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1 Vol.44, No.1, 1/7 28 Synchronzed Control for Blateral Teleoperaton wth Dfferent Confguratons and Communcaton Delays Hsanosuke Kawada,KoueYoshda and Toru Namerkawa Ths paper addresses the problem of the control of blateral teleoperaton wth dfferent confguratons and communcaton delays. We propose a synchronzed control law wth ndvdual gans and power scalng n the task space. Usng ths method, the end-effector moton and force relatonshp between the master and slave robots can be specfed freely n the task space and the control gans can be ndependently selected approprately for the master and slave robots. The passvty of the whole system s proven by usng an energy functon. Furthermore, the delay-ndependent asymptotc stablty of the orgn of the poston and velocty errors s proven by usng Lyapunov lke stablty methods n free space and the proposed control law acheves scaled synchronzaton of the teleoperaton. Several expermental results show the effectveness of our proposed method. Key Words: teleoperaton wth dfferent confguratons and communcaton delays, scaled synchronzaton, Lyapunov-Krasovsk functon, passvty 1. 1), 2) 3) 4) 7) 8) Graduate School of Natural Scence and Technology, Kanazawa Unversty, Kakuma-mach, Kanazawa Receved March 18, 28 Revsed August 4, 28 6) 8) 9), 1) 11), 12) (Synchronzaton) 11), 12) 11), 12) TR 1/8/441 1 c 28 SICE

2 2 T. SICE Vol.44 No.1 October n M m (q m ) q m +C m (q m, q m ) q m +g m (q m )=τ m +JmF T op M s (q s ) q s +C s (q s, q s ) q s +g s (q s )=τ s Js T F env 1 m s q m, q s R n τ m, τ s R n F op R n F env R n M m (q m ), M s (q s ) R n n C m (q m, q m ) q m, C s (q s, q s ) q s R n g m (q m ), g s (q s ) R n J m (q m ), J s (q s ) R n n ẋ = J q ẋ m ẋ s R n 1 J m J s ( ) ( ) ẍ = J q + J q (1) 13) M m (q m )ẍ m + Cm (q m, q m )ẋ m + g m (q m )=Jm T τ m +F op M s (q s )ẍ s + Cs (q s, q s )ẋ s + g s (q s )=Js T τ s F env M =J T M J 1 C =J T (C M J 1 2 J )J 1 g =J T g, =m, s (2) 1 13) 1 M (q ) 2 Ñ = M (q ) 2 C (q, q ) 2 Fg. 1 Teleoperaton system T m R T s R ), 8) 11) 3 1 Fg. 1 2 e m (t) :=α 1 x s (t T s ) x m (t) 3 e s (t) :=αx m (t T m ) x s (t) α > R e (t) as t, = m, s 4 ė (t) as t, = m, s 3 ẍ = ẋ =, = m, s βf op = F env 5 β > R

3 τ m = Jm{ T Mm Λẋ m Cm Λx m + g m + F m } 6 τ s = Js T { Ms Λẋ s Cs Λx s + g s + F s } Λ F m, F s (6) (2) M m (q m )ṙ m + Cm (q m, q m )r m = F op + F m 7 M s (q s )ṙ s + Cs (q s, q s )r s = F env + F s r m r s r m := ẋ m + Λx m 8 r s := ẋ s + Λx s (7) 11) r T (τ)f (τ)dτ σ, = m, s 9 F m = F m + F op F s = F s F env σ (8) (8) 3. 2 F m, F s F m (t) =K m (α 1 r s (t T s ) r m (t)) 1 F s (t) =K s (αr m (t T m ) r s (t)) K m = k m K K s = k s K K R n n k m > k s > R Fg. 2 11), 12) K m = K s = K (1) (7) (1) Fg. 1 F op r m F T op(ζ)r m (ζ)dζ σ ms σ ms R 11 ( ) x =[rm T rs T ] T V V (x)=αkm 1 rm(t) T Mm (q m )r m (t) +α 1 ks 1 rs T (t) Ms (q s )r s (t) + + t T m αr T m(ζ)kr m (ζ)dζ t T s α 1 r T s (ζ)kr s (ζ)dζ +2α 1 k 1 s {F T env(ζ)r s (ζ)}dζ α 1 k 1 s { F T env (ζ)r s (ζ) } dζ 13 V V 2 (7) V =2αkm 1 rmf T m +2ks 1 α 1 rs T F s + αk 1 m F T opr m + αr T mkr m + α 1 r T s Kr s αr T m(t T m )Kr m (t T m ) α 1 r T s (t T s )Kr s (t T s ) 14 Fg. 2 The synchronzed control archtecture for teleoperator (1) F m F s

