MmUm+FopX m Mm+Mop F-Mm(Fop-Mopum)M m+mop MSuS+FX S M S+MOb Fs-Ms(Mobus-Fex)M s+mob Fig. 1 Particle model of single degree of freedom master/ slave sy

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1 Analysis and Improvement of Digital Control Stability for Master-Slave Manipulator System Koichi YOSHIDA* and Tetsuro YABUTA* Some bilateral controls of master-slave system have been designed, which can realize high-fidelity telemanipulation as if the operator were manipulating the object directly. While usual robot systems are controlled by software-servo system using digital computer, little work has been published on design and analysis for digital control of these systems, which must consider time-delay of sensor signals and zero order hold effect of command signals on actuators. This paper presents a digital control analysis for single degree of freedom master-slave system including impedance models of both the human operator and the task object, which clarifies some index for the stability. The stability result shows a virtual master-slave system concepts, which improve the digital control stability. We first analyze a dynamic control method of master-slave system in discrete-time system for the stability problem, which can realize high-fidelity telemanipulation in the continuous-time. Secondly, using the results of the stability analysis, the robust control scheme for master-slave system is proposed, and the validity of this scheme is finally confirmed by the simulation. Consequently, it would be considered that any combination of master and slave modules with dynamic model of these manipulators is possible to construct the stable master-slave system. Key Words: master-slave manipulator, digital control, robust control * NTT Telecommunication Field Systems R&D Center, Naka-Gun, Ibaraki (Received June 1, 1991) (Revised May 28, 1992)

2 MmUm+FopX m Mm+Mop F-Mm(Fop-Mopum)M m+mop MSuS+FX S M S+MOb Fs-Ms(Mobus-Fex)M s+mob Fig. 1 Particle model of single degree of freedom master/ slave system

3 Fig. 2 Definition of sampling variable 6m=MM 0 6s M +Mm p s Mob

4 (KPcis+z 1Aob)(KP6m+z-1Aop) (1+KP6m)(1+KP6s) 1 Gebm 0 -i Gedop 0S e(4 I2-KeG ebs Ke 0 Gedex zm(z)s(z) pmmmop+msmop+msmob+mmmobtsk (M m+mop)(ms+mdb) Aop1(Mm-Mob)(Ms-Mop(M m+mop)(ms+mob) KP AOb-z+6S MM Ms+MzMMS A s s Cm KPz-lop+mMm+Ms+Mm+ sms MmMs M

5 APAob(M-M)<1(M+M ob) (M+Mon)

6 Mmuvs+Msuvm x m m+m, Fv M+M s(icus-asvm) GMSSB 1 (z-1)+ms+ms MB Gob Mob Mb Mob Fig. 5 Virtual master/slave system Fig. 6 Block diagram of proposed control scheme

7 Fig. 7 Simulation result of conventional master/slave control method Fig. 8 Simulation result of proposed master/slave control method

8 Fig. 9 Virtual multi degree of freedom master/slave system

9 Fig. 10 Simulation model Table 1 Specification of master manipulator for simulation (a) Tip locus of master manipulator (a) Tip locus of master manipulator (b) Tip locus of slave manipulator (b) Tip locus of slave manipulator Fig. 11 Simulation result of conventional master/slave control method Fig. 12 Simulation result of proposed master/slave control method

10 Fig. 13 Time response of Fm 7) G.J. Raju: Design Issues in 2-port Network Models of Bilateral Remote Manipulation, IEEE International Conference on Robotics and Automation, 1316/1321 (1989) 8) B. Hannaford: A Design Framework for Teleoperators with Kinesthetic Feedback, IEEE Transactions on Robotics and Automation, RA /434 (1989)

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