A study to compare trajectory generation algorithms for automatic bucket filling in wheel loaders

Reno Filla1, Martin Obermayr2, Bobbie Frank1, 3

1Volvo Construction Equipment, Emerging Technologies, 631 85 Eskilstuna, Sweden 2Fraunhofer ITWM, Fraunhofer Platz 1, 67663 Kaiserslautern, Germany

3Lund University, Faculty of Engineering, 221 00 Lund, Sweden

Abstract. In this paper we study how automatic bucket filling can be realised in wheel loaders. Based on observations of how experienced operators use their machines in bucket applications, four algorithms for parametric generation of bucket trajectories are investigated. The algorithms have been developed and tuned using a simplistic static integration-based approach. The Discrete Element Method is used to validate the predictive capability of the aforementioned algorithms. Results and limitations of the simplistic approach in comparison to the numerical results, as well as specific simulation-related challenges and findings are reported and discussed.

1 Introduction

Wheel loaders are highly versatile machines and need to fulfil complex design re-quirements, which are often interconnected and sometimes contradictory. Leaving aspects such as total cost of ownership, availability, legislation compliance, etc. aside, the most important machine properties during operation are productivity, fuel/energy efficiency, and operability. The challenge for the OEM is to find the perfect balance and to design machines with a natural, intuitive and workload-minimising way to op-erate them with highest possible energy efficiency at a productivity level as high as required. To achieve this goal, the operator can be actively or passively guided in controlling the machine or assisted by (partly) automated functions.

2 Short loading cycle and bucket filling

For wheel loaders, the short loading cycle, sometimes also dubbed V-cycle or Y-cycle for its characteristic driving pattern (Fig. 1), is highly representative of the majority of applications. Typical for this cycle is bucket loading of some kind of granular material (e.g. gravel, sand, or wood chips) on an adjacent load receiver (e.g. a dump truck, conveyor belt, or stone crusher) within a rather tight time frame of 25-35 seconds [1], in extreme situations even faster than that.

Fig. 1 Short loading cycle: phases and extension from V- to Y-cycle [1].

Such a short loading cycle represents several interesting challenges for the design

engineer: not only is the momentary power distribution between parallel subsystems hydraulics and drive train to be balanced in order to minimise losses, but also a bal-ance between the subsystems’ capacities in terms of forces and speeds needs to be achieved [2].

However, the human operator and its influence on overall productivity and energy efficiency must not be neglected. As mentioned previously, operability of the machine needs to be taken into account. Giving assistance to the operator in order to maximise productivity and/or energy efficiency is an increasingly utilised approach in the indus-try.

One opportunity in a bucket loading application as depicted in Fig. 1 lies in ques-tioning whether the classical V- or Y-cycle actually is the best choice or if the driving pattern itself can be optimised [3]. The focus would be on the tactical and strategical aspects of wheel loader operation.

However the main opportunity lies in operator assistance systems that help in the operational aspects of wheel loader use. The conclusion of a large study with 80 par-ticipants [4] is that even experienced operators would benefit from such assistance. Digging deeper into this matter (pun intended), it is found that assistance in bucket filling offers great potential. In Fig. 2 most of each operator’s deviation from baseline in terms of fuel consumption is accounted for in the bucket filling phase.

Fig. 2 Fuel consumed in a complete loading cycle vs. only bucket filling phase (each operators’

best result, baseline is operator with best result on average over several cycles) [4].

This means that additional fuel consumption in comparison to the overall best re-

sult often occurs during bucket filling. Fig. 2 provides compelling evidence, which, however, should not come as a large surprise considering the rate of fuel consumption during a short loading cycle is highest during the bucket filling phase. According to Fig. 3 the fuel consumption rate (expressed in volume or mass per time unit) is ap-proximately 60% higher during bucket filling than the cycle average. Expressed in absolute values, bucket filling accounts for 35-40% of the total fuel consumption per cycle, yet the time spent on filling the bucket is only 25% of the cycle time [5].

Fig. 3 Fuel consumption during short loading cycle [5].

