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High-fidelity sliding mode control of a pneumatichaptic teleoperation systemSean Hodgsona, Mahdi Tavakolia, Arnaud Lelevéb & Minh Tu Phamb

a Department of Electrical and Computer Engineering, University of Alberta, Edmonton, ABT6G2V4, Canada.b Laboratoire Ampère, UMR CNRS 5005, Université de Lyon, Insa-Lyon, F-69621 VilleurbanneCedex, France.Published online: 25 Feb 2014.

To cite this article: Sean Hodgson, Mahdi Tavakoli, Arnaud Lelevé & Minh Tu Pham (2014) High-fidelity sliding mode control ofa pneumatic haptic teleoperation system, Advanced Robotics, 28:10, 659-671, DOI: 10.1080/01691864.2014.888130

To link to this article: http://dx.doi.org/10.1080/01691864.2014.888130

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Advanced Robotics, 2014Vol. 28, No. 10, 659–671, http://dx.doi.org/10.1080/01691864.2014.888130

FULL PAPER

High-fidelity sliding mode control of a pneumatic haptic teleoperation system

Sean Hodgsona, Mahdi Tavakolia, Arnaud Lelevéb∗ and Minh Tu Phamb

aDepartment of Electrical and Computer Engineering, University of Alberta, Edmonton, AB T6G2V4, Canada; bLaboratoire Ampère,UMR CNRS 5005, Université de Lyon, Insa-Lyon, F-69621 Villeurbanne Cedex, France

(Received 4 October 2013; accepted 2 December 2013)

For a pneumatic teleoperation system with on/off solenoid valves, sliding mode control laws for position and forceensuring low switching (open/close) activity of the valves are developed. Since each pneumatic actuator has two pneumaticchambers with a total of four on/off valves, 16 possible combinations (‘operating modes’) for the valves’ on/off positionsexist, but only seven of which are both functional and unique. While previous work has focused on three-mode sliding-based position control of one pneumatic actuator, this paper develops the seven-mode sliding-based bilateral controlof a teleoperation system comprising a pair of pneumatic actuators. The proposed bilateral sliding control schemes areexperimentally validated on a pair of actuators utilizing position-position and force-position teleoperation architectures.The results demonstrate that leveraging the additional modes of operation leads to more efficient and smoother controlof the pneumatic teleoperation system. It was found that viscous friction forces were crippling haptic feedback in theposition-position architecture. Through the use of force sensors, the force-position architecture was able to compensatefor the heavy viscous friction forces.

Keywords: pneumatic actuator; on/off solenoid valve; teleoperation; transparency; sliding mode control

1. Introduction

Teleoperation aims to allow a human operator to carry outa sensing or manipulation task in an environment that isnot amenable to direct interaction. The interaction betweenthe human, the teleoperator, and the environment need tobe controlled in such a way as to ensure a high level of‘fidelity’ defined as the accurate transmissions of the en-vironment’s mechanical properties to the human operator.[1–4] Bilateral teleoperation systems have been developedfor a variety of applications ranging from telesurgery tospace exploration.[4–8]

In this paper, we investigate the performance of low-costpneumatic components when used as actuators in teleoper-ation systems. Pneumatic actuators offer many advantagesfor positioning applications such as low maintenance cost,high ratio of power to weight, cleanliness, and safety. Also,where it is not possible to use electric motors such as inrobot-assisted surgery under MRI guidance, it is possibleto use pneumatic actuators to drive robots. On the downside, pneumatic actuators typically suffer from stiction andsensitivity of the actuator dynamics to external loading andpiston position along the cylinder stroke.[9] Thus, designingan effective control architecture for a pneumatic actuator isfairly challenging and this is exacerbated by the nonlinearpressure dynamics in pneumatic chambers.[10]

∗Corresponding author. Email: arnaud.leleve@insa-lyon.fr

Some pneumatic system utilize servo valves, which allowfor a continuous change of the input mass flow rate.[11]However, servo valves are expensive devices. A low-costsubstitute to the servo valve is the on/off (i.e. open/close)solenoid valve, which does not require the expensive com-ponents used in manufacturing a servo valve. On the downside, due to the discrete-input nature of the on/off solenoidvalve, it cannot use continuous control laws as was thecase with the servo valve. The input discontinuity makesthe nonlinear dynamics of the pneumatic actuator harderto control. The noise they produce when actuated by aswitching controler may also be another drawback.

Past research has studied using solenoid-valve pneumaticactuators with a pulse width modulated (PWM) input.[12–15] In fact, a PWM input with a sufficiently high fre-quency to a solenoid valve can approximate the continuousinput properties of a servo valve.[16]

When considering a single pneumatic actuator that iscomprised of two chambers and four on/off solenoid valves,one would assume that there would be a total of 16 dis-tinct combinations of valves’on or off positions (‘operatingmodes’). Each chamber has two solenoid valves, one thatcan connect to a supply pressure, and one that can connect toan exhaust pressure. We do not want to connect the chamberto both pressure and exhaust at the same time, therefore we

© 2014 Taylor & Francis and The Robotics Society of Japan

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find that seven of the 16 possible valve combinations are in-valid. Of the remaining nine modes, three can be consideredfunctionally equivalent under no-load conditions. Thus, thesystem has a total of seven unique discrete modes. Thispoint is elaborated in Section 2.

