The flexible-membrane kite employed by some airborne wind energy systems uses a suspended control unit, which experiences a characteristic swinging motion relative to the top of the kite during sharp turning manoeuvres. This paper assesses the accuracy of a two-point kite model in resolving this swinging motion using two different approaches: approximating the motion as a transition through steady-rotation states and solving the motion dynamically. The kite is modelled with two rigidly linked point masses representing the control unit and wing, which conveniently extend a discretised tether model. The tether-kite motion is solved by prescribing the trajectory of the wing point mass to replicate a figure-eight manoeuvre from the flight data of an existing prototype. The computed pitch and roll of the kite are compared against the attitude measurements of two sensors mounted to the wing. The two approaches compute similar pitch and roll angles during the straight sections of the figure-eight manoeuvre and match measurements within 3°. However, during the turns, the dynamically solved pitch and roll angles show systematic differences compared to the steady-rotation solution. As a two-point kite model resolves the roll, the lift force may tilt along with the kite, which is identified as the driving mechanism for turning flexible kites. Moreover, the two-point kite model complements the aerodynamic model as it allows for computing the angle of attack of the wing by resolving the pitch. These characteristics improve the generalisation of the kite model compared to a single-point model with little additional computational effort.

Pumping airborne wind energy (AWE) systems with flexible-membrane kites are reaching a technology readiness level suitable for first commercial applications. Two prominent examples are the leading developers SkySails Power GmbH using ram-air kites and Kitepower B.V. using leading-edge inflatable (LEI) kites

AWE system with

At the present stage of development, AWE systems are not optimised yet in terms of power production. Instead, the priority is improving operational reliability and demonstrating long-term operation, as well as learning how the systems perform in different wind environments

Performance models estimate the energy generation of a specific system in a varying wind environment representative of the wind climate at a specific site. The models can be classified according to how the flight trajectory and the system configuration are represented. The modelled system configuration includes at least the kite and the tether.

The most simple flight trajectory representations idealise the flight with only one or a couple of steady-flight states calculated with Loyd's analytic theory of tethered flight

Simpler system model configurations represent the kite as a single point mass or rigid body and assume a straight tether with its mass and drag lumped to the kite point mass. More refined models also resolve tether sag induced by lateral forces on the tether, such as gravity, centrifugal force, and aerodynamic drag, often achieved through discretising the tether. Typically, the discretised tether is represented with lumped masses connected with rigid links or spring-damper elements

The choice of the kite model determines the level of abstraction required to introduce steering forces as demonstrated in the work of

In reality, the aerodynamics of the kite highly depend on the fluid–structure interaction involving the membrane wing and bridle. The LEI kite of Kitepower B.V. is steered by pulling the rear bridle lines attached to one side of the wing while loosening the lines on the other side. This asymmetric actuation of the bridle line system makes the wing deform and initiate a turn. Video footage of experiments sheds some light on the aero-structural deformation due to steering

The goal of this paper is twofold: to study the dynamics that induce the observed characteristic pitch and roll swinging motion of the kite during sharp turning manoeuvres and discuss the implications for performance modelling. Pertaining to the first goal, this paper introduces a two-point kite model that is used together with a straight and discretised tether. Firstly, the motion is approximated as a transition through steady-rotation states with both tether representations. Subsequently, the motion is resolved dynamically with the discretised tether to study the impact of transient effects. Instead of resolving the translational motion of the wing, we prescribe a cross-wind flight path from the flight data of Kitepower B.V. This removes the dependency of the model on the aerodynamics of the kite and, thereby, reduces uncertainties. Pertaining to the second goal, this paper provides a breakdown of the mechanisms that initiate and drive a turn of a flexible kite system with a suspended control unit.

This paper is organised as follows. In Sect.

The data used in the present study were acquired on 8 October 2019 using a 25 m

Fully instrumented V3.25B kite before launch (photo courtesy of Kitepower B.V.). The overlaid red, green, and white circles mark Pixhawk^{®} sensor 0, Pixhawk^{®} sensor 1, and the flow sensors, respectively.