The higher fuel consumption rate during bucket filling warrants a closer look at

this phase. The inner loop in Fig. 4 shows how the human operator interacts with the wheel loader. In order to fill the bucket, the operator needs to control three motions simultaneously: a forward motion that also exerts a force (traction), an upward motion (lift) and a rotating motion of the bucket to load as much material as possible (tilt). This is similar to how a simple manual shovel is used. However, in contrast to a man-ual shovel, the operator of a wheel loader can only observe, and cannot directly con-trol these three motions. Instead, he or she has to use different subsystems of the ma-chine to accomplish the task. The accelerator pedal controls engine speed, while the lift and tilt levers control valves in the hydraulics system that ultimately control movement of the linkage’s lift and tilt cylinder, respectively.

Fig. 4 Simplified power transfer and control scheme of a wheel loader [2].

The difficulty lies in that no operator control directly affects only one single mo-

tion. The accelerator pedal controls engine speed, which affects both the machine’s longitudinal motion and via the hydraulic pumps also affects the speeds of the lift and tilt cylinders. The linkage between the hydraulic cylinders and the bucket acts as a non-linear planar transmission and due to its design a lift movement will also change the bucket’s tilt angle and a tilt movement affects the bucket edge’s height above the ground.

Furthermore, Fig. 4 also shows how in the outer loop the primary power from the diesel engine is split up between hydraulics and drive train in order to create lift/tilt movements of the bucket and traction of the wheels, but is connected again when filling the bucket from for example a gravel pile. In this situation, shown in Fig. 5, the traction force from the drive train, acting between wheels and ground, creates a reac-tion force between gravel pile and bucket edge, which in turn creates a moment of forces around the loading arm’s centre of rotation that counteracts the moment of forces created by the push of the lift cylinder.

In effect, the traction force, indirectly controlled by the operator through the en-gine speed, reduces the available lifting force. Depending on lifting height and applied traction force, as well as performance envelope of the machine’s subsystems, the lift-ing force can be completely cancelled out, and the bucket cannot be moved upwards any further. The operator then has to either apply the tilt function or reduce the trac-tion force by reducing the engine speed – which is rather counter-intuitive as a com-

mon mental model of vehicle drivers is that an increase in accelerator pedal deflection leads to more torque from the engine until any external resistance can be overcome.

Fig. 5 Force balance during bucket filling [2].

In conclusion, filling the bucket of a wheel loader is a non-trivial task and the

overall energy efficiency of a complete short loading cycle is highly affected by how efficient the operator can perform bucket filling. It is therefore of great interest to study ways of assisting the operator in this task. As previously mentioned, such assis-tance can be rendered in form of active or passive guiding in controlling the machine or by means of (partly) automated functions. In this paper we focus on the latter and study possible bucket trajectories as part of a bucket filling automation.

3 Method

In this study we developed four different principle trajectories along which the bucket is controlled to move in a DEM simulation. Each principle bucket trajectory is the result of interviews with experienced wheel loader operators and represents a different bucket filling strategy commonly employed. The results of the particle simulations are used to compare simulated bucket fill factors with a priori estimations.

Apart from desired bucket fill factor most principle trajectories offer at least one parameter that is used to vary the individual shape. The bucket trajectories are gener-ated in MathCad using a kinematic model of the wheel loader’s front body, complete with linkage, hydraulic cylinders, bucket, and front axle. Controlling the bucket mo-tion indirectly through cylinder displacements and forward motion of the machine ensures that only valid bucket positions are prescribed. This will be explained in detail in the next section.

The particle simulations, utilising the DEM code Pasimodo, are described in detail in section 5. Postprocessing of the simulation results, mostly covering recalculating the forces acting on the bucket into cylinder forces and calculating machine stability is

done in MathCad. Data transfer between both programs is done sequentially using text files, i.e. no concurrent calculations or co-simulations are performed.

4 Trajectory generation

In this section the focus is on the problem of prescribing the nominal motion of the bucket, independent of any resistive forces that might interfere with the actual control.

4.1 Literature research

There are a great many publications, both academic papers and industrial patents (or patent applications) on the topic of bucket automation and autonomous excavation. The material referenced in this sector, restricted to front loaders (wheel loaders, LHD machines and the like) is only an excerpt. A brief history of autonomous excavation with references to important publications and a list of challenges to overcome can be found in [6], published by Hemami and Hassani.