In [17], a sliding mode control based on three of thesediscrete modes was applied to a two-chamber solenoid-valve actuator. It demonstrated good tracking and relativelylow steady-state position errors. One of the aspects thatcould be also analyzed while using solenoid valves is thevalve switching activity which is defined by the total countof switches performed by all the solenoid valves dividedby the total time of use. In [18], it has been demonstratedthat for a single pneumatic actuator, expanding the controlpossibilities from three-mode control to seven-mode controlreduces the tracking error and the valves’switching activity,causing an overall improvement in the pneumatic systemperformance. The use of such actuation and control in ateleoperation scheme has been studied in [6] but only with athree-mode control. In this paper, we design a seven-mode-based sliding control for application to position-positionand force-position control of a teleoperation system. It isexpected that the four additional modes of operation help toutilize just the necessary amounts of drive energy, allowingsmoother teleoperation control. To assess this conjecture,we compare in experimentations teleoperation performanceunder three-mode sliding control versus seven-modecontrol.

The organization of this paper is as follows. The discrete-input mode-based model of a single pneumatic actuator withsolenoid valves is given in Section 2. Sliding mode controlof a teleoperated pair of pneumatic actuators is reported inSection 3 at first for a position-position scheme and thenfor a force-position scheme. The experimental results arereported in Section 4 with the the analysis of the results inSection 5. Finally, the concluding remarks and directionsfor future research are presented in Section 6.

2. Discrete-input model

We consider a pneumatic actuator comprised of two cham-bers as shown in Figure 1. Each chamber is connected viaits two solenoid valves to either the supply pressure or theexhaust pressure. The model presented in this section isderived from the one in [18]. It is summed up here as it isnecessary for the comprehension of the rest of this paper.

To describe the air flow dynamics in a cylinder, weassume that:

• Air is an ideal gas and its kinetic energy is negligiblein the chambers,

• The pressure and the temperature are homogeneous ineach chamber,

• The evolution of the gas in each chamber is polytropic,• The mass flow rate leakages are negligible, and

• The supply and exhaust pressures are constant.

The pressure dynamics of the two chambers of the actu-ator can be approximated [19] as

PP = k

VP(rTP Q P − AP PP y)

PN = k

VN(rTN QN + AN PN y) (1)

where Q P and QN refer to mass flow rates (kg/s) of thechambers P and N, respectively; TN and TP refer to thetemperature (K) in chambers N and P, respectively. In ad-dition, VP and VN refer to volumes (m3) of the chambers Pand N, respectively, as shown below:

VP = AP (l/2 + y) VN = AN (l/2 − y) (2)

The mass flow rates Q P and QN can be derived in termsof the discrete voltage inputs U1, U2, U3, and U4 and thecontinuous pressure inputs PP and PN .

Q P = U1 Q(PS, PP) − U2 Q(PP , PE ) (3a)

QN = U3 Q(PS, PN ) − U4 Q(PN , PE ) (3b)

As shown below, the model for the mass flow rate has twoparameters: the critical pressure ratio bcrit and the mass flowrate constant Cval = Cρ0 where C is the sonic conductance(m3/(s Pa)) and ρ0 is the density of air (kg/m3) at a referencecondition T0 = 293 K [20]:

Q(PU p, PDown) = Cval PU p

√TAtm

TU p

×

⎧⎪⎪⎨⎪⎪⎩

√√√√1 −( PDown

PU p−bcri t

1−bcri t

) 2

, if PDownPU p

> bcrit (subsonic)

1, if PDownPU p

≤ bcrit (choked)

(4)

The value for bcrit = 0.433 comes directly from the datasheet of our solenoid valves, provided by Matrix-Bibus(BIBUS France S.A.S, Chaponnay, France). In the above,TU p is the upstream temperature of air and TAtm is theatmospheric temperature.

It may seem that the four on/off solenoid valves of theactuator allow a total of 16 possible combinations (‘modes’)in terms of the valves’ on/off positions. However, from afunctional perspective, we cannot allow a single chamberto both vent and pressurize at the same time, limiting theactuation possibilities to nine modes. In fact, as far as eachchamber of the pneumatic actuator is concerned, its twoon/off valves allow it to be in one of three ‘states’: con-nected to an air supply (pressurizing), connected to exhaustpressure (venting), or closed. Since each chamber is capableof being in one of the above-mentioned three states, thepneumatic actuator with two chambers can have a total ofnine discrete modes.

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Figure 1. Single pneumatic actuator with four on/off solenoid valves.

