Force control for electro-hydraulic servo actuator used ... · Force control for electro-hydraulic servo actuator used for a humanoid robotic arm A.Abdellatif, Tan Quang DUONG,

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:18 No:05

Force control for electro-hydraulic servo actuatorused for a humanoid robotic arm

A.Abdellatif*, Tan Quang DUONG*, S.ALFAYAD*, Olivier BRUNEAU**Laboratoire d’ingénierie des systèmes de Versailles, Université Paris-Saclay, 78140 Vélizy, Paris, France

Abstract—Due to the great power of hydraulic systemactuators, the control of electro-hydraulic actuators has been animportant and ever developing point of research in the field ofhumanoid robots. But due to the non-linearities of the hydraulicsystems, It is very difficult to implement either motion or forcecontrollers on the hydraulic actuators experimentally beforethe mechanism is modeled and simulated. This is due safetyreasons and complex control issues. So, taking into accountthe humanoid robot HYDROïD, this paper presents the designof PID position and force control algorithms, tested on anelectro-hydraulic servo actuator. This actuator is one of theactuators present on the robotic arm of HYDROïD. The virtualmodel of the system is built through co-simulation betweenADAMS [1] and EASY5 [2] software. The output results werelater validated using hardware implementation.

Index Terms—Humanoid Robot, HYDROïD, Force Control,PID Control, Hydraulic systems.

I. INTRODUCTION

For decades, advancement of robots has been proven bythe efforts and aspiration of the human being in making arobot to be a real human companion in life [3]. Humanoidrobots, in particular, can be used in assisting aging humansand children, replacing humans in hazardous environmentsand as a test-bed for new prosthesis and or-thesis devices.Hence, there have been a constant need for a convenientactuator for the joints of humanoid robots enabling a preciseand powerful actions in addition to a safe and compliancemotion.

Actuation of the humanoid robots have become one ofthe biggest challenges in robotics. Demanding performancesin actuation became needed to enhance the autonomy ofhumanoid robots. Within this field, essential and desirableproperties for actuators are required which include: 1) highpower to mass ratio; 2) ability to produce high torque atlow speed; 3) high integrated mechanism as it could occupyreduced volume or what can be called high power to volumeratio; 4) human-like movements; 5) for safety reasons, theactuator must also ensure active compliance of the robot forsafe interaction with humans [4].

Nowadays, actuation of humanoid robots depends mainlyon two disciplines. Electric actuation, which is for humanoidrobots like LOLA [5], HRP4 [6], and REEM-B [7]. It hasseveral advantages as it is low in cost and can be easilyused and controlled. But its main problem appears whileconnecting the electric motor to the load, where the limitation

of the gearbox torque and the inability to produce aninstantaneous high torque without using a large sized motor.The other actuation discipline is using hydraulic power. Thistechnology is characterized by its high power to weight ratio,high power to volume index, high durability, producing largeforces at high speeds and its high holding torque serve asan interesting factors in humanoid robots actuation. Some ofglobal known humanoid robots like ATLAS [8], SARCOS[9],HYQ[10] and the underdevelopment HYDROïD [11] areactuated hydraulically.

So, in traditional terms, the robot must perform tedious andrepetitive tasks with great speed and accuracy [13]. In which,the repetition of tasks and the controllable environment, theposition and force controlled robotic manipulators shouldtrace the predefined joint trajectories with ease. Hence,precise interaction with humans and objects, the desire for aforce controlled actuator would be of a great necessity.

But unfortunately, the dynamic characteristics of hydraulicactuated systems makes it very difficult for such type ofcontrol, due to the highly non-linear dynamics of suchsystems. This makes the force controlled actuators wouldhave always limitations in the form of impedance, friction andbandwidth. This limits the traditional linear controllers andmakes the electro-hydraulic actuator control a major point ofresearch. However, several strategies have been introducedto work around the force control deficiencies of the electro-hydraulic actuator. T. H. Lambert[12] derived the nonlinearequations representing the hydraulic servos and showed theassumptions necessary for linearizing such equations usinganalog computation. Such work, directed the attention to theinfluence of the hydraulic parameters on the nonlinear closedloop behaviors. After that, Liu[14] proposed a mathematicalmodel for a typical servo system and exposed the nonlinearparameters with a compensation adaptive algorithm [15].C.L. Hwang and C.H. Lan [16] succeeded in eliminatingthe non-linear behaviors of the hydraulic servo-mechansimsthrough variable structure system controller algorithm. While,Sohl and Bobrow[17] used a lyapunov derived function asa controller design methodology to provide a stable forcecontrol with position tracking. In which, the controlleris applied to an existing experimental hydraulic systemproviding force and position tracking without the complexityof variable structure or adaptive methods.

