the features s used in the control scheme.

All the methods proposed to estimate numerically the interaction matrix rely on observations of the variation of features due to a known or measured camera motion. More precisely, if we measure a feature's variation s due to a camera motion v c , we have from ( 1)

L s v c = s,
which provides k equations, while we have k × 6 unknown values in L s . Using a set of N independent camera motions with N > 6, it is thus possible to estimate L s by solving

L s A = B,
where the columns of A ∈ R 6×N and B ∈ R k×N are respectively formed with the set of camera motions and the set of corresponding features variations. The least squares solution is of course given by L s = BA + .

(

Methods based on neural networks have also been developed to estimate L s [START_REF] Suh | Visual servoing of robot manipulators by fuzzy membership function based neural networks[END_REF], [START_REF] Wells | Vision-based robot positioning using neural networks[END_REF]. It is also possible to estimate directly the numerical value of L + s , which provides in practice a better behavior [START_REF] Lapresté | An efficient method to compute the inverse jacobian matrix in visual servoing[END_REF]. In that case, the basic relation is

L + s s = v c ,
which provides six equations. Using a set of N measurements, with N > k, we now obtain

L + s = AB + . ( 6
)
In the first case (5), the six columns of L s are estimated by solving six linear systems, while in the second case [START_REF] Suh | Visual servoing of robot manipulators by fuzzy membership function based neural networks[END_REF], the k columns of L + s are estimated by solving k linear systems, which explains the difference in the results.

Estimating the interaction matrix online can be viewed as an optimization problem, and consequently a number of

Epipolar geometry can be used to estimate the 3-D parameters, which can then be used to construct the interaction matrix.

researchers have investigated approaches that derive from optimization methods. These methods typically discretize the system equation [START_REF] Ma | An Invitation to 3-D Vision: From Images to Geometric Models[END_REF], and use an iterative updating scheme to refine the estimate of L s at each stage. One such online and iterative formulation uses the Broyden update rule given by [START_REF] Hosada | Versatile visual servoing without knowledge of true jacobian[END_REF], [START_REF] Jägersand | Experimental evaluation of uncalibrated visual servoing for precision manipulation[END_REF]

L s (t + 1) = L s (t) + α v c v c ( x -L s (t) v c ) v c ,
where α defines the update speed. This method has been generalized to the case of moving objects in [START_REF] Piepmeier | Uncalibrated dynamic visual servoing[END_REF].

The main interest of using such numerical estimations in the control scheme is that it avoids all the modeling and calibration steps. It is particularly useful when using features whose interaction matrix is not available in analytical form. For instance, in [START_REF] Deguchi | Direct interpretation of dynamic images and camera motion for visual servoing without image feature correspondence[END_REF], the main eigenvalues of the Principal Component Analysis of an image have been considered in a visual servoing scheme. The drawbacks of these methods is that no theoretical stability and robustness analysis can be made.

Advanced Visual Servo Control Schemes

We now describe visual servo control schemes which have been proposed to improve the behavior of basic IBVS and PBVS. The first ones combine the respective advantages of these schemes while trying to avoid their shortcomings.

Hybrid Visual Servo

Suppose we have access to a clever control law for ω ω ω c , such as the one used in PBVS ω ω ω c = -λ θu, [START_REF] Wells | Vision-based robot positioning using neural networks[END_REF] where θu is obtained either from a pose estimation algorithm if the 3-D model of the object is available, or from the partial pose estimated using the epipolar geometry or the homography. How could we use this in conjunction with traditional IBVS? Considering a feature vector s t and an error e t devoted to control the translational degrees of freedom, we can partition the interaction matrix as follows:

ṡt = L s t v c = [ L v L ω ω ω ] v c ω ω ω c = L v v c + L ω ω ω ω ω ω c .
Now, setting ėt = -λe t , we can solve for the desired translational control input as

-λe t = ėt = ṡt = L v v c + L ω ω ω ω ω ω c ⇒ v c = -L + v (λe t + L ω ω ω ω ω ω c ). ( 8
)
We can think of the quantity (λe t + L ω ω ω ω ω ω c ) as a modified error term, one that combines the original error with the error that would be induced by the rotational motion due to

ω c . The translational control input v c = -L + v (λe t + L ω ω ω ω ω ω c
) will drive this error to zero.

The method known as two and one-half-dimensional (2 1/2-D) Visual Servo [START_REF] Malis | 2-1/2D visual servoing[END_REF] was the first to exploit such a partitioning in combining IBVS and PBVS. More precisely, in [START_REF] Malis | 2-1/2D visual servoing[END_REF], s t has been selected as the coordinates of an image point, and the logarithm of its depth, so that L v is a triangular always invertible matrix. More precisely, we have s t = (x, log Z ), s * t = (x * , log Z * ), e t = (xx * , log ρ Z ) where ρ Z = Z /Z * , and

L v = 1 Z * ρ Z -1 0 x 0 -1 y 0 0 -1 L ω = xy -(1 + x 2 ) y 1 + y 2 -xy -x -y x 0 .
Note that the ratio ρ Z can be obtained directly from the partial pose estimation algorithm described previously.

If we come back to the usual global representation of visual servo control schemes, we have e = (e t , θu) and L e given by

L e = L v L ω 0 L θu ,
from which we obtain immediately the control law ( 7) and ( 8) by applying ( 2). If we consider the example chosen in Part I of the tutorial to compare the behavior of the different control schemes, the results obtained using (8) are given in Figure 1. Here, the point that has been considered in s t is the center of gravity x g of the target. Note that the image trajectory of this point is a straight line as expected, and that there is a nice decrease of the camera velocity components, which makes this scheme very near the first PBVS approach.

As for stability, it is clear that this scheme is globally asymptotically stable in perfect conditions (refer to the stability analysis provided in the Part I of the tutorial: we are here in the simple case k = 6). Furthermore, thanks to the triangular form of the interaction matrix L e , it has been possible to analyze the stability of this scheme in the presence of calibration errors using the homography estimation approach [START_REF] Malis | Theoretical improvements in the stability analysis of a new class of model-free visual servoing methods[END_REF]. Finally, the only unknown constant parameter involved in this scheme, that is Z * , can be estimated on line using adaptive techniques [START_REF] Chen | Adaptive homographybased visual servo tracking for fixed and camera-in-hand configurations[END_REF].

Other hybrid schemes can be designed. For instance, in [START_REF] Morel | Explicit incorporation of 2D constraints in vision-based control of robot manipulators[END_REF], the third component of s t is different and has been selected so that all the target points remain in the camera field of view as far as possible. Another example has been proposed in [START_REF] Chaumette | 2 1/2 D visual servoing: a possible solution to improve image-based and position-based visual servoings[END_REF]. In that case, s is selected as s = ( c * t c , x g , θ u z ) which provides with a block-triangular interaction matrix of the form:

L e = R 0 L v L ω ,
where L v and L ω can easily be computed. This scheme is so that, in perfect conditions, the camera trajectory is a straight line (since c * t c is a part of s), and the image trajectory of the center of gravity of the object is also a straight line (since x g is also a part of s). The translational camera degrees of freedom are devoted to realize the 3-D straigth line, while the rotational camera degrees of freedom are devoted to realize the two-dimensional (2-D) straight line and compensate also the 2-D motion of x g due to the transational motion. As can be seen in Figure 2, this scheme is particularly satisfactory in practice. Finally, it is possible to combine differently 2-D and 3-D features. For instance, in [START_REF] Cervera | Improving imagebased visual servoing with three-dimensional features[END_REF], it has been proposed to use in s the 2-D homogeneous coordinates of a set of image points expressed in pixels multiplied by their corresponding depth:

s = (u 1 Z 1 , v 1 Z 1 , Z 1 , . . . , u n Z n , v n Z n , Z n ) .
As for classical IBVS, we obtain in that case a set of redundant features, since at least three points have to be used to control the six camera degrees of freedom (we here have k ≥ 9). However, it has been demonstrated in [START_REF] Schramm | Extended-2D visual servoing[END_REF] that this selection of redundant features is free of attractive local minima.

Partitioned Visual Servo

The hybrid visual servo schemes described previously have been designed to decouple the rotational motions from the translational ones by selecting adequate visual features defined in part in 2-D, and in part in 3-D (that is why they have been called 2 1/2-D visual servoing). This work has inspired some researchers to find features that exhibit similar decoupling properties but using only features expressed directly in the image. More precisely, the goal is to find six features so that each of them is related to only one degree of freedom (in which case the interaction matrix is a diagonal matrix), the Grail being to find a diagonal interaction matrix whose elements are constant, as near as possible of the identity matrix, leading to a pure, direct, and simple linear control problem.

The first work in this area partitioned the interaction matrix so as to isolate motion related to the optic axis [START_REF] Corke | A new partitioned approach to imagebased visual servo control[END_REF]. Indeed, whatever the choice of s, we have

ṡ = L s v c = L xy v xy + L z v z = ṡxy + ṡz ,
v xy = -L + xy (λe(t) + L z v z ).
As before, we can consider (λe(t) + L z v z ) as a modified error that incorporates the original error while taking into account the error that will be induced by v z . Given this result, all that remains is to choose s and v z . As for basic IBVS, the coordinates of a collection of image points can be used in s, while two new image features can be defined to determine v z .

