Development of an autonomous cow-milking robot control system

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Development of

an

Autonomous

Cow-Milking Robot Control

System

Cornelis

Klomp, Wim

Jongkind,

Ger

Honderd, Joost Dessing, and

Richard Paliwoda

This article describes the development of overall control for a robot system which is uscd to milk cows at the cow's own demand, without intervention by the farmer. The focus of the paper is on design of the inner and outer loop control of the robot arm developed especially for this system. The article highlights the milking-cups connection strategy, consisting of an approach mode, capture mode, and locking mode, to the teats of the cow. The position of the teats of the cow is measured with a specially designed ultrasonic sensor system.

Cornelis Klomp, Ger Honderd, and Wim Jonfikind are nith Delft Unilvrsiy ofTechnology. Department of Electrical Engineering, Control Laboratory, 2600 GA Delj?, The Netherlunds. Joost Dessing is with Virw International BV, 2150 BA Nieuw Ven- nep, The Netherlands. Richard Paliwodu is n'ith A.P.A. BV, 5500, AE Veldhoven, The Netherlands.

The kinematical and dynamical models of the robot arm have been derived for siniu- lation purposes with the aid of experimental data. In initial experimental implementation with live cows, the system performed well, and the complete system is currently undergoing practical tests. The first results of these tests have proved that it is feasible to milk cows autonomously.

Introduction

As part of a large overall farm automation project, an autonomous cow-milking robot system has been developed. The system will be able to milk cows fully automatically, i.e., without any help from human beings. The development of the overall system was carried out by VICON International BV [1]-[3]

in the Netherlands. The robot arm and its controller were developed in cooperation with robot manufacturer A.P.A. BV and with

the Control Laboratory of the Department of Electrical Engineering of the Delft Univer- sity of Technology. The main emphasis of the work done by the Control Laboratory has been on the modeling of the robot system and the development of a controller for the robot system.

It is anticipated that the milking machine will be able to milk cows four to five times a day at the cow's own demand. Usually cows are only milked two times a day, and the advantage of milking four to five times a day is the increase in milk productivity per cow by about 15%. A further advantage of autonomous milking is that the farmer does not have to attend the cow milking so there is time to cany out other tasks. The following functions will be carried out autonomously by the system: system entrance check; cleaning the udder and teats; connecting the milking-cups to the teats of the cow; milking; registration of the milk pro-

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duction per cow; checking and registration of health and milk quality for each cow; keeping the stored milk cool; cleaning the milk installation; and feeding the cow.

In the autonomous milking system, thcre is space for two cows to be milked simul-

about a robot control system for sheep-shear- ing [4] has recently been published.

In the following sections of this article the development of the robot control system for positioning the milking cups under the teats of the cow will be explained. First the strat-

Fig. I . Milking cups attached to the cow’s teats.

taneously, although only one robot arm is available for connecting the milking cups to the cow’s teats. The two sets of milking cups, one for each cow, are connected one at a time. The system has been built into a standard container which can be placed in any suitable spot inside or outside the barn. For identification purposes a collar with a transponder will be fitted on each cow’s neck. When the cow comes within a certain distance of the milking system, it will be recognized and an entrance check will be performed. Criteria for allowing entrance are the state of health of the cow and the time which has elapsed since the last visit. If this time is too short, the cow will be guided back to the other cows. In the case of sick- ness the cow can be guided away to a special box. Information as to the state of health of a cow is obtained from the quality of the milk produced which can be measured with the aid of sensors. The advantage of the above measurement system is that the farmer is quickly informed about the cow’s condi- tion. Although the application is completely different, it is interesting to note that a paper

egy for connecting the milking-cups and the construction of the robot arm is described. After that the derived simulation models for the robot links are outlined. The controllers for the robot movements (inner loop and outer loop control) are discussed in the following section, whereafter results of the simulations of the overall control system are shown and a comparison between measurement and simulation is made. The conclusions are drawn in the final section.

