DE102023110203A1 - Crane and method for automated positioning and/or movement of the load-carrying device of such a crane - Google Patents

Abstract

The present invention relates to a crane and a method for the automated positioning and/or automated movement of the load-carrying device of such a crane, with the following steps in a calibration phase:
- Collecting training data characterising positioning errors of the load hook in different areas of the crane's working range and at different lifting loads on the load handling device, by means of the following steps:
◯ Approaching different target positions and/or following different target paths of the load handling device by controlling the crane drives via a crane control system,
◯ Recording the actual positions reached and/or the actual path travelled by the load-handling device using a position recording device in absolute coordinates,
- Determining a crane model that describes the positioning errors of the crane over its working range for different lifting loads by regression of the collected training data, and the following steps in a compensation and/or work operation phase:
- Detection of a lifting load picked up and/or to be picked up on the load-handling device,
- Correcting the target position and/or the target path of a load lift based on the specific crane model depending on the detected lifting load, and
- Controlling the crane drives via the crane control system based on the corrected target position and/or the corrected target path.

Description

The present invention relates to a crane, in particular in the form of a tower crane, with a boom that can be pivoted about an upright axis, and a hoist rope that runs from the boom, carries a load-carrying device such as a load hook, and can be lowered and raised by a hoist. The invention further relates to a method for the automated positioning and/or movement of the load-carrying device of a crane, in which the load-carrying device is moved from a starting position to a target position and/or is moved automatically along a path. The invention also relates in particular to a method and a system for correcting position errors and/or deviations in the path of the load-carrying device in the absolute coordinates of a construction site.

For the automated construction of buildings, it is important to be able to carry out load lifts with a crane automatically, whereby the load attached to the load-handling device must be set down at the desired target position and/or moved along a desired lifting path with sufficiently high precision. The load-handling device must also be able to pick up the load at the desired starting position with sufficiently high precision.

It is important that the transported loads can be positioned or moved precisely in the absolute coordinates of the construction site, since the planning of a construction site is carried out in a fixed, georeferenced construction site coordinate system. On the other hand, a crane usually works in its own crane coordinate system. In order to move to a target position with the load hook or lifting device or to travel a specific lifting path or to calculate it in advance, the crane control system gives the crane drives target coordinates or lifting path coordinates as drive coordinates in the crane coordinate system, so that the crane drives are then actuated accordingly and the load hook moves to the lifting path points or the target position. For a tower crane, these drive coordinates of the crane typically include the angle of rotation around the upright tower axis, the trolley position along the boom and the rope length, and for a mobile crane with a luffing telescopic boom, also the angle of rotation around the upright axis, the luffing angle of the boom and the rope length and, if applicable, the telescopic length. By measuring the crane position on the construction site, the crane coordinate system can be compared with the georeferenced construction site coordinate system or the absolute coordinate system and, for example, a target position of a load in the georeferenced construction site coordinates can be transformed into crane coordinates.

In practice, however, significant positioning errors or deviations from the desired stroke path often occur due to various circumstances.

On the one hand, positioning errors of the load hook or lifting device are caused by deformations of the crane structure. Cranes used on construction sites, such as tower cranes or mobile cranes with telescopic booms, are designed ambitiously in terms of their load capacity and have long, slender structures that deform considerably due to the comparatively high load capacities and also due to the non-negligible dynamic stresses. In the case of a tower crane, deformations of the tower in particular occur, which bends forwards or in a radial direction, i.e. in an upright longitudinal center plane, when a load is picked up on the boom, which leads to a kind of pitching movement of the boom and influences the lowering depth or lifting height of the load hook. The boom itself also bends under the load or the lifting forces introduced by the hoist rope. In addition, there are transverse bends across the upright longitudinal center plane of the crane, which runs through the tower's longitudinal axis and the boom's longitudinal axis, due to dynamic loads that occur, for example, when the slewing gear is decelerated or accelerated, or due to wind loads. The dynamic loads can have a multiaxial effect if the load swings or is accelerated by operating the hoist rope.

On the other hand, positioning errors also occur due to the system's control of the hoist. The crane operator usually calibrates the lowering depth "zero" by pressing a button when the load hook is directly under the boom or 1 m or 2 m under the boom, and also the ground level when the load hook is fully lowered, for example -60 m. Between these two reference points, the crane control often calculates the lowering depths using linear interpolation and controls the hoist drive accordingly, but in practice this is not exactly correct and can lead to significant errors, since one revolution of the cable winch drum does not result in the same unwinding or retrieving length over the entire lowering depth range. This is caused by the hoist rope being wound in multiple layers on the drum, which changes the actual winding radius.

In addition, path errors due to errors in the sensor evaluation or sensor deviations occur as soon as the crane hook position is taken into account in a fixed georeferenced construction site system.

These systematic deviations result in positioning errors in the absolute construction site coordinate system, which pose a problem for automated crane lifts. Without correction, positioning errors of significant magnitude can occur, for example with a lowering depth of 1 m or even 2 m, which can have dramatic consequences when setting down a load.

Modern cranes have sway damping systems that use comprehensive sensors and sensor evaluation to monitor crane movements and intervene to correct the control of the crane drives, in particular the control of the slewing gear, which is used to rotate the boom around the upright axis, the trolley drive, which can be used to move a trolley along the boom, and the hoist, which can be used to raise and lower the load hook. It has also already been proposed that structural deformations of the crane should be taken into account for sway damping, in particular the deflection of the tower and the boom, see for example EP 37 84 616 A1 However, the positioning errors mentioned in the georeferenced construction site system as described above cannot be eliminated.

These systematic positioning errors in the absolute coordinate system have so far been countered by monitoring the actual, absolute crane hook position in georeferenced construction site coordinates, for which special position sensors are used, for example a GNSS sensor module on the crane hook or a tachymeter or local sensor tags operating in the ultra-wideband range, which can include one or more tags at calibrated positions on the construction site and one or more tags on the crane. However, such absolute position detection systems are very expensive and can operate with errors under certain operating conditions, such as unfavorable weather or environmental conditions or interfering objects such as steel structures or transmitters in the immediate vicinity. This often also requires the installation of peripheral devices and cables, which, depending on the construction site, can be difficult or even impossible to implement.

The present invention is therefore based on the object of creating an improved crane and an improved method of the type mentioned at the beginning, which avoid the disadvantages of the prior art and develop the latter further in an advantageous manner. In particular, automated lifts should be made possible with no or only negligible positioning errors or deviations from the lift path, without the need for permanent monitoring by expensive absolute sensor systems.

According to the invention, the above object is achieved by a method according to claim 1, a crane according to claim 12, a correction method according to claim 13 and a correction system according to claim 14. Preferred embodiments of the invention are the subject of the dependent claims.

It is therefore proposed to operate the crane in a calibration phase before regular crane operation with automated lifts, in which a sensor system working in georeferenced absolute coordinates monitors the positions actually approached or travelled to when the load handling device is moved and compares them with the positions recorded and/or specified in the crane coordinate system in order to determine any positioning errors that occur in the georeferenced absolute coordinates. A model is determined from the training data recorded in the calibration phase, with the help of which positioning errors can also be estimated or determined for positions and/or lifting paths for which no position data from the sensors working in absolute coordinates is available, so that the crane can work with automated lifts in a later regular crane operation phase without monitoring by the absolute sensors and the positioning errors can be corrected on the basis of the positioning errors estimated using the model.