Then, Prut et al.[18] excluded the need for position

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International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:18 No:05 2

knowledge for applying the force control law by usingforce, force rate and pressure for force tracking. Finally,K.Baghestan et al. in [19] proposed a linearized hydraulicsystem around an operating point, while the polytopicuncertainties that emerged were faced by a robust H∞controller. In general, all of these above advanced methodsimproved the quality of force controller in this kind ofsystem. However, the final result was not always the best.

This paper deals with the control of the hydraulic actuatorsof the humanoid hydraulic robot HYDROïD [20]. HYDROïDis humanoid robot having 52 degrees of freedom. It is weighsabout 125 Kg and is 1.8 m height. It is the first europeanrobot to have the hydraulic integration technology, in whichthe hydraulic oil is transmitted inside the robot parts bydrilling into the mechanical parts. Its main objective is tonavigate in rough terrains, assist the elders and interactsocially with humans. Therefore, the development of a safeinteraction capability for its joints is a necessity.

Under the mantle of HYDROïD ’s project, A prototypeof a 7 degree of freedom robotic arm is being developed, inwhich each joint is equipped with one servo valve actuator,sharing the same hydraulic source. The pressure and rotationdisplacement sensors are attached suitably at each joint, inorder to send the necessary feedback information to thecontroller. While, the geometrical and kinematics models aresolved, an inverse dynamic model is needed to estimate theforce required for each actuator. Therefore, a force controlleris needed on the hydraulic actuators fixed at the joints toensure the right positioning of hydraulic actuator with theright torque.

But implementing the controller algorithms on the armprototype directly may have some problems. As the highlynon-linear system and the powerful capacity of the hydraulicactuator makes it very dangerous to apply directly theexperimental controller to the prototype. Moreover, beforeapplying the controller algorithms on the arm prototypedirectly, all the tasks should be built and simulated in thesimulation software to ensure precision. Therefore, a linearactuator test bench was developed for one degree of freedomof motion and it is used for elementary implementationsubject. Where, the proposed force algorithm to be testedand verified with the a virtual model built in EASY5 andADAMS software.

So, this paper reviews the dynamic behaviors of hydraulicactuators through its mathematical model in section II. Thegeometrical and the kinematics models of the arm mechanismare presented in section III. The forces required for eachhydraulic actuator are estimated through the inverse dynamicmodel of the arm mechanism which is shown in sectionIV. Also, a force control technique using PID controller isadded to the virtual model of the joint mechanism built inADAMS software, in addition to the mathematical modelof the hydraulic system which is built in EASY5r. Thisco-simulation is shown in section V. After that the hardware

implementation is presented in section VI, showing thesystem components and the validation of the virtual modeland the controller. Finally, section VII is reserved for theconclusion and the future work.

II. MATHEMATICAL MODEL OF THE ELECTRO-HYDRAULICSYSTEM

Due to the fact of applying force/torque control on ahydraulic actuated system, a model based control is requiredto achieve high dynamic performance. Therefore, knowingthat each joint of the robot arm is coupled by one servovalve actuator, the dynamics of this kind of actuator shouldfirst be analyzed. These dynamic equations for the hydraulicsystem mainly come from the work of Merritt [21]. Thetransfer function between the control current Iin , and thespool displacement on valve, xv , is given by :

xv(s) =Kvω

2n

s2 + 2ζωns+ ω2nxv

Iin (1)

The control signal applied to the spool valve is directlyproportional to the spool position, meaning that the dynamicsof the valve motor/flapper are fast enough to be neglected.However, the effects of servovalve dynamics was included byother researchers [17] but in this case, it requires an additionalsensor to obtain the spool position and only minimal perfor-mance improvement is achieved for position tracking. So, theflow is related to the spool valve displacement, neglecting theleakage, can be described as :

Q1 = k1xv√

∆P1,∆P1 =

{Ps − P1 , xv ≥ 0

P1 − Pr , xv < 0

Q2 = k2xv√

∆P2,∆P2 =

{P2 − Pr , xv ≥ 0

Ps − P2 , xv < 0

Where k1, k2 are the flow gain coefficients of the valve;Ps and Pr are the supply pressure of the hydraulic oil andthe tank pressure, respectively.

