24
24 23 411M133
i 1 1 1.1........................................ 1 2 4 2.1...................................... 4 2.2.................................. 6 2.2.1........................... 6 2.2.2 viterbi........................... 9 2.3................................... 10 3 12 3.1...................................... 12 3.2...................................... 16 3.2.1................................ 16 3.2.2................................ 21 3.2.3.................................. 23 3.3...................................... 26 4 29
ii 30 32
iii 2.1 Algorithm for the proposed method (NS chart)................ 5 2.2 left-to-righthmm................................. 6 2.3 Timing of likelihood calculation......................... 10 3.1 The system of the small autonomous mobile robot MieC......... 13 3.2 Joystick map................................... 14 3.3 Two routes of straight and slalom for the experiment............. 15 3.4 The transition probability matrix........................ 16 3.5 The emission probability matrix (Output matrix)............... 17 3.6 The emission probability matrix S = 100, n = 30............... 19 3.7 The comparison between the learning data and the estimation data for slalom 20 3.8 The comparison between the learning data and the estimation data for straight...................................... 20 3.10 Transition of the likelihood on slalom...................... 21 3.9 Transition of the likelihood on straight..................... 22 3.11 Route for verifying the validity of the forcefeedback.............. 23 3.12 Joystick map in polar coordinate........................ 24 3.13 Transition of the likelihood for the curve course................ 26 3.14 Choice of the course............................... 27
iv 3.1.................................... 24 3.2......................... 25 3.3.............................. 27
1 1 1 ( HMM) 1.1
1 2 [1] 2
1 3. ( HMM) HMM DNA ([2][3][4]) [5] [6][7] HMM HMM [8] HMM HMM 2 3
2 4 2 2.1 HMM HMM
2 5 NS Fig. 2.1 Time Loop Observe human operation Select the maximum likelihood HMM Low Learn as a new model The likelihood High generates a maximum likelihood route Force feedback Correction by human Fig. 2.1 Algorithm for the proposed method (NS chart) Forward-Probability Backward-Probability Viterbi
2 6 2.2 2.2.1 HMM HMM O = {o 1,...,o N } ( ) S = {s 1,...,s N } s n s n 1 p(s n s n 1 ) A i s i j s j a ij A = {a ij } (1 i,j N) s i Π = {π i } i o b i (o) B = b i (1 i,j N,1 t T) λ = (A,B,Π) left-toright HMM Fig. 2.2 s 1 Fig. 2.2 left-to-righthmm HMM Baum-Welch Baum-Welch Forward-Backward
2 7 Probability Backward-Probability α β λ α β α t (j) = P(o 1,o 2,...,o t,s t = j λ) (2.1) β t (i) = P(o t+1,o t+2,...,o T,s t = i λ) (2.2) λ t O = o 1,o 2,...,o t s j λ s i t O = o t+1,o t+2,...,o T α β Forward Probability α 1 (i) = π i (2.3) N α t+1 (j) = α t (i)a ij b j (o t+1 ) (2.4) i=1 Backward P robability β T (i) = 1 (2.5) β t (i) = N a ij b i (o t+1 )β t+1 (j) (2.6) j=1 i = 1,2,...,N j = 1,2,...,N t = 1,2,...,T α
2 8 ξ γ ξ t (i,j) = α t(i)a ij b j (o t+1 )β t+1 (j) P(O λ) (2.7) γ t (i) = N ξ t (i,j) (2.8) j=1 P(O λ) = N α T (i) (2.9) i=1 ξ γ t s i t+1 s j t s i λ = (A,B,Π) π i = γ 1 (i) (2.10) ā ij = bj (k) = T 1 t=1 ξ t(i,j) T 1 t=1 γ t(i) T t=1,s.t.o t=v k γ t (j) T t=1 γ t(j) (2.11) (2.12) v = {v 1,v 2,...,v k } λ gradient left-to-right Ergodic
2 9 2.2.2 viterbi viterbi viterbi O = {o 1,o 2,...,o T } Q = {q 1,q 2,...,q T } viterbi t q t = S i δ t (i) = max q1,q 2,...,q t 1 Pr[q 1,q 2,...,q t 1 = S i,o 1,O 2,...,O t λ] (2.13) t δ t (i) ψ t (i) δ 1 (i) = π i b i (O 1 ), i = 1,...,N (2.14) ψ 1 (i) = 0 (2.15) δ t (j) = max 1 i N [δ t 1 (i)a ij ]b j (O t ), t = 2,...,T, j = 1,...,N (2.16) ψ t (j) = argmax 1 i N [δ t 1 (i)a ij ], t = 2,...,T, j = 1,...,N (2.17) T P qt P = max 1 i N [δ T (i)] (2.18) q T = argmax 1 i N [δ T (i)] (2.19)