Front view ^{®} sensors 0 and 1 are assumed to be fixed with respect to the TWS reference frame, while the relative flow sensors are assumed to be fixed with respect to the bridle reference frame. Adapted from

The published data set

For this flight test, two Pixhawk^{®} sensor units were mounted to the wing, one on each of the two struts adjacent to the symmetry plane of the kite (red and green cases in Fig. ^{®}. The velocity measurements used in the present analysis come from the same sensor. The tangential and radial components of these measurements are depicted together with those measured by sensor 1 in Fig.

Kinematics of the studied figure-eight manoeuvre measured with the two Pixhawk^{®} sensor units and the kinematics obtained with the flight trajectory reconstruction described in Appendix

Comparing the tether reel-out speed to the position of the wing indicates anomalies in the recorded wing position that manifest as unrealistically large jumps in radial position predominately occurring during left turns, as can be observed in Fig.

We illustrate our analysis using a figure-eight cross-wind manoeuvre of the wing shown in Fig.

The studied figure-eight cross-wind manoeuvre of the wing depicted with respect to the wind reference frame, shown in Fig.

Timestamps of the reference positions along the figure-eight path shown in Fig.

For simplicity, the present study assumes that the wind velocity is uniform and constant. The average wind speed measured at the ground for the reference pumping cycle is approximately 7 m s

The flight behaviour along the figure eight described in the previous section is analysed with two different methods for solving the motion of the two-point kite model with a discretised tether model. First, this section discusses the tether-kite model configuration. Next, the two methods for solving the motion are discussed. The first approximates the tether-kite motion as a transition through steady-rotation states. The second solves the motion dynamically.

The two-point kite model accounts for the two distinct mass concentrations of the wing and the KCU. During cross-wind flight, the bridle line system is tensioned by the aerodynamic force acting on the wing. Accordingly, the two point masses stay at a constant distance, considering that the effect of wing actuation, including deformation, is negligible. From a modelling perspective, the two rigidly linked point masses resemble a rigid-body model, with rotational inertia in pitch and roll but not in yaw. The yaw motion is irrelevant to the present analysis due to the exclusion of the wing aerodynamics. This would not be the case when solving the full, unconstrained kite motion.

The two-point kite model developed for the present analysis can be added in a straightforward way to a discretised tether model as an additional final element. An example with five tether elements of equal length

Two-point model of the kite expanding a tether discretised by

To account for a varying length

Aerodynamic drag is one of the forces considered to act on the point masses representing the tether. The drag is calculated as

Two aerodynamic forces act on the KCU point mass below the wing: the drag of the KCU itself,

Physical parameters of the airborne system model.

Equation (

The subroutine for solving the quasi-static tether shape proposed by

To facilitate the calculation of loads, the velocities and accelerations of the point masses are approximated by assuming that they collectively rotate around the tether attachment point at the ground with a constant angular velocity, treating the point masses as particles embedded in a rigid body. According to this kinematic assumption, the velocity

The great-circle angular velocity

A shortcoming of this great-circle angular velocity approximation is that it does not yield an acceleration representative of a turning kite. Calculating the corresponding acceleration according to the steady-rotation assumption (Eq.

A more generally applicable angular velocity

To assess the steady-rotation assumption along the studied figure eight, the generalised rotational velocity

Assessing the steady-rotation assumption with the generalised rotational velocity

To conclude, we incorporate the following model modifications with respect to the model of

We apply a more generally applicable angular velocity in the steady-rotation assumption by the addition of a radial angular velocity component to account for turning manoeuvres of the kite.

The elasticity of the tether elements is not considered.

A different lumping approach is used for the uppermost tether point mass than for the other tether point masses; i.e. the mass and drag of half a tether element are allocated to the former instead of the mass and drag of a full element.

We add an extra element (rigid link) to represent the kite as described in Sect.

The proposed dynamic model is a derivative of the generic model for multiple kite system architectures with fixed tether lengths introduced by

The model is described by a differential-algebraic system of equations (DAEs), with constraints originating from the use of non-minimal coordinates. The differential states

Without imposing the translational motion of the wing, the dynamics of the two-point kite model with two tether elements read as

The constraint equations in the lower three rows of Eq. (

To prevent inaccuracies of an aerodynamic model of the wing from interfering with the simulation, we do not resolve the dynamics of the point mass of the wing. Instead, the acceleration of the wing is prescribed and used as input. The wing acceleration is inferred from a cross-wind flight path from the flight data, as described in Appendix

Incorporating the accelerations of the point masses, except for the wing point mass, as algebraic states allows the DAE of the full model to be expressed in a semi-explicit form. The time derivatives of the differential states are

In contrast to the steady-rotation-state calculation in Sect.

