nating additional influences such as hydraulic or mechanic friction or other effects of the hydraulic power train. This makes it possible to evaluate specifically the.
Payload Estimation in Excavators Model-Based Evaluation and Comparison of Current Payload Estimation Systems Nureddin Bennett1 , Ashwin Walawalkar1 and Christian Schindler1 Lehrstuhl KIMA, Technische Universit¨at Kaiserslautern, Gottlieb-Daimler-Straße 42, 67663 Kaiserslautern
Abstract. The paper shows an investigation of the accuracy and reliability of industrially available payload estimation methods in construction machinery, specifically hydraulic excavators. “Payload” refers to the weight exerted at the operating end (bucket) of the working arm of an excavator due to the amount of material in the bucket. There are several challenges which make dynamic and accurate payload estimation a difficult task - the complex kinematics of the excavator, the complicated operations and movements of the arm, as well as the requirements on the robustness of the excavator operation etc. Current payload estimation systems are based on patent EP0736752A1 “W¨ageverfahren und Hubfahrzeug zur Durchf¨uhrung des Verfahrens” from 1995. This empirical method has three main inputs to the system, consisting of boom angle, arm angle and the pressure difference across the boom. Using these inputs, a characteristic matrix is generated by calibrating the system using several different position and load configurations. The dynamic effects such as mass inertia or centrifugal forces are partially or completely ignored in this method. It is therefore very sensitive to changes in measuring speed, accelerations during the measurement or changes in the relative center of gravity position of the payload. This paper examines and evaluates the functionality and performance of current payload estimation systems using a multi-body-simulation model of an excavator. Using this model-based approach, this investigation can be simplified by eliminating additional influences such as hydraulic or mechanic friction or other effects of the hydraulic power train. This makes it possible to evaluate specifically the influence of static and dynamic behavior of machine on the described method. Finally, based on the simulation results, possible improvements to the method are considered.
1
Introduction
Mobile excavators are one of the most important and flexible construction machines with diverse applications. Hydraulic excavators (henceforth referred to as simply ‘excavators’) are the most commonly used mobile construction machines where the required power is transmitted hydrostatically from high pressure oil cylinders and distributed to the individual members of the working attachment of the excavator [1]. Amongst the most common tasks performed by excavators are earth-moving and load-lifting operations. It is important to know the exact value of the digging forces exerted at the end of the excavator working attachment during such operations. Specifically, the value of
the mass of the payload in the bucket is useful in several important ways. For instance, transport trucks can always be loaded to their optimum capacity by (avoiding overloading or underloading) when the accurate mass of the material in the excavator bucket is known. Similarly, knowledge of payload is a crucial parameter in assessment of tip-over stability of the excavator, and accurate estimation of payload can lead to better stability assistant systems. However, accurate estimation of payload is a challenging task for several reasons, such as: 1. Complex kinematics: The excavator working attachment kinematics are quite complicated to determine. For a two-piece boom arrangement, the bucket has three degrees of freedom. 2. Center of gravity of payload: It is difficult to determine the position of the center of gravity (CG) of the payload. Moreover, it is also difficult to determine the CG of the various components of the working attachment itself. 3. Inertial parameters: The value of inertial forces and moments of the components of the working attachment needs to be known in real-time in order to estimate the payload dynamically. 4. Effect of friction: The effect of friction in the joints and in the hydraulic connections has a substantial influence on the accuracy of the payload estimation. But the exact nature of these non-linear frictional effects is complicated to assess. 5. Effect of joint tolerances: Tolerances withing the linkage joints vary throughout the excavator operational life and thus have an influence on the accuracy of a payload estimation method. 6. Robustness: Finally, any payload estimation method must be robust enough to adapt to the harsh working environment of the excavator which offers many external disturbances that interfere with the estimation process. The objective of this paper is an investigation of the functionality of commercially available payload estimation systems. The quality of the results given by this system will be discussed with respect to boundary conditions such as accuracy; reliability etc. and consequently it will be shown how sensitive this method is to the various external disturbances and internal parameter variations.