In an early work Hemami studies bucket trajectories in order to minimise energy consumption in the scooping and loading process [7]. He concentrates on the motion pattern itself and does not consider resistive forces in this paper. One of his conclu-sions is that simply estimating of the amount of loaded material as the area between the trajectory and the contour of the material will lead to deviations that need to be corrected by an experimentally determined factor. We use the same estimation in our study but determine the correction factor using a DEM simulation, instead.

Based on information from personal interviews with professional operators, litera-ture study, and statistical analysis of full-scale experiments, Wu reflects thoroughly upon the loading cycle and a human operator’s techniques and strategies [8]. The controller developed by Wu creates an ideal trajectory in advance (basically the same shape as Hemami), based on bucket volume, workspace, and rock pile parameters. During digging, this trajectory is roughly followed, but adjustments are made to ma-chine speed and bucket position. Wu recognises that different material properties require variations in the scooping strategy, and identifies three usable strategies, la-belled as “easy-scoop”, “normal-scoop”, and “hard-scoop”. In the latter small oscilla-tions in bucket tilt angle are implemented, while in the former the bucket is tilted backwards faster than in “normal-scoop” and without any oscillation.

The basic strategies of Wu are re-examined, improved upon, and implemented by Almqvist in [9]. Here the basic bucket trajectory is modified to be a polygon (called “J-curve”) with further improvements identified and implemented as “chic-chic” (ba-sically the oscillations Wu describes) and “aggression”. The latter imitates an experi-enced operator who finalises the bucket filling phase by flipping the loaded material from the cutting edge into the centre of the bucket. This is achieved by briefly and distinctly activating the tilt function, possibly in combination with a longitudinal jerk. With this manoeuvre the operator minimises the amount of material dropped from the bucket during the following transport phase.

A rudimentary control law has been published in 2006 by Kanai, Sarata and Ku-risu [10]: They advance the bucket in longitudinal direction until the reaction force reaches a threshold, then start lifting and if the reaction force does not decrease then

they also use the tilt function simultaneously. When a pre-defined height is reached the bucket is lifted straight up and out of the material.

Previous to the above reference, in early 2005 a similar algorithm, but with several additional control laws, was published by Filla, Ericsson and Palmberg in [11].

4.2 Type A: “Slicing cheese”

This type is a (perhaps impossibly) faithful implementation of a bucket filling strategy advocated by several professional machine instructors who were interviewed previous to our study. Their advice was to move the bucket such as if carving a slice of constant thickness off the material pile.

Fig. 6 Example trajectory acc. to type A, optimised for exit height at 2m and fill factor 1.14

In the diagram to the left in Fig. 6 we see the trace of the bucket tip moving at a

constant distance to the slope until a height of about 2.5m (corresponding to the hinge pin of the bucket being at 2m), at which point the bucket is fully tilted back. How this is accomplished can be seen in the middle and right diagram in Fig. 6: the bucket is constantly lifted from initial height to exit height (both set a priori), while at the same time being tilted back proportionally from initial angle (zero) to maximum angle (which is the slope angle of the material pile, because once the bucket is parallel with the slope, no further advancement can be made without the bucket’s bottom pushing into the material, which creates a large reaction force). After stopping at exit height the bucket is just tilted back and retracted. The forward motion of the complete ma-chine is controlled so that the bucket tip is always at a constant distance to the pile’s slope.

The exit height can be chosen freely; while the slice thickness is a result of the tar-geted fill factor and thus subject to parameter optimisation (i.e. an optimisation is performed to find the value that fulfils the target fill factor).

4.3 Type B: “Just in & out”

This simple algorithm mimics the bucket filling style of operators who rely mostly on initial rim pull (traction force) to fill the bucket. They basically just push the bucket into the pile, then tilt back and leave. No further advancement is made after the initial penetration of the material pile.

Fig. 7 Example trajectory acc. to type B, optimised for fill factor 0.94

In the diagram to the left in Fig. 7 we see the trace of the bucket tip accomplished

purely by the motions of the hydraulic cylinders without any further longitudinal mo-tion after initial penetration of the pile, as exhibited in the right diagram. The diagram in the middle discloses that in order to accomplish the targeted fill factor, the bucket’s hinge pin height also needed to be increased slightly (though not much) by using the lift function simultaneously with the tilt function that controls bucket angle.