As can be seen from the equations (2) and (3), the pres-surized flow provided by the servo valve can be decomposedin three components: a flow generated by the displacement ofthe piston, a flow induced by the compression of the oil in theactuator chamber, and a flow due to leakage in the actuator.

Q1 = A1x+V14βP1 +QLI +QLE1 (2)

Q2 = A2x+V24βP2 +QLI +QLE2 (3)

where V1 = V01 + A1x and V2 = V02 + A2x are the totalvolumes of the chambers; V01 and V02 are the extend andretract chamber volumes when x = 0; β is the effective bulkmodulus of the hydraulic oil; QLI is the internal flow leakageof the cylinder; QLE1 and QLE2 are the external flow leakageof the chambers.



Then, the dynamics of the actuator’s moving part is givenby :

mx = P1A1 − P2A2 − cx− Fs − Ff (4)

where, x is the actuator’s displacement; P1, P2 are the pres-sures inside the extend and retract chambers of the cylinder,respectively;A1 ,A2 are the piston areas facing the extend andretract chambers, respectively;Fs is the spring force; Ff isthe friction force; m is the mass of the moving part; c is theequivalent viscous damping coefficient.

III. THE KINEMATICS OF THE ARM MECHANISM

Most of the robots present are designed with rigid links,as Rigidty generates kinematic accuracy. So, the robotic linksare modeled as a rigid body systems to simplify modelingand to increase the computational efficiency [22]. Therefore,the arm mechanism can be considered as a system of rigidbodies connected together through joint elements as seen inFig.1, where, the arm mechanism can be considered a serialmanipulator of joints of revolute type. This model of the armmechanism will be main representation for calculating thegeometric, kinematic and dynamic models in the followingsections.

Fig. 1. The arm mechanism rigid model. The Base frame axis are denotedXr , Yr and Zr while the end effector frame axis are denoted Xe, Ye andZe

A. Geometrical Model

The kinematics of serial manipulators begins with the studyof the geometric relations between the joint variables, withone variable per joint. A seven axis manipulator, like the onedisplayed in Fig. 2 has seven joint variables, q1, q2,q3 .....qn. Denavit-Hartenberg notation was calculated and shown inFig. 2.

Here, the transformation from frame Ri+1 to frame Ri isrepresented by matrix T i+1

i , as:

T i+1i = Ti =

[Qi+1

i di+1i

0 1

](5)

Fig. 2. The arm mechanism coordinate frame.

In which, Qi+1i is the rotation matrix and di+1

i is thetranslation vector.

Qi+1i = Qi =

cos qi − cosαi sin qi sinαi sin qi

sin qi cosαi cos qi − sinαi cos qi

0 sinαi cosαi

(6)

di+1i = di =

ai cos qi

ai sin qi

bi

(7)

By applying the values of DH parameters in Fig.2 in Qi

and di as i ∈ 1 : 7 gives :

Qi+1i = Qi = ... = Q7 =

cos qi 0 sin qi

sin qi 0 − cos qi

0 1 0

(8)

d1 = d2 = d4 = d6 =

0

0

0

(9)

d3 =

l1 cos q3

l1 sin q3

0

(10)

d5 =

0

0

−l2

(11)

d7 =

l3 cos q7

l3 sin q7

0

(12)

B. Kinematic Model

Based on the general case of of a serial revolute axismanipulator seen in Fig.3, the angular velocity of the endeffector can be described as :



w0n+1 =

[e1 e2 .... en

]q1

q2

....

qn

(13)

While, the linear velocity of the end effector can be de-scribed as :

V 0n+1 =

[e1Xr1 e2Xr2 .... enXrn

]q1

q2

....

qn

(14)

Where, ri = di + di+1 + .... + dn. From both equation 15and equation 14, the linear and the velocity of the end effectorare represented as :

[w0

n+1 V 0n+1

]=

[e1 e2 .... en

e1Xr1 e2Xr2 .... enXrn

] q1

q2

....

qn

(15)

Where, the jacobian matrix can be described as J6xn whichequals :

J6Xn =

[e1 e2 .... en


](16)

Therefore, the direct kinematic model of the manipulator isdefined as :

[e1 e2 .... en


]=[J6Xn

]q1

q2

....

qn

(17)

In which, the angular velocity of each joint q1, q2,q3 .....qn are known, in order to calculate the angular and the linearvelocity of the end effector. Also, the inverse kinematic modelcan be described as :

q1

q2

....

qn

=[J−16Xn

] [e1 e2 .... en


](18)

Where, J−16Xn is denoted as inverse jacobian matrix. Whichis used to calculate the angular velocity of each joint from theknown velocities of the end effector.

