Constrained Bilateral Control with Master Force Scaling and Virtual Stiffness

R. M. Maheshi Ruwanthika1† and Seiichiro Katsura2

1,2Department of System Design Engineering, Keio University, Yokohama, Japan1(Tel: +81-80-8166-8746; E-mail: maheshi@katsura.sd.keio.ac.jp)

2( E-mail: katsura@sd.keio.ac.jp)

Abstract: Lack of sufficient workforce motivates the human-robot coexistence environment. The studies on man-machinesafety are essential in the fields of human tele support/care/assist. This paper proposes a safe operating technique forbilaterally controlled robots. It protects the remote slave environment from the excessive force applied by the masteroperator. The excess force beyond the safe limit is modeled via a virtual stiffness and a scaling factor to avoid transmittingto the slave side. The concept of parallel force position control is applied. Both force and position are limited on the slaveside while force and position on the master side are free to change accordingly with operator intention. The proposedmethod is verified through simulation.

Keywords: Bilateral control, Safety, Force limit, Virtual stiffness, Environment impedance.

1. INTRODUCTION

The world is experiencing an aging population witha declining birth rate. By 2060, in Japan 38.1% of thepopulation will be 65 years and above as at 2018 UnitedNations world population aging statistics projection [1].As a precaution, Japan is encouraging a robotics supportsociety in both industry and human living space. Thehyper-aged society needs more nursing/caring staff andthus more focuses on human assistant robots [2]. Ensur-ing safety of the human-robot coexisting environment isa vital challenge.

Safety is the primary concern in physical Human-Robot Interaction. The development of human assistantrobots with teleoperation capability may ensure safetyand social acceptance. The acceleration based bilateralcontrol technology facilitates contact with haptic sensa-tion to a distant environment via master-slave manipula-tors [3]. There are events to protect the slave environmentregardless of master force position commands. As anexample, consider a massaging robot that replicates realtime massage therapist movements or data saved on thedatabase. If the therapist or database apply excess forceon muscle, it is painful. In such an event, a slave robotcontrol system should be able to follow safe operatingsteps irrespective of the therapist or database commands.Therefore, research on constrained remote motion controlis important.

Constrained bilateral motion control studies aiminghazard avoidance have been conducted [4-6]. Taguchi etal. have designed a hazard avoidance controller with aselected ratio based on position and velocity informationfor acceleration based 4 channel bilateral controller [4].Sakaino et al. have successfully implemented constraintbilateral control based on oblique coordinate control forsafe robot motion by avoiding dangerous area [5, 6].

This paper proposes a constrained bilateral controlmethod based on virtual stiffness and a force scaling co-efficient on the master side. Section 2 describes model-

† R. M. Maheshi Ruwanthika is the presenter of this paper.

ing, section 3 demonstrates simulation results to verifythe proposed method and finally, section 4 concludes thepaper.

2. MOTION CONTROL

This paper proposes a constrained bilateral controlmethod based on virtual stiffness and a force scaling co-efficient on the master side. It protects the distant slaveenvironment beyond its safe force limit. Thus additionalforce applied by the master operator is not penetrating tothe slave side. Both force and position are limited on theslave side while force and position on the master side arefree to change accordingly with operator intention. Theconcept of parallel force position control is applied. Themodified method utilizes common mode force servoingand differential mode position control properties to main-tain acceleration based bilateral control structure. Thestudy applies disturbance observer (DOB) [7, 8] for ro-bust motion control and reaction force observer (RFOB)[9] for master-slave reaction force estimation.

2.1. Bilateral control

This paper focuses on acceleration based bilateral con-trol [10, 11]. In ideal bilateral control, both master andslave follow same position and force feedback obey thelaw of action and reaction. Thus, bilateral control systemwithout scaling follows Eq. (1) and Eq. (2). Those repre-sent the differential mode space and common mode spacecontrol goals.

xm − xs = 0 = xcmdd (1)

fextm + fexts = 0 = f cmdc (2)

The notations x, f , ©m, ©s, ©c, ©d, ©cmd, ©ext

represent position, force, master, slave, common mode,differential mode, command value, and external value re-spectively. Both position and force are combined in thecommon dimension of acceleration and master-slave ac-

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celeration references are given by Eq. (3) and Eq. (4).

xrefm =1

2Cp(x

ress − xresm )− Cf (f

extm + fexts ) (3)

xrefs =1

2Cp(x

resm − xress )− Cf (f

extm + fexts ) (4)

The notations x, ©ref , Cf , ©, ©res, Cp denote theacceleration, the reference value, the force feedback gain,the estimated value, the response value and the PD con-troller gain. The Cp is defined as in Eq. (5). Kp, Kd,gpd, and s correspond to the PD position controller pro-portional gain, the derivative gain, the gain of pseudo-derivation, and the Laplace operator.