This trajectory type offers no additional parameter since the initial penetration is a result of the targeted fill factor and thus subject to parameter optimisation.

4.4 Type C: “Parametric parabola”

This algorithm can be parameterised to generate trajectories of seemingly different shapes. The control in this algorithm is similar to type A, but instead of following a line with constant distance parallel to the slope, the bucket tip is controlled to follow a quadratic curve, i.e. a 2nd order polynomial. The parabola is controlled through a shape-influencing parameter (which has been chosen to be the height of that point on the trajectory that corresponds to the highest penetration depth counted from the slope surface).

Fig. 8 Example trajectory acc. to type C, optimised for exit height 0.55m and fill factor 1.05

In the diagram to the left in Fig. 8 we see the trace of the bucket tip moving on a

quadratic curve in relation to the slope until a height of about 1.1m (corresponding to hinge pin height of 0.55m) at which point the bucket is fully tilted back. This is ac-complished in a similar fashion as for type A, as can be seen in the middle and right

diagram in Fig. 8 – however this time the forward motion is controlled so that the bucket tip is always at that distance to the pile’s slope which is prescribed by the quadratic curve.

The exit height and the control point height where the maximum penetration depth counted from the slope is achieved can be chosen freely, while the maximum penetra-tion itself is a result of the targeted fill factor and thus subject to parameter optimisa-tion.

4.5 Type D: “Stairway”

This type is reminiscent of the approach described in [9, 11], however the important difference that the trajectory is composed of an adjustable, pre-defined number of steps, like a stairway. Within each step the wheel loader stands still and only the hy-draulic functions lift and tilt are executed. A new step is inserted by advancing ma-chine and bucket forward using the drive train.

Fig. 9 Example trajectory acc. to type D, optimised for two steps and fill factor 0.94

In the diagram to the left in Fig. 9 we see that this particular stairway consists of

two stairs after initial penetration. In between the steps the bucket is constantly lifted and tilted. During forward advancement the bucket height and angle also need to be controlled in order to avoid pressing the bucket’s bottom against the material. At the end of the sequence the bucket is tilted back fully and then retracted from the pile.

In this algorithm the number of stairs can be chosen freely, together with a depre-ciation factor that controls the subsequent advancements in relation to the initial pene-tration (a depreciation of 0.5 means that the depth of each subsequent penetration is only half of the previous one). The initial penetration depth itself and the bucket exit height are the result of parameter optimisation to achieve the targeted fill factor.

5 Particle simulation

The Discrete Element Method (DEM) has already shown its capability to model the soil-tool interaction for cohesionless soil [12]. Compared to the analytical algorithms for the prediction of bucket fill and draft forces, the DEM naturally captures complex effects, such as material outflow from the bucket and compaction of soil underneath the bucket.

5.1 Discrete element model for cohesionless soil

Only spherical particles are used in this study. The angle of internal friction that can be achieved by the DEM is limited in this case to very low values due to excessive rolling of the particles. At the same time, the friction coefficient has a limited effect on the macroscopic shear resistance [13]. This situation can be improved by using non-spherical particles, compounds of two or more spheres [14, 15, 16] or by introducing more complex contact laws including an additional rolling resistance with an elastic limit [12, 17, 18]. Another, more radical, approach is to completely lock particle rota-tions. It is shown in [12] that with this simplification one can still predict realistic draft forces for cohesionless soil. An advantage of the non-rotational model is the reduced numerical effort compared to the rotational model.

Normal contact: In case of spherical particles, the overlap δ between contacting

particles can be directly computed from their positions xi and radii ri and a repulsive contact force is calculated in case of δ > 0. At the angle normal to the contact surface, a linear spring and dashpot model is applied

N N NF k dδ δ= + (1)

with the normal stiffness kN = π/2 Er and the damping coefficient dN . In this formula-tion, the Young’s modulus E of an imaginary rod with radius r = (r1 + r2)/2 between the particle centres is the free parameter, see also [19]. In [20] it is shown, that this yields a scale independent model, which facilitates the practical usage.