Fig. 3. Serial n-revolute axis manipulator

IV. THE INVERSE DYNAMIC MODEL

Robot dynamics is the study of the relationship betweenthe applied forces/torques and the resulting motion of themanipulator. Similarly to kinematics, also for the dynamicsit is possible to define direct and inverse model. The directdynamic model is that once the forces/torques applied to thejoints knowing the joint positions and velocities, the jointaccelerations can be computed as: q = f (q,q,τ ) and then q =∫q dt , q =

∫q dt.

On the other hand, the inverse dynamic model is that oncethe joint accelerations, velocities and positions are known,the corresponding forces/torques can be computed as : τ =f−1(q,q, q) = g(q,q, q).

The main goal is to derive the dynamic model in short time.The number of link and joints in the kinematic chain, thetopology of the chain (e.g. serial or parallel), the position andorientation of the coordinate frames, and whether a recursiveprocedure is used or not, are factors that influence thecomputation time. The Newton/Euler formulation is usuallythe preferred choice for manipulators with many degreesof freedom. The reason is the recursive structure which theNewton/Euler formulation is based on. If the frames areattached in a convenient way, the recursions will be greatlysimplified. In this study, the Newton/Euler formulation isused to solve the inverse dynamic model.

Fig. 4. Analytical schematic of serial links dynamics



The Newton/Euler formalism is based on two fundamentallaws : the force balance 19 and the torque balance equation20. Fig.4 illustrates the internal and the external generatedforces applied to the i link.

∑link

f = m× a (19)

∑link

τ = ω × (Iω) + Iω (20)

So, in order to calculate the kinematic and the dynamicmodels for the case of 7 DOF arm mechanism are concludedas follows :

ωi = ωi−1 + ωi−1i (21)

αi = αi−1 + αi−1i + ωi−1 × ωi−1

i (22)

me,i = me,i−1 × rei−1,ei + ωi × (ωi × rei−1,ei) (23)

mc,i = me,i−1 + αi × rei−1,ci + ωi × (ωi × rei−1,ci) (24)

As the previous equations 21,22,23 and 24, are theequations for the inverse dynamic model to be applied forthe all the links of the mechanism in a recursive manner.The software Maple [23] was used to calculate the forwardand the backward recursive equations for the mechanism links.

V. MECHANISM CO-SIMULATION

In order to apply the required control algorithms, a virtualmodel of whole system has to be simulated. The whole armmechanism is a series of joints connected together to oneinput pressure source. But each joint has its electro-hydraulicservo system. The shoulder joint piston was taken as anexample to represent one degree of freedom for the actuatorson the arm mechanism. Once the the model and the appliedcontrollers are validated, They can be repeated for all otherjoints of the arm mechanism.

The virtual model of the hydraulic cylinder is built inADAMS and the mathematical model is built is EASY5r

and a C++ subroutine is created in EASY5r to write therequired controller functions to drive the virtual model inADAMS. This way, the physical responses are shown inADAMS, while the corresponding graphical response of themathematical model is shown in EASY5r (as seen in Fig5).

Moreover, the required sensory feedback is attained byadding a compression spring to the ADAMS model. Since itis difficult to model a feedback sensor in such simulation,the compression of the compliant element, which is here theadded spring, makes the force on the load can be calculatedusing Hooke′s Law. A feedback controller calculates the

Fig. 5. Block diagram showing the co-simulation of arm mechanism usingADAMS and EASY5

Parameter Value Unit

Ps 50 bar

Iin ±15 mA

β 1.5 GPa

Pa 1 bar

A1 0.0025 m2

A2 0.00125 m2

Q 6.666 ∗ 10−5 m3/s

ζ 0.8 −m 20 Kg

ωn 30 rad/s

c 3000 N.s/m

µ 300 N.s/m

K 1000 N/m

TABLE ITHE SIMULATION PARAMETERS FOR THE SYSTEM

error between the actual force and the desired force, applyingappropriate current to the motor to correct any force errors.

