TEMA 7_1 on the Control of Joint Integrated Servo Actuators for Mobile Handling

8/6/2019 TEMA 7_1 on the Control of Joint Integrated Servo Actuators for Mobile Handling

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On the Control of Joint Integrated Servo Actuators for Mobile Handling and Robotic Applications

Proc. of 1st FPNI-PhD Symp. Hamburg 2000, pp. 449-465

450

use hydraulic drives due to their minimum ten times higher power density for all mobile

devices, where payloads are 10 or 100 times higher than in common manufacturing

applications. Since a Diesel engine is used as primary energy source for all mobile machines

the disadvantage of energy conversion does not weigh too high.

2 STATE OF THE ARTTodays hydraulic drive technology of mobile machines is based almost completely on valve

controlled cylinders. The valves are located next to the driver, who is controlling the machine

by operating the valves directly. High positional precision and high repetitive precision are

not required for todays machines. Also the requirements on the dynamic behaviour are not as

high as they are for stationary robots or for stationary hydraulic systems. Differentialcylinders are preferred due to their more compact design. Currently the constant pressure net

is going to be replaced more and more by load sensing technology. Compared to a pump

working in a constant pressure net, in a load-sensing-system the high pressure pump adapts to

the maximum pressure currently required in the system. Thereby load sensing allows to

operate at least one cylinder at optimal conditions. However, all other cylinders are still most

likely to be operated far away from their optimal conditions. Though, a lot of energy is wasted

to heat due to throttle losses at the control valves. Especially at higher numbers of hydraulic

actuators the energy saving effect of load sensing will not be very high. Additionally load

sensing requires a lot of further hydraulic components compared to a constant pressure net.

Load sensing has also a tendency to positional and pressure oscillations. Furthermore it is not

very suitable for applying automatic control due to its permanently changing plant

parameters, what makes the controller design very complex. However, for automated

processes in mobile handling devices and robots closed loop control of each hydraulic axis is

absolutely essential. Even for half automated processes closed loop control is required, what

will e.g. allow the operator to control tools at the end-effector in Cartesian co-ordinates

instead of controlling each axis angle. Only Cartesian co-ordinate control makes straight line

operation possible, what is required for a lot of processes in automated or half-automated e.g.at building sites.

3 PUMP CONTROLLED JOINT INTEGRATED SERVO ACTUATORSA completely new way is the idea of a pump controlled joint integrated servo actuator. Here

the control element, the servo valve, is replaced by a servo pump, what eliminates all

throttling losses within the hydraulic power circuit. Only leakage and friction losses of motorand servo pump will then reduce the efficiency. Furthermore, the differential cylinders is


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replaced by a hydraulic swivel motor in the vane type form. This motor type is very compact

and allows an integration directly into the joint axis. This allow simultaneously a much

simpler design of the joint kinematics, since the original type of motion is a rotation and not a

translation. An additional advantage is that the pressure force is always applied at its optimal

lever arm, what makes the driving torque independent from the joint angle. Also higher anglesup to 270 are achievable by a vane type swivel motor without any disadvantages like long

cylinder strokes. The combination of these characteristics makes this new actuator design

highly suitable especially for end effector joints, where two or three actuators are required to

implement the required number of degree of freedom.

3.1 Principle of operationThe basic principle of the pump controlled joint integrated servo actuator is shown in figure 1.It consists of a servo pump (1), driven by small electric motor (2), rotating at very high

velocity. The pump is connected to the vane type swivel motor (3) by a closed hydraulic

circuit. The circuit has to two high pressure relief valves (4a and 4b), which release the high

pressure line to the low pressure line in case of overload. An integrated charge pump (5)

supplies the electro-hydraulic servo pump adjustment system (7) and charges the low pressure

line to a typical level of 20 bars to increase the load stiffness. An integrated micro controller

(6) is supplied with positional and/or velocity commands from a central control unit, operated

by the driver and provides all controls for pump adjustment as for velocity and positional

control of the hydraulic axis.