Coulomb friction: As soon as two particles get in contact for the first time, the contact points on both particles, measured in their particle coordinate systems, are stored. If the contact points undergo a relative displacement, the contact points do not coincide any more in the successive simulation steps. In order to measure the tangen-tial deformation, in every simulation step the contact points are transformed into the global coordinate system and the connecting vector of these two points xC,i, i.e.

,2 ,1ˆ = −T C Cx xξ (2)

is projected onto the tangential plane to get the tangential deformation vector ξT. The tangential force is then computed from

T T T T T= -k - kf ξ ξ (3)

with the tangential stiffness kT being a constant in this model, the tangential damping coefficient dT. If the tangential force exceeds the limit FT=µFN , where µ is the local friction coefficient, slipping friction occurs. This is accounted for by resetting the tangential spring to

* N T

T T

μF=kT

ξξξ

(4)

and updating the contact points accordingly, see [12] for more details. While it is absolutely necessary for the simulation of slow or quasi-static granular matter to ac-count for static friction, it is not so important to have different coefficients for static and dynamic friction.

5.2 Model and simulation setup

The discrete element model consists of about 16000 spherical and non-rotational par-ticles of diameters ranging from 8 to 12cm. A 5m high pile is modelled as a particle layer of 4m thickness over a solid inclined surface, as shown in Fig. 10. This setup avoids placing particles in areas of the model that would never get in contact with the bucket, which improves simulation speed.

Fig. 10 Initial configuration of particles into the shape of a gravel pile.

Furthermore, the model consists only of a 1m wide slice of material. This is re-

ferred to as 2.5–dimensional model. Comparison with a 5m wide, fully 3-dimensional, model has shown that forces are almost unchanged due to this simplification. Even with these modifications the computational costs are fairly high, as simulation of about 10 seconds real time takes about 15 hours on a single core.

In this paper, we do not study specific gravel, but use properties of a typical bulk material. The parameters of the discrete element model are summarised in Table 1.

Table 1 DEM simulation parameters

parameter value particle radii r=4…6 cm Young’s modulus E=40 MPa tangential stiffness kT=4·106 N/m friction coefficient µ=0.32 soil-tool friction µext=0.32 porosity N=0.48 bulk density ρb=1.65 t/m³ angle of internal friction φ=41°

An interesting finding from early simulation runs is that the bucket should not en-

ter the pile at the very bottom, since this can cause single particles to get caught un-derneath, between the bucket and the ground, resulting in unrealistically high vertical forces. To prevent this, ground and pile were lowered 0.3m relative to the bucket, so that even at “bottom position” there are always about three layers of particles between cutting edge and the ground.

The time step size is selected such that the particle simulation is stable. Once sta-bility is achieved, the forces do not change significantly if the time step size is further reduced. At the upper limit of the step size, sometimes individual particles are already beyond the stable limit and pop off the simulation domain (so-called “popcorn ef-fect”).

The bucket is 2.5m wide and as previously mentioned the simulation contains a slice of only 1m. It turned out that to transfer forces from the 2.5-dimensional model to the 3-dimensional model, a correction factor of 2.3 is best suited, instead of 2.5 as expected from the geometry. This is due to material that flows out of the bucket at both sides. This indicates that the simulation is not perfectly described by the 2.5-dimensional model.

5.3 Procedure

The aim of this study is to compare theoretical bucket fill factors to results from parti-cle simulations. Each trajectory type has been simulated varying each adjustable pa-rameter, each combination then with the estimated bucket fill factor varied in three steps: 0.85, 0.95 and 1.05 (which, for example, for type C resulted in 27 simulations because of two adjustable parameters, each varied in three steps).

The bucket fill factor achieved is determined as the ratio of the loaded mass to the rated mass of the bucket, the former obtained through the vertical force that is re-quired to balance the bucket after complete retraction from the pile.

Simply estimating the amount of material loaded into the bucket as the area be-tween the trajectory of the bucket tip and the contour of the material pile will lead to deviations, as already observed by Hemami [7]. Dividing the simulated bucket fill factors with the respective estimation will give a correction factor for each case. How-ever, the goal for an automatic bucket filling algorithm would be to generate a trajec-tory that leads to the originally targeted fill factor, not to conclude that the fill factor aimed for will be deviated from by a certain percentage. In other words, there is a need to compensate for the deviations. The obvious idea is to just multiply the correc-tion factor with the original target and aim for that higher target instead, hoping that the resulting deeper initial penetration will lead to the actually desired bucket fill fac-tor. We have found that this approach would require several iterations, as for such a pre-compensated trajectory the deviation, and therefore also the correction factor, will be different from the original one. The amount of iterations required varies, mainly dependent on the type of bucket trajectory.