Fig. 6. Position and Force control strategies of the robot arm

The nominal simulation values of the electro-hydraulicservoactuator system are listed in table I. In which the systemis simulated with a time interval of xs against the loadapplied of the hydraulic piston.

The hydraulic system was built in EASY5r, in whichthe auxiliary components are: The reservoir, relief valve,pipes, and the junctions are connected with the main sub-model(Actuator and Controller) which is shown in Fig.7.



Fig. 7. Modeling of the hydraulic system in EASY5

In this sub-model, as shown in Fig.8, the servo valvedenoted as (VI), the actuator chamber as (AC) and the springas (SF) are connected. Where, the specified inputs parametersof the servo valve and the actuators are given. From thisconnection, Some generated forces, that represent the forcebalance equation(Eq.25), can be measured from this model.These forces are :

Fa = Fp − Fs − Fd − Ff (25)

Fig. 8. Configuration of servo valve actuator in EASY5r

So, a new closed loop is built in EASY5r. This closed loop(seen in Fig.9), Where it can be divided into 6 main groups :

1) Actuator group:The servo valve controls the pressurized flows intoand out of the actuator, moving the piston, while thespring represents the external force on the actuator. Thevalve receives the pressurized flow from the hydraulicsystem (maximum rated pressure Pmax = 210bars)and the control current signal from Group 5 (maximuminput current Imax = 15m.A), while the actuator andspring can give the measured feedback values for thecontroller in Group 2 and 3.

2) Error group:It generates the error from the difference of thereference value and the measured feedback value.

3) PID controller group:It receives the error signal from the group 2 andgenerates the control signal(voltage)for Group 4.

4) Saturation group:Its function is to limit the control voltage signal fromthe controller in the suitable range. And the saturationlimits are −15v and 15v

5) Voltage to current group:It transforms the limited control voltage to the controlcurrent, putting into the servo valve in Group 1. And itis shown that transfer function equals 1

0.01s+1 .

6) ADAMS Simulation Block:It sends/receives the output signal from the mathematicalmodel built in Easy5 to the virtual model built inADAMS.

Fig. 9. Closed loop Co-simulation of an electro-hydraulic servo actuator withPID Controller

A. Position control

In spite of the fact that a force control is to be performedto the system, Acceptable position tracking should be alsoachieved. As the robot needs to perform a trajectory incertain directions while a precise control of the force isrequired in the same time. This means that in all otherdirections (and orientations), the robot needs to perform astandard, programmed position trajectory. Therefore, in realapplications, force control is in fact an hybrid force/positioncontrol for which the joint torques are computed using tworeferences [17]. On top of that, the control scheme needs tobe dynamically changed between two operations. Therefore aproper position control should be shown for the piston beforeapplying the algorithms of force control.

A PID control block was added to the proposed model.Where its gains are added to the simulated system usingZieglar Nichols tuning method to examine the systemresponse. Several simulations were performed with variousinput trajectories to determine the desired position. As aresult of such simulation, the desired trajectory is trackedwith minimum errors with gains Kp = 0.4, Ki = 0.08 and



Kd = 1 as shown in Fig.10.

Fig. 10. Position control tracking at xr = 20mm

B. Force control

As previously mentioned in section III-A, roboticmanipulators are modeled as a rigid body systems withtorques as its primary input. So, in order to achieve highcontrol performance, A controlled torque source is requiredfor each joint of the rigid body system.

Since the manipulator system at hand is hydraulicallyactuated, The hydraulic system control has to be studied. Byits physical nature, a hydraulic actuator is a velocity source,i.e., a given controlled flow rate into the actuator will resultsin a certain velocity. Hydraulic actuators are characterizedby its high impedance (mechanically stiff) systems. Due tothe need of having a force controlled joints in the humanoidrobot HYDROïD, force control strategies are needed to bedeveloped.