Figure 1: principle of the pump controlled joint integrated servo actuator

Since the joint integrated servo actuator takes its full advantages at the end effector joints, thisalso means, that long hydraulic hoses would be needed, when conventional design is assumed,


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where the servo pumps are located at a central distribution gear at the diesel engine. This

means also high hydraulic capacities with low stiffness, slowing down actuator dynamics

(response time to position commands). Additionally, long lines increase pressure losses due to

fluid friction and add significant installation mass to the system. A different concept is the

power by wire technology. This technology avoids long lines by transferring the energyelectrically. Instead of using a central power unit or a number of centrally installed pumps,

each actuator uses its own pump, installed locally at actuator. This means the line lengths can

be widely reduced by moving the pump right next to the motor and building a compact unit.

This compact unit brings also some other advantages with it as in case of malfunction or

maintenance this unit can easily be replaced and repaired. The complete testing of these units

can be easily done prior to installation and allows a control parameter adjustment very

comfortable.

3.2 Dynamic characteristicsFor analysis of the dynamic behaviour and for closed loop controller design a state space

model of the pump controlled joint actuator needs to be created. It can be derived by using

two basic equations. A complete mathematical model of the actuator was already explained in

Grabbel and Ivantysynova (1999). The continuity equation gives

p& =

&

21 ,M

pLiP

H

VpkQC , (1)

where CH= V/K hydraulic capacity,

V= VM+ Vline oil volume including lines and motor displacement volume.

The terms represent the pump flow (QP), pressure dependent volumetric losses at the

hydraulic pump and motor (coefficient kLi, p) and the motor inlet flow due to its movement

(motor displacement volume VM). The bulk modulus Kis assumed to be constant. The balance

of moments at the servo joint results is calculated to

&& ={

lossespressure

p

torquefriction

R

torqueload

loadload

torqueMotor

M MMglmpV

321 &444 3444 2143421

)(sin2

. (2)

Here the pressure dependent motor torque, the load (including the mass of the arm itself),

friction effects and pressure losses, which can be subtracted here, are considered.


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Looking at the fact, that the servo pump eigenfrequencies are much higher than the

eigenfrequencies of the main circuit, the dynamic behaviour is basically defined by the

eigenfrequencies of the main circuit. Further assuming the load torque as a disturbance,

reducing friction to pure (linear) viscous friction and finally reducing the model to velocity

control, a completely linear state space model of the order two can be derived.

0],10[,

0

1

,2,

==

=

=

DCBA H

vsp

M

H

pLi

C

rM

V

C

k

with the state vector

=

&

px ,

where pressure losses and fluid mass are also neglected. The third order model for positional

control contributes a third eigenvalue of zero, representing the integrating character of the

hydraulic motor. The load torque has to added, respectively. However, the load torque

function is nonlinear and cannot be added to a single state space model. The following

characteristics can be derived from analyzing the open loop plant of the main hydraulic

circuit:

The system has a dominating, conjugated complex pole pair, which represents the hydrauliceigenfrequencies of the main hydraulic circuit. This pole pair defines substantially the

dynamic behaviour of the system for applied velocity and positional control. The

eigenfrequencies of the servo pump are significantly higher (10 to 100 times) compared to the

main hydraulic circuit and have no significant impact on the system behaviour. The

dominating pole pair of the main hydraulic circuit is extremely low damped which is a typical

property of all pump controlled systems. This low damping ration is responsible for a

significant oscillations in the main circuit, if no other measures (by means of closed loop

control or added hydraulic components) are implemented. The closed loop system will

become instable already at low gain, when single proportional control is used.

The dynamic behaviour is obviously determined by the poles of the main hydraulic circuit.

Significant parameters for deriving the location of these dominant poles are

for the eigenfrequency

pipe and motor fluid volume and load torque and inertia;


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for the damping ratio

internal leakage and friction losses.