This reflects the maximum number of modes availablein a two-chamber pneumatic actuator, meaning that a con-troller can utilize only a subset of these modes. In general,the usage of more modes by the controller is expected tofacilitate the use of more optimal amounts of drive energy,meaning that improved positioning precision and reducedvalve switching (open/close) activity should result. This pa-per studies this issue in the context of teleoperation controlof a pair of pneumatic actuators equipped with solenoidvalves.

In [17], three out of nine discrete modes have been consid-ered for control of the two-chamber solenoid-valve actuatorof Figure 1. In [21], the three-mode model was expandedto a five-mode model. The five-mode control has two extramodes that utilize the option to have one chamber closedand the other chamber pressurized. In [22], the five-modemodel was further expanded to a new seven-mode modelutilizing two new modes. We mentioned previously thatthere are a total of nine discrete modes for the solenoidvalves. The question is whether there is any significantadvantage in further expansion of control possibilities fromseven to the full nine modes. The nine possible modes areshown in Table 1, refer to an open valve. Reviewing thesedifferent discrete modes, we observe that the modes M1,M8, and M9 are functionally similar (under no load) asthey correspond to the two chambers being both closed,both venting, and both pressurized, respectively. For allof these three modes, the pressure difference across thechamber P and chamber N is reduced to zero over time,implying that the piston acceleration profile will be similarfor them. In our research, the mode M1 was selected outof the three equivalent modes (M1, M8, and M9) because itprovides the highest resistance to piston motion, which willfacilitate reducing the position tracking error to zero. Thus,our modeling and control analysis from this point forwardwill focus on the modes M1 to M7.

The dynamics of the pneumatic actuator of Figure 1involving the chamber pressures and the resulting pistonmotion is

(AP PP − AN PN ) − bV y − τSt + τExt = M y (5)

where PP and PN refer to pressures (Pa) inside the chambersP and N, respectively; AP and AN refer to the piston cylin-der areas (m2) in the chambers P and N, respectively; bV isthe viscosity coefficient (N s/m), M is the total mass of theload and the piston (kg), τSt is the stiction force (N), τExt isthe external force (N), and y refers to the piston position (m)shown in Figure 1. Note the arrows for position y and forceFExt and Fst in Figure 1 refer to their positive directions.The stiction force τSt was considered to be negligible sincethe pneumatic actuator used in our experiments was anAirpel anti-stiction cylinder (All Air Inc., New York, USA).

It is possible to find the switched dynamical equation forthe seven-mode system by taking the derivative of (5) andsubstituting the pressure dynamics PP and PN :

...y =

{f + τExt

M , mode M1

f + (−1) j g j + τExtM , mode M j �= M1

(6)

where the integer j ranges from 2 and 7 and

f = −bV

My − k

M

(AP PP

l/2 + y+ AN PN

l/2 − y

)y

g2 = krT

M

Q(PS, PP)

(l/2 + y)g3 = krT

M

Q(PP , PE )

(l/2 + y)

g4 = krT

M

Q(PN , PE )

(l/2 − y)g5 = krT

M

Q(PS, PN )

(l/2 − y)g6 = g2 + g4 g7 = g5 + g3

where PS and PE are the pressures of the compressed airsupply and the exhaust (atmosphere), respectively; l is thetotal length of the chamber, k refers to the polytropicconstant, T is the supply temperature, and r refers to the

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Table 1. Nine discrete modes of the open-loop actuator.

M1 M2 M3 M4 M5 M6 M7 M8 M9

U1 0 1 0 0 0 1 0 0 1U2 0 0 1 0 0 0 1 1 0U3 0 0 0 0 1 0 1 0 1U4 0 0 0 1 0 1 0 1 0

universal gas constant (J/(kg K)). In general, Q(PU p, PDown),in which PU p is the upstream pressure and PDown is thedownstream pressure, refers to the expression for the massflow rate through an orifice. It should be noted that thefunctions g2 through g7 are all positive or equal to zero.

3. Sliding mode control of a dual pneumaticteleoperation system

3.1. Position-position control

For a teleoperation system, the master and slave dynamicswill be the same as those described previously with thedifference that the common variables will be re-labeled asshown in Table 2. The block diagram in Figure 2 showsthe architecture of a position-position bilateral teleoper-ation system (also called Position Error Based in [23]).In this setup, the human operator dynamics, Zh , and theenvironment dynamics, Ze, are unknown or uncertain; τh

and τe are the operator force applied on the master and theenvironmental force applied on the slave, respectively. Theτ ∗

h and τ ∗e variables are the continuous exogenous input

forces from the operator and the environment, which havelimited energy and as such are bounded.

The equations for the master and slave dynamics are

M ym = A(PP,m − PN ,m) − bV ym + τh

M ys = A(PP,s − PN ,s) − bV ys − τe (7)

Substituting the variables from Table 2 into (6), we obtain

...y m =

{fm + τh/M, mode M1fm + (−1)vgv,m + τh/M, mode Mv �= M1

...y s =

{fs − τe/M, mode M1fs + (−1)t gt,s − τe/M, mode Mt �= M1

(8)

where v ∈ {1, . . . , 7} and t ∈ {1, . . . , 7}.For sliding mode position control purposes, let us define

the switching function as

sp = ep

ω2p

+ 2ξpep

ωp+ ep (9)

in which ep = ym −ys and ξ and ω are constant and positivenumbers. It should be noted that the slave controller usesthis switching function (sp) whereas the master controlleruses its negative (−sp).