Running small packages of DEM simulations followed up by manual interventions to setup new iterations has been deemed not efficient. In order to enable running large bulks of simulations uninterrupted by manual work we chose a different approach:

each trajectory has been simulated several times with various horizontal offsets (for example varied in steps between 0 and +300mm, in one case also including -100mm offset). Through interpolation using the simulated fill factors we determined which profile offset was required to reach the exact bucket fill factor that has been originally aimed for. Then, new trajectories were generated with the profile offset added to the initial penetration in the beginning of the filling sequence and verified in a final simu-lation.

6 Results and discussion

The sizeable number of particle simulations performed has given an amount of results that is too large to account for in detail, especially in a conference paper of limited length as this one. In any case, the exact offset values required for the various variants of the principle trajectories to meet the targeted bucket fill factors is of no greater concern to the reader, since these values will differ with bucket geometry, material properties, and others.

Instead, the main research contributions of this paper are to be found in the de-scription of the four algorithms for generating bucket trajectories that mimic the buck-et handling of human operators, in the introduction and investigation of the offset method for arriving at the desired bucket fill factor, as well as in the specific usage of the DEM particle simulations, their setup and findings from them.

6.1 Offset method

The approach of performing bulk simulations with a priori-determined trajectory off-sets, then interpolate to find a suitable offset for the desired bucket fill factor, and use this to generate a new trajectory, worked well. With this method we were able to find target-fulfilling trajectories for the principle types A, B, and C.

Fig. 11 Offset values (left) and error in correction factor (right) for trajectory type A

The diagram to the left in Fig. 11 shows the final offset values for trajectories of type A and their dependency on targeted bucket fill factor and exit height. The alterna-tive approach would have been an iterative process, in which the targeted fill factor is gradually adjusted by a correction factor, in essence pretending to aim for a complete-ly different value in order to reach the actually desired fill factor. The diagram to the right in Fig. 11 shows that the initial guess was underestimating the required value of the correction factor by 8%, as a correction factor of 1.59 would have been used ini-tially, while the correct value was 1.72 according to Table 2.

Table 2 Correction factors for trajectory type A

Exit height 1m 2m 3m

Target fill factor 0.85 0.95 1.05 0.85 0.95 1.05 0.85 0.95 1.05 Corr. factor, initial 1.37 1.37 1.35 1.51 1.48 1.54 1.55 1.58 1.59 Corr. factor, final 1.35 1.40 1.44 1.50 1.52 1.58 1.55 1.57 1.72 Error, init. to final 2% −2% −6% 1% −3% −2% 0% 1% −8%

Due to this deviation of the initial correction factor, determined using the results

from the first batch of simulations, from the final correction factor, this iterative pro-cess would have required several steps. With no possibility to calculate the final cor-rection factor in advance, using the iterative process would have resulted in an overall longer time for this study, as the simulations would have been made in several batches with (manual) adjustments in between, instead of bulk simulations as possible when using the offset method.

Naturally, the offset method would not be possible to implement in a real machine, instead the iterative approach has to be used. Our method of calculating the trajectory profile by optimisation, with the targeted bucket fill factor as one parameter, is well suited for implementation in reality. After each working cycle the next correction factor is calculated as the ratio of previously targeted fill factor and the previously achieved one, as measured by using the wheel loader’s load weighing system. We propose to adapt continuously to deviations in the bucket fill factor, as disturbances due to changing material properties and so on are to be expected.

While the offset method generally worked well in simulations, to our initial sur-prise the trajectories of type D needed further adjustment with a correction factor. The explanation lies in how these trajectories are generated: the previously described de-preciation factor that controls the advancement in between steps is applied to the sum of originally calculated initial penetration depth and the required offset. This means that in this case the profile of the adjusted trajectory is not just the original trajectory being offset by a constant value, but rather by a value that is depreciated with the same factor as the initial penetration depth. However, the DEM simulations used to deter-mine a matrix of offset values just move the original trajectory by a constant value. This mismatch between simulations with a priori-determined offsets and how the in-terpolated offset is used in generating a new trajectory explains why another adjust-ment using a correction factor was required for all trajectories of type D.