• In der Kalibrierphase werden Trainingsdaten gesammelt, die Positionierfehler des Lasthakens in verschiedenen Abschnitten des Arbeitsbereichs des Krans und bei verschiedenen Hublasten am Lastaufnahmemittel charakterisieren, wobei zum Sammeln der Trainingsdaten verschiedene Soll-Positionen angefahren und/oder verschiedene Soll-Pfade mit dem Lastaufnahmemittel abgefahren werden, indem die Antriebe des Krans durch die Kransteuerung angesteuert werden, und die tatsächlich angefahrenen Ist-Positionen und/oder die tatsächlich abgefahrenen Ist-Pfade mittels einer in Absolutkoordinaten arbeitenden Positionserfassungseinrichtung erfasst werden. Anhand der gesammelten Trainingsdaten wird dann durch Regression der genannten Trainingsdaten ein Kranmodell bestimmt, das die Positionierfehler des Krans über dessen Arbeitsbereich für verschiedene Lasten beschreibt.

The following steps can be taken during the calibration phase and during the regular operation phase:

• In the calibration phase, training data is collected that characterizes positioning errors of the load hook in different sections of the crane's working area and at different lifting loads on the load-handling device. To collect the training data, different target positions are approached and/or different target paths are followed with the load-handling device by controlling the crane's drives via the crane control system, and the actual positions actually approached and/or the actual paths actually followed are recorded using a position detection device working in absolute coordinates. Based on the collected training data, Then, by regression of the training data mentioned, a crane model is determined that describes the positioning errors of the crane over its working range for different loads.

In the regular operating phase with automated load lifts, the lifting load picked up or to be picked up on the load handling device is then recorded by sensors in order to correct the target position and/or the target path of the load handling device for the automated load lift depending on the recorded lifting load and based on the specific crane model and then to control the crane drives via the crane control system based on the target position and/or the target lifting path corrected in this way.

The crane model determined by regression of the training data makes it possible to estimate the positioning error occurring in the georeferenced construction site coordinates over the entire working area of the crane and thus also to determine it for positions or sections of the working area in which no measurements were previously made with the absolute sensors in the calibration phase. Regardless of whether a position approached in the calibration phase for training purposes or a section of the working area traveled over for training purposes is to be approached or traveled away from, the crane can work in regular crane operation with automated lifts without the monitoring of a position detection sensor system working in absolute coordinates and still determine the systemic positioning error or the positioning error caused by deflections in absolute coordinates and correct the target position to be approached or the lifting distance to be traveled based on the estimated or determined positioning error.

The present invention thus achieves the significant advantage that, after a calibration phase, the positioning accuracy of the crane in georeferenced coordinates can be improved without additional and usually very expensive measuring systems. This means that a permanent and often cumbersome installation of such measuring systems can be avoided. The calibration and compensation phases mentioned can generally be applied to any type of crane, but are particularly advantageous for cranes with long, slender and ambitiously designed structures that show significant deformation under loads and can work with long hoist rope lengths. In addition, the system itself can achieve increased safety and the automation of the construction of buildings that are planned in a fixed construction site coordinate system can be further advanced.

In a further development of the invention, in the calibration phase for collecting training data, the lifting loads recorded on the load-handling device and the target positions approached or lifting paths traveled are varied over large areas within the load-bearing range and the working range of the crane in order to obtain the most meaningful training data possible. For example, different lifting loads can be recorded and the crane's radius can be changed, for example by moving the trolley drive, in order to represent at least 75% of the load-bearing range as training data. Alternatively or additionally, lifting paths can be traveled and/or target positions approached that represent at least 75% of the radial radius. Alternatively or additionally, lifting paths can be traveled and/or target positions approached that represent at least 75% of the lifting height, i.e. loads are lifted from ground level to close to the boom, for example, or lowered conversely. Large areas can also be traveled in the horizontal plane, whereby preferably at least the edge areas of the crane's working range can be traveled with training runs.

In a further development of the invention, in the calibration phase, on the one hand the position signal of the position sensors operating in absolute coordinates and, on the other hand, sensor signals and/or evaluated sensor signals and/or control signals are recorded in parallel in real time, which are stored in crane coordinates by the crane control and/or sensors present on the crane as training data.

In principle, various crane data can be collected as training data, in particular position data that determine the respective position of the crane drives and/or the crane components driven by them, for example the angle of rotation of the boom around the upright axis, the trolley position along the boom and the unwinding length of the hoist rope and/or the rotary position of the hoist rope drum. Depending on the sensors present on the crane, other crane operating parameters can also be collected as training data, for example strains of the crane structure such as strains in the longitudinal belts of the tower, bending deformations of the tower and/or the boom in one or more axes, and in particular also travel speeds of the crane drives mentioned, i.e. rotation speeds around the upright axis and/or trolley travel speeds and/or hoist rope speeds. Alternatively or additionally, accelerations can also be recorded by sensors and/or derived from other sensor-recorded variables and collected as training data, for example Hoist rope accelerations, load hook accelerations, trolley accelerations and/or rotational accelerations around the upright axis.

The sensors used in the calibration phase, which work in absolute coordinates, can fundamentally be designed in different ways. In an advantageous development of the invention, at least one GNSS sensor can be used, for example attached to the load hook or the load-carrying device. Alternatively or additionally, such GNSS sensors can also be attached to other crane components such as the trolley and/or boom tip.

Alternatively or in addition to such GNSS sensors, a tachymeter system can also be used to record the position of the crane's load-carrying device and possibly other crane components such as the trolley in absolute coordinates, whereby optical and/or electronic tachymeters can be used here. Tachymeters with automatic target detection can preferably be used.

Alternatively or additionally, the absolute sensor technology can also work with optical detection systems such as cameras, which determine the position of the load hook and possibly other relevant crane components such as the trolley in absolute coordinates.

Alternatively or additionally, the absolute sensor system can also have local, wireless signal transmission/reception devices that can, for example, record signal propagation times and/or signal strengths. For example, ultra-wideband tags can be provided that are mounted on the one hand at a location measured in the georeferenced coordinate system or at several georeferenced positions and on the other hand are attached to one or more positions on the crane, for example on the load hook and at one or more points on the boom, in order to determine the absolute position of the load-handling device from the signals exchanged between the tags, their propagation times and/or their received signal strengths.

In a further development of the invention, when regressing the training data, a linear regression can be carried out, preferably with non-linear basis functions.

Preferably, trolley positions can be taken into account in the regression to the second power and/or third power in order to achieve better accuracy, in particular to better represent deformations of the boom. Squared and cubic trolley positions allow a more precise prediction of bending of the boom in the vertical direction, since the bending curve of the boom can be described by a third-order polynomial, at least if one assumes that there is no load distribution or that all line loads distributed over the boom are neglected.

In particular, a so-called Lasso algorithm, i.e. “least absolute shrinkage and selection operator”, can be used in regression to select the most relevant parameters or properties of the training data.

In the compensation phase, the positioning error can be corrected in various ways. For example, path points defining a stroke path can be corrected by shifting the positions or coordinates defining the stroke path point by point.

Alternatively or additionally, the positioning correction can also include a correction of the trajectory, which characterizes the desired path of the load hook.

• 1: eine Seitenansicht eines Krans nach einer vorteilhaften Ausführungsform der Erfindung in Form eines Turmdrehkrans,
• 2: eine schematische, perspektivische Darstellung des Krans aus 1 zur Verdeutlichung der Freiheitsgrade und des Krankoordinatensystems,
• 3: eine Darstellung eines Hubpfades, der von einem Hubpfadplaner entlang mehrerer Pfadpunkte bestimmt wurde,
• 4: eine schematische Seitenansicht des Krans aus den 1 und 2 zur Verdeutlichung der auftretenden Positionierfehler,
• 5: eine perspektivische Darstellung eines Hubpfads um verschiedene Objekte herum, wobei Arbeitsbegrenzungen durch einen schwarzen Rahmen dargestellt sind,
• 6: eine Darstellung eines Hubpfads, der in der Kalibrierphase mit am Lasthaken angebrachtem GNSS-Sensor abgefahren wird,
• 7: eine Darstellung des Positionierfehlers in Polarkoordinaten in gemessenen Absolutkoordinaten im Vergleich zu dem durch das Kranmodell geschätzten Positionierfehler,
• 8: eine Darstellung der Lasthakenpositionen im festen Krankoordinatensystem, wobei neben dem Soll-Pfad die Korrekturpfade in strichlierten Linien und der in Absolutkoordinaten gemessene Soll-Pfad dargestellt sind, und
• 9: eine Darstellung des Positionierfehlers in polaren Koordinaten entsprechend den Darstellungen in 8.