◆ Define α, with 0 ≤ α < 2π as the angle between the horizontal axis of the image plane and the directed line segment joining two feature points. It is clear that α is closely related to the rotation around the optic axis. ◆ Define σ 2 to be the area of the polygon defined by these points. Similarly, σ 2 is closely related to the translation along the optic axis. Using these features, v z has been defined in [START_REF] Corke | A new partitioned approach to imagebased visual servo control[END_REF] as

v z = λ v z ln σ * σ ω z = λ ω z (α * -α).

IBVS with Cylindrical Coordinates of Image Points

As proposed in [START_REF] Iwatsuki | A new formulation of visual servoing based on cylindrical coordinate system[END_REF], another option is to use the cylindrical coordinates (ρ, θ) of the image points instead of their Cartesian coordinates (x, y). They are defined by

ρ = x 2 + y 2 θ = arctan y x (9)
as long as ρ = 0, in which case θ is not defined. We deduce from ( 9):

ρ = (x ẋ + y ẏ)/ρ θ = (x ẏ -y ẋ)/ρ 2 .
Using the interaction matrix L x given in Part I of the tutorial to express ẋ and ẏ, and then substituting x by ρ cos θ and y by ρ sin θ , we obtain immediately

L ρ = -c Z -s Z ρ Z (1 + ρ 2 )s -(1 + ρ 2 )c 0 L θ = s ρZ -c ρZ 00 c /ρ s/ρ -1 ,
where c = cos θ and s = sin θ . By looking at the third and sixth column of L ρ and L θ , we can note that ρ is invariant with respect to ω z while θ is invariant with respect to v z and linearly related to ω z , as were the two image features σ and α chosen previously. This explains why the behavior obtained in that case is quite satisfactory. Indeed, by considering the same example as before, and using now s = (ρ 1 , θ 1 , . . . , ρ 4 , θ 4 ) and L + e = L + e * (that is a constant matrix), the system behavior shown in Figure 3 has the same nice properties as using L + e = (L e /2 + L e * /2) + with s = (x 1 , y 1 , . . . , x 4 , y 4 ). If we go back to the example used in the geometrical interpretation of IBVS described in Part I of the tutorial, the behavior obtained will also be as expected, thanks to the decoupling between the third and sixth columns of the interaction matrix.

Advanced IBVS Schemes

Up until now, for all IBVS schemes presented, we have primarily considered image point coordinates in s. Other geometrical primitives can of course be used. There are several reasons to do so. First, the scene observed by the camera cannot always be described merely by a collection of points, in which case the image processing provides other types of measurements, such as a set of straight lines or the contours of an object. Second, richer geometric primitives may ameliorate the decoupling and linearizing issues that motivate the design of partitioned systems. Finally, the robotic task to be achieved may be expressed in terms of virtual linkages (or fixtures) between the camera and the observed objects [START_REF] Chaumette | Classification and realization of the different vision-based tasks[END_REF], [START_REF] Castano | Visual compliance: task directed visual servo control[END_REF], sometimes expressed directly by constraints between primitives, such as for instance point-to-line [START_REF] Hager | A modular system for robust positioning using feedback from stereo vision[END_REF] (which means that an observed point must lie on a specified line).

For the first point, it is possible to determine the interaction matrix related to the perspective projection of a large class of geometrical primitives, such as segments, straight lines, spheres, circles, and cylinders. The results are given in [START_REF] Espiau | A new approach to visual servoing in robotics[END_REF] and [START_REF] Chaumette | Classification and realization of the different vision-based tasks[END_REF]. Recently, the analytical form of the interaction matrix related to any image moments corresponding to planar objects has been computed. This makes possible to consider planar objects of any shape [START_REF] Chaumette | Image moments: A general and useful set of features for visual servoing[END_REF]. If a collection of points is measured in the image, moments can also be used [START_REF] Tahri | Point-based and region-based image moments for visual servoing of planar objects[END_REF]. In both cases, moments allow the use of intuitive geometrical features, such as the center of gravity or the orientation of an object. By selecting an adequate combination of moments, it is then possible to determine partitioned systems with good decoupling and linearizing properties [START_REF] Chaumette | Image moments: A general and useful set of features for visual servoing[END_REF], [START_REF] Tahri | Point-based and region-based image moments for visual servoing of planar objects[END_REF].

Note that for all these features (geometrical primitives, moments), the depth of the primitive or of the object considered appears in the coefficients of the interaction matrix related to the translational degrees of freedom, as was the case for the image points. An estimation of this depth is thus generally still necessary. Few exceptions occur, using for instance an adequate normalization of moments, which allows in some particular cases to make only the constant desired depth appear in the interaction matrix [START_REF] Tahri | Point-based and region-based image moments for visual servoing of planar objects[END_REF]. The main interest of using such numerical estimations in the control scheme is that it avoids all the modeling and calibration steps.

IEEE Robotics & Automation Magazine MARCH 2007 114

Performance Optimization and Planning

In some sense, partitioned methods represent an effort to optimize system performance by assigning distinct features and controllers to individual degrees of freedom. In this way, the designer performs a sort of off-line optimization when allocating controllers to degrees of freedom. It is also possible to explicitly design controllers that optimize various system performance measures. We describe a few of these in this section.

Optimal Control and Redundancy Framework

An example of such an approach is given in [START_REF] Papanikolopoulos | Visual tracking of a moving target by a camera mounted on a robot: A combination of vision and control[END_REF] and [START_REF] Hashimoto | LQ optimal and nonlinear approaches to visual servoing[END_REF], in which linear quadratic Gaussian (LQG) control design is used to choose gains that minimize a linear combination of state and control input. This approach explicitly balances the tradeoff between tracking errors (since the controller attempts to drive ss * to zero) and robot motion. A similar control approach is proposed in [START_REF] Nelson | Strategies for increasing the tracking region of an eye-in-hand system by singularity and joint limit avoidance[END_REF] where joint limit avoidance is considered simultaneously with the positioning task.

It is also possible to formulate optimality criteria that explicitly express the observability of robot motion in the image. For example, the singular value decomposition of the interaction matrix reveals which degrees of freedom are most apparent and can thus be easily controlled, while the condition number of the interaction matrix gives a kind of global measure of the visibility of motion. This concept has been called resolvability in [START_REF] Nelson | Force and vision resolvability for assimilating disparate sensory feedback[END_REF] and motion perceptibility in [START_REF] Sharma | Motion perceptibility and its application to active vision-based servo control[END_REF]. By selecting features and designing controllers that maximize these measures, either along specific degrees of freedom or globally, the performance of the visual servo system can be improved.

The constraints considered to design the control scheme using the optimal control approach may be contradictory in some cases, leading the system to fail due to local minima in the objective function to be minimized. For example, it may happen that the motion produced to move away from a robot joint limit is exactly the opposite of the motion produced to near the desired pose, which results in a zero global motion. To avoid this potential problem, it is possible to use the gradient projection method, which is classical in robotics. Applying this method to visual servoing has been proposed in [START_REF] Espiau | A new approach to visual servoing in robotics[END_REF] and [START_REF] Castano | Visual compliance: task directed visual servo control[END_REF]. The approach consists in projecting the secondary constraints e s on the null space of the vision-based task e so that they have no effect on the regulation of e to 0 e g = L + e e + P e e s , where e g is the new global task considered and P e = (I 6 -L + e L e ) is such that L e P e e s = 0, ∀e s . Avoiding the robot joint limits using this approach has been presented in [START_REF] Marchand | Using the task function approach to avoid robot joint limits and kinematic singularities in visual servoing[END_REF]. However, when the vision-based task constrains all the camera degrees of freedom, the secondary constraints cannot be considered since, when L e is of full rank 6, we have P e e s = 0, ∀e s . In that case, it is necessary to inject the constraints in a global objective function, such as navigation functions which are free of local minima [START_REF] Marchand | Dynamic sensor planning in visual servoing[END_REF], [START_REF] Cowan | Visual servoing via navigation functions[END_REF].

Switching Schemes

The partitioned methods described previously attempt to optimize performance by assigning individual controllers to specific degrees-of-freedom. Another way to use multiple controllers to optimize performance is to design switching schemes that select at each moment in time which controller to use based on criteria to be optimized.

A simple switching controller can be designed using an IBVS and a PBVS controller as follows [START_REF] Gans | An asymptotically stable switched system visual controller for eye in hand robots[END_REF]. Let the system begin by using the IBVS controller. Consider the Lyapunov function for the PBVS controller given by L = 1 2 e(t) 2 , with e(t) = ( c t o -c * t o , θu). If at any time the value of this Lyapunov function exceeds a threshold γ P , the system switches to the PBVS controller. While using the PBVS controller, if at any time the value of the Lyapunov function for the IBVS controller exceeds a threshold, L = 1 2 e(t) 2 > γ I , the system switches to the IBVS controller. With this scheme, when the Lyapunov function for a particular controller exceeds a threshold, that controller is invoked, which in turn reduces the value of the corresponding Lyapunov function. If the switching thresholds are selected appropriately, the system is able to exploit the relative advantages of IBVS and PBVS, while avoiding their shortcomings.