arameter

Milking-Cup Connection Strategy

After a cow has been allowed to enter, it is locked within a certain area of the milking system, and the milking cups are connected to the teats. The control strategy for connecting the milking cups has been divided into three modes, approach mode, capture mode, and lock mode. The milking cups are attached to a rack which is connected to a two link passive arm, which can be moved easily. The connection strategy starts when the passive arm is in a parked position with the arm retracted completely. When a signal is received that a cow has to be milked, the rack containing the milking cups is connected to the active robot arm with the aid of a gripper. Thus, the active robot arm and gripper cause the milking cups to move. The approach mode operates as follows: the robot arm with the rack containing the milking cups on its end is moved upwards towards the cow. During approach, the robot has to move slowly to the edge of the area where the teats are to be expected. To attach the milking cups correctly, a control system with its relevant sensor system is necessary. The reasons a control system is required, is that cows are not of the same size and that each cow has teats which keep changing in shape throughout the day as well as throughout its lifetime and also that the cow is still able to make (relatively small) movements. The first teat detected during the approach mode is the right front teat, which we have chosen to be the point of reference. The random position, within certain boundaries, of the point of reference is found with the aid of a set of ul-

trasonic sensors, which are called the coarse sensors. The coarse sensors are attached to the rack that contains the milking cups. The sensors have been constructed such that they emit a wide, flat bundle perpendicular to the Z-axis. The robot is moved in the upward direction until the reference teat is detected. Once the reference teat has been detected the approach mode ends and the capture mode

Table I Model Parameters

Description

Effective output voltage of PWM (V)

Angular displacement of motor axis (rad) Resistance of motor armature winding ( Q )

Torque constant (NmlA) Back emf constant (Vsirad) Inertia of actuator shaft (Nms’irad) Damping of actuator shaft (Nmsirad) Flexibility constant (Nmirad) Damping of link (Nmsirad) Inertia of link (Nms2/radl

Long link input output 5.8 1.9e- 1 I .9e- 1 2.0e-4 1 .Oe-2 4.4 4.2e-3 1.3e-3 Short link input output 5.8 1.9e-1 1.9e-1 2.0e-4 1 .Oe-2 4.4 1.3e-3 5.3e-4

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starts. During the capture mode the robot positions the milking cups under the teats of the cow. After the point of reference has been detected, the Z-position remains fixed while in XY-direction the movements of the cow are followed via the information from

I n t e r - L o c a l m o t o r .,.

ll..ll..ll.l.l...I.L

b p o l a - + c o n t r o l l e r - - - , o f t h e t o r l o n g a x i s long a x i s r

SHORT LINK

j/

{THTH=\,

I n t e r - p o l e - c o n t r o l l e r L o c a l o f t h e s h o r t a n i s s h o r t a n i s Fig. 2 . Illustration of the robot arm.

r o b o t

ll.lll..l.lll.

{

+ r a c k

the coarse sensors. The positions of the other teats relative to the point of reference are measured with the aid of another ultrasonic sensor (the fine sensor), that is also specially developed. Finally, in the lock mode, the movements of the cow are followed with little tolerance in order to be able to attach the milking cups. Fig. 1 shows a picture of a cow after the milking cups have been attached.

The milking cups are attached one at a

time. After all the milking cups have been attached the actual milking process can start and the active robot arm will be retracted and then the robot arm can be used to attach a

second set of milking cups to another cow that is waiting to be milked in the second box.

T-1

Construction of the Robot Arm

Fig. 2 is an illustration of the robot arm

used in the autonomous milking system. The two links closest to the gripper are called the short and the long link. Movements of these links cause the gripper to displace in the hor- izontal plane (XY). The complete construction of the long link and the short link can be moved upwards and downwards by means of the Z-link. Springs are used for the com- pensation of gravity effects. The motor axes are attached to spindles to convert the rota- tion into a translation movement. The dis- placement of all links is realized with ar-

mature-controlled dc motors. The motors are

driven by pulse width modulated power sup- plies (PWM). The output signal of the PWM switches from zero to V,,, (48 V) or - V,,,

+ c o n t r o t t e l e c t r o - ler n i c s 300 280 - 260

-

240

-

220 - 200 -

g

180 - 1 160

-

140 - U) Y x U f 120 - 2 100 -

>m

₈₀_- 60 - 40 - 20 - 0 - 0 D O 5 0 1 0 1 5 0 2 0 2 5 0 3 0 3 5 0 4 0 4 5 0 5 0 5 5 0 6 0 6 5 T I N [SI

Fig. 3. Measured velocity response of the open system.