The invention is explained in more detail below using a preferred embodiment and associated drawings. In the drawings:

• 1 : a side view of a crane according to an advantageous embodiment of the invention in the form of a tower crane,
• 2 : a schematic, perspective view of the crane from 1 to clarify the degrees of freedom and the crane coordinate system,
• 3 : a representation of a lifting path determined by a lifting path planner along several path points,
• 4 : a schematic side view of the crane from the 1 and 2 to clarify the positioning errors that occur,
• 5 : a perspective view of a lifting path around various objects, with work boundaries shown by a black frame,
• 6 : a representation of a lifting path that is travelled during the calibration phase with the GNSS sensor attached to the load hook,
• 7 : a representation of the positioning error in polar coordinates in measured absolute coordinates compared to the positioning error estimated by the crane model,
• 8 : a representation of the load hook positions in the fixed crane coordinate system, where in addition to the target path, the correction paths are shown in dashed lines and the target path measured in absolute coordinates, and
• 9 : a representation of the positioning error in polar coordinates according to the representations in 8 .

How 1 shows, the crane 1 can be designed as a tower crane, the tower 2 of which carries a boom 3 which can be rotated about an upright axis 4, in particular the longitudinal axis of the tower, by a slewing gear. A trolley 5 can be moved along the boom 3 by a trolley drive cable 6 in order to be able to change the outreach of the load hook 7. The trolley travel cable 6 can be adjusted by a corresponding trolley travel drive.

The load hook 7 can be lowered or raised from the boom 3 by a hoist rope 9 in order to be lowered and raised along the upright axis 10, cf. 1 .

The planning level of the construction site usually works with a locally fixed, georeferenced coordinate system that requires automated tower cranes to position the transported payload absolutely. However, the error, which includes bending displacements, sensor offsets and sensor evaluation errors, cannot yet be compensated for by modern controls that only work with relative sensors on the tower crane. The corresponding path error causes the payload to deviate from the desired path, which can lead to collisions with obstacles.

The degrees of freedom and the crane coordinate system K are in 2 highlighted.

The tower crane 1 transports payloads with mass m _pl by hanging them on the crane hook 7. The tower crane 1 can be equipped with at least three drive systems. The slewing drive actuates a joint below the tower crane cabin or, in the case of a bottom-slewing crane, slews the entire tower 2 including the boom 3, which determines the slewing angle γ of the boom. The trolley travel drive controls the trolley position x _tr and the hoist drive changes the rope length l _r .

The movement of the drives can cause the payload to swing with the swivel angles ϕ _x in the vertical direction and ϕ _y in the radial direction of the boom. The origin of the crane coordinate system K is located according to 2 above the cabin.

und in tangentialer Richtung q_vy sowie die des Auslegers 3 in tangentialer Richtung q_wy und in vertikaler Richtung q_wz zugrundeliegen, zu berücksichtigen.For the tower crane 1, a known vibration damping controller and a trajectory tracking controller can be provided in order to carry out automated load hoists. In this case, the elastic degrees of freedom that correspond to the bending of the tower 2 in the radial direction q _vx ∈ R

and in the tangential direction q _vy as well as those of the boom 3 in the tangential direction q _wy and in the vertical direction q _wz shall be taken into account.

wobei der Zustandsvektor des Turmdrehkrans definiert wird als x = [q, q̇]^T, während die entsprechende Soll-Zustandstrajektorie wie folgt bezeichnet wird: x_d.In the following, the vector containing all degrees of freedom of the tower crane is considered as follows $$q=\left[{\mathrm{\varphi }}_x,{\mathrm{\varphi }}_y,q_{\text{vxT}},{\text{q}}_{\text{vy}},{\text{q}}_{\text{wy}},{\text{q}}_{\text{wz}}\right]\in R^7$$

where the state vector of the tower crane is defined as x = [q, q̇] ^T , while the corresponding desired state trajectory is denoted as follows: x _d .

die Steuereingänge zu den Antriebssystemen mit u indiziert.Sensors of the drive systems measure the positions q _d = [γ, x _tr , l _r ] ^T and the speeds q̇ _dr = [γ̇, ẋ _tr , l̇̇ _r ] ^T . The target positions and speeds of the drive systems are given by q _dr,d and $q_{\text{dr}\text{,d}}$

the control inputs to the drive systems are indexed with u.

von N_p sogenannten Bahnpunkten p_i, die einen kollisionsfreien Weg von einem Startort zu einem Zielort in Bezug auf das gemeinsame georeferenzierte Bodenkoordinatensystem G darstellen und nach bestimmten Kriterien optimiert werden können. Der Hubpfad kann dabei mit einem ebenfalls per se bekannten Algorithmus zwischen jedem aufeinanderfolgenden Punktpaar p_i und p_i+1 berechnet werden, wobei die Hakenposition dem flachen Ausgang z des Systems entsprechen kann. Aus der gewünschten Hubtrajektorie und ihren Ableitungen ${\text{z}}_{\text{d}}^{\ast }=\left[{\text{z}}_{\text{d}},\dots ,{\text{z}}_d^{\left(4\right)}\right]$

kann die Ableitung der Soll-Zustandstrajektorie $x_d={\mathrm{\psi }}_x\left(Z_d,\dots ,\stackrel{\dots }{Z_d}\right)$

und der Vorwärtssteuerungseingangstrajektorie $u_{FF}={\mathrm{\psi }}_u\left({\text{Z}}_d^{\ast }\right)$

unter Verwendung der flachen Parametrisierungen ψ_x, ψ_u gewonnen werden.The fully automatic payload transport or automated payload lifting is prepared by planning a collision-free crane hook path to a specified destination, which further corresponds to the lifting path, and calculating the corresponding trajectory in the coordinate system K. A known algorithm can be used for the path planning. The path planning algorithm preferably calculates a sequence $$P=\left({\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="DE102023110203A1\_0062.png"\; state="\{\{state\}\}">p</figure-callout>}}_1,\dots ,p_{N_p}\right)$$

of N _p so-called trajectory points p _i , which represent a collision-free path from a starting point to a destination in relation to the common georeferenced ground coordinate system G and can be optimized according to certain criteria. The lifting path can be calculated using an algorithm that is also known per se between each successive pair of points p _i and p _i+1 , whereby the hook position can correspond to the flat output z of the system. From the desired lifting trajectory and its derivatives ${\text{z}}_{\text{d}}^{\ast }=\left[{\text{z}}_{\text{d}},\dots ,{\text{z}}_d^{\left(4\right)}\right]$

the derivation of the target state trajectory $x_d={\mathrm{\psi }}_x\left(Z_d,\dots ,\stackrel{\dots }{Z_d}\right)$

and the feedforward control input trajectory $u_{FF}={\mathrm{\psi }}_u\left({\text{Z}}_d^{\ast }\right)$

using the flat parameterizations ψ _x , ψ _u .