Thus, the switching function sp provides a measure ofthe distance from the sliding surface based on the position,

velocity, and acceleration errors. Take the derivative of (9)to get

s p =...e p

ω2+ 2ξ ep

ω+ ep

=...y m − ...

y s

ω2+ 2ξ ep

ω+ ep (10)

Considering the slave actuator (the workflow is symmet-ric for the master), by substituting the actuator dynamics(6) into (10) through ys , we obtain

s p ={

λs, mode M1

λs + (−1)i gt,s/ω2, mode Mt , (2 ≤ i ≤ 7)

(11)where λ = ( fs − ...

y m + τExt/M)/ω2 + 2ξ ep/ω + ep withτExt = −τe for the slave or τh for the master.

To ensure the convergence to the sliding surface sp = 0,we wish to have the s p such that sp is always approachingzero regardless of its sign. To ensure this, we will invokethe seven different modes of the open-loop system based onthe current value of sp relative to five distinct regions forthe value of sp. These regions of sp and the operating modeof the system as selected by the sliding mode controller areillustrated in Table 3. This attempts to ensure s p < 0 whensp > 0 and s p > 0 when sp < 0, leading to the convergenceto sp = 0. The choice rules concerning modes M3 vs M5and M2 vs M4 are detailed in [18].

When we utilize the pneumatic controller that alters theoperating mode of the pneumatic actuator system based onTable 3, for the lowest error band |sp| < ε, we use themode M1 which has no active effect on the system (i.e. noactuation). For the highest positive error band sp > β, weuse the mode M7, which exerts the highest drive (causingthe highest piston acceleration) in the negative direction.Conversely, for the largest negative error sp ≤ −β, weutilize mode M6, which has the highest drive in the positivedirection.[22] Evidently, this control action is designed toensure that the system is always approaching the sp = 0surface. For methodology on the selection of β and ε, pleaserefer to [18].

To be able to analyze the closed-loop position trackingperformance, consider the Lyapunov function candidate

Vlya = 1

2s2

p (12)

which is positive definite. Therefore, if Vlya < 0, then Vlya

will be decreasing. If Vlya is decreasing, |sp| will also be

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Figure 2. Position-position-based teleoperation.

Table 2. Master/slave actuator variable namesa.

Single y Pq τExt gi f

Master ym Pq,m τh gv,m fmSlave ys Pq,s −τe gt,s fs

Note: a where q ∈ {P, N }, v ∈ {1, . . . , 7}, and t ∈ {1, . . . , 7}.

Table 3. Selection of the operating mode based on the value of sp .

Region of sp Selected Magnitude of resultingoperating mode s p from (11)

sp > β M7 Large negativeβ ≥ sp > ε M3 and M5 Medium negativeε ≥ sp > −ε M1 Small−ε ≥ sp > −β M2 and M4 Medium positive−β ≥ sp M6 Large positive

decreasing. Assuming sp is initially bounded and |sp| isalways decreasing, then sp will always be bounded. Thismeans that sp will approach zero if we control the systemso that

Vlya = s psp < −ηp|sp| (13)

for some positive constant ηp > 0.[24] This condition canbe rewritten as {

s p > ηp if sp < 0s p < −ηp if sp > 0

(14)

In the above, s p is found by taking the derivative of (9):

s p =...e p

ω2p

+ 2ξpep

ωp+ ep (15)

Let us consider two possible cases for the sign of s p inthe following.

−sgn(sp) · s p > ηp (16)

Based on the aforementioned sliding mode control(specifically, see Table 3), the master and slave systems’closed-loop dynamics become

...y m = fm − sgn(sp) · gv,m + τh/M v ∈ {3, 5, 7}...y s = fs + sgn(sp) · gt,s − τe/M t ∈ {2, 4, 6} (17)

because, as noted earlier, the slave controller uses theswitching function sp while the master controller uses theswitching function −sp. Given

...e p = ...

y m − ...y s = ( fm − fs) − sgn(sp).

× (gv,m + gt,s) + (τh + τe)/M (18)

Substituting (18) into (15), we find

s p = λp − sgn(sp) · (gv,m + gt,s)/ω2p (19)

where

λp = ( fm − fs) + (τh + τe)/M

ω2p

+ 2ξp

ωpep + ep (20)

Finally, by substituting (19) into (16), we find that condition(16) is fulfilled if and only if the following condition is met:

(gv,m + gt,s) > (ηp + sgn(sp) · λp+)ω2p (21)

Therefore, if the positive-valued functions gi,m and gi,s

for i ∈ {2, · · · , 7} are sufficiently large, then the controlstrategy can satisfy condition (14) (or equivalently (21)) aslong as λp is bounded.