Fig. 4 . Model of the long link including motor

I n t e r - p o l e -

cow

c o a r s e s e n s o r s Mechanical E l e c t r o n i c a l c o n n e c t i o n ~ c o n n e c t i o n 1.1.111111111.1

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with a variable duty cycle. This duty cycle is controlled by a nine (eight

+

sign) bit input signal. The switching frequency of 16 kHz is high compared to the fastest sampling frequency in the system (200 Hz). The po-

sitions of the different motor axes are registered by optical encoders which are mounted on the motor axes. These encoders are incremental, which means only displacements from some predefined starting point can be registered.

Fig. 6 . Model of the inner loop controller:

Modeling of the Robot Links

Including Motors

The models of the motor-driven links are obtained experimentally by measuring the angular velocity response of the motor axes of the open system with the PWM-input set to a certain (constant) value. One of these responses is illustrated in Fig. 3. The unit for the angular velocity is given in sliced5 ms, which corresponds to the measured number of pulses from the encoders per sample period. The numbers that are displayed at the end of each line in the graph are the PWM-input value and the final value of the angular velocity. The response (Fig. 3)

shows some flexibility effects of the arm.

For the long link this flexibility effect cannot be neglected and therefore it is incorporated in the model. The resulting model with some parametric modifications is also used for the simulation of the short link and the Z-link behavior. The model is based on a standard dc motor model in which some changes have been made in order to incorporate the flexibility effects. The resulting model is shown in Fig. 4. The descriptions and values of the parameters used in the diagram (Fig. 4) are listed in Table I. The simulated response of the long link, based on the model shown in Fig. 4, is similar to the measured response shown in Fig. 3 . The controller design, which is discussed in the next section, is based on these models for both the inner loop and the outer loop.

Control of the Robot Arm

The robot arm is computer controlled. The control system is shown in Fig. 5 ; it consists

of an inner loop and an outer loop. The inner loop controllers provide the control signal for the PWM. There is an inner loop controller for the position control of each sep- arate motor. Each motor position is measured by an encoder. The task of the inner loop controllers is to make the motor move in a controlled way to the desired position

as quickly as possible. The sample time of the inner loop controllers is 5 ms. The outer loop consists of the ultrasonic sensor system, the trajectory controller and robot dynamics. The ultrasonic sensors measure the location of the teats of the cow. The measured dis- tances are the input for the outer loop controller. This controller generates a new setpoint for the robot in Cartesian space and the setpoint is converted into the encoder positions of the different motor axes by means of the inverse kinematic formulas (T-I). The sampling rate of the outer loop is a factor 10 slower than that of the inner loop, thus the sample time of the outer loop is 50 ms. For each of the links, an interpolator is present to generate the setpoints for the inner loop controllers.

Inner Loop Controller

The inner loop controllers are for control- ling the desired joint angles of the robot ann.

The position and the velocity signals of each joint are used for state feedback. The states which depend on the flexibility effects in the model of Fig. 4 are not used for feedback. Fig. 6 illustrates the inner loop controllers. The angular velocity is related to the mea-

sured difference in increments of the position encoders of the present motor position and the motor position one sample before. To obtain the angular velocity this difference is divided by the sample time (T, = 5 ms), and by a gain (lO00/7r), which represents the number of encoder pulses per revolution of the motor axis. The gains Kp and Ku are the parameters of the controller. The sampling rate for the inner loop controllers was derived with the aid of the simulation model. Slow sampling rates ( T , 2 10 ms) produce moderately large errors. High sampling rates

(T, 5 2.5 ms), on the other hand, are dif- ficult to realize in the real-time control system although they lead to better results and less jerky motion. A sample time of 5 ms has been chosen as a compromise between the desired smoothness of the robot movements and the expected implementation dif- ficulties. A standard controller design rule

(T, I 0.1

.