The tether length time derivatives are added to the dynamic equations to enable modelling pumping AWE systems.

Drag is computed directly at the point masses instead of being computed at the centres of the tether elements and then lumped to the adjacent point masses.

The acceleration of the wing point mass is not solved. Instead, the wing acceleration inferred from measurements is directly imposed.

We add an extra element (rigid link) to represent the kite as described in Sect.

Firstly, the steady-rotation-state approximation is used to study the motion of the tether and kite along the figure-eight manoeuvre. A discretisation by 30 tether elements is compared with a minimal discretisation using only a single-tether element. Secondly, the motion is simulated with the dynamic model using 30 tether elements. Subsequently, the resulting roll and pitch along the figure eights from the different models are compared with measurements. Finally, the motion of the tether and kite along a full pumping cycle is studied.

The steady-rotation-state approximation uses the measured tether force, wing position, and optimised angular velocity to determine the instantaneous positions of the point masses. The line formed by the elements between these point masses is referred to as the tether-kite line. Figure

Tether-kite lines for the nine reference instances resulting from the steady-rotation-state approximation with the tether discretised by 30 elements in 3D

Variations in the deformation of the tether-kite line are hard to identify with the naked eye in the previous plots. Therefore, the cross-axial displacement is plotted against the radial position for the first five reference instances with the solid lines in Fig.

Tether-kite lines with cross-axial displacement decomposed with respect to the tangential apparent wind velocity of the wing (see Fig.

The negated vertical unit vector

The discontinuities in the tether-kite lines at the KCU indicate that it has a substantial effect on the attitude of the kite element. The high mass and drag lumped to the KCU point relative to the mass and drag lumped to the tether points cause these discontinuities.

The pitch and roll of the kite derived from the attitude of the kite element (with respect to the

To investigate the imposed kite attitude more precisely, it is quantified using the pitch and roll of the kite element with respect to the

Figure

The analysis is repeated using a single-tether element. Figure

The dynamic simulation requires the wing acceleration, imposing the flight path, and the tether reel-out acceleration as input. The flight trajectory is reconstructed as described in Appendix

Figure

Tether force evolution along the figure eight resulting from the dynamic simulation and from the flight data. The shaded intervals indicate the turns.

The resulting tether-kite lines are plotted in Fig.

The transient effects on the tether-kite line that arise from the highly dynamic flight behaviour during turns are accounted for by the dynamic model but not by the steady-rotation states. This explains why in Fig.

Despite including transient effects, the dynamic model does not necessarily enhance accuracy as it requires significant assumptions, e.g. for acquiring the tether reel-out acceleration input. Moreover, the dynamic simulation is expected to be more sensitive to neglecting tether elasticity and damping. One aspect that demonstrates this sensitivity is the relatively large oscillations observed in the pitch and roll of the kite computed with the dynamic model.

The wing attitude measurements enable estimating the pitching and rolling motion of the kite assembly and, thereby, can be used to validate the computed results. Validating the rotational motion of the kite is particularly important for performance model development, as accurate descriptions of this motion are essential for incorporating the aerodynamics and the turning mechanism. The tether motion cannot be validated as no measurements are taken directly from the tether.

Figure

Both sensors measure a similar roll along the whole figure eight, as shown in Fig.

Relations between

Video stills obtained from a recording from a test flight on 30 March 2017 with a kite largely identical to the V3.25B kite and a GoPro^{®} camera mounted to the KCU (video stills extracted from video recordings provided by Kitepower B.V.).

Figure

The possible inaccuracy of the kite model structure in highly dynamic states pertains to the assumption that the kite assembly (consisting of the wing, bridle, and KCU) is rigid. In reality, the kite deviates substantially from the CAD geometry in Fig.

In general, the steady-rotation states perform reasonably well in estimating the kite attitude, both with a single-tether element and 30 tether elements. This suggests that the coarse discretisation is equally effective in capturing the inertial effect of the KCU during turns. Despite including transient effects, the dynamic model does not necessarily show better agreement with measurements than the steady-rotation-state model. This suggests that improving the method for solving the motion may not be effective unless the configuration of the kite model itself is refined to compute pitching motion more accurately. However, a definite conclusion cannot be drawn because the uncertainty in the measurements might distort the view of the model validity.