The controller to be applied is a conventional PIDcontroller, where it can be simply added to the mathematicalmodel built in EASY5r (as will be shown in sectionV).But in spite of PID controllers are considered the mostwidely used controller in industrial applications [24], theoutput desired performance in the closed loop systems cannot be guaranteed. As the presence of non linear plantparameter variations and external disturbances greatly affectthe controller applied. As for hydraulic servo systems, themain parameters causing non-linearity for the system are : Thehydraulic fluid compressibility, complex flow properties of theservo valve, friction, system mass and variable loading [17].Further research showed that the two common approaches tocompensate the nonlinear behavior of hydraulic servo systemswhich are : adaptive control and variable structure systems.But, both are very complex in implementation [18].

The output force calculated by the mathematical model inEASY5r is applied to the virtual model present in ADAMS

Fig. 11. Simulation of the hydraulic actuator in ADAMS

as shown in Fig.11 and it is simulated, In which the resultantforce is compared to force applied as shown in Fig.12. ThePID gains were found to be Kp = 4.4, Ki = 0.02 andKd = 0. Moreover, the damping and the spring force valuesare shown in Fig.16. Also, the pressure forces Pextensionand Pretraction are displayed in Fig.14 as blue dotted lineand a black continuous line respectively.

Fig. 12. Closed loop force control output using PID controller

Fig. 13. The output graphs of the Co-simulation of the hydraulic piston.(a)shows the damping force Fd while (b) shows the spring force Fs.

VI. HARDWARE IMPLEMENTATION

After achieving acceptable results in simulation, the controllaw was implemented on the existing hydraulic test systemshown in Fig.15. In which, the whole hydraulic circuit wasbuilt on a test bench having its main components shown intable II. The real target for control implementation is to applyit on the actuators of the arm mechanism. Therefore, theshoulder joint piston was chosen to apply the control law.The dimensions of the used cylinder 0.185 stroke and a 42



Fig. 14. Pressure forces acting on the hydraulic piston

Mechanical Part Specification Manufacturer Model

Hydraulic radial pump up to 220 bars MTS Series 505.6 SilentFlowHydraulic servo valve ±15 mA MOOG MOOG30

Pressure sensors up to 1000 bar Keller Series 4 LCPressure gauges Scale up to 1000 bars WIKA Model 213.53

Pressure relief valve 200 bar MTS Integrated in 505.6 MTS pumpLoad Cell up to 50 KN ELAF piezo resistive load cell

Linear Position Sensor 0 to 50 cm range ASM magnetic position sensor

TABLE IITHE MAIN COMPONENTS FOR THE HYDRAULIC TEST BENCH

mm outer diameter diameter. The same load that was appliedin EASY5r simulation model is added here. The piston wasconnected to 4 kg of weights mounted on a horizontal linearpulley track system. Fluid pressure was supplied at 50 bar bya MTS 505 silent flow hydraulic group. A 12 bit A/D andD/A board connected to personal computer, which is used toobtain system data from the two pressure sensors and outputthe control signal to the servovalve. A sampling rate of 100KS/s was used. A screen-shot for the hardware is shown inFig.16.

Fig. 15. The hardware schematic used to control the electro-hydraulic servoactuator system

The position sensor provides the precise position of thepiston, while the load cell measures the force imparted onthe load by the actuator. The feedback controller calculatesthe error between the measured force and the desired forceand applies the appropriate current to the motor to correct

any discrepancies. The active force sensing and closed loopcontrol work together to decrease the effects of friction andinertia, thereby attaining a higher force fidelity and lowerimpedance than with current control alone.

Fig. 16. A screen-shot for the developed electro-hydraulic servo system.(1)Servo-valve, (2)Integrated Pressure sensors, (3)Load cell, (4)Hydrauliccylinder piston and (5)Linear Position Sensor

The output position and force outputs are shown in Fig.17and Fig.18 respectively. The PID gains for the position loopwere found to be Kp = 3.46, Ki = 1.11 and Kd = 0.Meanwhile, the PID gains for the force control loop wereKp = 22.5, Ki = 0.0196 and Kd = 0.

Fig. 17. Position control response at reference value xr = 3 cm

The output response of position control is shown in Fig.17.The reference position of the piston xr and the outputdisplacement xp are shown in blue dotted line and black linerespectively. There were no steady state error in the outputbut there is a small delay which is negligible in our case.