To ensure continuous movement of the hook, a sphere with a certain radius around the sphere center p _i is defined for all i = 1, ..., N _p . Once the crane hook cuts through the sphere while following the target trajectory p _i , the crane determines an updated lifting path at p _i+1 . An example lifting path is shown in 3 shown.

durch die Vorwärtskinematik FK(x, q_d) basierend auf dem nominellen Starrkörpermodell und einem Fehler berechnet werden, der durch die Biegung e_bend des Turms 2 und des Auslegers 3 des Turmdrehkrans 1 sowie die Dehnung des Hubseils 5, Sensorabweichungen e_off und Sensorauswertefehler e_obs zustandekommen kann. Diese Fehlerquellen sind in 4 dargestellt.Overall, the crane operates in its own crane-centered coordinate system K, but all other operations on the construction site are planned by the planning layer in relation to the common georeferenced ground coordinate system G. In a previous step, the transformation between the ground coordinate system G and the crane system K is therefore determined by measurements, preferably for the case where there is no load hanging on the hook, the hoist rope is as short as possible and the trolley is close to the tower under the boom. Here, G can be the local UTM projection. Within G, the actual hook position can be $$z=FK\left(x,q_{\text{d}}\right)+e_{\text{bend}}+e_{Off}+e_{Obs}$$

by the forward kinematics FK(x, q _d ) based on the nominal rigid body model and an error that can arise from the bending e _bend of the tower 2 and the boom 3 of the tower crane 1 as well as the stretching of the hoist rope 5, sensor deviations e _off and sensor evaluation errors e _obs . These error sources are in 4 shown.

The orbit error is then defined as $$e=z_d-z=FK\left(x_d,q_{dr,d}\right)-FK\left(x,q\right)-e_{bend}-e_{Off}-e_{Obs}$$

The trajectory error e also includes the control error FK(x _d , q _dr,d ) - FK(x, q) of the trajectory follower controller. The sensor deviations lead to the drive systems stopping at constantly shifted positions. In addition, the sensor evaluation errors cannot be neglected, because validation measurements have shown that the pendulum angle in the radial direction ϕ _y is incorrectly evaluated by up to 3°, which leads to a trajectory error, especially during transitions.

In order to compensate for the mentioned trajectory error e, a first step can be to predict this trajectory error. The prediction of the error e is carried out using a regression model.

wobei $$f_{\xi }={\left[\mathrm{1,}{f}_{\xi }{,}_1,\dots ,f_{\xi }{,}_{N_{{}_{\xi }}}\right]}^T\in R^{N_{\xi }X1}$$

$${\mathrm{\Theta }}_{\xi }={\left[{\mathrm{\theta }}_{\xi }{,}_0,\dots ,{\mathrm{\theta }}_{\xi }{,}_{N_{{}_{\xi }}}\right]}^T\in R^{N_{\xi }X1}$$

für ξ ∈ (γ, x_tr, Z). Die Konstanten N_ξ beschreiben die Anzahl der Merkmale, die für die Vorhersage jeder Komponente verwendet werden. Die Koeffizienten Θ_ξ werden durch einen Regressionsanpassungsalgorithmus ermittelt, der auf die Trainingsdaten angewendet wird. Die Trainingsdaten umfassen vorzugsweise Messungen von Merkmalen f_ξ und die jeweiligen Fehler Δγ_e, Δx_tr,e und ΔZ_e. Mögliche Merkmale sind die Soll-Zustandstrajektorie x_d, der Zustandsvektor x , der durch die Sensorauswertung berechnet wird, die Positionen q_dr, sowie die Geschwindigkeiten q_d, der Antriebssysteme des Turmdrehkrans, die vom Lastsensor gemessene Nutzlast m_pl, und die Steuerbefehle, die vom implementierten Regler berechnet werden. Weitere Merkmale sind die quadratische und kubische Katzposition $x_{tr}^2$

und $x_{tr}^3$

sowie die angenäherten Nutzlastschwankungsabstände l_rϕx und l_rϕ_y. Die quadratische und kubische Laufkatzenposition kann eine genauere Vorhersage der Biegung des Auslegers in vertikaler Richtung ermöglichen, da die Durchbiegungskurve des Auslegers ein Polynom dritter Ordnung ist in x_tr unter der Annahme, dass es keine verteilte Last gibt.The three components [Δγ _e , Δx _tr,e , ΔZ _e ] ^T representing e in polar coordinates are considered as the results of the regression model. The error of the angle of rotation Δγ _e is calculated with respect to the origin of the coordinate system attached to the tower crane. Therefore, based on linear regression, the output y of the regression model is defined as follows $$y={\left[\Delta {\mathrm{\gamma }}_e,\Delta x_{tr,e},\Delta Z_e\right]}^T={\left[f_{\mathrm{\gamma }}^T{\mathrm{\Theta }}_{\mathrm{\gamma }},f_{tr}^T{\mathrm{\Theta }}_{tr,}{f}_Z^T{\mathrm{\Theta }}_Z\right]}^T$$

where $$f_{\xi }={\left[\mathrm{1,}{f}_{\xi }{,}_1,\dots ,f_{\xi }{,}_{N_{{}_{\xi }}}\right]}^T\in R^{{\mathrm{<figure-callout\; id="1"\; label="N\; \xi \; X"\; filenames="DE102023110203A1\_0062.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\xi }X1}$$

$${\mathrm{\Theta }}_{\xi }={\left[{\mathrm{\theta }}_{\xi }{,}_0,\dots ,{\mathrm{\theta }}_{\xi }{,}_{N_{{}_{\xi }}}\right]}^T\in R^{{\mathrm{<figure-callout\; id="1"\; label="N\; \xi \; X"\; filenames="DE102023110203A1\_0062.png"\; state="\{\{state\}\}">N</figure-callout>}}_{\xi }X1}$$

for ξ ∈ (γ, x _tr , Z). The constants N _ξ describe the number of features used to predict each component. The coefficients Θ _ξ are determined by a regression fitting algorithm applied to the training data. The training data preferably includes measurements of features f _ξ and the respective errors Δγ _e , Δx _tr,e and ΔZ _e . Possible features are the target state trajectory x _d , the state vector x , which is calculated by the sensor evaluation, the positions q _dr , as well as the speeds q _d , of the drive systems of the tower crane, the payload m _pl measured by the load sensor, and the control commands calculated by the implemented controller. Other features are the quadratic and cubic trolley position ${\mathrm{<figure-callout\; id="2"\; label="x\; t\; r"\; filenames="DE102023110203A1\_0062.png,DE102023110203A1\_0066.png"\; state="\{\{state\}\}">x</figure-callout>}}_{tr}^{}$

and ${\mathrm{<figure-callout\; id="3"\; label="x\; t\; r"\; filenames="DE102023110203A1\_0062.png"\; state="\{\{state\}\}">x</figure-callout>}}_{tr}^{}$

and the approximate payload sway distances l _r ϕx and l _r ϕ _y. The quadratic and cubic trolley position can provide a more accurate prediction of the boom deflection in the vertical direction since the boom deflection curve is a third order polynomial in x _tr assuming that there is no distributed load.

