24 26,,,,,,,,, Nsho [7] Nakadokoro [8],,,, 2 (Tradtonal estmaton of mage Jacoban matrx), f(t 1 ) p(t 2 ) : f(t 1 ) = [f 1 (t 1 ), f 2 (t 1 ),, f m (t

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1 Control Theory & Applcatons Vol 26 No 1 Jan 2009 : (2009) , (, ) :,,,,,,,, : ; ; : TP24 : A The estmaton of mage Jacoban matrx wth tme-delay compensaton for uncalbrated vsual servong GAO Zhen-dong, SU Jan-bo (Department of Automaton, Shangha Jao Tong Unversty, Shangha , Chna) Abstract: A novel onlne estmaton of mage Jacoban matrx wth tme-delay compensaton for uncalbrated vsual servong s proposed The tradtonal methods ddn t consder the tme-delay whch causes larger estmaton error In order to compensate the tme-delay, local fttng Jacoban matrx wth tme-delay compensaton based on polynomal fttng s employed to obtan more accurate Jacoban estmaton and mage precompensaton Smulatons and experments of uncalbrated moble robot and uncalbrated vsual sensors show that ths method mproves the system dynamc performance and reduces the steady-state error, demonstratng the feasblty and valdty of the tme-delay compensaton Key words: uncalbrated vsual servong; tme-delay compensaton; mage Jacoban matrx estmaton 1 (Introducton) Herve [1], [2] Hashmoto,, [3] Pepmeer,, [4] 3-D [5],,,, ( ),,,,,, [6], : ; : : ( )

compensaton for uncalbrated vsual servong s proposed The tradtonal methods ddn t consder the tme-delay whch causes larger estmaton error In order to compensate the tme-delay, local fttng Jacoban

2 24 26,,,,,,,,, Nsho [7] Nakadokoro [8],,,, 2 (Tradtonal estmaton of mage Jacoban matrx), f(t 1 ) p(t 2 ) : f(t 1 ) = [f 1 (t 1 ), f 2 (t 1 ),, f m (t 1 )] T, (1) p(t 2 ) = [p 1 (t 2 ), p 2 (t 2 ),, p n (t 2 )] T (2), t 1 = t 2 : f(t 1 ) = J(p) ṗ(t 2 ) = J(p) ṗ(t 1 ) (3) : f, ṗ, J(p) m n, J(p) : J(p) = f 1 p 1 f m p 1 f 1 p n f m (4) p n, (3) : τ f(t 1 ) = J t2 τ(p) ṗ(t 2 τ) (5), k, T, p,, f,,,, 1 ht p f h, 1 Fg 1 Tradtonal estmaton of IJM wth tme-delay

: f(t 1 ) = J(p) ṗ(t 2 ) = J(p) ṗ(t 1 ) (3) : f, ṗ, J(p) m n, J(p) : J(p) = f 1 p 1 f m p 1 f 1 p n f m (4) p n,

3 1 : 25 3 (Estmaton of mage Jacoban matrx wth tme-delay compensaton), h, 2 k h 2 Fg 2 Estmaton of IJM wth tme-delay compensaton [4] k h Ĵk h: Ĵ k h =Ĵk h 1 + (f k h f k h 1 )ṗ T k h P k h 1 λ + ṗ T k h P k h 1ṗ k h (Ĵk h 1ṗ k h f k h T )ṗ T k h t P k h 1 λ + ṗ T k h P, (6) k h 1ṗ k h P k h = 1 λ (P k h 1 P k h 1ṗ k h ṗ T k h P k h 1 λ+ṗ T k h P k h 1ṗ k h ) (7) : Ĵ k h k h, f k h k h, ṗ k h, T, λ, 0 < λ 1, f t T,, f t T = 0 J ( = 1,, k h) ṗ ( = 1,, k), ṗ ( = k h + 1,, k) J ( = k h + 1,, k), k, f J p, J ( = 1,, k h) ṗ ( = 1,, k) J, J k (p k ) J p : j 11 (p,1 ) j 1n (p,n ) J (p ) = (8) j m1 (p,1 ) j mn (p,n ) p n, j 11,, j mn J(p) J(p), : j(p) = a 0 + a 1 p + + a v p v (9) : a 0, a 1,, a v, v a 0, a 1,, a v, k h r+1 k h, r J (p ), ( = k h r+1,, k h) 0 < β 1 1 v : mn(ϕ(a 0, a 1,, a v )) = mn( r e 2 ) = mn( r β (a 0 + a 1 p + + a v p v j ) 2 ) (10)