An example for this system is shown in Figure 4, for the case of a rotation by 160 • about the optical axis. Note that the system begins in IBVS mode and the features initially move on straight lines toward their goal positions in the image. However, as the camera retreats, the system switches to PBVS, which allows the camera to reach its desired position by combining a rotational motion around its optic axis and a forward translational motion, producing the circular trajectories observed in the image. Other examples of temporal switching schemes can be found, such as for instance the one developed in [START_REF] Chesi | Keeping features in the field of view in eye-in-hand visual servoing: A switching approach[END_REF] to ensure the visibility of the target observed.

Feature Trajectory Planning

It is also possible to treat the optimization problem offline, during a planning stage. In that case, several constraints can be simultaneously taken into account, such as obstacle avoidance [START_REF] Hosoda | Trajectory generation for obstacle avoidance of uncalibrated stereo visual servoing without 3D reconstruction[END_REF], joint limit and occlusions avoidance, and ensuring the visibility of the target [START_REF] Mezouar | Path planning for robust image-based control[END_REF]. The feature trajectories s * (t) that allow the camera to reach its desired pose while ensuring the constraints are satisfied are determined using path planning techniques, such as the well known potential field approach.

Coupling path planning with trajectory following also allows to improve significantly the robustness of the visual servo with respect to modeling errors. Indeed, modeling errors may have large effects when the error ss * is large, but have few effects when ss * is small. Once desired features trajectories s * (t) such that s * (0) = s(0) have been designed during the planning stage, it is easy to adapt the control scheme to take into account the fact that s * is varying, and to make the error ss * remain small. More precisely, we now have The new second term of this control law anticipates the variation of s * , removing the tracking error it would produce. We will see in the next section that the form of the control law is similar when tracking a moving target is considered.

Target Tracking

We now consider the case of a moving target and a constant desired value s * for the features, the generalization to varying desired features s * (t) being immediate. The time variation of the error is now given by

ė = ṡ = L e v c + ∂e ∂ t , ( 10
)
where the term ∂e ∂ t expresses the time variation of e due to the generally unknown target motion. If the control law is still designed to try to ensure an exponential decoupled decrease of e (that is, once again ė = -λe), we now obtain using [START_REF] Jägersand | Experimental evaluation of uncalibrated visual servoing for precision manipulation[END_REF]:

v c = -λ L + e e -L + e ∂e ∂ t , ( 11)
where ∂e ∂ t is an estimation or an approximation of ∂e ∂ t . This term must be introduced in the control law to compensate for the target motion.

Closing the loop, that is injecting [START_REF] Piepmeier | Uncalibrated dynamic visual servoing[END_REF] in [START_REF] Jägersand | Experimental evaluation of uncalibrated visual servoing for precision manipulation[END_REF] Otherwise, tracking errors will be observed. Indeed, by just solving the scalar differential equation ė = -λe + b, which is a simplification of ( 12), we obtain e(t) = e(0) exp(-λt) + b/λ, which converges towards b/λ. On one hand, setting a high gain λ will reduce the tracking error, but on the other hand, setting the gain too high can make the system unstable. It is thus necessary to make b as small as possible.

Of course, if the system is known to be such that ∂e ∂ t = 0 (that is the camera observes a motionless object), no tracking error will appear with the most simple estimation given by ∂e ∂ t = 0. Otherwise, a classical method in automatic control to cancel tracking errors consists in compensating the target motion through an integral term in the control law. In that case, we have

∂e ∂ t = µ j e( j),
where µ is the integral gain, which must be tuned. This scheme allows to cancel the tracking errors only if the target has a constant velocity. Other methods, based on feedforward control, estimate directly the term ∂e ∂ t through the image measurements and the camera velocity, when it is available. Indeed, from [START_REF] Jägersand | Experimental evaluation of uncalibrated visual servoing for precision manipulation[END_REF], we obtain

∂e ∂ t = ė -L e v c ,
where ė can, for instance, be obtained as ė(t) = (e(t)e(tt))/ t, with t being the duration of the control loop. A Kalman filter [START_REF] Corke | Controller design for high performance visual servoing[END_REF] or more elaborate filtering methods [START_REF] Bensalah | Compensation of abrupt motion changes in target tracking by visual servoing[END_REF] can then be used to improve the estimated values. If some knowledge about the target velocity or the target trajectory is available, it can of course be used to smooth or predict the motion [START_REF] Allen | Automated tracking and grasping of a moving object with a robotic hand-eye system[END_REF]- [START_REF] Rizzi | An active visual estimator for dexterous manipulation[END_REF]. For instance, in [START_REF] Ginhoux | Active filtering of physiological motion in robotized surgery using predictive control[END_REF], the periodic motion of the heart and of the breath are compensated for in an application of visual servoing in medical robotics. Finally, other methods have been developed to remove as fast as possible the perturbations induced by the target motion [START_REF] Papanikolopoulos | Visual tracking of a moving target by a camera mounted on a robot: A combination of vision and control[END_REF], using for instance predictive controllers [START_REF] Gangloff | Visual servoing of a 6 dof manipulator for unknown 3-D profile following[END_REF].

A simple switching controller can be designed using an IBVS and a PBVS controller.

Eye-in-Hand and Eye-to-Hand Systems Controlled in the Joint Space

In the previous sections, we considered the six components of the camera velocity as input of the robot controller. As soon as the robot is not able to realize this motion, for instance because it has less than six degrees of freedom, the control scheme must be expressed in the joint space. In this section, we describe how this can be done, and in the process develop a formulation for eye-to-hand systems.

In the joint space, the system equations for both the eyeto-hand configuration and the eye-in-hand configuration have the same form

ṡ = J s q + ∂s ∂ t . ( 13
)
Here, J s ∈ R k×n is the feature Jacobian matrix, which can be linked to the interaction matrix, and n is the number of robot joints.

For an eye-in-hand system [see Figure 5(b)], (∂s/∂ t) is the time variation of s due to a potential object motion, and J s is given by

J s = L s c V N J(q), (14)
where ◆ c V N is the spatial motion transform matrix (as defined in Part I of the tutorial) from the vision sensor frame to the end effector frame. It is usually a constant matrix (as soon as the vision sensor is rigidly attached to the end effector). Thanks to the robustness of closed loop control schemes, a coarse approximation of this transform matrix is sufficient in visual servoing. If needed, an accurate estimation is possible through classical handeye calibration methods [START_REF] Tsai | A new technique for fully autonomous and efficient 3D robotics hand-eye calibration[END_REF]. ◆ J(q) is the robot Jacobian expressed in the end effector frame. For an eye-to-hand system [see Figure 5(b)], (∂s/∂ t) is now the time variation of s due to a potential vision sensor motion and J s can be expressed as

J s = -L s c V N N J(q) ( 15) = -L s c V 0 0 J(q). (16)
In ( 15), the classical robot Jacobian N J(q) expressed in the end effector frame is used but the spatial motion transform matrix c V N from the vision sensor frame to the end effector frame changes all along the servo, and it has to be estimated at each iteration of the control scheme, usually using pose estimation methods. In ( 16), the robot Jacobian 0 J(q) is expressed in the robot reference frame and the spatial motion transform matrix c x 0 from the vision sensor frame to that reference frame is constant as long as the camera does not move. In that case, which is convenient in practice, a coarse approximation of c V 0 is usually sufficient.

Once the modeling step is finished, it is quite easy to follow the procedure that has been used above to design a control scheme expressed in the joint space, and to determine sufficient condition to ensure the stability of the control scheme. We obtain, considering again e = ss * , and an exponential decoupled decrease of e q = -λ J + e e -J + e ∂e ∂ t . [START_REF] Chaumette | 2 1/2 D visual servoing: a possible solution to improve image-based and position-based visual servoings[END_REF] If k = n, considering the Lyapunov function L = 1 2 e(t) 2 , a sufficient condition to ensure the global asymptotic stability is given by

J e J + e > 0. ( 18)
If k > n, we obtain by following the developments of the stability analysis of basic IBVS (see Part I of the tutorial):

J + e J e > 0 [START_REF] Schramm | Extended-2D visual servoing[END_REF] to ensure the local asymptotic stability of the system. Note that the actual extrinsic camera parameters appears in J e , while the estimated ones are used in J + e . It is thus possible to analyse the robustness of the control scheme with respect to the camera extrinsic parameters. It is also possible to estimate directly the numerical value of J e or J + e using, as described previously, the Broyden update rule. In the joint space, the system equations for both the eye-to-hand configuration and the eye-in-hand configuration have the same form.

Finally, to remove tracking errors, we have to ensure that J e J + e ∂e ∂ t = ∂e ∂ t .

Finally, let us note that, even if the robot has six degrees of freedom, it is generally not equivalent to first compute v c using (2) and then deduce q using the robot inverse Jacobian, and to compute directly q using [START_REF] Chaumette | 2 1/2 D visual servoing: a possible solution to improve image-based and position-based visual servoings[END_REF]. Indeed, it may occur that the robot Jacobian J(q) is singular while the feature Jacobian J s is not (that may occur when k < n). Furthermore, the properties of the pseudo-inverse ensure that using (2), v c is minimal while using [START_REF] Chaumette | 2 1/2 D visual servoing: a possible solution to improve image-based and position-based visual servoings[END_REF], q is minimal. As soon as J + e = J + (q) N V c L + e , the control schemes will be different and will induce different robot trajectories. The choice of the state-space is thus important.