7) also justifies the choice of the sample time (5 ms), because the principal time constants of the long link and of the short link are about 125 ms and 75 ms re- spectively. The PWM has been modelled by a limiter, a dead zone that appeared to be present in the implemented electronic and mechanical system, and a gain. The limiter guards the input values which are not to ex- ceed -255 or 255. The dead zone accounts for the effect that small values of the input signal do not result in ann movements. The gain of 48/255 represents the effective voltage output per PWM-input (V,,,,, = 48 V,

PWM,,, = 255). 300 280 260 240 220 200 180 160 140 120 100 80 60 40 20 0 I

1

I

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Optimization

The parameters Kp and

Kv

were optimized with the aid of the designlsimulation tool of the Interactive Simulation Program (PSI) [ 5 ] .

The criterion was chosen in order to obtain fast step responses with limited overshoot. The criterion to be minimized is therefore: the integral of the absolute position error (Zip)

plus the absolute value of the change in the

smooth. There are two reasons for this requirement. First, if the robot were to move quickly and jerkily, the cow could get ner- vous. Second, the control algorithm would not work properly; if the sensors should produce bursts of wrong sensor data of short duration, which can happen occasionally, the robot could react too quickly to that wrong data, and as a result the teat that is the point of reference might move outside the sensor’s

1

positions

1

Fig. 8. Simulation model of the inverse Jacobian controller.

control signal (bPWM):

10 + s i

Criterion =

1

_lEpl

+

_c

.

_IAPWMI

_dt. 0

The factor c in ( I ) is chosen such that the last term in the equation contributes to 114 of the total criterion value. The input signal used during the optimization procedure is a step function. The time to is defined as the time where the motor and controller are no longer in saturation. The reason for this choice is obvious: as long as there is saturation, the system keeps moving at maximum slew-rate, and altering the parameters by optimization does not cause changes in the system’s behavior. Starting at time to the criterion value is calculated over a period of time corresponding to five times the principal time constant of the link concerned, after which the final value of the step response should have been reached. A step response of the long link is shown in Fig. 7 . The contollers of the short and Z-link are designed in a similar way. After implementation in the real system, the inner loop controllers showed results similar to those obtained during the simulations.

Outer Loop Controller

To attach the milking cups, sensor information from the coarse ultrasonic sensors which measure the position of the reference teat is used. A requirement for the cow is that the movements of the robot must be

workspace. Smoothing the error signal over- comes this problem. This smoothing is realized by filtering and limiting the measured error signal. Because of the differences in the behavior (speed and smoothness) required of the robot during the approach, capture and lock mode, it is desirable to create a control system which provides the possibility of ad- justing for these different behavior requirements by means of a parameter. In order to enable the development engineers to adjust

the controller to those requirements, it is desirable to perform this adjustment using a single parameter. However it is not intended to have the farmer perform any of these ad- justments. The bandwidth of the cow move- ment is about 1 Hz. Thus the robot should be able to follow sinusoidal setpoints with limited amplitudes and frequencies up to 1

Hz. Overshoot should remain small to pre- vent the robot arm touching the cow. The desired accuracy is relatively small. The sen-

sors have a maximum accuracy of about 1 mm. Tests have shown that an accuracy of

5 mm is sufficient for correctly attaching the milking-cups, so this requirement has been more than fulfilled by the sensors. Of the possible outer loop controllers two have been investigated in more detail: the inverse Ja- cobian controller, and the Cartesian controller.