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State of the Art
Payload estimation is an active research area, especially payload estimation for construction machines in general [2], [3], [4], [5]. However, there is no research work that targets payload estimation specifically for the case of excavators. These aforementioned research works tackle the payload estimation problem from different approaches, such as estimation based on kinematic and dynamic modelling of the machine configuration [5], estimation based on a neural networks approach [4], [6], or on approaches based in the field of robotics and control [6], [7]. There are several commercial products available which offer payload estimation systems as well, such as those by Gritzke Lasertechnik OHG, Loadrite (Actronic Ltd.), VEI Payload Management Systems etc. Commercial solutions for payload estimation
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are largely based on the working principle as described in the patent EP0736752A1 [8], where an estimation for payload is generated using an empirical approach. The basic concept has largely remained unchanged as is evident in later patents for commercial products [9]. According to the methodology described in this patent, the payload estimation system is calibrated using two different, known payloads. For each payload, the excavator working attachment is moved through a pre-defined range of motion (refer figure 1). Dynamic effects or inertia are not considered, therefore, using constant speeds, dynamic effects are minimized. This motion is achieved by only varying the lower boom angle φ1 and arm angle φ3 from a certain minimum to maximum value with a constant angular speed. The upper boom angle φ2 and the bucket angle φ4 are not varied. During the motion of the excavator working attachment, the hydraulic pressure difference dP across the main cylinder is measured. The set of these three values (φ1 , φ3 , dP) over the range of the working attachment movement generates a set of points which is called the characteristic map (refer figure 2). Once the system is thus calibrated for two reference payloads, in order to determine any arbitrary payload, the three parameters (φ1 , φ3 , dP) are measured continuously during the motion of the working attachment. Comparing the actual measured values against the characteristic map from the calibration, an estimate for the actual payload is obtained using interpolation.
3
Influences on the accuracy of the payload estimation method
The accuracy of this payload estimation method is sensitive the numerous external disturbances as well as possible deviations from the many conditions under which calibra-
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tion/measurement needs to be performed. Important factors that affect the accuracy are as follows. 1. Acceleration of the excavator working attachment links: The payload estimation gives best results when the working attachment moves with constant angular velocity (constant φ˙1 , φ˙3 ) so that dynamic effects can be neglected. In fact, only the parameter φ˙1 is moved during the calibration. All other parameters are adjusted before the actual movement begins. Any deviation to this will cause minor or major errors. Moreover, since the angular motion of the links of the working attachment is controlled by the translational motion (stroke) of the hydraulic cylinders (refer figure 1), this is a difficult condition to achieve throughout the range of motion. 2. Velocity of the excavator working attachment links: During measurement of payload, if the angular velocity of the excavator working attachment links deviates from the velocity at which the system was calibrated, the accuracy of the payload estimation is adversely affected. 3. CG of payload: (a) The CG of the payload is assumed to be coincident with the CG of the bucket. This assumption does not hold true for all bucket filling conditions, and the payload CG shifts as more material is filled in the bucket. This adversely affects the accuracy of the payload estimation. (b) The CG of the payload also moves according to movement of the bucket. Ideally this motion is to be restricted (φ˙4 = 0), however, under real world conditions this bucket angle cannot be kept constant by the operator for all payload requirements. 4. Motion of the arm and/or the superstructure: It is necessary during the calibration as well as the actual measurement that the arm and the superstructure remain stationary. This might not always be the case under real-world conditions. Thus, the
velocity as well as the acceleration of these two components - since unaccounted for by the payload estimation method - has an undesirable effect on the its accuracy. 5. Friction and effect of manufacturing tolerances: Under real world working conditions, friction in the working attachment joints and hydraulic connections as well as the manufacturing tolerances in the kinematic linkages also influences the accuracy of the payload estimation. However it is the aim of this paper to investigate solely the functionality of the payload estimation algorithm in absence of external disturbances. 6. Inclination of superstructure: The stationary inclination of the excavator has an influence on the payload estimation. However, this factor is accounted for by the payload estimation method by considering the appropriate angular component of the gravity vector (projection onto the 2D plane of the kinematics of the working attachment). It is also important to note that during digging and material-transport operations, the excavator is usually stabilized on level ground with the help of the outriggers.
4 4.1
Modelling Multi-body model of the excavator
For the proposed investigation, a multi-body simulation (MBS) model of an actual mobile two-piece boom excavator was created in the MBS tool Simpack. Of relevance to this investigation is the model of the excavator working attachment, which is shown in figure 1. The working attachment is joined to the superstructure which is not shown here. The MBS model is composed of rigid bodies. The main components of the working attachment - the lower and upper boom, the arm and the bucket are rigid bodies connected to each other through revolute joints. The motion of the working attachment is achieved through the extension and retraction of the multiple piston-cylinder arrangements. The piston-cylinder bodies are mutually connected using a translational joint element. Each piston-cylinder arrangement is connected to the working attachment at both ends using a revolute joint element. In order to model the stiffness effect due to the hydraulic fluid inside the cylinder, a simplified approach was adopted using a spring force of very high stiffness between the piston and the cylinder. Finally, the payload is modelled as a rigid element connected to the bucket. 4.2
Mathematical model of the payload estimation system
The payload estimation system was modelled using MATLAB/Simulink. Both systems - the MBS model as well as the payload estimation system - run parallel in a cosimulation (refer figure 3). Inputs to the MBS model from Simulink are the cylinder strokes (translational motion) in order to control the relative angles of the working attachment links φ1 to φ4 , as well the inclination angles α and β of the superstructure. Furthermore, there is also a possibility to change the CG of the payload from Simulink which allows for the possibility to analyze the influence of this effect on the accuracy of the payload estimation. Outputs from the MBS model to Simulink are all the measured values of the excavator model during simulation including the current values of
Fig. 3. Co-simulation between Matlab and Simpack
all the relative angles φ1 to φ4 as well as the force in the main hydraulic cylinder and the inclination angles α and β of the superstructure. Using the Simulink model, the payload estimation system is first calibrated for two reference payload values. During the calibration, the lower boom angle φ1 is varied from a certain minimum value to a maximum value for a set of user defined angular positions of the arm (refer figure 2 - left). This gives a ‘mxn’ array of (φ1 ,φ3 ) values. For each of these pairs, the force (analogous to the pressure difference) across the main cylinder is measured. This gives a ‘mxn’ characteristic map, one for each of the reference payloads, as shown in figure 2 right. These maps are stored in lookup tables in Simulink, which offer linear and cubic interpolation methods. The process flow of the calibration and actual measurement is modelled using a state machine in Simulink. In order to avoid any possible copyright infringements, all results will be normalized.