Conclusion

In this tutorial, we have only considered velocity controllers. It is convenient for most of classical robot arms. However, the dynamics of the robot must of course be taken into account for high speed tasks, or when we deal with mobile nonholonomic or underactuated robots. As for the sensor, we have only considered geometrical features coming from a classical perspective camera. Features related to the image motion or coming from other vision sensors (fish-eye camera, catadioptric camera, echographic probes, etc.) necessitate to revisit the modeling issues to select adequate visual features. Finally, fusing visual features with data coming from other sensors (force sensor, proximetry sensors, etc.) at the level of the control scheme will allow to address new research topics. Numerous ambitious applications of visual servoing can also be considered, as well as for mobile robots in indoor or outdoor environments, for aerial, space, and submarine robots, and in medical robotics. The end of fruitful research in the field of visual servo is thus nowhere yet in sight.

Numerous ambitious applications of visual servoing

can be considered.

Figure 1 .

 1 Figure 1. System behavior using s = (x g , log (Z g ), θu).

  in which L xy includes the first, second, fourth and fifth columns of L s , and L z includes the third and sixth columns of L s . Similarly, v xy = (v x , v y , ω x , ω y ) and v z = (v z , ω z ) . Here, ṡz = L z v z gives the component of ṡ due to the camera motion along and rotation about the optic axis, while ṡxy = L xy v xy gives the component of ṡ due to velocity along and rotation about the camera x and y axes. Proceeding as before, by setting ė = -λe we obtain -λe = ė = ṡ = L xy v xy + L z v z , which leads to

Figure 2 .

 2 Figure 2. System behavior using s = ( c * t c , x g , θu z ).

Figure 3 .

 3 Figure 3. System behavior using s = (ρ 1 , θ 1 , . . . , ρ 4 , θ 4 ) and L + e = L + e * .

Figure 4 .

 4 Figure 4. Image feature trajectories for a rotation of 160 • about the optical axis using a switched control scheme (initial points position in blue and desired points position in red).

  ė = ṡ -ṡ * = L e v c -ṡ * , from which we deduce, by selecting as usual ė = -λe as desired behavior v c = -λ L + e e + L + e ṡ * .

Figure 5 .

 5 Figure 5. Top: (a) Eye-in-hand system. (b) Eye-to-hand system. Bottom: Opposite image motion produced by the same robot motion.


Nicolas Raimbault
email: nicolas.raimbault@ifsttar.fr

Wouter Jacobs
email: wouter.jacobs@ua.ac.be

Frank Van Dongen
email: frank.vandongen@pbl.nl.

Port regionalisation from a relational perspective. The rise of Venlo as Dutch international logistics hub

Keywords: Port Regionalisation, Logistics, Netherlands, Relational Approach, Greenport Venlo

. While this process largely results from the decisions of shippers and logistics providers, the scope of public policy can also shape it. This includes the strategic capacity of stakeholders to couple not only locally available assets with the needs of global flows, but also to provide meaning through the constitution of symbols, frames and discourses. We propose the application of a relational perspective to port regionalisation, which allows us to analyse how various actors engage strategically in actor-networks and coalitions across scales to stimulate growth based on logistics. This is accomplished by presenting the rise of Venlo in the Netherlands as an inland logistics hub within the corridor of the port of Rotterdam.

Introduction

The rise of global supply chain systems and geographical dispersion of related inland logistics centres has led to a new phase in the evolution of port systems and port-city interface. [START_REF] Notteboom | Port regionalization: towards a new phase in port development[END_REF] have referred to this phase as port regionalisation, which is characterised by seaports becoming integral parts of extensive intermodal hinterland networks, corridors and inland intermodal terminals. According to the seminal paper of Notteboom and Rodrigue, the process of port regionalisation is largely the result of the location and routing decisions of shippers and logistics service providers; however, the scope of public policy can also shape the spatial contours of the process, although it remains case-specific and dependent on various types of local and national contingencies and institutional contexts (cf. [START_REF] Wilmsmeier | The directional development of intermodal freight corridors in relation to inland terminals[END_REF][START_REF] Monios | Giving a direction to port regionalisation[END_REF].

The spatial and functional-economic outcomes of the port regionalisation process have indeed become a reality in many countries [START_REF] Wilmsmeier | The directional development of intermodal freight corridors in relation to inland terminals[END_REF] and under different institutional contexts. Many inland locations have been identified by transport geographers as hubs (e.g., Liège, Tilburg, Venlo, Duisburg in the Rhine-Scheldt Delta) in multiport gateway-hinterland transport networks [START_REF] Notteboom | Complementarity and substitutability among adjacent gateway ports[END_REF]. Nonetheless, according to [START_REF] Monios | Giving a direction to port regionalisation[END_REF] 4 , the main theoretical issue raised by the port regionalisation concept is the direction of its development and identification of the main drivers. They compared two directions of port regionalisation: landside-driven (referred to as inside-out) or seaside-driven (outside-in). These two directions correspond to the interests of different types of actors driving the regionalisation process: public port authorities and private terminal operators on the one hand and rail operators and public organisations on the other hand.

However, such a dichotomy of development trajectories and outcomes is problematic because it precludes the possibility that both directions can be at play simultaneously. Certain actors, such as firms (e.g., private terminal operator) or higher levels of government beyond the local scale, can have stakes at multiple locations that include the seaside and landside of the logistics chain. Many of the problems in the current theories, as we will argue throughout the paper, have to do with how agency is considered in relation to institutional structure (cf. [START_REF] Hesse | Cities and flows: re-asserting a relationship as fundamental as it is delicate[END_REF] for similar approach). Therefore, port regionalisation as it is currently studied applies actor-network thinking, but is logistics-centric and follows a reductionist ontology or instrumental logic with regards to regional development. Networks are primarily perceived as transport flows and logistics chains, but they do not consider, for instance, how agency can lobby governments and align with institutional actors to secure interests or pursue development agendas through networking. The issue of governance mostly refers to coordination problems within the logistics chain (e.g., [START_REF] Horst | Coordination in hinterland transport chains: a major challenge for the seaport community[END_REF] and largely ignores how governance takes place in terms of regional-economic and spatial (strategic or land use) planning. As such, contemporary studies neglect the roles that other actors beyond the logistics scenery play in facilitating or constraining the port regionalisation process. These actors must not be in favour of logistics-based development at all, and developing a location into an inland logistics hub is just one among many alternative routes for regional development to proceed. Indeed, it is striking that the economic impacts of port regionalisation on inland locations have hardly been studied until now (see: [START_REF] Heuvel | Spatial concentration and location dynamics in logistics: the case of a Dutch province[END_REF].

However, the various degrees of power that actors might hold and the ways that such power is exercised in the port regionalisation process is an issue that is mostly overlooked in the literature (see: [START_REF] Jacobs | An evolutionary perspective on regional port systems: the role of windows of opportunity in shaping seaport competition[END_REF]. Not every actor holds the same degree of power or can mobilise the same type of (institutional) resources as support. In this case, much depends on the spatial scale at which actors operate and how they gain leverage across scales (from the global to the local) and within relational networks (cf. [START_REF] Cox | Spaces of Dependence, Spaces of Engagement and the Politics of Scale[END_REF][START_REF] Jacobs | Strategic Coupling as Capacity. How seaports connect to globalized flows of containerized traffic[END_REF]. Finally, spatio-temporality is also a neglected issue in the literature on port regionalisation. While port regionalisation suggests a process, one that has been ongoing for at least 20 years, contemporary case study analyses primarily focus on the outcomes. These case studies neglect to a large extent historical or evolutionary accounts of how inland logistic hubs developed and became institutionally endorsed.

To overcome these problems, we propose the application of a relational perspective to port regionalisation (see also [START_REF] Jacobs | An evolutionary perspective on regional port systems: the role of windows of opportunity in shaping seaport competition[END_REF][START_REF] Jacobs | Strategic Coupling as Capacity. How seaports connect to globalized flows of containerized traffic[END_REF]. This allows us to focus on how regional development results from relational constructs and social formations that are constituted through ongoing actorspecific practices and processes across territorial scales within institutionalised structures. As such, we will be able to overcome the problem of the institutional context perceived as a constraining factor in the understanding of nationally different outcomes in the port regionalisation process. Rather, a relational perspective understands institutions as one of many assets to be mobilised by agency in the pursuit of their goals (cf. [START_REF] Jacobs | Political economy of port competition. Institutional analysis from Rotterdam, Southern California and Dubai[END_REF]. Central to our approach is the concept of 'strategic coupling' (cf. [START_REF] Coe | Globalizing regional development: a global networks perspective[END_REF]) and how we can apply it to analyse the role of agency in aligning various forms of locally available assets (inside-out) with 'global' network demands (outside-in) in a dynamic context. This is accomplished by presenting the rise of Venlo in the Netherlands as an inland logistics hub within the corridors of the ports of Rotterdam and Antwerp. The case of Venlo is compelling because it has been labelled in previous transport geographical studies as a "satellite terminal for Rotterdam" (Rodrigue et al. 2010: 525) and an "extended gate" to the ECT Delta Terminal located in the port of Rotterdam (Rodrigue and Notteboom 2009: 177). These very real observations led [START_REF] Monios | Giving a direction to port regionalisation[END_REF] to conclude that the development of Venlo has followed an outsidein logic-driven process led by a private port terminal operator, which is in contrast to their more general conclusion that port regionalisation in Europe and the US has followed an inside-out pattern. Therefore, the case of Venlo stands out; however, in light of the problematic issues addressed above, it also deserves closer empirical inquiry. If we accept the proposition that port regionalisation is both an outcome of inside-out and outside-in drivers and driving agents, how can we understand its rise through relational processes across scales and within institutional contexts? Therefore, the aim of this research is to add to the debate on port regionalisation, both theoretically and empirically. Theoretically, we add a relational perspective that allows port regionalisation to be viewed as a mutual constitutive process among actors, networks and structures. Empirically, we revisit Venlo as an internationally outstanding case that has barely been empirically investigated until now beyond the logic of the ECT business model. Through the case study of Venlo, we would like to induce further theoretical thoughts on port regionalisation; in particular, we would like to discuss how to move beyond its functionalist account of regional development and overcome the problem of institutional contexts. Therefore, we also hope to direct the discussion beyond that of 'hard-core' transport geographers and induce insights from other scholars interested in the classical port-city interface, such as planners, urban geographers and urban historians.