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664 S. Hodgson et al.

On the other hand, since all 12 functions gi,m and gi,s

are proportional to Cval , the valve’s mass flow rate con-stant, then choosing a large enough valve will ensure thatthese scalar functions will be sufficiently large and thusthe convergence to the sliding surface sp = 0 over time isguaranteed.

One of the distinct advantages of the position-positioncontrol architecture is that it does not require any forcesensors for ensuring master/slave force tracking and thusproviding some level of haptic feedback to the operator,but in general, it comes at the cost of nonideal master/slaveforce tracking.[4] As a remedy, the force-position control inthe next section is proposed.

3.2. Force-position control

The block diagram in Figure 3 shows the architecture fora force-position bilateral teleoperation system (also calledDirect Force Reflection in [23]); the slave side of the systemis identical to that in the position-position teleoperationcase. This means that the slave actuator controller usesthe same switching function (9) as in position-position ar-chitecture, and therefore the position tracking performanceand stability of the slave subsystem is ensured in the sameway as before. This teleoperation architecture is known toprovide better transparency than the position-position onebut requires two additionnal force sensors.

Force-position control is different from position-positioncontrol in that the control action for the master actuatorcomes from the readings of a sensor measuringslave/environment contact forces. Thus, the master’s slidingmode controller uses a new switching function given by

s f = e f

ω2f

+ 2ξ f e f

ω f+ e f (22)

where e f = −τh − τe is the force tracking error betweenthe master and the slave (according to (7) τh and τe haveopposite signs, thus (−τh − τe) is the force error). To beable to analyze the force tracking performance, considerthe following Lyapunov function candidate

Vlyb = 1

2s2

f (23)

Evidently, Vlyb is a positive-definite function and, ifVlyb < 0, Vlyb will be decreasing. If Vlyb is decreasing, |s f |will also be decreasing. Assuming s f is initially boundedand |s f | is decreasing, s f will approach zero. This requiresthat we control the master robot so that

Vlyb = s f s f < −η f |s f | (24)

for some positive constant η f > 0. This condition can berewritten as {

s f > η f if s f < 0s f < −η f if s f > 0

(25)

Take the derivative of (22) to obtain

s f =...e f

ω2f

+ 2ξ f e f

ω f+ e f (26)

Let us consider two possible cases for the sign of s f inthe following.

• Case 1: If we consider that s f is positive,according to (25), we have the following condition

s f < −η f (27)

Based on the aforementioned sliding modecontrol, the master and slave dynamics become

...y m = fm − gt,m + τh/M t ∈ {3, 5, 7}

...y s = fs + (−1)i gi,s − τe/M i ∈ {1 − 7}

(28)Substituting (28) into (26), we find

s f = λ f − gt,m M (29)

where

λ f = (−...y m + fm − (−1)i gi,s + ...

y s − fs)M

+...e f

ω2f

+ 2ξ f e f

ω f(30)

Also, substituting (29) into (27) we find

gt,m >λ f + η f

M(31)

Therefore, (27) is true if and only if condition (31) ismet.

• Case 2: If we consider that s f is negative,according to (25), we have the followingcondition

s f > η f (32)

Based on the aforementioned sliding modecontrol, the master and slave dynamics become

...y m = fm + gv,m + τh/M v ∈ {2, 4, 6}

...y s = fs + (−1)i gi,s − τe/M i ∈ {1 − 7}

(33)Substituting (33) into (26) we find

s f = λ f + gv,m M (34)

Finally, substituting (34) into (32) we find

gv,m >η f − λ f

M(35)

Therefore, (32) is true if and only if condition (35) ismet.

Therefore, if the positive-valued functions gi,m for i ∈{2, · · · , 7} are large enough, the control strategy can satisfy

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Figure 3. Force-position-based teleoperation.

condition (25). All six functions bi,m are proportional toCval , the valve’s mass flow rate constant, thus choosing alarge enough valve will ensure that these scalar functionswill be sufficiently large, and thus, ensure the convergenceto the sliding surface s f = 0 within finite time.

4. Experimental results

The purpose of this section is to test the advantage offered byseven-mode over three-mode control in the context of tele-operation control of a pneumatic actuator. We first evaluatethe position-position teleoperation architecture where thetwo robots are position controlled with the position of eachrobot serving as the reference position for the other robot.We then consider the force-position architecture where theslave robot utilizes position control and the master robotutilizes force control. For both of these architectures, we willcompare three-mode versus seven-mode control in termsof position tracking, force tracking, and valve switchingactivity.

To test the teleoperation control schemes discussed previ-ously, a quasi-periodic input motion pattern was applied bythe operator’s hand to the master. This input resembled threecycles of back-and-forth motion with an approximately 10mm RMS amplitude when the slave was in free space,followed by approximately two seconds of motion causingcontact between the slave and its environment, which wasa soft material located 14.5 mm away from the slave’s zeroposition. This entire motion pattern was repeated by thehuman operator three times over a 20 second period. Theposition and force profiles of the master and the slave robotswere measured via position and force sensors.