Fig. 4. Mass estimation using linear interpolation
As mentioned previously, the actual value of payload is estimated using interpolation and curve fitting. Thus, the current payload value can be estimated from the values of current cylinder force and the values of the forces and corresponding reference masses from the calibration. This is illustrated from the following equation and accompanying figure 4: mre f − m0 ∗ (F − F0 ) + m0 (1) mactual = Fre f − F0
Speed compensation: The described method is carried out with constant angular speed of φ˙1 . When there is a change in speed the results of the estimation will deviate due to the uncompensated inertia effects. In order to improve the estimation by accommodating for variation in speeds, a second calibration procedure is performed with varying φ1 and φ˙1 for different positions of φ3 , using a known reference load and recording the estimated mass. The speed φ˙1 at each run is held constant. This results in an array of the dimension ‘mxnxo’ of the (φ1 ,φ˙1 ,φ3 ) values. Additionally, a second characteristic map of dimension ‘mxn’ for (φ1 ,φ3 ) is created with the estimated mass at reference speed. The compensated mass estimation becomes therefore: mcomp =
mvre f (φ1 , φ3 ) · mactual m(φ1 , φ˙1 , φ3 )
(2)
One drawback is that the angular speed φ˙1 is the outcome of the linear movement of the boom cylinder and the gear ratio of the mechanism transforming linear to rotational motion. By nature, it is only the cylinder speed that can be kept constant, while there will always be some angular acceleration of the boom.
5
Discussion of simulation results
The system is calibrated for quasi-static conditions with two different reference loads. It is also required that angular speeds φ˙1 , φ˙3 need to be kept constant so as to prevent occurrence of dynamic effects. However, this condition is not entirely satisfied since the angular motion is controlled by the translational motion of the cylinder strokes and therefore the cylinder stroke velocity is kept constant during calibration of the model. Optimum measurement range within calibration range: As seen in figure 5, even within the calibration conditions, there is a specific ‘optimum’ range of φ1 and φ3 (and the corresponding velocities φ˙1 φ˙3 ) where the best estimate for payload is achieved. This is further illustrated in figure 6 which shows the relative error for results produced with calibration conditions. The plots show the relative error in payload estimation for three different values of arm angle φ3 as the lower boom angle φ1 is varied. It is seen that the best results are obtained for arm angles 165◦ and 90◦ . An angle of 50◦ shows 3% deviation from actual payload mass. Thus, it seen that even when calibration conditions are closely followed, the accuracy of the payload estimation is not consistent throughout the range of calibration. Variation in angular speed: When the measurement is done at angular speeds of the boom (φ˙1 ) different than that at which the system is calibrated (calibration speed = 0.2m/s), the method shows even greater errors. The top row of plots in figure 7 shows a variation of payloads measured at different angular speeds of the boom. Estimation errors of greater than 20% occur when deviating from the reference speed used at calibration. The lower row of plots in the same figure shows estimation results with speed compensation. Payloads in the closer range of the reference payload show good results. As the actual payload deviates further from the reference payload, the error also increases. It should be noted that mre f refers to the higher of the two reference payloads
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Fig. 5. Determining valid measurements: At time (A) the measurement range of the lookup table starts, and goes until time (B). The measurement range in this project work is defined for φ1 from 20◦ (E) to 80◦ (F). At time (C) the range is re-entered, but this time with a negative angular speed φ˙1 . In between time (A) and time (B), a correct estimation can be done, see (G)
i.e. when the bucket is fully loaded. Since most digging/loading operations will consist of the operator trying to load the bucket to its maximum capacity, it is favorable that the error is least when m = mre f . Variation position of CG of bucket: Another major influence is the variation of the center of gravity of the bucket i.e. bucket position. Figure 8 shows the influence of variation of bucket positions and arm angles on payload estimation accuracy. Good results
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Fig. 6. Variation of arm angles using reference speed of 0.2m/s; mre f = higher of the two reference payloads
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Fig. 7. Variation in angular speed; mre f = higher of the two reference payloads