Inverse Jacobian Outer Loop Controller

A Jacobian [6] is used in robotics to convert joint velocities into Cartesian velocities. The conversion from Cartesian velocities to joint coordinate velocities can be performed by applying equation ( 2 ) , where 0 is the 2

x 1 vector of joint angles of the manipula- tor, x is the 2 x 1 Cartesian position vector, and J - ’ is the inverse of the 2 x 2 Jacobian matrix of partial derivatives.

dOldt = J - ‘

.

dxldt. ( 2 )

For small displacements we can assume that the matrix J - ’ is fixed in time and small changes in 0 ( 6 0 ) are assumed proportional

440 430 420 410 400 390 380 370 360 350 34 0 330 320 310 300 290 280 270 260 250 240 0 0 2 0 4 0 6 0 8 1 2 T i m e [s]

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1'"

yy

L

trollers

p o s i t i o n s

J

Fig.

IO.

Simulation model of the Cartesian controller.

0 22 0 2 0 18 0 16 0 14 Q 22 0 1 0 08 0 06 0 04 0 02 0 0 7 0 65 0 6 0 55 0 5 0 45 0 4 0 35 0 3 I,@"&"'- 0 . 5 1 1 . 5 2 2 5 3 3 . 5 4 4 . 5 5 Banawiatn [HZ]

Fig. 11. DC gain and damping ratio as a function of the bandwidth,

to small changes in x (6x): When the displacements remain small, equation (3) can be applied. However the Jacobian is position dependent. Recalculat- (3)

6 0 = J - '

.

6x.

ing the inverse Jacobian every sampling period is too time consuming for the real-time control system. Therefore the inverse Jaco- bian was taken fixed over the whole workspace, taking the center of the workspace as reference for the fixed Jacobian. Because the matrix is part of the feedback loop of the system, the influence of changes in the matrix on the control of the robot remains relatively small. Fig. 8 shows the scheme of the simulation model of the system with the inverse Jacobian controller. The error signal ( e ) , which is directly measured by the sen-

sors in the real system, is obtained in the simulation model by subtracting the current robot position (1st x , y) from the setpoint. The setpoint represents the Cartesian position of the teat that is the point of reference. The robot position is determined by transformation of the motor positions, resulting from the motor models, to the Cartesian robot position with the forward kinematics transformation (T). The factor

z-'

represents the dead time of three sampling periods present in the system. The dead time is caused by the duration of the communication between the different computer systems used to control the milking robot. Sensor information is immediately available to the inner loop controllers, but before the information reaches the outer loop controller one sample has passed and this also applies to the information flow from the outer loop controller back to the inner loop controllers. The filter, chosen in order to smooth the sensor data,

is a second-order autoregressive filter (ao, a ,

.

z - ' ,

a2

.

z - ~ ) which has different parameter settings for each link.

Simulations showed that the controller in-

corporating the inverse Jacobian worked poorly. Responses when moving towards a non-moving cow (constant setpoint), starting from some predefined position, resulted in undesirable behavior. Where the distance to be traveled is small the robot shows a heavily damped motion without overshoot. Increas- ing the travel distance by a factor 2.5 resulted in an overshoot of about 35%. The above-described responses are shown in Fig. 9. These effects can be explained because equation (3) is only correct if the measured errors remain small. This is not the case if the distance increases. A demand is that the

control system should be able to function well with both small and large errors. There- fore the inverse Jacobian control would require some adaptive characteristics, if it were to perform well. Updating the inverse Ja- cobian in the simulation model by recalcu- lating the matrix each sample made little difference in comparison with responses where the matrix was taken constant, with the cen-

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ter of the workspace as reference. If larger setpoints, or setpoints far away from the center of the workspace had been applied, these differences would probably have been considerably larger. Because of the problems previously mentioned these tests were not attempted, and the control algorithm based on the inverse Jacobian was not further investigated.

Cartesian Outer Loop Controller

Due to the unsatisfactory results with the inverse Jacobian controller described above, another method was investigated and suc- cessfully applied. Instead of filtering the sep- arate joint position errors, which are obtained using the inverse Jacobian described above, the Cartesian errors are filtered. The errors measured by the coarse sensorx (e.g., the difference between the setpoint and the robot position (1st x, y ) in the simulation model) are filtered and added to the previous setpoint to result in the new Cartesian setpoint. After the new Cartesian setpoint is calculated, it is converted into positions for the motor axes with the inverse kinematics

(TI).