4 4 T. SICE Vol.44 No.1 October 28 V = α{α 1 r s (t T s ) r m (t)} T K{α 1 r s (t T s ) r m (t)} α 1 {αr m (t T m ) r s (t)} T K{αr m (t T m ) r s (t)} + αkm 1 Fopr T m 15 (15) 1 2 V αk 1 m F T opr m V (x) V (x()) αk 1 m F T op(ζ)r m (ζ)dζ F op = F env = (7) (1) (3) ( ) 1 F op =F env = V = α{α 1 r s (t T s ) r m (t)} T K{α 1 r s (t T s ) r m (t)} α 1 {αr m (t T m ) r s (t)} T K{αr m (t T m ) r s (t)} 18 r m r s L (18) {α 1 r s (t T s ) r m (t)} L 2 L {αr m (t T m ) r s (t)} L 2 L (1) F m F s L (7) ṙ m ṙ s L 14) lm t α 1 r s (t T s ) r m (t) = lm t αr m (t T m ) r s (t) = α 1 r s (t T s ) r m = ė m +Λe m αr m (t T m ) r s = ė s +Λe s 19 2 ( {α 1 r s (t T s ) r m } {αr m (t T m ) r s } ) ( ) e m e s lm t ė m = lm t ė s = lm t e m = lm t e s = 15) 3 1 ẋ (t) = ẍ (t) =,= m, s (7) (1) βf op = F env 21 β = α k s k m > ( ) (7) (1) βf op β( Mm ṙ m + Cm r m )+k s K(r s (t T s ) r s ) = k s K(αr m r s ) = F env +( Ms ṙ s + Cs r s ) k s Kα(r m (t T m ) r m ) 22 ẍ (t) =ẋ (t) = = m, s βf op = k s KΛ(αx m x s )=F env α>1: α<1: α =1: (β ) β 2 β α k m k s k m k s k m k s (23) k m k s (22) 3 3 (1) k m k s k m k s 3 X Y 16)

44 1 28 1 5 5. 2 Fg. 3 2 2 (l m,l s ) Fg. 3 F op F env dspace DS114 1[ms] T m = T s =.5[s] Λ = dag(5, 5) K = dag(5, 5) k m =1 k s =6 α, β (l s /l m =1.5625 1.5) α =1.5 β = αk s /k m =9 1.

5 Fg (l m,l s ) Fg. 3 F op F env dspace DS114 1[ms] T m = T s =.5[s] Λ = dag(5, 5) K = dag(5, 5) k m =1 k s =6 α, β (l s /l m = ) α =1.5 β = αk s /k m =9 1.5(=α) 9(=β) Case1 Case2 Case1 k m = k s =1 k m = k s =1 Case1 Fg. 4 5 k m =1 k s =6 Case1 Fg. 6 7 Fg. 4 (a) X (b) (a) Fg. 5 Fg. 4 K Fg. 5 (.3 [Nm] 5[Nm]) Fg. 6 7 Fg. 6 7 X Y Case2 Fg. 8 1 Fg. 8 (a) Tme response (b) Scaled and shfted data Fg. 4 Poston data n Case 1 (equvalent gan as k m = k s =1) (a) Master robot (b) Slave robot Fg. 5 Input torque commands n Case 1 (equvalent gan as k m = k s =1) (a) Tme response (b) Scaled and shfted data Fg. 6 Poston data n Case 1 (ndvdual gan as k m =1,k s =6) Fg. 3 Experment setup (a) Master robot (b) Slave robot Fg. 7 Input torque commands n Case 1 (ndvdual gan as k m =1,k s =6)