Cp = Kp +sgpds+ gpd

Kd (5)

Fig. 1 represents the control block diagram of acceler-ation based bilateral control system which obeys Eq. (3)and Eq. (4).

2.2. Excess force control with virtual stiffnessRobot when touches an environment, exerts force

to either comply with the workpiece or overcome theimpedance of the working environment. Exerting excessforce is not desirable as it could damage the workpiece byexceeding the bearable safe force limit. This section ad-dresses the proposed control method to protect the slaveenvironment from the excessive force applied by the mas-ter operator.

The proposed virtual stiffness controller consists ofa position control loop and a force control loop. Theposition-force references are combined in the commondimension of acceleration.The excess force amount ap-plied by the master operator is modeled as a virtual en-vironment force fsp, represented as in Eqs. (6) and (7).Then Eq. (8) can be derived.

fsp = fextm + fexts (6)fsp = (xeqs − xresm )(Ksp +Ds) (7)

xeqs − xresm =fextm + fexts

Ksp +Ds(8)

+

_

+

+

_

+

+

_

++

_

+

+

+

𝑀𝑛

𝐾𝑓𝑛

1

𝐾𝑓𝑛

1

𝐾𝑓𝑛

𝑀𝑛

𝐾𝑓𝑛

𝑥𝑠𝑟𝑒𝑠

𝑥𝑚𝑟𝑒𝑠

𝑥𝑠𝑟𝑒𝑠

𝑥𝑠𝑟𝑒𝑠

𝑥𝑚𝑟𝑒𝑠

𝑥𝑚𝑟𝑒𝑠

𝐶𝑝

𝐶𝑝

𝐶𝑓

መ𝑓𝑚𝑒𝑥𝑡

መ𝑓𝑠𝑒𝑥𝑡

𝑓𝑚𝑒𝑥𝑡

ሷ

𝑥𝑚𝑟𝑒𝑓

ሷ

𝑥𝑠𝑟𝑒𝑓

𝐼𝑚𝑑𝑖𝑠

𝐼𝑠𝑑𝑖𝑠

𝐼𝑚𝑟𝑒𝑓

𝐼𝑠𝑟𝑒𝑓

Master system with

DOB and RFOB

𝑓𝑚𝑑𝑖𝑠

Slave system with

DOB and RFOB

𝑓𝑠𝑒𝑥𝑡

1

2

1

2

Fig. 1 Acceleration based bilateral control system.

Notations xeqs , Ksp, and D correspond to the slaveequilibrium position at the slave environment safe forcelimit, the spring force coefficient, and the damping forcecoefficient.

The slave side force and position are limited at cor-responding environmet safe force limit while both forceand position on the master side are free to change accord-ingly with operator intention.Thus, control goal given inEq. (1), modifies as in Eq. (9a) and (9b). Based on Eq.(6), the control goal in Eq. (2) is modified as in Eq. (10).

xeqs − xresm < 0 master (9a)xeqs − xress = 0 slave (9b)

fextm − fsp + fexts = 0 (10)

When considering the master side, the portion of ac-celeration reference from the force loop xf is given byEq. (11). The force scalling coefficient α is introduced.The portion of acceleration reference from the positionloop xp and the acceleration reference to master xrefm aregiven in Eqs. (12) and (13) respectively. Then, the valueof α can be derived as in Eq. (14) substituting from Eqs.(6), (8), (11), and (12) to Eq. (13).

xf = Cf

(fexts + α(fextm − fsp)

)(11)

xp =1

2Cp(x

eqs − xresm ) (12)

xrefm = xp − xf = 0 (13)

α = 1− Cp

2Cf (Ksp +Ds)

(1 +

fextm

fexts

)(14)

The effect of low pass filters in DOB, RFOB and PDposition controller are omitted assuming ideal operationof the system. Fig. 2 shows the modified control blockdiagram of the master acceleration reference xrefm .