A scheme containing this outer loop controller is shown in Fig. IO. The previously mentioned dead time of three sampling periods ( z - ~ ) may lead to slowly damped os-

cillations around the setpoint. Therefore the desired specifications cannot be met. The effect of this dead time was taken into consid- eration during the controller development. Based on parabolic extrapolation of the three previous errors, the developed controller tries to predict its future error. In this way better information is available for control which results in well damped behavior of the arm.

The reason extrapolation was chosen instead of the prediction of the future error from the previously derived simulation model is that the time required for the extrapolation cal- culation is considerably less than that required to predict the error signal from the simulation model. A parabolic extrapolation was used since this matched well with the relatively slow movements of the cow, in comparison to the sample time of the system which is 50 ms. The filter used is a second- order autoregressive filter (ao, a ,

.

z - ' ,

a 2 . z - ~ ) , which has an adjustable bandwidth,

adjustable dc gain and adjustable damping ratio.

Parameter Settings

The filter bandwidth is based on the required robot behavior and will be the only adjustable parameter in order to obtain some degree of user friendliness. Therefore the other two filter parameters, dc gain and damping ratio, are made dependent on the

/ /

-

410 I 400

I

,

34 0 Y c 0 cl UI Q X 320 330

4 Y

/

250 260

3

0 2 0 4 0 6 0 8 1 2 T i m e [ s ]

Fig. 12. Simulated responses of moving towards a constant setpoint

320

,

I I I 310 300 290 280 270 260 250 240 230 220 210 200 190 180 0 0 2 0 4 0 6 0 8 1 1 2 1 4 1 6 1 8 2 2 2 2 4 T l W [SI

Fig. 13. Simulated sinewave response frequency = I Hz

chosen filter bandwidth. As mentioned previously the term user applies to the development engineers and not to the farmer. The user will be able to set the bandwidth to a value between 0.2 Hz and 5 Hz. A bandwidth near the lower boundary (0.2 Hz) results in rather slow and smooth robot movement. Slower movements than obtained using a bandwidth of 0.2 Hz are of no practical

value. Considering the time constants of the links and the mechanical vibrations of the robot system the upper boundary of the filter bandwidth is chosen at 5 Hz. A filter band-

width setting larger than the 5 Hz specified cannot be handled by the inner loop controllers, and also problems with mechanical vibrations can be expected. At the maximum setting, the movements of the robot are

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340 330 320 310 300 U C 2 290 4 01

-

280 & 270 260 250 240 $. rn 0 0 2 0 4 0 6 O E 1 1 2 1 4 1 6 T l W [SI

Fig. 14. Simulated responses of moving towards a constant setpoint, f o r different bandwidth settings. 440

,

430

4

420 410 400 390 380 370 360 350 340 330 320 310 300 290 280 270 260 250

i

mbot p o s i t r o n T i m e [ s ]

Fig. 15. Simulated versus measured sinewave responses frequency = 0.5 Hz.

faster, and accordingly less smooth, than normally would be required to position the milking-cups in the lock mode therefore under normal conditions the maximum bandwidth will not be used, which means that some margin to deal with abnormal conditions is preserved. The other parameters, dc gain and damping ratio, were made dependent on the chosen bandwidth, and were obtained with the aid of the simulation model. Appropriate dc gains and damping ratios were determined for six different settings of

the bandwidth. The parameters were chosen in such a way that when moving towards a teat from the predefined starting position, the robot was within the 5 mm margin of the setpoint as quickly as possible and also re- mained within this margin, which ensures that the milking cups can be attached quickly once the cow has settled itself in the system. As stated earlier, these parameter settings (PAR,,

. . .

, PA%) are obtained for six different bandwidths

(fi,

. . .