To study the pitching motion of the kite outside the reel-out phase, we zoom out and evaluate multiple pumping cycles, including the 65th cycle, which contains the previously investigated figure-eight manoeuvre. During the reel-in phase, the kite only requires small steering adjustments. Consequently, the kite does not show significant rolling. In contrast, the pitching of the kite increases due to the increased tether sag. The increased sag results from a decrease in tether tension, which makes the weight and drag of the tether more dominant.

Figure

Each cycle shows an increase in pitch after the last turn in the reel-out phase as the kite transitions into the reel-in phase. The model overestimates the pitch at the start of the reel-in and underestimates it towards the end but gives good overall agreement. There are many factors that may cause this discrepancy. One plausible explanation is that the reduced load during the reel-in phase leads to the deformation of the kite struts on which the sensors are mounted. The deformation is measured but not accounted for in the model and, thus, not incorporated in the computed results. Note that during the reel-in, the steering input is non-zero, as shown in Fig.

The pitch of the kite element with respect to the

In this section, we discuss the turning mechanism and the implications of the observed swinging motion for the performance modelling of a kite system. Different mechanisms initiate and drive a turn of a flexible kite system with a suspended control unit.

The initiation mechanism relies on twisting the wing tips, as discussed in Sect.

The driving mechanism for turning flexible kites with a suspended control unit is the rolling of the kite. As soon as the turn is initiated, the kite will roll into the turn to exert a centripetal force on the relatively heavy KCU, pulling it along. Together with the kite, the lift force generated by the top wing surface rolls into the turn and contributes to the centripetal force. The higher the mass of the KCU, the more roll is required to execute the same turn. Consequently, a smaller fraction of the lift is available to carry the weight of the airborne components and pull the tether. While the aerodynamic side force is still necessary to maintain turning, it is the roll of the kite that accommodates the largest contribution to the centripetal force and is thus considered to drive the turn.

To incorporate this turning mechanism, a single-point kite model would need the roll of the kite as an input, relying on the user to provide realistic roll angles. Another option is modelling the roll, e.g. using an empirical relationship between the roll and the steering input, as shown in Fig.

Although the kite pitch does not change substantially during the reel-out phase, the tether-kite motion changes the pitch substantially outside this phase. The sag-induced pitch concerns performance modelling as it affects the angle of attack experienced by the wing, which in turn affects the generated aerodynamic forces. Resolving the pitch also requires modelling the kite with at least two point masses and enables incorporating an aerodynamic model for the wing with a dependency on the angle of attack.

Given the coarse discretisation of a two-point representation of the kite, it is reasonable to adopt a rigid-kite assumption when employing this kite model. The adequacy of using a two-point kite model for performance modelling pertains to the validity of the rigid-kite assumption. Despite the fact that the kite assembly is subject to a changing geometry, the errors arising from the rigid-kite assumption are expected to be limited. Therefore, this assumption can be justified by the necessity to limit computational complexity as required for some types of analysis for which the performance model can be useful.

Employing the developed models for performance modelling requires that the model is complemented with an aerodynamic model of the wing. This enables the dynamic model to resolve the flight path and a quasi-steady model to compute the kite speed along a partially prescribed flight path. Note that incorporating the wing aerodynamics makes the models much more sensitive to the wind input.

The inertia of the suspended control unit has a large effect on the roll of a flexible kite during turns in the reel-out phase. During the reel-in phase, the pitch of the kite changes due to the weight and drag of the control unit and increased tether sag. These effects are not resolved when the kite is modelled with a single point mass. With two point masses, one at the wing and one at the control unit, the steady-rotation-state model performs reasonably well in capturing the pitch and roll with little extra computational effort. A two-point model of the kite can thus be a powerful tool for the performance modelling of flexible kite systems.

The swinging motion of a kite with a suspended control unit is assessed with two approaches: approximated as a transition through steady-rotation states and solved dynamically. In contrast to the dynamic model, the steady-rotation-state model neglects transient effects. Both approaches employ a two-point kite model extending a discretised tether model using an additional rigid element for the kite. By prescribing the cross-wind flight path of the wing, no aerodynamic model of the kite is required.