The master and the slave acceleration references dur-ing constrained bilateral motion control are given in Eqs.(15) and (16). Fig. 3 shows the modified control blockdiagram for constrained bilateral control.

xrefm =1

2Cp(x

reseq − xresm )− Cf

(α(fextm − fsp) + fexts

)(15)

xrefs =1

2Cp(x

reseq −xress )−Cf (f

extm −fsp+ fexts ) (16)

1

𝐾𝑓𝑛

Master system with

DOB and RFOB

𝑀𝑛

𝐾𝑓𝑛

መ𝑓𝑚𝑑𝑖𝑠

+

𝑓𝑚𝑒𝑥𝑡

_

𝑥𝑠𝑒𝑞

መ𝑓𝑚𝑒𝑥𝑡

𝑓𝑠𝑝

𝐼𝑚𝑑𝑖𝑠

𝐼𝑚𝑟𝑒𝑓

ሷ

𝑥𝑚𝑟𝑒𝑓_

+

+

+_

+

ሷ

𝑥𝑝

ሷ

𝑥𝑓

𝛼

𝐾𝑠𝑝+𝐷𝑠

+መ𝑓𝑠𝑒𝑥𝑡

𝐶𝑓

𝐶𝑝

𝑥𝑚𝑟𝑒𝑠

+

1

2

𝑥𝑚𝑟𝑒𝑠

Fig. 2 Master side acceleration reference modificationwith virtual stiffness and scaling coefficient.

708

1

𝐾𝑓𝑛

Master system with

DOB and RFOB

𝑀𝑛

𝐾𝑓𝑛

መ𝑓𝑚𝑑𝑖𝑠

+

𝑓𝑚𝑒𝑥𝑡

_

መ𝑓𝑚𝑒𝑥𝑡

𝑓𝑠𝑝

𝐼𝑚𝑑𝑖𝑠

𝐼𝑚𝑟𝑒𝑓

ሷ𝑥𝑚𝑟𝑒𝑓_

+

+

+_

+ሷ𝑥𝑝

ሷ𝑥𝑓

𝛼

𝐾𝑠𝑝+𝐷𝑠 +

𝐶𝑓

𝐶𝑝

𝑥𝑚𝑟𝑒𝑠

𝑥𝑚𝑟𝑒𝑠

1

𝐾𝑓𝑛

Slave system with

DOB and RFOB

𝑀𝑛

𝐾𝑓𝑛

መ𝑓𝑠𝑑𝑖𝑠 መ𝑓𝑠

𝑒𝑥𝑡𝐼𝑠𝑑𝑖𝑠

𝐼𝑠𝑟𝑒𝑓ሷ𝑥𝑠

𝑟𝑒𝑓

_

++

+ _+

+

𝐶𝑓

𝐶𝑝

𝑥𝑠𝑟𝑒𝑠

𝑥𝑠𝑟𝑒𝑠

𝑓𝑠𝑒𝑥𝑡

+

𝑥𝑠𝑒𝑞

Mas

ter

sid

eSl

ave

sid

e

+

1

2

1

2

Fig. 3 Modified control block diagram for constrainedbilateral control.

3. SIMULATION

The proposed method was tested with simulation. Aforce profile exerted on a real environment object wasused as human applied force fextm on the master side. Aspring damper model was considered as the slave envi-ronment 625x + 15x and its safe force limit is taken asFlimit = 1.5N. The relevant parameters of the simulationare listed in Table 1.

When human applied force is lower than the safe forcelimit both master and slave follow the acceleration basedbilateral control. The proposed method is applied be-yond the safe force limit. The master operator is chang-ing force and position as he wishes and the slave side ismaintaining the safe force limit and the slave equilibriumposition under constrained bilateral motion control. Re-fer Fig. 4 and 5.

The results are shown for two sets of values of DOBcut off frequency gd and RFOB cut off frequency gr.Both master and slave have equal values for gd, gr. AsDOB, RFOB cut off frequencies are increasing the slaveside force and position responses are oscillating aroundthe safe force limit and the corresponding equilibriumposition during constrained bilateral motion. As futureworks, the algorithm should develop to attain smooth op-eration on the slave side during constrained bilateral mo-tion and should conduct experiments to validate the pro-posed method. Further, stability and reproducibility anal-ysis when virtual stiffness presence on the master sideshould be carried out.