mit 48 Einträgen. Um die relevantesten Merkmale für jede Ausgabe zu identifizieren und eine Überanpassung zu vermeiden, wird eine sog. LASSO-Regularisierung für jede Ausgabe Ψ ∈ (Δγ_e, Δx_tr,e, ΔZ_e) unter Verwendung von Trainingsdaten berechnet. Genauer gesagt, kann das Optimierungsproblem $$min\left({\mathrm{\omega }}_{\xi }\right)\left(\frac{1}{2N}{\displaystyle {\sum }_{k=1}^N{\left({\mathrm{\Psi }}_k-\left[\mathrm{1,}{d}_k\right]{\mathrm{\omega }}_{\xi }\right)}^2+\lambda {\displaystyle {\sum }_{j=1}^{N_{\xi }}\left|w_{\xi ,j}\right|}}\right)$$

für verschiedene Werte von λ mit Matlab-Simulink gelöst werden. Dabei steht der Index k für den Zeitschritt der Trainingsdaten. Die Koeffizienten ω_ξ ∈ .R

und seine Komponenten ω_ξ,j bezeichnen den unbekannten Koeffizientenvektor, wenn alle 48 Merkmale und ein konstanter Offset berücksichtigt werden.All features considered are summarized as follows $$d={\left[x^T,{\text{q}}_{dr}^T,q_{dr}^{\dot{T}},m_{pl},u^T,x_d^T,q_{dr,d}^T,q_{dr,d}^{\dot{T}},{\mathrm{<figure-callout\; id="2"\; label="x\; t\; r"\; filenames="DE102023110203A1\_0062.png,DE102023110203A1\_0066.png"\; state="\{\{state\}\}">x</figure-callout>}}_{tr}^{},{\mathrm{<figure-callout\; id="3"\; label="x\; t\; r"\; filenames="DE102023110203A1\_0062.png"\; state="\{\{state\}\}">x</figure-callout>}}_{tr}^{},l_r{\mathrm{\varphi }}_x,l_r{\mathrm{\varphi }}_y\right]}^T$$

with 48 entries. To identify the most relevant features for each output and avoid overfitting, a so-called LASSO regularization is computed for each output Ψ ∈ (Δγ _e , Δx _tr,e , ΔZ _e ) using training data. More specifically, the optimization problem can be $$min\left({\mathrm{\omega }}_{\xi }\right)\left(\frac{1}{2N}{\displaystyle {\sum }_{k=1}^N{\left({\mathrm{\Psi }}_k-\left[\mathrm{1,}{d}_k\right]{\mathrm{\omega }}_{\xi }\right)}^2+\lambda {\displaystyle {\sum }_{j=1}^{N_{\xi }}\left|w_{\xi ,j}\right|}}\right)$$

for different values of λ using Matlab-Simulink. The index k stands for the time step of the training data. The coefficients ω _ξ ∈ .R

and its components ω _ξ,j denote the unknown coefficient vector when all 48 features and a constant offset are considered.

The higher the value of λ, the more coefficients ω _ξ are zero, while the remaining coefficients sufficiently minimize the squared error between the measured output and the outputs of the regression model and thus indicate the features that are best suited for reconstructing the respective output.

$$f_{tr}={\left[\mathrm{1,}{\mathrm{\varphi }}_y,q_{vx}^T\mathrm{,}{\mathrm{\varphi }}_y^{.},l_r,m_{pl},u_{tr},u_r,x_{tr}^3\right]}^T,$$

$$f_Z={\left[\mathrm{1,}{q}_{vx}^T,l_r,m_{pl},u_{tr},u_r,l_{r,d}^{.},x_{tr}^3\right]}^T.$$

After examining the non-zero coefficients of the solution for several values of λ, the following features are obtained for predicting the errors by regression $$f_{\mathrm{\gamma }}={\left[\mathrm{1,}{\mathrm{\varphi }}_x,q_{wy},\dot{\gamma }\mathrm{,}{\mathrm{\varphi }}_x^{.},x_{tr},l_r,u_{\mathrm{\gamma }},x_{tr,d},l_{r,d},l_d^{.},{\mathrm{\varphi }}_{x,d}\right]}^T,$$

$$f_{tr}={\left[\mathrm{1,}{\mathrm{\varphi }}_y,q_{vx}^T\mathrm{,}{\mathrm{\varphi }}_y^{.},l_r,m_{pl},u_{tr},u_r,x_{tr}^3\right]}^T,$$

$$f_Z={\left[\mathrm{1,}{q}_{vx}^T,l_r,m_{pl},u_{tr},u_r,l_{r,d}^{.},x_{tr}^3\right]}^T.$$

und enthalten den Pendelwinkel in radialer Richtung ϕ_y und die Kranseillänge l_r, stattdessen. Die radiale Biegung des Turms q_vx ist wichtiger als die vertikale Biegung q_wz des Auslegers. In Bezug auf ΔZ_e sind die wichtigsten Merkmale in (10c) die Last m_pl, und die kubische Katzstellung $x_{tr}^3$

die die Durchbiegungskurve in Abhängigkeit von der Fahrwerksposition darstellt.The features (10a) for the prediction Δγ _e do not include the payload m _pl . The influence of the bending of the boom in the tangential direction q _wy exceeds the influence of m _pl . The pendulum angle ϕ _x and the target angle ϕ _x,d are both relevant features because their difference directly determines Δ _γe , which is also an angle. The features (10b) for the prediction of Δx _tr,e do not include the product ${\mathrm{\varphi }}_y{l}_r$

and contain the pendulum angle in the radial direction ϕ _y and the crane rope length l _r , instead. The radial deflection of the tower q _vx is more important than the vertical deflection q _wz of the boom. In relation to ΔZ _e the most important Features in (10c) the load m _pl , and the cubic cat position ${\mathrm{<figure-callout\; id="3"\; label="x\; t\; r"\; filenames="DE102023110203A1\_0062.png"\; state="\{\{state\}\}">x</figure-callout>}}_{tr}^{}$

which represents the deflection curve depending on the chassis position.

In a further step of deriving the regression model, the coefficients Θ _ξ are calculated using the iteratively reweighted least squares fitting algorithm. The result of the regression model is thus formulated as follows $$y\left(x,q_{dr},q_{dr}^{.},m_{pl},u,x_d,q_{dr,d},q_{dr,d}^{.},x_{tr}^3\right)={\left[f_{\mathrm{\gamma }}^T{\Theta }_{\mathrm{\gamma }},f_{tr}^T{\Theta }_{tr},f_Z^T{\Theta }_Z\right]}^T.$$

sowie die entsprechende Hubtrajektorie $\widetilde{z_d^{*}}$

angewendet werden, wobei die Soll-Zustandstrajektorie $\widetilde{x_d}$

und Vorwärtssteuerung $\widetilde{u_{FF}}$

des Turmdrehkrans zur genaueren Verfolgung der geplanten Bahn in georeferenzierte Koordinaten umgerechnet warden kann. Die korrigierten Trajektorien werden bezeichnet mit $\widetilde{z_d},\widetilde{x_d}\text{ und }\widetilde{u_{FF}}$

To compensate for path or positioning errors, several approaches can be used to calculate a corrective stroke path $\widetilde{z_d}$

and the corresponding lifting trajectory $\widetilde{z_d^{*}}$

be applied, whereby the target state trajectory $\widetilde{x_d}$

and forward control $\widetilde{u_{FF}}$

of the tower crane can be converted into georeferenced coordinates for more precise tracking of the planned path. The corrected trajectories are denoted by $\widetilde{z_d},\widetilde{x_d}\text{and}\widetilde{u_{FF}}$

ist jeweils rot und blau gestrichelt hervorgehoben und ergibt sich durch Verschiebung der Soll-Hakenposition z_d um den vorhergesagten Bahnfehler y als Ergebnis von (11). Die Steuerung des Turmdrehkrans zielt darauf ab, den Haken an der Ausgleichsposition $\widetilde{z_d}$

zu positionieren. Aufgrund des noch vorhandenen Bahnfehlers wird die Hakenposition gleich der gewünschten Hakenposition z_d (schwarz in 4), was das Gesamtziel ist.The correction and measurement results of a load stroke using two different approaches are shown in 4 The corrected hook position $\widetilde{z_d}$

is highlighted in red and blue dashed lines and is obtained by shifting the target hook position z _d by the predicted path error y as a result of (11). The control of the tower crane aims to position the hook at the compensation position $\widetilde{z_d}$