,

fs)

of the filter. But since it must be possible to specify

any bandwidth that lies between 0.2 Hz and

5 Hz the following solution has been cre- ated. A fifth-order polynomial relation between each parameter (dc gains and damping ratios) and the adjustable bandwidth is derived, based on interpolation. For each parameter, equation (4) can be applied, where PAR, is the parameter corresponding with the ith chosen bandwidth, J is the ith chosen bandwidth in hertz, and a , b, c , d , e , and g are the polynomial coefficients:

PAR, = a .

f;

+

b f :

+

c ' f , '

+

d

.

f;

+

e

.

J

+

g, 1 s i s 6 . Matrix notation results in (5):

(4)

FR1]

=

[i:

-q

.

[j

( 5 )

PAR,

f 2

_{. . .}

f:

The polynomial coefficients are determined directly by inverting the six-by-six matrix in equation ( 5 ) .

The outcome of these calculations was verified in two different ways. First the resulting functions were drawn and checked for local or global minima and maxima and smoothness. Second if the first verification was considered correct, the resulting fifth- order function was inserted into the simulation model. Several bandwidths between the

0.2 Hz and 5 Hz were investigated and the responses were checked. The functions which finally resulted for damping ratio and dc gain are shown in Fig. 11.

Simulation Results

Finally some responses of the developed controller are shown. First a response of the robot moving towards a constant setpoint. This seems to be a step response but actually no discontinuity appears in the sensor data because of the initialization of the controller. This response is shown in Fig. 12. The developed controller ensures that the setpoint is reached quickly and that the robot remains within the 5 mm margin of the setpoint. Fig. 13 elucidates a simulated sinewave response with a sinewave input of 1 Hz. The setpoint is followed correctly but a considerable phase shift occurs. This phase shift is mostly due to the dead time. Fig. 14 shows a simulated response of the robot for different settings of the filter bandwidth: 5 Hz, 3.2 Hz, 1.9 Hz, 1.3 Hz, and 0.8 Hz.

After implementation some measurements were performed to verify the simulation re-

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sults. Fig. 15 shows both simulated and measured sinewave responses with a frequency of 0.5 Hz. The responses are almost identical which shows that the simulation model derived is a good description of the actual system.

Some practical tests using real cows were performed. The robot was capable of following the cow’s movements. Even when the cow moved abruptly the robot remains close to the desired position. To investigate whether the control system is robust enough, especially with respect to bursts of erroneous

sensor data, extended practical tests using a number of cows are now in progress.

Conclusions

Considering the overall performance of the autonomous cow-milking robot system, the control system should be able to attach the milking cups correctly to almost any cow. The control system performs well within the required boundaries: the accuracy is better than 5 mm. The application of a parabolic extrapolation filter for the estimation of the future error, thus compensating part of the dead time in the system, proved to be useful. With the developed controller the robot ar- rives quickly within a margin of 5 mm of a constant setpoint. The time required depends

on the distance to be traveled, but is normally between 0.3 and 0.8 s . This means that shortly after the cow stops moving the milking cups can be attached. Sinusoidal movements with frequencies up to 1

Hz,

the maximal frequency of the normal cow movements, can be followed. The appearing phase shift is mainly due to the dead time in the system. The designed controller is user friendly. The development engineers can easily change the robot behavior by means of a single parameter. This parameter is the bandwidth of the adjustable filter that is used in the Cartesian controller. The controller is to a certain degree resistant to error bursts of short duration that can occur in sensor data. The complete system is currently undergoing extensive practical tests, where the cows are to be milked autonomously. During these tests the robustness of the controller and the behavior of the complete system in general are examined.

References

[I] E. de Gelder, “Design of digital position controllers for the motors of the cow-milking robot system,” Rep. A88.027(455), Dept. of Elec- trical Engineering, Delft University of Technol- ogy, 1988 (in Dutch).

[2] C. Klomp, “Design of a Cartesian setpoint controller for the inner loop controllers of the cow-

milking robot system,” Rep. A89.017(492), Dept. of Electrical Engineering, Delft University of Technology, 1989 (in Dutch).