An alternative expression for the angular velocity underlying the steady-rotation assumption is derived that accounts for the turning of the kite. This angular velocity expression accommodates lateral accelerations on the point masses and, thereby, allows for studying the lateral swinging motion of the kite. The angular velocity for turns is approximated with flight data and shows good agreement with the kite kinematics. Unlike the original angular velocity expression, the proposed expression yields a good approximation of not only the wing velocity but also the wing acceleration.

The tether-kite lines resulting from the steady-rotation states show discontinuities at the junction between the tether and the kite. These indicate that the control unit has a substantial effect on the attitude of the kite and stress the need for including a separate point mass for the control unit in performance models for flexible kite systems. The steady-rotation states perform reasonably well in estimating the roll of the kite, both with a single-tether and 30-tether element. The computed pitch and roll angles match the measured angles within 3° during the straight sections of the figure-eight manoeuvre. During the turns, the peaks in the roll are overestimated, and the instantaneous differences in roll may exceed 5°, whereas the pitch exhibits more systematic differences. These systematic differences could partially be explained by the fact that the model did not account for transient effects. However, drawing a definite conclusion is challenging, as the measurements include steering-induced pitch, making the wing measurements a poor reference.

Although the dynamic model considers transient effects, it does not prove to be more accurate in capturing the roll and pitch behaviour during turns than the steady-rotation states. This is expected to be primarily caused by inaccuracies in the wing acceleration and tether reel-out acceleration inputs. Due to anomalies in the flight trajectory measurements, a reconstruction was necessary to generate consistent inputs, enabling a running simulation. The reconstruction assumes that the tether slack length, defined as the difference between the tether length and radial position of the kite, remains constant. The large modifications imposed by the reconstruction add further uncertainty to the results. Moreover, since the developed model aims for simplicity to increase computational efficiency, it does not incorporate all relevant mechanical effects, such as tether elasticity and damping. In addition to solving the motion dynamically, it could be necessary to refine the configuration of the kite model in order to increase the accuracy of solving the pitching motion and explain the observed differences between the measured and computed pitch.

Two separate mechanisms have been identified that initiate and drive a turn of a flexible kite system with a suspended control unit. A steering input causes an aerodynamic side force that initiates the turn. As soon as the turn is initiated, the kite starts to roll as it needs to pull the relatively heavy control unit into the turn. The rolled lift force provided by the top wing surface of the kite provides the largest contribution to the centripetal force and is said to drive the turn. Since a two-point kite model resolves the roll, the lift force may tilt along with the kite to drive turns. Hence, it avoids making large assumptions to model the centripetal force, as seen in a single-point kite model. Furthermore, by resolving the pitch, the kite model allows for computing the angle of attack of the wing, which is crucial for obtaining an accurate aerodynamic model. This becomes particularly important when solving the wing motion instead of prescribing a flight path, as done in the current study. Further study is needed to assess how refined the pitching motion needs to be solved to accurately calculate the angle of attack of the wing.

The results of this study could be significantly improved with better-quality flight data, more raw data, and information about how measurements are conditioned and calibrated. Currently, the sensor units are mounted to the flexible wing. As a result, wing deformation and actuation of the depower angle of the wing are also measured. This could be prevented by mounting the sensor units to the kite control unit. To find a better match between the measured and simulated tether forces, it would be interesting to incorporate variable tether slack and account for stretching in the dynamic simulation. A stepping stone could be to wrap the simulation in an optimisation problem to find the tether acceleration input that produces the measured tether force and cross-check the results with the tether lengths resulting from the steady-rotation states. More accurate tether length information in the experimental data would greatly help such analysis. Moreover, the flight trajectory reconstruction could be enhanced with this information, as well as with more advanced state estimation techniques. Finally, both the steady-rotation state and the dynamic model could still benefit from refining the wind modelling and fine-tuning the model parameters.

The kinematics of the wing recorded in the flight data show inconsistencies in the measured tether reel-out speed and are reconstructed in a preprocessing step to remove anomalies. The dynamic simulation relies on the recorded wing kinematics and tether reel-out speed for its input. Directly using these recorded quantities as input leads to faulty simulations, and a workaround is needed to obtain coherent input. The reconstruction is carried out for the full 65th pumping cycle.