Especially relevant for the controller design is the fact, that load torque and inertia willchange during operation. What is quite normal for all mobile machines carrying different

loads, makes the controller design difficult, what will discussed later. Since the

eigenfrequencies are dependent on the load torque and inertia, a variation in the load inertia,

will also lead to a variation in the hydraulic eigenfrequencies. Combined with the very low

damping ratio this will basically rule all efforts for an adequate controller design.

3.3 Control strategiesRegarding automated process management and precise, collision free positioning the

following demands have to be fulfilled by designing a suitable control strategy:

overcritical damping ratio for collision free positioning, high bandwidth for short work cycle duration.

It has to be pointed out, that an overcritical damping ratio is the most important demand, all

other goals are of secondary importance. Since for a significant number of applications

velocity control is required additionally, if the system is subject to trajectory control, where a

drag error is to be minimised, a closed loop velocity control has to be applied as well.

Considering all demands, the controller design can be divided into four major steps:

servo pump swash plate control (not further explained at this stage), velocity control, positional control, increase of system damping.

Considering the swash plate control as integrated into the servo pump a two cascade control

concept is proposed (figure 2). The inner cascade is the velocity control loop, while the outer

cascade is the positional control loop. This kind of axis controller would allow digital

implemention and can be integrated into a power-by-wire- modul as mentioned before.

Positional and velocity commands for axis and trajectory control will than be submitted by

signal wiring from a centralized control unit. For this centralized control unit the power-by-

wire-module appears as a smart actuator unit, what only needs signals of desired position and

maximum velocity.


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ML= f( )

QP integration1/s

epositioncontroller

velocitycontroller actuator

load torque

e cc

Figure 2: two cascade control strategy

3.4 Velocity controlPrevious investigations have shown the achievement of overcritical damping to be the mostdifficult one, especially if the bandwidth has to be kept as high as possible. For velocity

control a PI-controller has shown to be very effective, where the integrative part is necessary

to compensate control deviation in the velocity control loop, because an integrative part is

missing in the plant. This control structure is shown in figure 3, where for the integrative part

a limited semi-integrator is used.

+

Arm

Soll Schwenk-

arm

Servo-

pumpe-Regler

Quasi-Integrator

Druck-rckfhr.Ts+1

k

figure 3: velocity control using a limited semi-integrator

Investigations have shown that a carefully designed velocity controller, including measure to

increase the damping ratio to desired values, would allow to use simple proportional controlfor the positional loop without losing (further) bandwidth.

3.5 Principle of the limited semi-integratorLooking at other studies done in the field of closed loop control for hydraulic and all other

mechanical systems involving friction, the problem of limit cycles and wind up effects has

always been a considerable problem, where a number of solutions where derived to be more

or less effective, e.g. switching integrators. A new method was developed at the Institute forAircraft Systems Engineering (Berg 1999), where the system is prevented from carrying out


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limit cycles without any typical integrator problem like wind-ups or defining switching

conditions. This principle, called limited semi-integrator, is shown in figure 5. But first,

consider the transfer function derived from figure 4:

1)()( ++= Tsk

sEsU , (3)

where kis to be considered as tuning screw and

Tis the integrator time constant.

++

e

Ts+1k

u

Figure 4: unlimited semi-integrator

This transfer function can be transformed as follows:

)()()1()()1( sUksETssUTs ++=+ (4)

and then )()1()()1( sETssUkTs +=+ . (5)

Finally the transfer function yields

T

ks

Ts

kTs

Ts

sE

sUsGBI

+

+=

++

==1

1

1

1

)(

)()( . (6)

It is now easy to see, that this transfer function has a zero at s0 = 1/Tand a pole at sP = (1

k)/T. This means, the semi-integrator consist of pole and of zero, where the position of thezero depends on Tonly, while the position of the pole depends on Tand k. In case k= 1 this

transfer function can be simplified to

sTsT

sT

sE

sUsG

II

IBI

11

1

)(

)()( +=

+== (7)

with a zero at s0 = 1/Tand a pole at sP = 0. For this case the semi-integrator becomes a true

integrator. In other words reducing k to values from k = 0.95 .. 1.00 would allow to simply

adjust the systems to its friction and stop it from carrying out limit cycles.