4.1. Experimental setup

In this paper, experiments were performed with a pair of1-DOF pneumatic actuators as the master and theslave – see Figure 4. The low friction cylinders (Airpelmodel M16D100D) have a 16 mm diameter and a 100mm stroke. The piston and shaft mass for each actuator

Figure 4. Experimental setup.

is approximately M = 900 g. In terms of sensors, a low-friction linear variable differential transformer is connectedto the cylinder in order to measure the linear positions.

The pneumatic solenoid valves (Matrix model GNK821213C3K) used to control the air flow have switching times ofapproximately 1.3 ms (opening time) and 0.2 ms (closingtime). With such fast switching times, the on/off valves areappropriate for the purposes of the proposed control. Thecontroller is implemented using a dSPACE board (DS1104),running at a sampling rate of 500 Hz. The double differen-ciation required for the sliding mode control has been per-formed with Matlab Simulink Discrete derivative blocks.Asnumerically differentiating twice produces a considerableamount of numerical noise, we compensated for this byfiltering the measured (resp.) position and force error bya second-order low-pass Butterworth filter with a cut-offof (resp.) 70Hz and 10 Hz. This reduces this noise to anacceptable level but introduces a small delay which thesliding mode control successfully compensates for. Thissampling rate has been chosen according to the open/closebandwidth of the valves and to enable an acceptable trackingresponse. The experimental setup has the model parameterslisted in Table 4.

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Figure 5. Position and force tracking profiles for the master and the slave robots in position-position architecture: (a) with three-modesliding control and (b) with seven-mode sliding control.

Table 4. System’s model parameters.

Var. Value Label

l 0.1 m Chamber LengthT 296K Supply TemperatureCval 3.4 × 10−9 kg/(s Pa) Mass Flow Rate Const.r 287.0 J/(kg K) Gas ConstantPS 300, 000 Pa Supply Air PressurePE 100, 000 Pa Exhaust Air Pressurek 1.2 Polytropic ConstantAP , AN 1.814 cm2 Piston Cylinder AreabV 50 N s/m Viscosity CoefficientM 0.9 kg Total Mass of load

4.2. Position-position teleoperation control

In this section, we review the experimental results for theposition-position architecture using the sliding mode con-trol design in Section 3.1. For this experiment, the follow-ing controller parameters were selected from preliminaryexperiments: ωp = 50 rad/s, ξp = 0.5, εp = 1 mm,β = 3.4 mm. The position-position scheme relied eitheron the three-mode or the seven-mode sliding control. Theresults are depicted in Figure 5. From these results, we cansee that there is a 58% improvement in the RMS error of

position tracking with the seven-mode-based control com-pared to the three-mode-based control. We can also see fromthese results that, in terms of the switching activity of thesolenoid valves, there is a 28% reduction in the seven-mode-based control compared to the three-mode-based control.The reason for this is that, in the three-mode control, eachchange of mode involves two switch transitions (betweencolumns M1 to M6 or M7 of Table 1). In the seven-modecontrol, however, each change of mode involves either onlyone switch transition (between columns M1 to M2–M5 or

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Figure 6. Position and force tracking profiles for the master and the slave robots in force-position architecture: (a) with three-mode slidingcontrol and (b) with seven-mode sliding control.

M2–M5 to M6 or M7 of Table 1) or two (between columnsM1 to M6 or M7 of Table 1) switch transitions. As a result,seven-mode control leads to less switching activity.

The force tracking performance is approximately the samefor the three-mode and the seven-mode control schemes asit is evident from Figure 5. When the slave is in contactwith the environment (τe �= 0), there is good force trackingas τh ≈ τe. However, under the free motion case, (i.e.when τe ≈ 0, because the slave is not in contact withthe environment), we see a sizable force feedback of about±10 N applied by the master to the operator.

4.3. Force-position teleoperation control

In this section, we review the experimental results for theforce-position architecture defined in Section 3.2. For thisexperiment, the following force controller parameters wereselected for the master controller: ω f = 50 rad/s, ξ f =1.0, ε f = 0.5 N, β = 1.7 N. The slave controller uti-lized the same control parameters described in Section 4.2.The force-position scheme was used with both three-modeand seven-mode sliding control. The results are charted inFigure 6. From these results, we can see that there is a44% improvement in position tracking error and a 20%

improvement in force tracking error for the seven-modecontrol when compared to the three-mode control underforce-position-based control. We can also see from theseresults that, in terms of the switching activity of the solenoidvalves, there is a 27% reduction in the seven-mode-basedcontrol compared to the three-mode-based control.