Due to the remaining path error, the hook position is equal to the desired hook position z _d (black in 4 ), which is the overall goal.

wobei die N_p Punkte die Bahnpunkte in Polarkoordinaten in K beschreiben, erhält man die korrigierten Bahnpunkte durch $$\widetilde{p_l}=p_i+y\left(\mathrm{0,}{p}_i\mathrm{,0,}{m}_{pl}\mathrm{,0,0,}{p}_i\mathrm{,0,}{x}_{tr}^3\right).$$

The path calculated with the path planning algorithm [8] consists only of a sequence of points in the working space of the tower crane. Therefore, the only known features of (10) are the positions of the drive systems q _dr and the permanently measured load m _pl at these points. Therefore, in a first approach (blue in 4 ) the regression model is evaluated at the position of each trajectory point, assuming that the hook is in a stationary state. The remaining features required for the prediction by the regression model are not known. Suppose that the path calculated by the trajectory planning algorithm used is represented as a set $P=\left({\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="DE102023110203A1\_0062.png"\; state="\{\{state\}\}">p</figure-callout>}}_1,\dots ,p_{N_p}\right)$

where the N _p points describe the trajectory points in polar coordinates in K, the corrected trajectory points are obtained by $$\widetilde{p_l}=p_i+y\left(\mathrm{0,}{p}_i\mathrm{,0,}{m}_{pl}\mathrm{,0,0,}{p}_i\mathrm{,0,}{x}_{tr}^3\right).$$

und die entsprechende Hubtrajektorie $\widetilde{z_{d\mathrm{,1}}^{\ast }}$

werden durch Anwendung des zuvor beschriebenen Algorithmus zur Erzeugung von Bahnen auf den Satz von Ausgleichsbahnpunkten $\widetilde{P_1}=\left\{\widetilde{p_1},\dots ,\widetilde{p_{N_p}}\right\}$

verwendet. Die flachen Parametrisierungen ψ_x, ψ_u ergeben dann die Soll-Zustandstrajektorie $\widetilde{x_{d\mathrm{,1}}}$

und die Vorwärtssteuerungseingabe $\widetilde{u_{FF\mathrm{,1}}},$

die dem Trajektorienfolgeregler zugeführt werden.In it, the drive systems q _dr are set to p _i . Neglecting all other features reduces the quality of the predicted error y in (12) and the regression model therefore only describes static deflections and sensor displacements. The corrected stroke path $\widetilde{z_{d\mathrm{,1}}}$

and the corresponding lifting trajectory $\widetilde{z_{d\mathrm{,1}}^{\ast }}$

are obtained by applying the previously described algorithm for generating trajectories to the set of adjustment trajectory points $\stackrel{}{P_{}}$$\widetilde{{}_1}=\left\{\tilde{{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="DE102023110203A1\_0062.png"\; state="\{\{state\}\}">p</figure-callout>}}_1},\dots ,\widetilde{p_{N_p}}\right\}$

used. The flat parameterizations ψ _x , ψ _u then yield the target state trajectory $\widetilde{x_{d\mathrm{,1}}}$

and the forward control input $\widetilde{u_{FF\mathrm{,1}}},$

which are fed to the trajectory follower controller.

und die Hubtrajektorie $\widetilde{z_{d\mathrm{,2}}^{*}}$

basierend auf der gewünschten Hubbahn des Hakens $z_d^{*}$

berechnet warden. Die Zustandstrajektorie x_d umfasst dabei die erwarteten Pendelwinkel, elastischen Freiheitsgrade und Fahrgeschwindigkeiten. Unter der Annahme, dass die Hubtrajektorie perfekt verfolgt wird, gilt x = x_d und u = u_FF. Dann sind die Sensorwerte der Positionen der Antriebssysteme q_dr = q_dr,d und die Geschwindigkeiten $q_{dr}^{.}=q_{dr,d}^{.}$

ebenfalls gleich den Werten der entsprechenden Sollwerte. Die korrigierten Bahnpunkte können dann berechnet werden nach $$\widetilde{z_{d\mathrm{,2}}}=z_d+y\left(x_d,q_{dr,d},q_{dr,d}^{.},m_{pl},u_{FF},x_d,q_{dr,d},q_{dr,d}^{.},x_{tr,d}^3\right).$$

Alternatively or additionally, the corrected stroke path can be used as a second approach $\widetilde{z_{d\mathrm{,1}}}$

and the lifting trajectory $\widetilde{z_{d\mathrm{,2}}^{*}}$

based on the desired lifting path of the hook $z_d^{*}$

be calculated. The state trajectory x _d includes the expected pendulum angles, elastic degrees of freedom and driving speeds. Assuming that the lifting trajectory is perfectly tracked, x = x _d and u = u _FF apply. Then the sensor values of the positions of the drive systems are q _dr = q _dr,d and the speeds $q_{dr}^{.}=q_{dr,d}^{.}$

also equal to the values of the corresponding target values. The corrected path points can then be calculated according to $$\widetilde{z_{d\mathrm{,2}}}=z_d+y\left(x_d,q_{dr,d},q_{dr,d}^{.},m_{pl},u_{FF},x_d,q_{dr,d},q_{dr,d}^{.},x_{tr,d}^3\right).$$

Daher werden die Ableitungen ${\tilde{z}}_{d\mathrm{,2}}^{.},{\tilde{z}}_{d\mathrm{,2}}^{\mathrm{..}},$

des korrigierten Hubpfads $\widetilde{z_{d\mathrm{,2}}}$

berechnet, indem der per se vorhandene Trajektoriengenerierungsalgorithmus für einen neuen Satz von Bahnpunkten, die wie folgt definiert sind, erneut verwendet wird $$\widetilde{P_2}=\left\{p_i\in R^3|p_i=\widetilde{z_{d\mathrm{,2}}}\left(t_i\right),i=\mathrm{0,}\dots ,N_t\right\},$$

wobei die Zeitschritte t_i gleichmäßig über die Zeitspanne verteilt sind, die den Übergang zwischen Start- und Zielort beschreibt. Die Zeitschritte t_i sind somit bestimmt durch $t_i=i\Delta t\text{ mit }\Delta t=\frac{\text{max}\left\{T_{\gamma },T_{tr},T_Z\right\}}{N_t}$

wobei T_γ, T_tr, T_Z die Übergangszeit in jeder Koordinate von $\widetilde{z_{d\mathrm{,2}}}$

ist. Die Anwendung des Trajektorienalgorithmus auf $\widetilde{P_2}$

liefert $\widetilde{z_{d\mathrm{,2}}^{*}}$

und damit die Soll-Zustandstrajektorie $\widetilde{x_{d\mathrm{,2}}}$

sowie die Vorwärtssteuerungseingabe $\widetilde{u_{FF\mathrm{,2}}}$

nach Verwendung der flachen Parametrisierungen.However, it should be noted that only the position of the hook is corrected in polar coordinates. The derivatives ż _d , z̈ _d , do not match the compensated position $\widetilde{z_d}.$

Therefore, the derivatives ${\tilde{z}}_{d\mathrm{,2}}^{.},{\tilde{z}}_{d\mathrm{,2}}^{\mathrm{..}},$

the corrected stroke path $\widetilde{z_{d\mathrm{,2}}}$

calculated by reusing the existing trajectory generation algorithm for a new set of trajectory points defined as follows $$\widetilde{P_2}=\left\{p_i\in R^3|p_i=\widetilde{z_{d\mathrm{,2}}}\left(t_i\right),i=\mathrm{0,}\dots ,N_t\right\},$$

where the time steps t _i are evenly distributed over the time period that describes the transition between the start and destination locations. The time steps t _i are thus determined by $t_i=i\Delta t\text{with}\Delta t=\frac{\text{max}\left\{T_{\gamma },T_{tr},T_Z\right\}}{N_t}$

where T _γ , T _tr , T _Z is the transition time in each coordinate of $\widetilde{z_{d\mathrm{,2}}}$

The application of the trajectory algorithm to $\tilde{{\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="DE102023110203A1\_0062.png,DE102023110203A1\_0066.png"\; state="\{\{state\}\}">P</figure-callout>}}_2}$

delivers $\widetilde{z_{d\mathrm{,2}}^{*}}$

and thus the target state trajectory $\widetilde{x_{d\mathrm{,2}}}$

and the forward control input $\widetilde{u_{FF\mathrm{,2}}}$

after using the flat parameterizations.