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Figure 5 shows the same principle, where only a saturation characteristic is added. The

saturation limits the output signal and finally prevents the integrator from running upwards

(wind-up effect).

++

e

Ts+1k

u

Figure 5: limited semi-integrator without wind-up effect

3.6 Measures to increase the damping ratioAs mentioned before the basic disadvantage of pump controlled hydraulic systems is the

extremely low damping ratio of the dominant pole pair of about d = 0.01 .. 0.2. Since

overcritical damping (d> 1) is required to prevent the system from overshooting the damping

has to be increased by suitable measures. As mentioned in the introduction, the design of an

energy efficient actuator was a main reason for the change from valve control to pump

control. That means that a typical hydraulic mean to increase damping, using a bypass

throttle, has to be avoided, since this would also increase the losses. On the other hand, a

number of control measures to increase damping are known. Two of those are discussed here:

Compensation of the low damped pole pair by a complementary pair of zeros(cancellation), replacing the old pair by a new one with overcritical damping.

Pole placement by stated feedback or reduced state feedback allows free choice ofeigenfrequency and damping ratio, limited only by saturation and eigenfrequency of the

control element.

3.7 CompensationA good approach to increase the damping ratio is the design of a second order compensator. Itconsists of a of complex conjugated pair of zeros and two poles, either complex conjugated or

on the real axis. The purpose of the pair of zeros is to cancel the low damped pole pair of the

plant, while the two poles will replace the cancelled pole pair by forming a new dominant

pole pair. Figure 6 is illustrating this design approach, considering a complex conjugated pole

pair (keep in mind, that the integrator added by the controller is shown here as well since its

dynamic has influence on the pole trajectories). For this case the compensator transfer

function gives


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1

11

)(2

21

22

++

++=

sd

s

sd

s

sG

cp

cp

cp

cz

cz

czcomp

(8)

where cz - the compensator zero pair eigenfrequency,

cp - the compensator pole pair eigenfrequency,

dcz - the compensator zero pair damping ratio and

dpz - the compensator pole pair damping ratio.

ML= f( )

QP integration

1/s

epositioncontroller

velocitycontroller

PIcontroller

compen-sator

2nd order

actuator

load torque

e cc

Figure 6: block diagram, showing PI-compensator velocity control

The basic advantage of a compensator is its comparatively easy design method, especially for

time discrete implementation state of the art today. Furthermore, this design approach only

needs the positional signal, what needs to be measured anyway. The velocity signal is derived

subsequently by a differential filter. On the other hand, care has to be taken onto the choice of

the eigenfrequencies of the compensating zero pair and poles. It has to be pointed out, that acomplete cancellation of the low damped pole is not possible by a fixed parameter controller

design due to the variation of the plants poles, what is basically provoked by varying loads

(causing varying torque Tloadand inertia load). This means, even with closed loop control the

low damped pole will remain, practically, since the compensating pair of zeros is fixed, while

the plants pole pair is moving with varying load. A dominant behaviour of the compensation

pole pair can only be achieved by reducing the compensators eigenfrequency to values below

those of the lowest hydraulic eigenfrequency of the plant. This means explicitly

cp!

< hydr., min.


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-35 -30 -25 -20 -15 -10 -5 0

-15

-10

-5

0

5

10

15

Root Locus Design

Imag

Axes

Real Axis

dominant pole pairof main hydraulic circuit

compensatorzero pair

integratorzero

integratorpole

compensatorpoles

cp

Closed Loop

Figure 7: pole-zero-map of the velocity control loop (PI + Kompensator)