The outline of this paper is as follows. In the first section, we discuss the process of port regionalisation as an extension of James Bird's classical Anyport model (1963), which was identified by [START_REF] Notteboom | Port regionalization: towards a new phase in port development[END_REF]. In the second section, we then make our case for a relational approach to port regionalisation and put forward the concept of strategic coupling as a method of understanding how structure and agency interact in regional development processes. In the third section, we revisit the case of Venlo and demonstrate the status of Venlo as a Dutch inland logistics hub within the Rhine-Scheldt Delta (outcome). The fourth section explains the rise of Venlo as a logistics hub through the lens of strategic coupling (process). We emphasise that the development of Venlo is best understood as an interplay between inside-out and outside-in and global and local forces. The fifth section presents the conclusions.

II) Port Regionalisation from a Relational Perspective

From Anyport to Port Regionalisation-The spatial and functional evolution of port systems, in particular the dynamic and fraught relationship between ports and cities, are well-conceptualised phenomena among geographers and planners [START_REF] Bird | The major seaports of the United Kingdom[END_REF][START_REF] Bird | Of central places, cities and seaports[END_REF][START_REF] Hayuth | The port-urban interface: an area in transition[END_REF][START_REF] Hoyle | The port-city interface: trends, problems and examples[END_REF]Norcliff et al. 1996). The most influential work regarding this phenomena is that of James [START_REF] Bird | The major seaports of the United Kingdom[END_REF] and his concept of the Anyport, wherein three phases (settlement, expansion and specialisation) are distinguished in the evolution of port cities. Because of the rise of spatially extensive supply chain systems and development of inland container hubs along transport corridors, [START_REF] Notteboom | Port regionalization: towards a new phase in port development[END_REF] added a new phase to Bird's Anyport model: port regionalisation.

The essence of this phase is that warehouse, distribution and logistics activity moves further inland and away from the initial port city. The move is driven by various structural pull and push factors. The most important push factor is the lack of affordable land close to the port in combination with congestion on the main highways and container terminals. Most of the commodities shipped by container are consumer goods or production components in demand in the port's hinterland and to a far lesser degree in the direct urban economy. In other words, once arriving at the port, there is no need for the container to stay much longer in the port's vicinity. Therefore, the most important pull factor to move logistics activity inland is the proximity to the consumer market and to benefit from a strategic location along transport corridors where land (and labour) is abundant and accessibility is superior. The most strategic location is where several transport modes converge so that the location can be served by several seaports in the wider region (cf. [START_REF] Heuvel | Spatial concentration and location dynamics in logistics: the case of a Dutch province[END_REF], also referred to as a multiport gateway region [START_REF] Notteboom | Complementarity and substitutability among adjacent gateway ports[END_REF].

Therefore, Notteboom and Rodrigue added a much needed phase in Bird's outdated model that focuses on the continuation of port and related logistics activity and is contrary to others who have primarily focused on the struggles of the redevelopment processes at the initial waterfront in the city (Norcliff et al. 1996;[START_REF] Wiegmans | Changing port city relationships at Amsterdam: a new phase in the interface[END_REF][START_REF] Hein | Port Cities. Dynamic Landscapes and Global Networks[END_REF]. Not only did port regionalisation extend the Anyport model into the container age, it also addressed the issues of scale and agency. The port-city interface was regionalised with externalities and values operating beyond the local scale and classical 20 th century urban perimeter (cf. [START_REF] Hall | Cities, Regions and Flows[END_REF][START_REF] Hesse | Cities and flows: re-asserting a relationship as fundamental as it is delicate[END_REF]. Moreover, port regionalisation involves the simultaneous functional-economic and spatial integration of ports, inland logistics zones, suburban and urban economies and hinterlands. It views ports and inland hubs as nodes in international freight flows, transportation networks and logistics chains. [START_REF] Monios | Giving a direction to port regionalisation[END_REF] raised the issue of the direction and drivers of port regionalisation. The original paper of [START_REF] Notteboom | Port regionalization: towards a new phase in port development[END_REF] insisted on a market-driven nature of port regionalisation that developed "from logistics decisions and subsequent actions of shippers and third-party logistics providers" (2005: 306). Furthermore, in the context of the "terminalisation of supply chains," private port based terminal operators were becoming active in inland supply chain management and deeply involved in port regionalisation strategies [START_REF] Rodrigue | The terminalization of supply chains: reassessing the role of terminals in port/hinterland logistical relationships[END_REF]. Likewise, local governments in the hinterland were involved because they might facilitate or prevent such logistics developments in their jurisdiction through all types of politically mediated land use plans. For example, Valburg near Nijmegen in the Netherlands was initially planned to be the inland logistics hub because of its directplanned connection with the to-be-constructed Betuweline freight rail line and strong support by the Dutch logistics industry for its development, most notably the support of the Port of Rotterdam Authority and Rotterdam-based private terminal operator ECT. Nonetheless, local politicians in Nijmegen ultimately blocked its development because they doubted the forecasted benefits for the local economy.

The latter example raises an important point: port regionalisation can be successfully opposed. Developing a location into an inland logistics hub or 'extended gateway' is only one among many economic alternatives. Different actors have different interests and hold different degrees of 'power,' both within actor-networks (e.g., a value chain) and institutionally (e.g., regulations). Power should be viewed here not as 'power over,' such as in the command of resources, but as 'power to,' which is to employ such resources strategically in multi-actor games. Institutions are in this context not only as a set of constraining rules but also as enablers and 'territorial assets' when they are actively employed by the appropriate agencies. Therefore, when analysing port regionalisation as an outcome, not only must the direction (outside-in or inside-out) be determined and drivers (private or public actors) be identified, but the methods by which these factors are strategically aligned through the process of agency must also be determined. For that, we want to address a relational approach.

Strategic coupling as a relational approach to port regionalisation-

The relational approach gained scholarly ground within economic geography and planning within the previous decade [START_REF] Storper | The Regional World. Territorial Development in a Global Economy[END_REF][START_REF] Dicken | Chains and networks, territories and scales: towards a relational framework for analysing the global economy[END_REF]Bathelt and Glückler, 2004;[START_REF] Yeung | Rethinking relational economic geography[END_REF][START_REF] Sunley | Relational Economic Geography: a partial understanding or a new paradigm?[END_REF]. The essence of the relational approach is that we cannot understand spatial processes without considering specific relationships that exist between places, between different actors in places and between actors and their institutional contexts. Spatial dynamics are therefore relationally constituted through interactions and place-specific (traded and non-traded) interdependencies among actors [START_REF] Storper | The Regional World. Territorial Development in a Global Economy[END_REF].

The relational approach "allows us to avoid the two polarised frameworks in contemporary economic geography -actor networks and institutional structures" (Yeung, 2005: 38), and thus to "identify the complex relational geometry comprising local and non-local actors, tangible and intangible assets, formal and informal institutional structures, and their interactive power relations." The relational approach in economic geography is particularly profound in work on global production networks (GPN) (cf. [START_REF] Dicken | Chains and networks, territories and scales: towards a relational framework for analysing the global economy[END_REF][START_REF] Coe | Globalizing regional development: a global networks perspective[END_REF][START_REF] Coe | Global production networks: realizing the potential[END_REF][START_REF] Yeung | Regional development and the competitive dynamics of global production networks: An East Asian perspective[END_REF] that focus on 'globalising regions.' In particular, the GPN approach is concerned with how regions become inserted in various global flows (information, capital and goods) and align with various functions of transnational corporations. The insertion and alignment is not only a process imposed by global forces on 'the region' because a scope remains for action by locally dependent interests to strategically engage with other centres and networks of 'social power' to gain leverage, mobilise agents and resources, or build strategic coalitions (cf. [START_REF] Cox | Spaces of Dependence, Spaces of Engagement and the Politics of Scale[END_REF][START_REF] Jacobs | Strategic Coupling as Capacity. How seaports connect to globalized flows of containerized traffic[END_REF]. A key concept within the GPN approach on regional development is strategic coupling.