6.2 Observed phenomena from DEM particle simulations

Visualising the simulation results of the various trajectory variants in a rendered video has been found a very suitable approach to both debug models and algorithms, and to learn about various phenomena that occur during the filling.

Fig. 12 Snapshots from DEM particle simulation of trajectory type D.

Fig. 12 shows snapshots from a simulation with trajectory type D. At the begin-

ning, the bucket enters the pile horizontally. During the filling phase, a wedge of grav-el is moved together with the bucket. This is indicated by the velocity of the particles. When the bucket is tilted back, some material gets lost. It is difficult to predict the amount of material loss in advance without the help of a particle simulation.

In the theoretical approach, we estimate the bucket fill from the area that is formed between the bucket tip trajectory and the pile contour, starting and ending with respec-tive point of intersection. This approach assumes the pile to remain at rest and there-fore cannot account for material flow. In order to demonstrate the importance of mate-rial flow for the bucket filling, Fig. 13 and Fig. 14 show snapshots from trajectories types A and B plotted with a vector plot of the particle velocities.

Fig. 13 shows two snapshots from a simulation with trajectory type A, with a large exit height and high bucket fill factor. During the forward and lifting motion, the ma-terial moves together with the bucket. The shape of the pile is according to expecta-tions. The theoretical approach works very well in that phase, shown on the left in Fig. 13. However, when lifting the bucket out of the material and tilting back at the end of the trajectory, some material is lost (right in Fig. 13) due to the fact that the granular

material can only support a certain angle of repose. Excess particles flow back in an avalanche flow.

Fig. 13 Bucket filling using trajectory type A: particle velocities (arrows) during the lift motion

(left) and at final tilt (right). Brown: current shape of the pile, light blue: initial shape.

In the case of trajectory type B this effect is even more pronounced. Fig. 14 shows

a snapshot from a simulation with a large bucket fill factor. Two lines drawn on top of the plot indicate the material that flows underneath the bucket and forms a new angle of repose. This observed material loss has an impact on energy efficiency of the work-ing process, since the excess material has been pushed forward and lifted upwards by the bucket, requiring mechanical energy, but instead of keeping it in the bucket it flows back onto the pile. A way to prevent or at least minimise this loss of material would be to combine a forward motion together with tilt-in, however still adhering to the rule of not pushing the bucket’s bottom into the pile.

Fig. 14 Bucket filling using trajectory type B: particle flow (arrows). The two lines indicate the

material that flows underneath the bucket.

Fig. 15 shows that there is also a loss of material during bucket retraction: when

the filling of the bucket is finished, the wheel loader starts accelerating backwards to get out of the pile. In our simulations the acceleration is significantly higher than what is possible in reality, which means that the simulation exaggerates the magnitude of

this loss. In any case, the amount of material lost through outflow during bucket re-traction is difficult to predict by conventional means.

Fig. 15 Material loss during bucket retraction.

Fig. 15 also displays that the material does not flow fully into the bucket, but re-

mains near the cutting edge instead. It would be desirable to fill the bucket more even-ly, which human operators achieve by the “flipping movement”, i.e. by briefly and distinctly activating the tilt function, possibly in combination with a longitudinal jerk, as mentioned previously.

7 Conclusion and Outlook

Four principle methods to generate bucket trajectories have been shown and dis-cussed, all usable for the development of an automated bucket filling assistant.

A challenge in the generation of trajectories is that due to the complexity of the granular flow the desired bucket fill factor cannot be exactly met. For implementation in real machines we have proposed a continuously adaptive process that is run once per wheel loader working cycle. When simulation is used we have shown that a meth-od utilising pre-calculated offsets leads to valid results in a shorter time than the itera-tive process.

DEM particle simulations have been found a good method to study the complete bucket filling process over time. Examples have been given for dynamic effects that in a simulation can be easily recognised, but are difficult to assess through real-life tests. Such analyses are useful not only when developing new control algorithms, but also for optimisation of the bucket’s geometry or the design of the machine’s loading unit.

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