Figure 7 shows the pole zero map of this approach. This also shows the weak spot of this

approach or a any fixed parameter controller design, respectively. As shown above the closed

loop eigenfrequency will also be below the lowest open loop eigenfrequency what causes a

loss of bandwidth especially for low level signal response. This loss of bandwidth can be

quite high, especially for small pays loads, where the open loop eigenfrequency gets very

high. It depends on the dynamic requirements, whether this type of controller design with its

dynamic weakness can be tolerated or not. However, this dynamic weakness concerns

basically the acceleration and deceleration of a procedure, while the total time for large

positional steps is not effected too much.Figures 8 and 9 show the effect of incomplete pole compensation for different load torque. In

the first case load mass and design mass (the load mass assumed for the controller design)

are almost identical. The second case shows incomplete compensation here the true load

mass is mload = 500 kg, while the design mass is mload, design = 1500 kg. In both cases the

velocity signal shows overlaid oscillations of the incompletely cancelled pole pair

eigenfrequency. Since the commanded velocity is controlled well within its desired values,

this behaviour may be tolerated in most cases.


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Following statements can be made as a conclusion of the compensator design

The dynamic is limited by the lowest frequency of hydraulic pole pair (derived from thehighest pay load). The dominant eigenfrequency of the compensator has to be chosen

significantly below this frequency.

For insufficient compensation the transition behaviour shows underlaid oscillations of theinsufficiently compensated eigenfrequency, what has no effect on the total transition time.

0 1 2 3 4 50

5

10

15

20

25

30Angular position

Time [s]

Position[]

0 1 2 3 4 50

5

10

15Angular velocity

Time [s]

Velocity[/s]

Figure 8: Design for mload, design =1500 kg, Step response for mload= 1500 kg

0 1 2 3 4 50

5

10

15

20

25

30Angular position

0 1 2 3 4 50

5

10

15Angular velocity

Time [s]

Velocity

[/s]

Figure 9: Design for mload, design =1500 kg, Step response for mload= 500 kg


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Improvements

An improvement can be expected for an adaptive controller adjustment depending on the

current pay load. This would require a load identification method, what can be achieved e.g.

by using pressure sensors. However, only for low and medium pay loads a dynamicimprovement can be expected, since for high pay loads, open loop and closed loop frequency

are quite close to each other. Another idea could be a compensator of higher order, what

would allow eventually to partially eliminate the underlaid oscillations.

4 EXPERIMENTAL RESULTSFor verification of simulation results a test rig was designed to create a real environment for

the joint integrated servo actuator. This test rig consists of an adjustable arm, where the lengthand position of the pay load can be changed during operation to simulate varying pay load

mass and inertia during a manoeuvre. This test rig allows the verification of the controller

performance and positional precision in a real situation as well as recording leakage and

friction behaviour of the used hydraulic motors. The angle is measured by TTL angle meter

with a resolution of 0.01. This signal is differentiated to get the velocity signal. The torque at

the motor shaft and pressure in line A and B are measured as well. While the pressure signal

could be used for a future state feedback control concept to increase the damping ratio of the

main hydraulic circuit, the installed torque meter is only needed for result verification.

Figure 10: test rig for experimental verifications


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First test rig results have shown the compensator design to work acceptable within its desired

parameters. A step response is shown in figure 11. Here the velocity signal shows a

significant ripple. This has several reasons. One reason can certainly be found in the

incomplete cancellation of the underdamped poles. A second reason, however, is the method

to generate the velocity signal. Since the velocity signal is calculated from the measuredposition, the accuracy and time delay of the velocity signal depend on the method used, the

sampling time and the resolution of the angle sensor. For the shown measurements the time

delay of the speed signal is approx. 70 ms, what will consequently lead to a time delay in the

velocity control and to further oscillations. The improvement of the velocity signal calculation

will be one further step of improvement. Future investigations will focus on the optimization

of the compensator design and the implementation of the pressure feedback, a reduced pole

placement design. Implementation of load identification will be considered, if pressure

sensors give satisfactory results.