The output response of force control is shown in Fig.18.The reference position of the piston Fr and the outputdisplacement Fp are shown in blue dotted line and blackline respectively. There were no steady state error in theoutput but there is an overshoot in a very limited timeduring flipping the current signal. This overshoot due toeither presence a high coefficient of static friction or someuncontrollable current overshoot from the servo actuatorboard. Such overshoot can be smoothed through the additionof capacitors in the electronic board controlling the servovalve. More performance enhancement can be done through



Fig. 18. Force control response at reference value Fr between 100 and 300N

further research on friction compensation techniques toeliminate the overshoot error. Moreover, the pressure outputvalues during extension and retraction are shown in Fig.19.

Fig. 19. Pressure values during extension and retraction of the hydrauliccylinder.

VII. CONCLUSION

This paper presents the mathematical model of the electro-hydraulic actuators used for arm mechanism of the robotHYDROïD. Based on Newton/Euler formalism, the kinematicmodel and inverse dynamic models of the HYDROïD armmechanism were calculated. The mathematical model ofthe electro-hydraulic servo system was used in EASY5r

to drive the virtual model of shoulder joint cylinder inADAMS software. PID controllers for both position and forcewere theoretically revised for this mechanism. Furthermore,experimental validation for these controllers was presentedand the results were shown and discussed.

For future work, the dynamic results reached in this studycan be applied on all the joints of the arm mechanism notjust for one actuator. In which the practical responses canbe compared with the model simulation and find out thebest controller gains for each joint. Further research canbe done to compensate the error present in controller gainswhile controlling position and force. As the correct controllershould control both features simultaneously. Moreover, furtherresearch in achieving precise torque control for the hydraulicservo system acts as the first step in achieving a compliancecontrol joints for an overall safe interaction hydraulic robot.Also, the addition of the new integrated electro-hydraulic

actuator will greatly enhance the mobility of the mechanismand will decrease the nonlinear problems caused by the servovalves and the hydraulic connections.

REFERENCES

[1] MSC Software. www.mscsoftware.com/products/caetools/adams.aspx. Website, March 2015.

[2] Claude Ginsburg. Modeling and simulation of complexhydraulic valves using easy5 software. 1997

[3] N. G. Tsagarakis, G. Metta, G. Sandini, D. Vernon, R.Beira, F. Becchi, L. Righetti, J. Santos-Victor, a. J. Ijspeert,M. C. Carrozza, and D. G. Caldwell, “iCub: the design andrealization of an open humanoid platform for cognitive andneuroscience research,” Adv. Robot., vol. 21, no. 10, pp.1151–1175, 2007.

[4] A. Abdellatif, Samer Alfayad, Fethi B. Ouezdou, SalemA. Haggag, Faycal Namoun,“Mathematical Modeling ofan Electro-Hydraulic Actuator for Humanoid Robots”,WSEAS Transactions on Circuits and Systems, ISSN /E-ISSN: 1109-2734 / 2224-266X, Volume 16, 2017, Art.# 22, pp. 187-195

[5] Thomas Buschmann, Sebastian Lohmeier, and Heinz Ul-brich. Humanoid robot Lola: Design and walking con-trol. Journal of Physiology Paris, 103(3-5):141–148, 2009.ISSN 09284257. doi: 10.1016/j.jphysparis.2009.07.008.

[6] Kenji Kaneko, Fumio Kanehiro, Mitsuharu Morisawa,Kazuhiko Akachi, Go Miyamori, Atsushi Hayashi, andNoriyuki Kanehira. Humanoid robot HRP-4 - Humanoidrobotics platform with lightweight and slim body. IEEEInternational Conference on Intelligent Robots and Sys-tems, pages 4400–4407, 2011. ISSN 2153-0858. doi:10.1109/IROS.2011.6048074.

[7] Ricardo Tellez, Francesco Ferro, Sergio Garcia, EstebanGomez, Enric Jorge, Dario Mora, Daniel Pinyol, JoanPoyatos, Oriol Torres, Jorge Velazquez, and Davide Fa-conti. Reem-B : an autonomous lightweight human-sizehumanoid robot.

[8] Scott Kuindersma, Robin Deits, Maurice Fallon Andr,Hongkai Dai, Frank Permenter, Koolen Pat, and MarionRuss. Optimization-based Locomotion Planning , Estima-tion , and Control Design for the Atlas Humanoid Robot.