4.4. Performance comparison with more traditionalcontrollers

We performed a series of experiments where the proposedsliding mode control was replaced by a PD controller. ThePD gains (K pp and Kdp ) were set experimentally so thatthe system reacts as fast as possible with small trackingerrors. Results we obtained are depicted in Figures 7 and 8.It is difficult to compare the performances between 3 and7 modes as the input of the system is applied by a humanand is therefore not exactly reproducible. Nevertheless, itis clear that better performances were obtained with thesliding mode controller (Figure 5 and 6) compared to theP(D) controller. It is noteworthy that we could not furtherincrease more the proportional gain K pp as oscillationsappeared while K pp was greater than 0.04. For the forcecontroller, we could not significantly improve the response

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with a PI controller. This is why we show here only plotswith a proportional controller (K p f ) for the force loop.

5. Analysis and discussion

5.1. Position-position teleoperation control

In this section, we analyze the experimental results for theposition-position architecture reported in Section 4.2 anddepicted in Figure 5. From these results, we can observereasonable position tracking. This architecture also demon-strates good force tracking when the slave is in contact withthe environment. However, under the free-motion case (i.e.τe ≈ 0), while the slave is not in contact with the environ-ment, we see a sizable and varying force feedback of about±10 N in magnitude applied by the master to the operator.This severely disrupts the perception of free motion forthe operator and is undesirable. In the following, we try

to understand the cause of this unwanted force feedback tothe operator.

To illuminate the reason for the large force feedback ofabout ±10 N experienced by the operator when the slaveis in free space, let us examine the sum of forces actingon each actuator. The dynamics of the master and the slaveaccording to (5) are

M ys = −τe + τs − τF,s (36)

M ym = τh + τm − τF,m (37)

where τs = (AP PP,s − AN PN ,s), τm = (AP PP,m −AN PN ,m), τF,s = bV ys is the slave viscous friction force,and τF,m = bV ym is the master viscous friction force. Infact, in Figure 2, τs and τm are the inputs to the two ActuatorDynamics blocks, and we have τs = −τm because τs isimplemented based on the switching function sp, while τm

is implemented based on the switching function −sp. First,

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Figure 9. Position-position seven-mode simulated results.

consider the slave actuator in the free motion case whereτe = 0. We have

τs = M ys + τF,s (38)

As mentioned above, in position-position control ofFigure 2, the master’s control action is in the oppositedirection to that of the slave:

τm = −τs (39)

Substituting (38) into (39) gives us

τm = −M ys − τF,s (40)

Substituting (40) into (37) and solving for τh leads to

τh = M(ym + ys) + τF,m + τF,s (41)

Therefore, the operator has to overcome the viscous frictionand the inertias of both the master and the slave actuators inorder to accelerate the master – this is a serious deficiencyof position-position control especially in pneumatic systemswhere the viscous friction is high.

In our experiments, the peak accelerations are low (ym ≈ys = 0.8 m/s2) and the mass M = 0.1kg, so inertia effect isaround 8·10−2N. Peak velocity is ym ≈ ys = 100 mm/s andbV = 50 N s/m. Therefore, the peak of the viscous frictionforce will be τF,m ≈ τF,s = 5 N or a total unwanted force ofτF,m +τF,s ≈ 10 N. Therefore, it is the viscous friction thatis causing a heavy loading in terms of the haptic feedbackto the operator when the slave is in free space.

To further evaluate this phenomenon, we simulated inSimulink the free motion case. The results of this simu-lation are shown in Figure 9. These results also demon-strate a ±10 N force, which corroborates the analytical andexperimental results that we have obtained.

For the case where the slave actuator is in contact with theenvironment (τe �= 0), the hand was stopped by the forcefeedback and, as a result, the hand velocity decreased tonear zero. Since the unwanted force is caused by the viscousfriction, which is proportional to the actuators velocity, inFigure 5, the unwanted force vanished as the master andslave velocities went towards zero.

5.2. Force-position teleoperation control

In this section, we analyze the experimental results for theforce-position architecture reported in Section 4.3 and de-picted in Figure 6.

From these results, we can observe that during bothcontact motion and free motion cases, there is good forcetracking (−τh ≈ τe) as well as good position tracking.The force-position control scheme with pneumatic actuatorsdoes not have the sizable force feedback in free motion thatwas observed in the position-position control scheme.

The force controller on the master side minimizes thedifference in measured force between the slave and masterside. As a result, the controller on the master side com-pensates for the force of friction on the master actuator.The force measured by the slave actuator does not includethe force of friction on the slave side. Therefore, the onlyfeedback felt by the hand through the haptic interface is theenvironmental force measured on the slave actuator.

This makes the force-position teleoperation architecturemore advantageous then the position-position teleoperationarchitecture in terms of free motion force tracking.Althoughthe force-position had better force tracking, it was observedthat the position-position control architecture had a 16%improvement in position tracking when compared to theforce-position control architecture.

6. Concluding remarks

We described a pneumatic open-loop actuator system withseven modes of operation based on the state of the on/offsolenoid valves. For such a pneumatic system, sliding modecontrol laws were developed for position and forcecontrol. The sliding control laws were utilized in twodifferent teleoperation architectures: position-position andforce-position. The sliding controllers for the pneumaticsystem selects one of these seven modes of operation atany given time based on the magnitudes and signs of theswitching functions sp and s f for the position and forcecontrollers, respectively.