0 1 2 3 4 5-5

0

5

10

15

20

25

30

35Angular position

Time [s]

Position

[]

0 1 2 3 4 5-2

0

2

4

6

8

10

12

14

16Angular velocity

Time [s]

Velocity

[/s]

Figure 11: Test rig results - Design for mdesign = 1500 kg, Step response for mload 1000 kg

5

CONCLUSION

This paper introduced a new concept for a directly driven joint integrated hydraulic servo

actuators, based on the concepts of displacement control, joint integration and electrical

power distribution (power by wire). This new concept is called joint integrated servo actuator

and combines these three concepts for a number of advantages:

Wide swivel angles (up to 270 with vane type motor), High efficiency due to pump (displacement) control),

Compact mounting, saving structure and space, Displacement control allows energy return to other consumers,


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Power by wire reduces pipe mass, energy losses due to fluid friction and improves thedynamic behavior by increasing the hydraulic stiffness.

Especially at the end-effector of mobile handling systems and robots, where these joint drives

can be combined to a compact unit with two or three joint axes, this approach appearspromising. The proposed control concepts appear promising for a fast and easy installation

and initial operation phase. Simulations have shown, that both concepts will be able to

achieve an efficient increase in damping while the overall performance is acceptable.

However, even if pressure feedback is likely to achieve higher bandwidth, compared to a

compensator design, it needs to estimate the current load torque to adapt its pressure

feedback. As long as no load identification is not implemented this will always result in a

certain estimation error, causing the velocity control to either overshoot (if estimation is too

low) or undershoot (if estimation is to high). This makes the pressure feedback design most

likely to gain significant improvement from load identification methods.

Different to control concepts a second major subject to further investigation is the efficiency

and the hereby influenced heat balance in the system. Since an energy efficient actuator

design is desired the loss characteristic of servo pump and motor need to be analyzed. They

determine basically the efficiency and the heat balance in the system. To estimate the

efficiency and the heating of the actuator a mathematical model of the loss behaviour and the

heat transfer has to be developed. This would allow to integrate these system characteristics

into simulation models to derive the efficiency for given work cycles and procedures without

rebuilding each situation with a test rig.

6 LIST OF NOTATIONS motor shaft angle

arms inertia kgm

Eigenfrequency Hzcp Eigenfrequency of compensator Hz

hydr. min Minimal Eigenfrequency of hydraulic pole pair Hz

p differential pressure at the motor barCH hydraulic capacity of the pipes from pump to motor m/bar

d damping ratio -

e input of limited semi-integrator

g gravity m/s

k tuning gain of limited semi-integrator -

kLi, p coefficient for internal motor leakage l/min/barK bulk modulus of compression N/m


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l line length m

lload distance of arms center of mass to rotational axis m

mArm arms mass kg

mload payloads mass kg

MR function for friction losses NmMp function for pressure losses Nm

QP servo pump volume flow l/min

T Time constant of limited semi-integrator s

u output signal of limited semi-integrator -

VM motor displacement volume ccm

A System matrix -

B Input matrix (here vector) -

C Output matrix (here vector) -

D Pass through matrix (here scalar) -

x State vector -

7 REFERENCESBoes, C. 1986. Hydraulische Achsantriebe im digitalen Regelkreis. Dissertation. Aachen:

RWTH Aachen.

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Springer.

Chiang, M.-H. (1998). Adaptive Achsregelung fr den Hydraulikbagger. 1. Internationales

fluidtechnisches Kolloquium, Aachen.

Eberle, C. 1998. Simulation mobiler Arbeitsmaschinen durch Kopplung der mechanischen

und hydraulischen Teilsysteme. 1. Internationales Fluidtechnisches Kolloquium, Aachen.

Grabbel, J., Ivantysynova, M. (1998). Hydraulic servo joint actuators for mobile

manipulators, 1stBratislavian fluid power symposium, Slovakia.

Grabbel, J.; Ivantysynova M. (1999). Integrated Servo Joint Actuators for Robotic

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Manipulators and Robots. 2nd

Tampere International Conference on Machine AutomationICMA `98. Tampere, Finland.


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Ivantysynova, M. (1998). Die Schrgscheibenmaschine eine Verdrngereinheit mit groem

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Mar, J.-C., Laffite. J.-M. (1995). A Study of the different pole assignment strategies for

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Documents

TEMA 7_1 on the Control of Joint Integrated Servo Actuators for Mobile Handling