[9] N Pollard, J K Hodgins, M J Riley, and C G Atkeson.Adapting Human Motion for the Control of a HumanoidRobot. Proc. IEEE Intl Conf. on Robotics and Automation(ICRA), 2002.

[10] C. Semini, N. G. Tsagarakis, E. Guglielmino, M. Foc-chi, F. Cannella, and D. G. Caldwell. Design of HyQ- a hydraulically and electrically actuated quadrupedrobot. Proceedings of the Institution of Mechanical En-gineers, Part I: Journal of Systems and Control Engineer-ing, 225(February):831–849, 2011. ISSN 0959-6518. doi:10.1177/0959651811402275.

[11] A. Abdellatif, S. Alfayad, Arne-Christoph Hildebrandt,F.B. Ouezdou, N. Mechbal, Yahya Zweiri. Development ofa New Hydraulic Ankle for HYDROïD Humanoid Robot,Journal of Intelligent & Robotic Systems, 2018. Pages:1-16, DOI: 10.1007/s10846-017-0750-z



[12] T. H. Lambert and R. M. Davies, Investigationof the Response of an Hydraulic Servomechanismwith Inertial Load. Journal of Mechanical Engineer-ing Science, Vol5, N3, pages = (281-294), 1963. doi:10.1243/JMES/JOUR/1963/005/037/02.

[13] Jerry E Pratt and Benjamin T Krupp. Series ElasticActuators for legged robots. Proceedings of SPIE 5422,Unmanned Ground Vehicle Technology VI, 5422:135–144, 2004. ISSN 0277786X. doi: 10.1117/12.548000.

[14] R Liu. Nonlinear control of electro-hydraulic servosys-tems: theory and experiment. page 122, 1998.

[15] Andrew Alleyne. Tracing Control for Hydraulic. 121(April 1998):184–190, 2013.

[16] C.L. Hwang and C.H. Lan. The position control of elec-trohydraulic servomechanism via a novel variable struc-ture control. Mechatronics, 4(4):369–391, 1994. ISSN09574158. doi: 10.1016/0957-4158(94)90018-3.

[17] G a Sohl and J E Bobrow. Experiments and simulationson the nonlinear control of a hydraulic servosystem.Proceedings of the 1997 American Control ConferenceCat No97CH36041, 1(2):238–247, 1999. ISSN 10636536.doi: 10.1109/87.748150.

[18] Prut Nakkarat and Suwat Kuntanapreeda. Observerbasedbackstepping force control of an electrohydraulic actuator.Control Engineering Practice, 17(8):895–902, 2009. ISSN09670661.

[19] K. Baghestan, S.M. Rezaei, H.a. Talebi, and M. Zareine-jad. Robust force control in a novel electro-hydraulicstructure using polytopic uncertainty representation. ISATransactions, 53(6):1873–1880, 2014. ISSN 00190578.doi: 10.1016/j.isatra.2014.08.002.

[20] M Elasswad, A Tayba, A. Abdellatif, S.Alfayad,K.Khalil. Development of lightweight hydraulic cylinderfor humanoid robots applications. Proceedings of theInstitution of Mechanical Engineers, Part C: Journal ofMechanical Engineering Science, September 21, 2017,https://doi.org/10.1177/0954406217731794

[21] Herbert E. Merrit. hydraulic control systems -Herbert EMerritt.pdf, 1967.

[22] Wei Wang, Robert N.K. Loh, and Edward Y. Gu. Pas-sive compliance versus active compliance in robot-basedautomated assembly systems. Industrial Robot: An Inter-national Journal, 25(1):48–57, February 1998. ISSN 0143-991X. doi: 10.1108/01439919810196964.

[23] Michael B. Monagan, Keith O. Geddes, K. Michael Heal,George Labahn, Stefan M. Vorkoetter, James McCarron,and Paul DeMarco. Maple 10 Programming Guide. Maple-soft, Waterloo ON, Canada, 2005.

[24] Valery D Yurkevich. PI / PID Control for NonlinearSystems via Singular Perturbation Technique. pages 0–30.


Documents

Force control for electro-hydraulic servo actuator used ... · Force control for electro-hydraulic servo actuator used for a humanoid robotic arm A.Abdellatif*, Tan Quang DUONG*,

Force control for electro-hydraulic servo actuator used ... · Force control for electro-hydraulic servo actuator used for a humanoid robotic arm A.Abdellatif, Tan Quang DUONG,