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These closed-loop controls were experimentally verifiedon a setup consisting of a pair of symmetric pneumaticactuators. For comparison, the experiments were conductedfor both the new seven-mode control and the traditionalthree-mode control. It was demonstrated that, for both tele-operation architectures, there was a 44–58% improvementin position tracking error and up to 27% reduction in theswitching activity with the seven-mode controller whencompared to the three-mode controller. It was also demon-strated that there was a 20% improvement in force trackingerror for the seven-mode controller in the force-positionarchitecture when compared to the three-mode controller inthe same architecture.

In the position-position architecture, it was found that dy-namic friction forces were causing large force applications(±10 N) on the operator hand under the free motion case(τe = 0). Thus, in terms of force tracking error, the force-position architecture is preferable for pneumatic actuators.We can see in Figure 5 that the free motion input impedancedisplayed to the operator was greatly reduced for the force-position architecture compared to the position-position ar-chitecture. The seven-mode-based teleoperation control hasperformed well in the experiments. This controller wouldbe a viable choice for use whenever a teleoperated robotuses on/off valves for actuation of the pneumatic chamber.

As written above, one of the main drawbacks of this sys-tem is the sound produced by the solenoid valves. However,this phenomenon could be diminished by putting the valvesaway from the cylinders. Unfortunately, the length of thehoses between valves and cylinders introduces an air prop-agation delay. Having studied the positive effects of seven-mode control (compared to 3-mode control) on positioningaccuracy and switching activity in a teleoperation system,the next step would be to examine the effect of this timedelay on this system.

In this paper, we had neglected the time delays. In general,time delay may destabilize an otherwise stable system. Ashas been demonstrated in [25], a regular sliding mode con-troller with some modification can control a slave system toperform a task well independently of time delay. Therefore,future research can explore using sliding mode control tohandle time delays in a pneumatic system.

AcknowledgementWe thank M. Christophe Ducat for the design of the testbed.

FundingThis work was supported by the Natural Sciences and Engineer-ing Research Council (NSERC) of Canada under grants [RGPIN372042-2009] and [CRDPJ 411603-2011].

Notes on contributorsSean Hodgson earned his BSc degree inElectrical Engineering and his BSc degreein Computer Science from the University ofSaskatchewan in 2004. After six years ofindustrial-based work experience he earned hisMSc in Electrical and Computer Engineering atthe University ofAlberta in 2011 with his thesis:Sliding-Mode Control of Pneumatic Actuatorsfor Robots and Tele-robots.

Mahdi Tavakoli received his BSc and MScdegrees in Electrical Engineering from Fer-dowsi University and K.N. Toosi University,Iran, in 1996 and 1999, respectively. He thenreceived his PhD degree in Electrical andComputer Engineering from the Universityof Western Ontario, London, ON, Canada, in2005. In 2006, he was a post-doctoral researchassociate at Canadian Surgical Technologies

andAdvanced Robotics (CSTAR), London, ON, Canada. In 2007–2008, and prior to joining the Department of Electrical andComputer Engineering at the University of Alberta as an assistantprofessor, Dr. Tavakoli was an NSERC Post-Doctoral Fellowwith the BioRobotics Laboratory of the School of Engineeringand Applied Sciences at Harvard University, Cambridge, MA,USA. Dr. Tavakoli’s research interests broadly involve the areasof robotics and systems control. Specifically, his research focuseson haptics and teleoperation control, medical robotics, and image-guided surgery. Dr. Tavakoli is the first author of the book ‘Hapticsfor Teleoperated Surgical Robotic Systems’ (World Scientific,2008).

Arnaud Leleve graduated in Electrical Engi-neering from the Ecole Normale Superieure deCachan, Cachan, France, in 1996. He receivedhis MSc degree in 1997 and his PhD degreein 2000, both in Automatic Control fromthe Universite de Montpellier 2, Montpellier,France. He was Assistant Professor at thisuniversity to teach Computer Networks (2000-2001). Since, he has been Associate Professor

with the Industrial Engineering Department of INSA Lyon,Universite de Lyon in Lyon, France. Dr Leleve worked atICTT/LIESP research laboratories (2001–2011) laboratorieswhere he focused on Virtual/Remote Laboratories in E-Learningapplications. Then, he joined the Automatic Control team ofAmpere research laboratory (CNRS UMR 5005) in 2011. Hisresearch interests now broadly involve the areas of robotics andsystems control, and focus on telerobotics and medical robotics.

Minh Tu Pham received the MS and PhDdegrees in control engineering from EcoleCentrale de Nantes and University of Nantes,France in 1998 and 2001, respectively. Hejoined the Laboratoire Ampere – UMR CNRS5005, Lyon, France, in 2003 and is currentlyan Associate Professor with the MechanicalEngineering Design Department of INSA,Lyon, France. His research interests include

robot identification, control, and the applications to medicalrobotics.

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