In its original meaning, strategic coupling involves the deliberate employment of regional assets to accommodate the demands and needs of 'global' players, plugging the region into global networks of exchange and flows of goods (cf. [START_REF] Coe | Globalizing regional development: a global networks perspective[END_REF]). Yeung (2009, p. 332) defines strategic coupling "as a mutually dependent and constitutive process involving shared interests and cooperation between two or more groups of actors who otherwise might not act in tandem for a common strategic objective." This definition echoes earlier US-based work on the politics of local economic development, such as the growth machine [START_REF] Logan | Urban Fortunes. The Political Economy of Place[END_REF] and urban regimes [START_REF] Stone | Regime Politics: Governing Atlanta, 1946-1988[END_REF]. However, such a 'localist' or 'regionalist' view on economic development should be avoided. Rather, strategic coupling should be viewed as a relational process across various scales in which actors assign a particular meaning and value to certain locally available assets (cf. [START_REF] Yeung | Regional development and the competitive dynamics of global production networks: An East Asian perspective[END_REF].

Strategic coupling is a relational capacity that accumulates from continuous interactions among agents and institutions and materialises in various networks, governance arrangements, discourses and the actual employment of resources and production factors [START_REF] Jacobs | Strategic Coupling as Capacity. How seaports connect to globalized flows of containerized traffic[END_REF]:

"One should therefore understand strategic coupling as networked power relations in the mobilization of resources (including the constitution of symbols of 'centrality,' 'competitiveness' or 'sustainability') that support and improve a territory's position in global flows." (Jacobs and Lagendijk, 2014, p. 59).

The mobilisation of resources (material and institutional) and employment of certain local or regional assets may therefore involve certain relationally constituted symbols, or what are also known in planning and public policy debates as frames and discourses. These frames and discourses can help to align actors around common objectives and opportunities or to consider collective action problems [START_REF] Hajer | The politics of environmental discourse : ecological modernization and the policy process[END_REF][START_REF] Brink | Rijkswaterstaat on the horns of a dilemma[END_REF]. According to Rein and Schön (1986, p. 4), framing stands for "a way of selecting, organizing, interpreting and making sense of a complex reality so as to provide guideposts for knowing, analyzing, persuading and acting." According to the planning theorist [START_REF] Faludi | Framing with Images, Environment and Planning B: Planning and Design[END_REF], important to the formulation of frames is their naming and institutional endorsement or sponsorship in various governance arenas and policy circles. Naming allows certain elements or issues to be focused on or demarcated while neglecting others. It allows for the structuration of cognition and common understanding across actors on what is at stake so that a shared and meaningful perspective can facilitate appropriate collective action. Spatially visualised images, conceptual metaphors and narratives all form powerful communicative tools in the framing process.

Therefore, a relational approach to port regionalisation is focused on how actors engage strategically in actor-networks across scales and how they employ various available assets (material, institutional and discursive) to stimulate growth based on logistics at certain inland locations. We will apply these thoughts to the case study of Venlo, the Netherlands, which is an inland logistics hub strategically located between the major seaports of Rotterdam and Antwerp and the Rhine-Ruhr area in Germany. We will reconstruct how Venlo-based stakeholders manage to secure their interests through three phases of "strategic coupling": first by the formation of a locally based coalition, second by strategic engagement with the national spatial planning-framework through discursive practices and third by the implementation of new governing tools. The empirical research is based on desktop research of policy documentation5 , data analysis of regional economic development6 and 10 interviews with key-representatives in Venlo and Rotterdam conducted by the lead author in 2012 and 2013.

III) Venlo as inland logistics centre

Venlo is strategically located in the east of the Netherlands along the border with Because of its strategic geographical location, Venlo has benefitted from the local demand for logistics services. First, the region has historically been an important agrofood production centre that was mainly dedicated to exports. Second, the presence of a small but innovative business electronics cluster surrounding home-grown Océ (now part of Canon) led to a local market in need of forwarding and logistics solutions. Venlo is the birthplace of a number of transport firms, such as Frans Maas (now part of DSV), Janssen Distribution, Gaston Schul, Emons Group and Seacon Logistics. These transport firms took full advantage of the location of Venlo by specialising in bonded warehouses and customs clearance services of goods coming from the ports of Rotterdam and Antwerp and destined for Germany. Especially after the Schengen Agreement of 1985 in the advent of the Common Market (1992), certain large shippers using the port of Rotterdam selected Venlo as the location for their European Distribution Centres. At that time, Rotterdam-based terminal operating company ECT selected Venlo to develop inland rail and barge terminals, allowing ECT to offer extended gateway services to its marine terminals located in Rotterdam. In its wake, major international logistics players, such as DHL, UPS, DB Schenker, Géodis, Ziegler and DSV, began to set up operations in Venlo as well.

Since 2005, Venlo has been elected six times as the logistics hotspot of the Netherlands by the professional magazine "Logistiek." It confirms both the economic specialisation of Venlo in logistics activities (tab.1) and the importance of Venlo in the national logistics structure (tab.3). Our analysis of employment 7 over time (1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011) through a location quotient index shows the increased specialisation of Venlo in logistics activities 8 . Taking into account only transport firms, the Venlo region increased from number 4 in 1996 to number 1 in 2011 (tab. 2). In terms of wholesaling activities, it increased from number 25 to number 15. According to our definition of logistics activities, Venlo is ranked number 3, whereas it was only the 13 th region in 1996 (tab. 1). Thus, logistics activities now represent 30% of the GDP of the Venlo region (cf. Viaport Venlo) compared with the national average of 7.5% GDP. With a stock of 1.3 million m², the Venlo region is one of the most important concentrations of warehousing space in the Netherlands after the regions of Rotterdam, Amsterdam and West-Noord-Brabant (tab. 3).

Urban Region Warehouses stock (m²) Rank

West-Noord-Brabant 2,625,000 1

Groot-Amsterdam 1,950,000 2

Groot-Rijnmond (Rotterdam region) 1,573,000 3

Noord-Limburg (Venlo region) 1,385,000 4

Midden-Noord-Brabant 1,275,00 5

Noordoost-Noord-Brabant 965,000 6

Zuidoost-Noord-Brabant 860,000 7

Oost-Zuid-Holland 855,000 8

Utrecht region 595,000 9

Arnhem/Nijmegen region 516,000 10

The rise of Venlo as an inland logistics hub is not only explained by geographical factors or pure market forces alone but also by different local public and private actors in support of logistics-based regional economic development. Thus, our aim is to study the interplay between these different drivers. As such, we use the concept of strategic coupling as introduced above.

IV)

The Greenport Venlo: strategic coupling at work

Strategic coupling is the way in which actors align themselves relationally to insert Venlo into global (logistics) networks and can be analysed through three phases. The first phase started in the 1980s with a locally based coalition of private and public actors working in tandem to promote Venlo as a logistics centre. These local actions were primarily aimed at securing land for logistics development, setting up appropriate governance mechanisms and forging ties with stakeholders related to the Mainport Rotterdam. The second phase started in the late 1990s and is characterised by discursive practices aimed at securing national government recognition through the Greenport-policy frame. In the third phase from the 2000s onwards, we see a further 'territorialisation' of the Greenport policy and continuation of the logistics-based growth. Only recently have truly global logistics players, especially real estate developers, become an essential developmental force.

Strategic Coupling I: local coalition formation, land-based development and capacity building-

Venlo was far from a 'globalising region' in the 1980s in terms of the GPN-approach [START_REF] Coe | Globalizing regional development: a global networks perspective[END_REF]; however, logistics-based development began to dominate the local agenda after the advent of the European Common Market. Coalitions between the local business sector and municipality were forged at that time and focused on accommodating logistics interests through three main policies: land-based development, connection to the Port of Rotterdam and local capacity building:

"How can we facilitate this [logistics development]? By having enough space with terminals and through a dedicated team led by a program manager."

(Interview: Municipality of Venlo)

"Venlo clearly said we want logistics. And that makes business easier."

(Interview: Prologis)

The main asset of Venlo at that time was the availability of municipal land. Logistics development requires huge plots of land, and the municipality of Venlo supported logistics-based growth by assigning land use and formal planning mechanisms. In the Netherlands, local governments traditionally have strong positions on the land market, and municipalities are involved in land assembly and development before such land is sold to the private sector (cf. [START_REF] Needham | Land policy in the Netherlands[END_REF][START_REF] Buitelaar | A theory of institutional change: illustrated by Dutch city-provinces and Dutch land policy[END_REF]). Thus, facilitating logistics growth by means of land policy is an opportunity for the municipality to earn revenue to finance other municipal policies. This can be understood as the physical or material dimension of the strategic coupling process. The business zones dedicated to logistics are the Venlo Trade Port East, West and North and total 1,400 ha (fig. 3) developed by the municipality on former farm land along the main infrastructure corridors northwest of the historic city of Venlo.

The second aspect of this first phase of strategic coupling was the connection with the port of Rotterdam. Since the mid-1980s, the port of Rotterdam had regained its national momentum for growth and successfully launched its Mainport policy in conjunction with a more fundamental neo-liberal driven paradigm shift in the Dutch political economy [START_REF] Jacobs | Political economy of port competition. Institutional analysis from Rotterdam, Southern California and Dubai[END_REF]. Links with the port of Rotterdam date back to that time because the Rotterdam-based ECT9 was granted the management contract of the rail-terminal in 1982 (and of the barge terminal in 2010) in the Venlo inland port. The municipality of Venlo took a pro-active role in forging these connections:

"It is because we were invited by the municipality. The municipality was the owner at that time, and the mayor was very interested in attracting the development of Rotterdam and its containers and being connected."