To validate the regression model (11) using experimental data and to investigate the performance of the presented approaches for error compensation, a real Liebherr 154 EC-H Litronic 6 tower crane was used, as in 1 shown, a payload with a weight of 1000 kg is moved from a starting point to a destination point in the working area of the tower crane 1. The starting and destination points are given by $${\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="DE102023110203A1\_0062.png"\; state="\{\{state\}\}">p</figure-callout>}}_1={\left[202°\mathrm{,24.5}\text{m}\text{,16m}\right]}^T,p_{105}={\left[29°\mathrm{,34}m\mathrm{,17}m\right]}^T.$$

The path planning algorithm calculates path points between the start and destination locations, taking into account that the payload must not be moved through restricted areas in the tower crane's working area, and minimizes the total path length. The resulting path points consist of 105 points, which are divided into 5 are shown.

It should be noted that there is a vertical transition of 1 m between the last two points p ₁₀₄ and p _105. The desired hook path z _d is calculated using the trajectory algorithm. The trajectory follower of the tower crane is used for path tracking and dampens the swaying of the payload.

The training data can be obtained by performing several benchmark payload transitions preferably at the edge of the tower crane's working area. The features (10) and the trajectory tracking error (4) are recorded while a GNSS sensor is attached to the hook 7 of the tower crane 1. The georeferenced position of the GNSS sensor is determined using real-time kinematics that achieves an accuracy of up to 2 cm.

The benchmark transitions consist of a transition in the swivel direction, a transition in the radial direction, a combination of a swivel and a radial transition and a combination of a swivel, a radial and a vertical transition. The target hook position of all benchmark transitions is in 6 highlighted in red. Looking at the training data as a whole, points 1 to 6 are only run through for two different rope lengths and transported payloads of 0 t and 2.25 t. The latter is the maximum payload that can be lifted with the test crane at a trolley position of 35 m.

7 shows the error predicted by the regression model (11) and the error e reconstructed from the measured data.

During t ∈ [70,215] the boom bends in the horizontal direction against the slewing direction, so that Δγ _e increases. The error Δx _tr,e becomes negative at the beginning of the automated load lift because the radial target hook position becomes smaller than the actual radial hook position. This is caused by an incorrect determination of the actual hook position by the sensor evaluation of the tower crane, since the sensor evaluation of the slewing angle in the radial direction has a smaller value than the actual one.

During the slewing movement, Δx _tr,e remains constant, which means that the position of the trolley 5 is shifted. If the trolley 5 is moved away from the tower 2, the same sensor evaluation error occurs as when the trolley 5 moves towards the tower 2. Since the direction of movement is changed, Δ _xtr,e becomes even larger at t ≈ 215s.

The vertical error ΔZ _e is dominated by the static bending of the boom 3 and the stretching of the crane rope. For wide-reaching trolley positions, the bending moment acting on the boom 3 is larger, which is why the payload hangs lower and the error thus increases. Since the scenario is terminated by lowering the payload by 1 m, the target height becomes smaller. Since the hoist drive is moved with a short delay, the target height is equal to the real height and causes ΔZ _e = 0 for a short period of time of about t ≈ 303s.

The mean absolute errors (MAEs) between the regression model result and the measured error are given by MAE _γ = 0.24°, MAE _tr = 5.4cm, and MAE _Z = 3cm. All MAEs are influenced by the measurement accuracy of the GNSS sensors, which is about 2 cm in the best case. Since the MAEs have almost the same values as the measurement accuracy, the prediction by the regression model works impressively well. The rest of the MAEs result from only including measurements for different transitions and different payloads or random disturbances such as wind or the bearing play of the rotary drive.

(gestrichelt) und die GNSS-Position des Kranhakens (durchgezogen), die während der Verfolgung des gewünschten Hubpfads (grün) und während der Verfolgung des durch den ersten (blau) und zweiten (rot) obengenannten Ansatzes Annäherung korrigierten Hubpfads gemessen wurde. Das Zeitraster für die Bestimmung der Ausgleichsbahn durch die zweite Annäherung z_d,2 wird berechnet mit N_t = 105. 8 shows the desired stroke path z _d (black), the corrected stroke paths $\widetilde{z_{d\mathrm{,1}}},\widetilde{z_{d\mathrm{,2}}}$

(dashed) and the GNSS position of the crane hook (solid) measured during the tracking of the desired lifting path (green) and during the tracking of the lifting path corrected by the first (blue) and second (red) approach mentioned above. The time grid for the determination of the compensation trajectory by the second approach z _d,2 is calculated with N _t = 105.

It can be observed that the height of the dashed compensation trajectories increases the more the trolley is from the tower. This is important because the bending deviation of the tower and boom is greater the further the trolley is from the tower. Therefore, the green line drops while the solid red and blue lines remain in the same horizontal plane. The bending in the vertical direction is not completely eliminated because there is an offset between the black and the solid blue and red lines, respectively. This offset is in the range of the MAE determined in the previous subsection and is also justified by the negatively affected measurement accuracy of the GNSS sensors. The results also show that the accuracy of the GNSS sensors used is significantly disturbed by the metal structure of the crane: although Real Time Kinematic is used, large peaks in the solid green, red and blue lines occur in the middle and at the end of the slewing operation.

In 9 the components of the trajectory error are shown. It should be noted that the correction of the individual trajectory points leads to a different transition time between the individual trajectory point pairs. Thus, the overall path obtained by approaches 1 and 2 has a different transition time than the original black path. To evaluate the trajectory tracking error, the components Δγ _e , Δx _tr,e, and ΔZ _e are determined by formulating the vector that connects each GNSS measurement with the closest point on the desired path in polar coordinates. Consequently, the errors Δγ _e and Δx _tr,e are zero during t ∈ [83,187] and t ∈ [20,66], and t ∈ [211,294], respectively, because the components are determined by the nearest point on the desired lift path that has the same swing angle or the same chassis position.

The errors Δγ _e and Δx _tr,e are already small due to the good performance of the tracking controller and are also dominated by unexpected disturbances that lead to only a small improvement in the results. These disturbances include wind gusts, a permanent vibration when moving the payload and bearing play. During the long rotation in the time interval t ∈ [70,210], the offset in the landing gear position Δx _tr,e is eliminated by both approaches.