6 6 T. SICE Vol.44 No.1 October 28 Fg. 8 Trajectores n Case Fg. 1 (15 [s]-35 [s]) 9 Fg. 1 1 [s] 35 [s] ( ) 6. Fg. 9 Tme responses n Case Fg. 1 Shfted and scaled response results of Fg. 9 Remote envronment Start Slave contacts wth envronment End Fg. 9 X Y F op, F env X Y Fg. 1 Fg , 794/82 (1993) 2 / / 42-7, 356/362 (1998) 3 P.F. Hokayem and M.W. Spong: Blateral Teleoperaton: An hstorcal survey, Automatca, 42-12, 235/257 (26) , 149/154 (1994) , 441/448 (1995) 6 (C ) , 34/39 (1998) /56 (27) 8 R.J. Anderson and M.W. Spong: Blateral Control of Teleoperators wth Tme Delay, IEEE Transactons on Automatc Control, 34-5, 494/51 (1989) 9 N. Chopra, M.W. Spong, R. Ortega and N.B. Barabanov: On Trackng Performance n Blateral Teleoperaton, IEEE Transacton on Robotcs, 22-4, 861/866 (26)

1 T. Namerkawa and H. Kawada: Symmetrc Impedance Matched Teleoperaton wth Poston Trackng, In Proc.

Spong: On Synchronzaton of Networked Passve Systems wth Tme Delays and Applcaton to Blateral Teleoperaton, In Proc.

Spong: Adaptve Synchronzaton of Blateral Teleoperators wth Tme Delay, Advance n Telerobotcs, M. Ferre et al.

7 1 T. Namerkawa and H. Kawada: Symmetrc Impedance Matched Teleoperaton wth Poston Trackng, In Proc. of 45th IEEE the Conference on Decson and Control, 4496/451 (26) 11 N. Chopra and M.W. Spong: On Synchronzaton of Networked Passve Systems wth Tme Delays and Applcaton to Blateral Teleoperaton, In Proc. of the SICE Annual Conference 25, 3424/3429 (25) 12 N. Chopra and M.W. Spong: Adaptve Synchronzaton of Blateral Teleoperators wth Tme Delay, Advance n Telerobotcs, M. Ferre et al. (Eds), 257/27, Sprnger- Verlag (27) 13 C.C. de Wt, B. Sclano and G. Bastn (Eds): Theory of Robot Control, Sprnger (1996) 14 G. Tao: A Smple Alternatve to the Barbalat Lemma, IEEE Trans. on Automatc Control, 42-5, 698 (1997) 15 R. Ortega and M.W. Spong: Adaptve Moton Control of Rgd Robots: a Tutoral, Automatca, 25-6, 877/888 (1989) (26) ( )IEEE

> σ, σ j, j σ j, σ j j σ σ j σ j (t) = σ (t ) σ j (t) = σ () j(t ) n j σ, σ j R lm σ = σ j, j V (8) t σ R σ d R lm σ = σ d V (9) t Fg.. Communcaton ln

> σ, σ j, j σ j, σ j j σ σ j σ j (t) = σ (t ) σ j (t) = σ () j(t ) n j σ, σ j R lm σ = σ j, j V (8) t σ R σ d R lm σ = σ d V (9) t Fg.. Communcaton ln IIC-- Dstrbuted Cooperatve Atttude Control for Multple Rgd Bodes wth Communcaton Delay Yoshhro achbana, oru Namerkawa (Keo Unversty) Abstract hs paper descrbes dstrbuted cooperatve atttude consensus and