(Interview: ECT)

The relationship with the port of Rotterdam is symbolic. Until now, they remain of utmost importance for Venlo-based stakeholders. Coordination between the Port of Rotterdam Authority and Venlo still happens on a regular basis.

"We do have a lot of contacts with people in Venlo of course. Venlo is very important for us. (…)We really help parties (…) to develop logistics: participation in projects; all kinds of institutional groups we participate in, speaking at conferences. There you present your hinterland strategy and mention the importance of this hinterland."

(Interview: Port of Rotterdam Authority) This is, however, a two-way relationship. Venlo provides the port of Rotterdam with space and 'extended gates' in the hinterland (i.e., port regionalisation), whereas Rotterdam secures Venlo international leverage because it allows Venlo to strategically connect with global players and the flows they control:

"The Port of Rotterdam can sell Venlo to global investors; they have more contacts internationally than we have. Sometimes we say: we are 'Rotterdam East!'" (Interview: Municipality of Venlo) Furthermore, the local logistics-based coalition was also built on local governance arrangements. The local logistics firms are highly organised to voice their concerns visà-vis the municipality. 'Venlo Freight Village Association,' 'Ondernemend Venlo Tradeport' and 'Ondernemend Limburg' are the more important firms. To lobby the local government, they mainly use the local arena formed by the local promotion and innovation program for logistics called "Viaport Venlo." The firms define the agenda of this program, but it is financed by the municipality. This way, they are associated in every public project concerning freight and logistics. Therefore, Viaport Venlo strengthens the organising capacity of the logistics interests and to a certain degree institutionalises the private participation in local economic governance: Consequently, the municipality of Venlo is lobbying itself to the national government and province of Limburg for its logistics development:

"Logistics is one of their [Venlo's] target sectors, so they do a lot of lobbying at The Hague [the national government] and the province of Limburg. It is good. They know logistics is very important so they really make an effort to improve it."

(Interview: Venlo Freight Village Association) Furthermore, logistics became a formalised concern within the municipal administrative apparatus that was carefully linked with the private sector through personal networks. Some civil servants of the economic development department in Venlo are dedicated solely to logistics, and key politicians and civil servants work or have worked in the logistics sector. Thus, the local logistics-based coalition materialised as a network of key persons -entrepreneurs, civil servants and politicians -sharing common paradigms on regional development. For instance, the current Alderman for economic affairs previously worked for logistics firms and was the head of a powerful national logistics lobby:

"Our Alderman was the director of the national association "Holland International Distribution Council." He knows what to do and who to talk when we are in the United States and in Asia to attract new logistics business to Venlo."

(Interview: Municipality of Venlo) At the same time, Venlo has slowly constituted itself as a port authority. It collects port dues and now prefers to lease land in the Venlo Trade Port rather than sell it (as it did with the barge container terminal). In this way, the Venlo Municipality is more and more financially dependent on logistics growth and not just land development.

Eventually, the main output of the local logistics-based coalition will perhaps be symbolic. Venlo appears to investors as the natural place for logistics:

"For Venlo, logistics is their foundation, their existence because they are at the crossroads of river and roads. It is absolutely a history of organic things. You cannot create it. (…) It is in Venlo's genes." (Interview: ECT) In substance, this first strategic coupling corresponds to a local public private coalition whose aim is to strengthen the competitiveness of the local firms to take advantage of the port regionalisation of Rotterdam. Thus, the inland global -regional market mechanisms and local policies could be joint drivers of an "inside-out" port regionalisation process. Moreover, the presence of ECT in the coalition shows that "inside-out" and "outside-in" strategies are not necessarily totally disconnected processes.

Strategic Coupling II: Engagement with national policy discourses-

The policy frame of 'Greenport' has its origins in the Dutch horticultural sector of the early 2000s. The frame was launched by key stakeholders in preparation of a newly commissioned national spatial planning vision, the Nota Ruimte ( 2004). Of particular significance in the policy frame is the use of '-port'; in contrast to 'green,' it is not something one immediately associates with horticulture. The use of '-port' was deliberately used to invoke a particular meaning and to assign a certain level of importance: framing is naming [START_REF] Faludi | Framing with Images, Environment and Planning B: Planning and Design[END_REF]. By framing the interests of the Dutch horticultural sector in terms of a 'port,' specific links were made with the existing policy frame of 'Mainport' used since the mid-1980s in official policy circuits and documentation to promote the growth and competiveness of the port of Rotterdam and Schiphol Airport as the main carriers of the Dutch economy. The use of 'port' in the frame also allowed for the explicit link with the horticultural sector's orientation on export and consequential importance of supply chains, logistics and physical accessibility of the Dutch horticultural clusters.

Next to naming, the policy frame required institutional endorsement or sponsorship. The strategic and economic importance of the Greenport(s) became formally acknowledged by the national government in their 'Nota Ruimte' of 2004: "Netherlands is the market leader in agribusiness sectors. They form the basis of a knowledge-intensive agribusiness complex that is concentrated in a few locations of national importance: the 'Greenports.' The future development of the Dutch Greenports is closely related to the development of the Mainports [Port of Rotterdam and Schiphol Airport] in terms of innovation, transport, accessibility and spatial accommodation within the urbanised areas of the country. To strengthen the international competitiveness of the Netherlands, the Dutch government supports the development of Greenports." (original in Dutch, italics added by authors)

The Dutch government granted six areas the status of 'Greenport': Venlo, Westland, Boskoop, Duin and Bollenstreek, Aalsmeer (in 2005) and Noord-Holland Noord (in 2011). Representatives from both the public and private sector from these Greenports first convened officially in 2005 and resulted in an official implementation agenda 'Greenport(s) Nederland. Manifest voor Uitvoering' in 2006. Because it was named a Greenport, the economic importance of Venlo was recognised for the first time in national policy circles and development strategies.

"The meaning of Greenport is excellence. Venlo is indeed good in these sectors, but the problem was that nobody knew about it. (…) Then, we said 'wait a minute, we are a Greenport!' That was the first time we said 'we host excellence'. And we obtained the Floriade. It was the first time the national government recognised our regional excellence. (…) It worked!" (Interview: Municipality of Venlo)

The political momentum and institutional endorsement at a national scale offered by the Greenport policy enabled local logistics stakeholders in Venlo to strategically couple their concerns with national development programs. In other words, the new context brought by the Greenport frame represented a window of opportunity for Venlo to engage more efficiently in logistical 'actor-networks' across scales to stimulate growth. The Venlo coalition succeeded in adapting the Greenport frame to its logistics project, i.e., they "territorialised" [START_REF] Faure | Territoires/Territorialisation[END_REF] it, meaning that Venlo defined its own localised economic problems around logistics competiveness leads to a territorial differentiation of the Greenport policy compared to the national definition and the redefinition of sectors and actors involved in this public policy beyond the influential lobby of the Dutch horticultural sector:

"When we say Greenport Venlo, everybody thinks only about agribusiness or agro and foods, perhaps agro logistics. We must be clear: Greenport Venlo is more than that. Yes, it is agribusiness, it is agro foods and it is also industry. However, it is always logistics. Logistics in general."

(Interview: Municipality of Venlo)

The local territorialisation of the Greenport as a "cluster of agro food industries and horticulture and logistics activities important to competitiveness"10 has been explicitly recognised by the national spatial planning a posteriori. Finally, the policy frame entails new legitimacy for logistics development. The Floriade organised in 2012 offered "a landmark because we are a Greenport" and displayed the local discourse around the, linking agribusiness, logistics and regional development.

"This year, we will have a lot of events thanks to the Floriade: the Netherlands distribution association will be in Venlo, the congress of the association of Dutch inland ports -all of them are at the Floriade. For us, the Floriade is more than agribusiness, it is really business to business, next to attracting visitors."

(Interview: Municipality of Venlo) However, although the Greenport frame secured a national endorsement for growth and linked logistics with export-based agribusiness, its meaning for logistics companies remained limited:

"When we profile ourselves to logistics companies, we refer to Tradeport, which works better for logistics: the Tradeport in the umbrella of the Greenport." (Interview: DCGV) "Which label is the best for us: Greenport or tradeport? None of them. Just Venlo. That is known. Our customers don't care about labels, they just think about logistics zones."

(Interview: Prologis) Therefore, from a regional development perspective, being included in the Greenport discourse offers the opportunity to obtain more attention from the national government in terms of formal recognition and financing:

"The central government has no money anymore. However, we caught the national government's attention. This is important. When they are investing in the rail network, they know we are an important region, so they will think about us. The chances that will we obtain money for development are bigger."

(Interview: Municipality of Venlo) Eventually, this discursive phase of strategic coupling secured national policy recognition and support. This way, national policies can constitute resources for local strategies without directly shaping port regionalisation. Moreover, the discursive practices with regards to the Greenport are accompanied with new governance arrangements that allows for further strategic engagement with global logistics.