A preliminary evaluation of the wing kinematics in the flight data shows that the vertical speed does not fully agree with the derivative of the vertical position of the wing, even though it does for the horizontal components. The largest mismatch occurs during the turns, where the recorded vertical speed is more negative than the derivative of the vertical position. The recorded vertical position is GPS data enhanced with barometer measurements. However, we expect that the vertical speed was not updated accordingly.

The inconsistent vertical speed leads to a discrepancy between the time derivative of the measured radial position

As an additional check, the time derivative of the measured radial position of the wing

Figure

The residual between the inferred tether length and measured radial position

The maxima in the recorded radial position do not need to be purely physical. Another possible cause is GPS inaccuracy during manoeuvres, which has previously been reported in the literature.

The flight trajectory reconstruction is obtained using a discrete-time optimisation problem that minimises the error between the modelled radial wing speed and recorded tether reel-out speed while limiting the bias between the modelled and recorded wing position:

In line with the dynamic simulation, the fitting problem uses discrete control input trajectories. It assumes a constant acceleration within each simulation time step of 0.1 s. Between the corresponding control intervals, the values may vary. Due to the step function form of the acceleration, the velocity and position are linear and quadratic functions, respectively, within the control intervals. These low-order forms allow for sufficient detail due to the small time step. The fitting problem is solved in CasADi using a multiple-shooting approach. This approach is not hindered by integration drift causing an accumulating error with time.

The flight trajectory reconstruction results are shown with the orange lines in Fig.

We use the reconstructed radial wing acceleration

We acknowledge that the flight trajectory reconstruction might not be strictly valid. However, it serves the main objective of this study by enabling the simulation of a short interval that encompasses a figure-eight manoeuvre during reel-out. A more educated reconstruction would require a lot more resources and probably more testing and is recommended as a possible future improvement.

Expressing the attitude of the kite using pitch and roll angles with respect to the wind reference frame gives large variations in these angles along the flight trajectory. Consequently, the kite attitude is difficult to interpret from these angles. Variations are smaller when the pitch and roll angles are expressed with respect to the tangential plane (

Earth reference frame

The rotation matrix for the transformation from the earth to the tangential reference frame is calculated by

The measured pitch, roll, and yaw of the wing of the kite are expressed using 3–2–1 Euler angles. The corresponding rotation matrix for the transformation from the earth to the top wing surface reference frame is calculated by

The attitude of the kite is not affected by the depower signal and can be approximated by pitching the wing reference frame with the negative of the depower angle

The rotation matrix for the transformation from the tangential to the bridle reference frame is derived from the previously presented matrices:

A rotation matrix can be represented with a set of 3–2–1 Euler angles. The yaw, pitch, and roll corresponding to these three angles can be calculated using the lower expressions:

Last two rotations in the 3–2–1 sequence (Euler angles) to get from the tangential to the bridle reference frame:

Expressing the Euler angles of the kite element of the model requires assigning a local reference frame to the element. The model does not specify a full reference frame but only specifies the axial direction of the element. This axial direction is used as the

Other than for securing the alignment between the roll and pitch definitions of the measured and modelled kite attitude, the yaw of the tether is not of interest to this study. It does not affect the kite attitude itself, and, therefore, the resulting yaw angles are left out of Fig.

The complete test flight data, including 87 pumping cycles spanning a total flight time of 265 min, are available in open access from

Conceptualisation: MS and RS; methodology: MS; software: MS; investigation: MS; writing (original draft preparation): MS; writing (review and editing): RS; supervision: RS; funding acquisition: RS. All authors have read and agreed to the published version of the paper.

At least one of the (co-)authors is a member of the editorial board of

Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors.

The authors are grateful to Kitepower B.V. for making the flight data available in open access and for sharing expertise about the system and in particular to Joep Breuer for asking critical questions. We would also like to thank Arthur Roullier, whose MSc thesis this work builds upon, and Jochem de Schutter for his tips on implementing the dynamic simulation.

This research was part of the project REACH (H2020-FTIPilot-691173), funded by the European Union's Horizon 2020 research and innovation programme under grant agreement no. 691173, and the project AWESCO (H2020-ITN-642682), funded by the European Union's Horizon 2020 research and innovation programme under Marie Skłodowska-Curie grant agreement no. 642682.

This paper was edited by Alessandro Croce and reviewed by three anonymous referees.