are achieved only when the bucket (φ4 ) is close to the position at the time of calibration. In the plots, the value of φ4 at which the calibration was done is 149◦ . Even a variation of approximately 20◦ in the value of φ4 results in a deviation from 6% to more than 20% depending on the arm position. These plots show results for payload m = mre f , i.e. fully loaded bucket. Influence of dynamic parameter changes: When parameters change during the measurement i.e. while the working attachment is in motion, the accuracy of the payload estimation is affected considerably. This is investigated by varying two parameters dyanmically:
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Fig. 9. Variation of bucket position (φ4 ) at different arm positions with empty bucket
1. Influence of bucket movement (φ4 ) during measurement: This phenomenon is illustrated in the figure 10. The bucket starts moving at t=3s, which brings about a considerable dip in the accuracy of the payload estimation. 2. Influence of arm movement (φ3 ) during measurement: It is required that the measurement is done only when the boom moves up (i.e. change in φ1 ) with all other parameters remaining constant. Hence, the movement of the arm (change in φ3 ) has a significant influence on the accuracy of the payload estimation. This is illustrated in the figure 11 shows that a deviation in φ3 while φ1 increases causes a considerable increase in the relative error.
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Fig. 10. Influence of bucket movement during measurement: The test is carried out with a measurement in ideal (calibration) conditions, with a constant boom movement. At time t=3s the bucket starts moving. The estimated payload immediately shows an error up to 40%.
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Fig. 11. Influence of arm movement during measurement: The top graph shows the relative error in estimated payload. The second graph from the top shows φ1 and φ3 , note that φ3 changes at t = 4s. The graph below that shows the corresponding angular speeds φ˙1 and φ˙3 followed by the angular acceleration at the bottom. During a measurement with a constant speed of the boom, the arm angle (φ3 ) is varied by -10◦ . Beginning with the motion of the arm movement, the measurement results deviate substantially with a peak of approx. 30% relative error.
6
Conclusion
It can be seen from the simulation results that the payload estimation method is not only sensitive to parameter variations but even within the limits specified for measurement, the accuracy varies considerably across the measurement range. The following measures are proposed in order to improve the accuracy and reliability of the estimation. 1. Improved calibration: If the calibration can account for more parameters than φ1 and φ3 , the system will be more robust against the corresponding parameter variations. This is the most straight forward yet expensive (in terms of time and effort) measure to improve the estimation accuracy. 2. Bucket position compensation: The method needs to compensate for changes in bucket position, since this has a substantial effect on the accuracy of the payload estimation (refer figure 10). This is all the more crucial since for any digging and load operation, it is highly probable that the bucket angle will not remain unchanged across the motion of the working attachment. 3. Improvement of speed compensation: It is seen from the figure 7 that the payload estimation method compensates for variations in angular speed of the working attachment to a certain extent. However, there is much scope for improvement, especially for payload values which deviate considerably from the reference payload value. 4. Measurement under ‘optimum’ conditions: As seen from the figure 5, the payload estimation gives best results for a certain optimum range of the parameter values. The method can therefore be so configured that it performs an estimation of the payload only when the parameters fall under this defined range within the measurement range. On the contrary to the benefits of better estimation, the number of test runs required for calibration get more complicated with additional every effect taken into consideration. The method remains a approach that is based on a single degree of freedom. Even with corrections for the influence of even the effects not explicitly mentioned in this report, such as coriolis effects or changed direction of the gravity, it can only be applied within a very limited band of application. Another drawback is the fact that the method is not capable of measuring statically with no movement of the working attachment.
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6. Nho, H.; Meckl, P. (2003) Proceedings of the IEEE/ASME Transactions on Mechatronics 8(2), 277-283. 7. Verdonck, W. (2004) Experimental robot and payload identification with application to dynamic trajectory compensation. PhD Thesis: Katholieke Universiteit Leuven, Leuven Belgium. 8. Silvy-Leligois, B.; Giroud, J. (1995) W¨ageverfahren f¨ur Bagger, Patent no. EP0736752A1, Deutsches Patentamt, (Filed by Ascorel Controle et Regulation Electronique). 9. Hsu, H. P.; King, J. C. (2012) Weight estimation for excavator payloads, Patent no. US8271229B2, US Patent, (Filed by Actronic Ltd).