The trajectory error resulting from following the compensation trajectory generated with the second approach gives relatively large peaks at the end of the long curve at t ≈ 190s and after lowering the payload at t ≈ 295s. These peaks are caused by the application of the trajectory generation algorithm, which involves P ₂ introduction of spheres with a radius of 1 m. Due to the spheres, the hook performs the transitions earlier than the desired trajectory. Compensation with both approaches is most worthwhile in terms of the error ΔZ _e in the vertical direction. The uncompensated error in the considered example increases with more extended trolley positions and shows an average error of 22cm in ΔZ _e , while compensation keeps the error almost zero during the entire transition and reduces the average trajectory error in ΔZ _e to 4.3 cm and 5.1 cm, respectively.

für die Kompensation stattdessen $\widetilde{z_{d\mathrm{,1}}}$

gering ist. Die MAE wird beim betrachteten Beispiel von 24cm auf 9cm bzw. 12cm reduziert, was einer durchschnittlichen Fehlerreduktion von 50% entspricht. Beide Kompensationsansätze sind besonders geeignet, um die Positioniergenauigkeit des Turmdrehkrans zu erhöhen, indem Offsets und Abweichungen durch Biegung eliminiert werden. Die MAE an der Zielposition des vorgestellten Experiments wird von 44 cm auf 10 cm und 5 cm reduziert.Overall, the presented compensation works well in the vertical direction and improves the tracking performance in the horizontal direction mainly by eliminating offsets. the advantage of using the corrected stroke path $\widetilde{z_{d\mathrm{,2}}}$

for compensation instead $\widetilde{z_{d\mathrm{,1}}}$

is low. The MAE is reduced from 24 cm to 9 cm and 12 cm in the example considered, which corresponds to an average error reduction of 50%. Both compensation approaches are particularly suitable for increasing the positioning accuracy of the tower crane by eliminating offsets and deviations due to bending. The MAE at the target position of the experiment presented is reduced from 44 cm to 10 cm and 5 cm.

QUOTES INCLUDED IN THE DESCRIPTION

This list of documents listed by the applicant was generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA accepts no liability for any errors or omissions.

Cited patent literature

• EP 3784616 A1 [0009]

Claims (14)

Method for automated positioning and/or automated movement of the load-handling device (7) of a crane (1), in particular the load hook of a tower crane, with the following steps: in a calibration phase: - collecting training data that characterize positioning errors of the load hook (7) in different areas of the crane's working area and at different lifting loads on the load-handling device (7), by means of the following steps: ◯ approaching different target positions and/or traveling different target paths of the load-handling device (7) by controlling the drives of the crane (1) by a crane control, ◯ recording the actual positions actually approached and/or the actual path traveled by the load-handling device (7) by means of a position detection device in absolute coordinates, - determining a crane model that describes the positioning errors of the crane over its working area for different lifting loads, by regression of the collected training data, in a compensation and/or working operation phase: - detecting a lifting load picked up and/or to be picked up on the load-handling device (7), - correcting the target position and/or the target path of an automated load lift based on the specific crane model depending on the detected lifting load, and - controlling the drives of the crane by the crane control based on the corrected target position and/or the corrected target path. Method according to the preceding claim, wherein when collecting the training data in the calibration phase, the actual positions and/or the actual path are recorded in absolute coordinates in real time and load handling device positions are recorded in crane coordinates. Method according to one of the preceding claims, wherein the position detection device operating in absolute coordinates is only used in the calibration phase and in the working operation phase with automated load lifts the crane (1) is operated without said position detection device operating in absolute coordinates. Method according to one of the preceding claims, wherein in the calibration phase operating parameters of the crane drives including setting positions and/or setting speeds and/or target positions in crane coordinates are recorded as training data. Method according to one of the preceding claims, wherein in the calibration phase, sensor and/or control command data of a pendulum damping system of the crane including the positions (q _dr ) and the speeds $\left({\dot{q}}_{dr}\right)$

the drive systems of the crane (1), the payload measured by the load sensor (m _pl ), control commands of the crane control, the square and cubic trolley positions $\left(x_{tr}^2\right)$

and $\left(x_{tr}^3\right)$

and the approximate payload fluctuation distances (l _r ϕ _x ) and (l _r ϕ _y ). Method according to one of the preceding claims, wherein when determining the crane model by regression of the training data, a linear regression with non-linear basis functions is carried out. Method according to one of the preceding claims, wherein when determining the crane model by regression of the training data, position data $\left(x_{tr}^2\right)$

and $\left(x_{tr}^3\right)$

a trolley (5) of the crane (1) in second power and/or third power. Method according to one of the preceding claims, wherein in the regression of the training data the number of independent variables is reduced and a subgroup of variables is selected for the crane model, in particular a Least Absolute Shrinkage and Selection Operator (LASSO) is applied. Method according to one of the preceding claims, wherein the actual positions and/or the actual path of the load-carrying means (7) are recorded in absolute coordinates by means of at least one GNSS sensor and/or a tachymeter system and/or a local ultra-wideband tag system. Method according to one of the preceding claims, wherein the calibration phase is carried out on the construction site at which the operational phase is also carried out. Method according to one of the Claims 1 - 9 , wherein the calibration phase is carried out on a test site and the working operation phase is carried out with automated load lifts on a construction site different from the test site, wherein in the calibration phase on the test site a reference location is determined and the crane model is related to it and the installation location of the crane (1) in the construction site for the working operation phase is selected depending on the said reference point and a reference point of the georeferenced construction site coordinate system. Crane, in particular a tower crane, with a boom (3) which can be pivoted about an upright axis (4), and a hoist cable (9) which runs from the boom (3), carries a load-carrying device (7) such as a load hook and can be lowered and raised by a hoist, and an electronic crane control for controlling the drives of the crane, in particular a slewing gear, a trolley drive and a hoist, characterized in that the crane control has a calibration module and a compensation module, wherein the calibration module is designed, in a calibration phase: - collecting training data which characterize positioning errors of the load hook (7) in different areas of the working area of the crane and at different lifting loads on the load-carrying device (7), by means of the following steps: ◯ moving to different target positions and/or traveling along different target paths of the load-carrying device (7) by controlling the drives of the crane (1) by a crane control, ◯ Collecting position data of the actual positions actually approached and/or the actual path traveled by the load handling device (7), provided by a position detection device in absolute coordinates, - determining a crane model which describes the positioning errors of the crane over its working range for different lifting loads, by regression of the collected training data, and said compensation module is designed to carry out the following in a working operation phase: - detecting a lifting load picked up and/or to be picked up on the load handling device (7), - correcting the desired target position and/or the desired path of an automated load lift based on the determined crane model depending on the detected lifting load, and - controlling the drives of the crane by the crane control based on the corrected desired target position and/or the corrected desired target path. Method for correcting position errors and/or deviations in the path of a load-handling device (7) of a crane in georeferenced coordinates of a construction site, with the following steps: - Collecting training data that characterize positioning errors of the load hook (7) in different areas of the crane's working area and at different lifting loads on the load-handling device (7), by means of the following steps: ◯ Approaching different target positions and/or traveling different target paths of the load-handling device (7) by controlling the drives of the crane (1) by a crane control, ◯ Recording the actual positions actually approached and/or the actual path of the load-handling device (7) traveled by means of a position detection device in absolute coordinates, - Determining a crane model that calculates the positioning errors of the crane over its working area for different lifting loads, including for sections of the working area in which no target positions and/or target paths were approached, describes, by regression of the collected training data. System for correcting position errors and/or deviations of the path of a load-handling device (7) of a crane (1) in georeferenced coordinates of a construction site, comprising a calibration module and a compensation module, wherein the calibration module is designed to: - collect training data that characterize positioning errors of the load hook (7) in different areas of the working range of the crane and at different lifting loads on the load-handling device (7), by means of the following steps: ◯ approaching different target positions and/or traveling different target paths of the load-handling device (7) by controlling the drives of the crane (1) by a crane control, ◯ detecting the actual positions actually approached and/or the actual path traveled by the load-handling device (7) by means of a position detection device in absolute coordinates, - determining a crane model that describes the positioning errors of the crane over its working range for different lifting loads, by regression of the collected training data, and said compensation module is designed to: - detecting a lifting load picked up and/or to be picked up on the load handling device (7), - correcting the desired target position and/or the desired path of an automated load lift based on the specific crane model depending on the detected lifting load.

Images