2 10 q t = ψ t (q t+1 ), t = T 1,T 2,...,1 (2.20) viterbi t+1 B 2.3 Fig. 2.3 Fig. 2.3 Timing of likelihood calculation
2 11 t O = {o 1,o 2,...,o t } P(o 1,o 2,...,o t λ) λ
3 12 3 3.1 MieC (Fig. 3.1)
3 13 Fig. 3.1 The system of the small autonomous mobile robot MieC MieC 2 CCD (Logicool QCAM-200R) LAN CPU FPGA CPU FPGA MieC (Logitech FORCE 3D PRO) Fig. 3.2 x,y [0-255] 8
3 14 Fig. 3.2 Joystick map Force-FeedBack Fig. 3.3 2 HMM HMM
3 15 Fig. 3.3 Two routes of straight and slalom for the experiment MieC t O = o 1,o 2,...,o t 2 HMM Foward-Probability 20 192[step](19.2[sec])
3 16 3.2 3.2.1 λ A i j (3.1) (3.2) a 11 a 12 a 1N. a.. 21 a2n A ij =. a ij., i = 1,...,N (3.1)..... a N1 a N2 a NN B j (v k ) = b 11 b 12 a 1K b 21... a2k. b jk...... b N1 b N2 a NK, j = 1,...,N, k = 1,...,K(3.2) n 1 1 [0-255] Fig. 3.4 Fig. 3.5 S(j) S(j) S(j) S(i) S(i) S(i) (a)initial model (b)learned model (c)learned model n = 0 n = 5 n = 30 Fig. 3.4 The transition probability matrix
3 17 v(k) S(j) (a)initial model v(k) S(j) (b)learned model n = 5 v(k) S(j) (c)learned model n = 30 Fig. 3.5 The emission probability matrix (Output matrix) S(i) S(j) 20x20 i j i j
3 18 S(j) v(k) j k S(j) v(k) x 20x64 flat start left-to-right HMM Fig. 3.4(a) 2 0.5 Fig. 3.5(a) 6 Fig. 3.4(b) Fig. 3.4(c) Fig. 3.5 20 S = 100 Fig. 3.6
3 19 v(k) S(j) Fig. 3.6 The emission probability matrix S = 100, n = 30 viterbi Fig. 3.7 Fig. 3.8
3 20 40 35 learning data output data 30 25 symbol 20 15 10 5 0 0 20 40 60 80 100 120 140 160 180 200 step Fig. 3.7 The comparison between the learning data and the estimation data for slalom 35 30 learning data output data 25 20 symbol 15 10 5 0 0 20 40 60 80 100 120 140 160 180 200 step Fig. 3.8 The comparison between the learning data and the estimation data for straight HMM HMM 96.3% 97.9%
3 21 3.2.2 Fig. 3.9 Fig. 3.10 HMM HMM Fig. 3.9 HMM 1 0.01 0.0001 straighthmm slalomhmm 1e-06 likehood 1e-08 1e-10 1e-12 1e-14 1e-16 0 5 10 15 20 25 30 35 40 step Fig. 3.10 Transition of the likelihood on slalom
3 22 1 0.01 0.0001 straighthmm slalomhmm 1e-06 likehood 1e-08 1e-10 1e-12 1e-14 1e-16 0 5 10 15 20 25 30 35 40 step Fig. 3.9 Transition of the likelihood on straight HMM Fig. 3.10 HMM 0 HMM HMM HMM
3 23 3.2.3 MieC Force-Feedback 4 0 [-5 +5] Fig. 3.11 80cm 80cm 40cm Fig. 3.11 Route for verifying the validity of the forcefeedback
3 24 Table 3.2.3 Table 3.1 [ -5 +5 ] Force-Feedback Fig. 3.12 360[ ] 15[ ] 24 3 36 37 27 28 29 26 14 15 16 17 18 30 25 13 24 12 3 4 5 6 7 12 8 11 10 9 20 19 31 36 23 22 21 32 35 34 33 Fig. 3.12 Joystick map in polar coordinate Table 3.2.3
3 25 Table 3.2 A B C D 3 2-2 0 0.75 0 0 0 0 0-2 4 1 3 1.5 0 0 0 0 0 4 Force-Feedback
3 26 3.3 3 3.2.3 3.2.3 37 20 160[step](16.0[sec]) Fig. 3.13 1 1e-20 Curve model Straight model 1e-40 likelihood 1e-60 1e-80 1e-100 1e-120 0 20 40 60 80 100 120 140 step Fig. 3.13 Transition of the likelihood for the curve course 40[step] Fig. 3.14 40[cm] 60[cm]
3 27 Straight model Corve model Fig. 3.14 Choice of the course Table 3.3 A B C D 5 2 2 3 3 0 0 0 0 0 4 5 3 5 4.25 0 0 0 0 0 3.2.3
3 28
4 29 4 HMM HMM
30 [1] Vol. 13 No. 4 1995 pp.545-552 [2] Hidden Markov Model. MVE, 97(207), 95-100, 1997-07-25 [3] HMM GMM [4] DNA Vol.40 No.2 1999 pp750-767 [5] HMM (D-II) vol.j85-d-ii no.7 July 2002 pp.1265-1270 [6] Vol.22 No.2 pp.256 263 2004 [7] vol.27 No.5
31 pp.564-574 2009 [8],, / (C ) 67 656 (2001-4) No.00-0257(173-180) [9] C.M. : Pattern Recognition and Machine Learning.,pp.323-349,2006 [10] :,,pp.112-128,2007
32