[3] G. Honderd, W. Jongkind, C. Klomp, J. Dessing, and R. Paliwoda, “An autonomous cow milking robot system,” in Proc. Int. Symp. Ad- vanced Computers for Dynamics and Design (AC&D), Tsuchiura, Japan, Sept. 6-8, 1989, pp.

53-58.

(41 J. P. Trevelyan, “Sensing and control for sheep-sheering robots,” in IEEE Trans. Robotics Auromarion, Vol. 5 , pp. 716-727, Dec. 1989. [ 5 ] P. P. J. van den Bosch, in “Interactive computer aided control system analysis and design,” in M. Janshidi and C. J. Herget, Ed. Amster- dam: North Holland Pub., 1985, pp. 229-312.

[6] J. J. Craig, Introduction to Robotics (Mechanics

and Control). Reading, MA: Addison-Wesley, 1986.

Cornelis Klomp was born in The Hague, The Neth- erlands, in 1966. In 1989 he graduated from the Delft University of Tech- nology at the Faculty of Electrical Engineering. The same year he became a member of the Control Laboratory to work on a Ph.D. thesis about intel- ligent robot control. His main research interests are robotics in general, sensor feedback control, sensor integration and fu- sion and artificial intelligence techniques.

linear systems. In 19:

Ger Honderd was born in Amsterdam, The Neth- erlands, in 1933 and received the Ing degree in electrical engineering in 1954 from HTS, Amster- dam, and the 1R degree in electrical engineering in 1961 from the Delft Uni- versity of Technology, with a thesis on grafo-an- alytical synthesis of non- $8 he joined the group on fundamental research of the Institute for Mechan- ical Constructions of the Organization for Applied Physics (TNO). In 1961 he became Member of the Scientific Staff of the Control Laboratory of the Department of Electrical Engineering of the Delft University of Technology. He was ap- pointed Lector in 1968, and in 1980 Full Professor at that university. In his work at the university he has initiated several projects together with indus- trial co-workers on the application of control engineering. He has given special attention to the field of power generation; primary and secondary control as well as economic optimization of elec- tric power production, actively promoting the development of especially adaptive control strategies and optimization methods. In the last few years

he has paid special attention to the field of robotics. His main research interest is in the field of sensitivity analysis and adaptive control, especially model-reference adaptive control.

Wim Jongkind was born in Haarlemmermeer in 1941 and received the master’s degree in electrical engineering from the Delft University of Tech- nology. He worked at the European Space Agency where he was responsible for the specification, integration, and testing of sun-pointing systems for sounding rockets. After leaving Delft University he was a Research Fellow at ESA-ESTEC Noord- wijk, The Netherlands, after which he worked in the aerospace depanment of Fokker. At Fokker he was involved in engineering analysis and design of the control system for the American-Dutch-An- glo satellite IRAS. At present he is an Assistant Professor at the Control Laboratory of the Faculty of Electrical Engineering at the Delft University of Technology.

Joost Dessing was born in 1962 and graduated in 1986 from the Technical College of Amsterdam in the field of information technology. Since 1987 he has been with the High Tech Farming division of Vicon BV, Nieuw-Ven- nep, a company that spe- cializes In the develop-

ment and production of agricultural machines. He has been involved in the application of microcontrollers, and more recently in the development of the automatic milking system (AMs). His main interests in this project are the ultrasonic sensor system and the development of the software (on a VME machine using OS-9) for the integration of all the pans in the AMs.

Richard Paliwoda graduated from the Delft Uni- versity of Technology, Faculty of Electrical En- gineering, in 1983. Since 1984 he has worked at Advanced Production Au- tomation b.v. in Veld- hoven, The Netherlands, as a Senior Systems En- gineer. His task is development of multiaxial controls for robotic applications with sensor feedback. These controls are integrated in several machines varying from assembly to laser beam processing. This development consists of hardware, software, and mechatronical design.