Table 1 Parameters of simulation

Parameter Value Parameter ValueMn 0.23 Kg Kp 900.0Kfn 3.214 N/A Kd 60.0Cf 4.35 gpd 500.0 rad/sFlimit 1.5 N gd1, gr1 150 rad/sdt 1 ms gd2, gr2 300 rad/sKsp 900 N/m D 5 Ns/m

(a)

0 5 10 15 20 25 30 35 40

Time (s)

-3.5-3

-2.5-2

-1.5-1

-0.50

0.51

1.52

Fo

rce

(N

)

(b)

0 5 10 15 20 25 30 35 40

Time (s)

-3.5-3

-2.5-2

-1.5-1

-0.50

0.51

1.52

Fo

rce

(N

)

Fig. 4 Master and slave force responses. (a). gd1, gr1 =150 rad/s and (b). gd2, gr2 = 300 rad/s.

(a)

0 5 10 15 20 25 30 35 40

Time (s)

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

Po

sitio

n (

cm

)

(b)

0 5 10 15 20 25 30 35 40

Time (s)

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

Po

sitio

n (

cm

)

Fig. 5 Master and slave position responses. (a).gd1, gr1 = 150 rad/s and (b). gd2, gr2 = 300 rad/s.

709

4. CONCLUSIONSThe virtual stiffness and the feedback scaling factor

on the master side realizes common mode force controlby compensating the loss of reaction force coming fromthe remote environment during state space transition be-tween normal and constrained bilateral motion. The dif-ferential mode position control is conducted on the equi-librium position corresponding to the slave environmentsafe force limit. On the slave side, both position and forceare limited at the corresponding safe limits. The masteroperator is free to modify his force and position. Theproposed method successfully stops the master appliedexcess force from transmitting to the slave side.

REFERENCES[1] Statistical handbook of Japan 2018, Ministry of

Internal Affairs and Communications, Statistics Bu-reau, Tokyo, Japan, 2018, ISSN 0081-4792.

[2] D. Neumann, “Human Assistant Robotics in Japan -Challenges and Opportunities for European Compa-nies,” EU-Japan Centre for Industrial Cooperation,Tokyo, Japan, Mar. 2016.

[3] S. Sakaino, A. M. H. S. Abeykoon and K. Ohnishi,“Keynote paper – Real world haptics applied to for-ceps in robot surgery,” 2010 Fifth International Con-ference on Information and Automation for Sustain-ability, Colombo, 2010, pp. 571-574.

[4] K. Taguchi, S. Hyodo, and K. Ohnishi, “A designmethod of autonomous hazard avoidance controllerwith selected ratio in bilateral teleoperation,“ in 10thIEEE International Workshop on Advanced MotionControl, pp. 607-612, 2008.

[5] S. Sakaino, T. Sato and K. Ohnishi, “Task hierar-chy for position limitation and bilateral control byoblique coordinate control,” in 35th Annual Confer-ence of IEEE Industrial Electronics, pp. 1794-1799,2009.

[6] S. Sakaino, T. Sato and K. Ohnishi, “Constrainedbilateral control by oblique coordinate control takingpriority of tasks into account,” in The 2010 Interna-tional Power Electronics Conference - ECCE ASIA -,pp. 2540-2544, 2010.

[7] K. Ohishi, K. OhnishiI, and K. Miyachir, “Torque- Speed Requlation of DC Motor Based on LoadTorque Estimation Method,” JIEE/1983 Interna-tional Power Electronics Conference, pp. 1209–1218, 1983.

[8] K. Ohnishi, M. Shibata, and T Murakami, “MotionControl for Advanced Mechatronics,” IEEE/ASMETransactions on Mechatronics, Vol. 1, pp. 56–67,March. 1996. doi: 10.1109/3516.491410

[9] S. Katsura, Y. Matsumoto, and K. Ohnishi, “Mod-eling of Force Sensing and Validation of DisturbanceObserver for Force Control,” IEEE Transactions onIndustrial Electronics, pp. 530–538, Feb. 2007. doi:10.1109/TIE.2006.885459

[10] Y. Matsumoto, S. Katsura, and K. Ohnishi, “Ananalysis and design of bilateral control based on dis-

turbance observer,“ in IEEE International Confer-ence on Industrial Technology, pp 802–807, Dec.2003.

[11] W. Iida, and K. Ohnishi, “Reproducibility and op-erationality in bilateral teleoperation,“ in The 8thIEEE International Workshop on Advanced MotionControl, pp 217-222, Mar. 2004.

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