Strategic Coupling III: New enabling governance tools-

The governance arrangements created by the Greenport framework allowed for local stakeholders to remove the municipal political constraints on economic and land development policies and govern logistics development through new tools. In a way, this arrangement resembled the more general shift towards what is referred to by critical scholars as 'urban privatism' and the 'post-democratic city' (cf. [START_REF] Macleod | Urban politics reconsidered. growth machine to post-democratic city?[END_REF]. Among the policy transformations, new ways of governing the built environment are emerging. This transformation has become highly strategic to capture the global logistics players [START_REF] Hesse | Land for logistics: locational dynamics, real estate markets and political regulation of regional distribution complexes[END_REF], Raimbault, 2013a[START_REF] Raimbault | Les firmes de l'immobilier logistique -2. Prologis : "Local partner to global trade[END_REF]. Two of the leading global real estate firms are Prologis and Goodman, and they are especially important in aligning the region with global networks: Above all, the new governance structure, called Greenport Venlo, is politically and operationally in charge of the Greenport project (cf. figure 2). Greenport Venlo is a foundation under private law; therefore, it is less constrained than a municipal administrative department. The municipalities of the region, the province of Limburg and the local employers' association ("enterprising Limburg") sit on its board. Greenport Venlo implements most of the local economic development policies that were once the responsibility of the municipality:

"Greenport Holland, that structure is very public. However, Greenport Venlo, that is a cooperation with firms. And if you look at logistics, you see we are very successful in this kind of cooperation."

(Interview: Municipality of Venlo) "In the municipality, you have not only to go to the alderman but also to the municipal council. That does not work. In a private organization, it is safe." (Interview: Prologis)

In fact, Goodman has just developed a park that includes three huge distribution centres in the Venlo Tradeport North, which is the first logistics zone of the Klavertje 4. Thus, a new coalition has been forged through the DCGV that involves the global real estate developers and investors. This new coalition is able to attract bigger logistics providers, such as DHL, UPS and Géodis, and logistics real estate developers and investors are also selling Venlo to global markets:

"One of the points I always say to the municipality is: see us as an ambassador of your region. Because we are financially interested in your region, your problem is my problem. (…) And I want to develop. So I am one of the ambassadors of Venlo."

(Interview: Prologis)

The coalition around the DCGV is not a substitute for the first coalition of the regional firms forged through the Viaport Venlo. This latter coalition is still at work under the umbrella of the Greenport Venlo foundation within the "Innovation Centre," which is the institution dedicated to innovation and research programs (cf figure 2). The two coalitions are partly disconnected because the real estate investors and global logistics providers do not participate in the promotion and innovation programs.

The territorialisation of the Greenport frame in Venlo, therefore, has led to a new mode of production of logistics spaces that aligns material, institutional and symbolic assets with growth based on logistics. Conversely, it embeds the interests of global logistics players through the built environment. In terms of strategic coupling, this last phase is characterised by a real estate-based coalition that intends to attract new distribution centres of the largest international logistics services providers and shippers. In particular, it is changing the way local economic development is governed locally so that it is more attuned to the business model of international real estate developers.

V) Conclusions

The conceptual understanding of port systems and the port-city interface has moved beyond Bird's classical 'Anyport' model. However, whereas planners and urban geographers focused on the antagonistic processes involved in waterfront redevelopment, transport geographers introduced a regionalisation phase to the Anyport model. This phase is characterised by containerised, integrated and spatially extensive supply chains in which multi-modal logistics hubs develop inland and away from the port-city. Although the port regionalisation phase is largely driven by both push and pull factors, a scope of action remains for public policy to shape its spatial contours.

In this paper we have argued for the inclusion of a relational perspective of port regionalisation that shows how agency constructs places in a (global) system of flows that is not a functionalist logic of the 'global' imposing development on the 'local' places (i.e., ECT's extended gate). Rather, port regionalisation as a pure spatial outcome is the result of a delicate relational process in which interests from various scales converge in the formation of policy agendas and strategic decision-making and materialise through the process of strategic coupling. This is why the issue of the 'direction' of the regionalisation phase is more delicate and subtle than the functionalist logic of the 'outside-in' or 'inside-out' dichotomy. Indeed, both forces are at work in the rise of Venlo as an inland logistics hub, with many other actors and interests involved than the private terminal operating company ECT. A relational approach thus reveals that the proliferation of Venlo as an inland logistics hub is more nuanced than the accommodation of ECTs extended gateway business model. Only by looking at how agents employ assets (land and location) and confer meaning to a place through discursive practices (Greenport) across scales (national planning support) and within networks (ECT's extended gateway but also the promotional alignment with the PA of Rotterdam, the agri-business sector and the client portfolio of globally specialised real estate-firms) can we fully appreciate how Venlo has become constituted as a logistics hub and, eventually locking-in a development path.

In general, we think that port regionalisation as a process and outcome is also of interest to planners and urban geographers. Planners, urban geographers and historians remain absent in the discussion of this extension of Bird's Anyport model because their studies largely focus on the urban waterfront redevelopment stage. Port regionalisation shows that the development of inland logistics hubs in semi-urban and semi-peripheral locations are as much a part of the wider structural changes as the actual retreat of transport activity from waterfront locations in urban cores. The case study of Venlo shows how 'global-local spaces' emerge 'beyond the waterfront' and materialise in specifically built forms, governance arrangements and economic development trajectories.

Figure 1 :

 1 Figure 1: The location of the Greenport Venlo in the Rhine-Scheldt Delta (own compilation)

"

  In the governance structure [of both the Viaport Venlo and the region of Venlo], the private sector is leading. So (…) [the local-based entrepreneurs are] more important than the Alderman. (…) It is very unique in the Netherlands. [In this program] we pay, but we don't decide." (Interview: Municipality of Venlo)

"

  Nowadays, Prologis and Goodman attract companies too. They are in the global network. In 2011, Goodman started developing a new DC for DSV's Unilever supply chain. So you see because they invest, DSV acquired this 5-year contract with Unilever. So I think that Goodman and Prologis are very important for our region." (Interview: Municipality of Venlo)

(

  Interview: Municipality of Venlo) It also leads to a new scale of implementation of local economic development policies. This used to be the only responsibility of the municipality of Venlo; but now it is conducted at the scale of the wider region: "Before Greenport and Floriade, we never worked together. All the municipalities were looking at each other in concurrence. Since then, they have worked well together, in cooperation. It is very unique. Not a lot of regions work together in this way." (Interview: Municipality of Venlo)

Figure 2 :

 2 Figure 2: Greenport Venlo governance arrangements (own compilation)

Figure 3 :

 3 Figure 3: Logistics parks, agribusiness and infrastructure in the Venlo region (own compilation)

  Germany in the north of the province of Limburg; it is approximately 150 km from both the ports of Rotterdam and Antwerp and only 50 km from Europe's largest inland port Duisburg. Venlo offers multimodal options because it is directly connected by major highways with both Rotterdam (A15-A73) and Antwerp (A-67/E-34) that extend into Germany. Through the Maas River (which is directly linked with the Rhine through a canal), Venlo is also accessible by barge and connected with Europe's main inland waterway system. By rail, Venlo is connected with the port of Rotterdam through the socalled 'Brabant-route'. The rail and barge (container) terminals in Venlo are operated by Rotterdam-based ECT through a joint venture with a locally based firm, Seacon Logistics.

ECT developed their first inland (rail) terminal in 1982 and a second terminal in 1992, which was followed by a barge terminal in 2010. In 2010, ECT handled approximately 200,000 TEU in Venlo.

Table 1 :

 1 Importance of logistics activities in the regional economy in terms of location quotient (Source: LISA, 2011). We conducted our data analysis at the regional scale (NUTS III in EU standardised data collection) because logistics poles generally fall outside of municipal borders, which is the case with Venlo. Furthermore, Noord-Limburg is now at the political scale of Venlo Regio, which is in charge of land and economic development policies (see section 4).

	Logistics

8

Similar to

Van der Heuvel et al. (2013)

, we defined logistics employment as the total of wholesaling employment and transport employment.

Table 2 :

 2 Importance of transport activities in the regional economy in terms of location quotient (Source:LISA, 2011)

	Transport

Table 3 :

 3 Warehouse stock and occupancy rates in Dutch logistics centres (source:CBRE, 2011)

"

  Because the Greenport company is also real estate people, they understand business. Municipality, it is difficult. It is not real estate. (…) So it is easier to communicate."According to Prologis, working with a development company instead of a municipal board could permit this firm to implement its strategy of developing logistics parks, which necessitates privatising the land development process:"What is different compared to central Europe and also France, where we have parks with five or six buildings, is that in the Netherlands, we have municipalities that are only selling land per plot. So we can only buy land for one warehouse. And the road in front is still owned by the municipality. So we have to do case by case, plot by plot, and because of that, you get a warehouse here, a warehouse there. (…) However, in Venlo (…), we are now negotiating with Greenport to let us develop the land as a main developer. (…) There is one of the plots[of Venlo Trade Park North] that is big enough. (…) It is the only plot I think almost in all the Netherlands."

	(Interview: Prologis)

Their perspective, inspired by actor-network thinking, echoes a similar approach as in planning theory developed byBoelens (2009).

Available upon request

For the data analysis, the LISA register was used. For all business establishments with paid jobs in the Netherlands, this database contains information regarding the location, amount of jobs, and industrial activity (NACE-codes) on a yearly basis.

In the 1980s, ECT's stakeholders included the Dutch state-owned national railway company NS.

Ontwerp Structuurvisie Infrastructuur en Ruimte, 2011 : p71