λ, 0 < λ 1, f t T,, f t T = 0 J ( = 1,, k h) ṗ ( = 1,, k), ṗ ( = k h + 1,, k) J ( = k h + 1,, k), k, f J p, J ( = 1,, k h) ṗ ( = 1,, k) J, J k (p k ) J p : j 11 (p,1 ) j 1n (p,n ) J (p ) = (8) j m1

4 26 26 e j (p) : ϕ = r β p q a (a 0 + a 1 p++a v p v j )=0, q q = 0, 1,, v (11) β 1, β 2,, β r = 1, 1 p p v p p 2 p v+1 p v+1 p v p v+v a 0 a 1 a v = j p j (12) p v j a 0, a 1,, a v j (p) (8) Ĵk h+1,, Ĵk ˆ f (p) 4 (Smulaton), τ 1500 mm, 15 mm [0 mm, 480 mm], [0 mm, 0 mm] 2 k m 5 k m, m = 2 3, τ,, 4, 8, 20, 20,,,,, Fg 3 3 τ = 2T Robot trackng rng trajectores at τ = 2T 4 Fg 4 Fg 5 τ = 2T Robot trackng errors at τ = 2T 5 Robot trackng trajectores

(Smulaton), τ 1500 mm, 15 mm [0 mm, 480 mm], [0 mm, 0 mm] 2 k m 5 k m, m = 2 3, τ,, 4, 8, 20, 20,,,,, Fg 3 3 τ

5 1 : 27,, 5 (Expermentaton) ActveMeda Poneer2DX 100 M,, 350, 30, 12 5,,, 6 (Concluson),,, (References): [1] HERVE J, SHARMA R, CUCKA P Toward robust vson-based control: Hand-Eye coordnaton wthout calbraton[c] //Proceedngs of IEEE Internet Symposum on Intellgent Control Sngapore: IEEE Computer Socety Press, 1991: [2] SUTANTO H, SHARMA R, VARMA V Image based autodockng wthout calbraton[c] // Proceedngs of IEEE Internet Conference Robotcs and Automaton Albuquerque: IEEE Computer Socety Press, 1997: [3] HASHIMOTO H, KUBOTA T, SATO M, et al Vsual control of robotc manpulator based on neural networks[j] IEEE Transactons on Industral Electroncs, 1992, 39(6): [4] PIEPMEIER A J, MCMURRAY V G, LIPKIN H Uncalbrated dynamc vsual servong[j] IEEE Transactons on Robotcs and Automatons, 2004, 20(1): [5] SU J, QIU W, MA H, et al Calbraton-free robotc eye-hand coordnaton based on an auto dsturbance-rejecton controller[j] IEEE Transactons on Robotcs, 2004, 20(5): [6] HIGASHI S, KOMADA S Obstacle avodance of redundant manpulators on vsual servo system usng estmated mage features[c] // Proceedngs of Internatonal Workshop on Advanced Moton Control Sngapore: World Scentfc, 1998: [7] NISHIO D, NAKAMURA M, KOMADA S, et al Trackng of movng object by manpulator usng estmated mage feature and ts error correcton on mage planes[c] // Advanced Moton Control Kawasak, Japan: IEEE Computer Socety Press, 2004: [8] NAKADOKORO M, KOMADA S, HORI T Stereo vsual servo of robot manpulators by estmated mage features wthout 3D reconstructon[c] // IEEE Conference on Systems, Man, and Cybernetcs Mchgan: IEEE Computer Socety Press, 1999, 1: : (1977 ),,,, E-mal: mgordon@163com; (1969 ),,,,, E-mal: jbsu@sjtueducn

calbraton[c] // Proceedngs of IEEE Internet Conference Robotcs and Automaton Albuquerque: IEEE Computer Socety Press, 1997: 974 979 [3] HASHIMOTO H, KUBOTA T, SATO M, et al Vsual control of robotc

34 7 S R θ Z θ Z R A B C D PTP θ t 0 = θ 0 θ t 0 = 0 θ t 0 = 0 θ t = θ θ t = 0 θ t = 0 θ t V max θ t a max 3 θ t A θ t t 0 t / V max a max A = 3 4 S S

34 7 S R θ Z θ Z R A B C D PTP θ t 0 = θ 0 θ t 0 = 0 θ t 0 = 0 θ t = θ θ t = 0 θ t = 0 θ t V max θ t a max 3 θ t A θ t t 0 t / V max a max A = 3 4 S S 7 0 7 No. 7 Modular Machne Tool & Automatc Manufacturng Technque Jul. 0 00-65 0 07-0033 - 06 *. 0040. 04 PTP s TH6 TP4. A The Moton plannng of Handlng Robot Based on Tme Optmal CAO Bo CAO Q-xn TONG Shang-gao