Grund.dvi

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たつやひがき
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3 i viterbi

2.1................................ 16 3.2.2................................ 21 3.2.3.................................. 23 3.3...................................... 26 4 29

4 ii 30 32

5 iii 2.1 Algorithm for the proposed method (NS chart) left-to-righthmm Timing of likelihood calculation The system of the small autonomous mobile robot MieC Joystick map Two routes of straight and slalom for the experiment The transition probability matrix The emission probability matrix (Output matrix) The emission probability matrix S = 100, n = The comparison between the learning data and the estimation data for slalom The comparison between the learning data and the estimation data for straight Transition of the likelihood on slalom Transition of the likelihood on straight Route for verifying the validity of the forcefeedback Joystick map in polar coordinate Transition of the likelihood for the curve course Choice of the course

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.

6 iv

7 1 1 1 ( HMM) 1.1

8 1 2 [1] 2

9 1 3. ( HMM) HMM DNA ([2][3][4]) [5] [6][7] HMM HMM [8] HMM HMM 2 3

10 HMM HMM

11 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

Learn as a new model The likelihood High generates a maximum likelihood

12 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

13 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

..,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.

14 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

15 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)

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 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

17 2 11 t O = {o 1,o 2,...,o t } P(o 1,o 2,...,o t λ) λ

18 MieC (Fig. 3.1)

19 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

20 3 14 Fig. 3.2 Joystick map Force-FeedBack Fig HMM HMM

21 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 [step](19.2[sec])

22 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 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

23 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

24 3 18 S(j) v(k) j k S(j) v(k) x 20x64 flat start left-to-right HMM Fig. 3.4(a) Fig. 3.5(a) 6 Fig. 3.4(b) Fig. 3.4(c) Fig S = 100 Fig. 3.6

25 3 19 v(k) S(j) Fig. 3.6 The emission probability matrix S = 100, n = 30 viterbi Fig. 3.7 Fig. 3.8

26 learning data output data symbol step Fig. 3.7 The comparison between the learning data and the estimation data for slalom learning data output data symbol step Fig. 3.8 The comparison between the learning data and the estimation data for straight HMM HMM 96.3% 97.9%

27 Fig. 3.9 Fig HMM HMM Fig. 3.9 HMM straighthmm slalomhmm 1e-06 likehood 1e-08 1e-10 1e-12 1e-14 1e step Fig Transition of the likelihood on slalom

28 straighthmm slalomhmm 1e-06 likehood 1e-08 1e-10 1e-12 1e-14 1e step Fig. 3.9 Transition of the likelihood on straight HMM Fig HMM 0 HMM HMM HMM

29 MieC Force-Feedback 4 0 [-5 +5] Fig cm 80cm 40cm Fig Route for verifying the validity of the forcefeedback

30 3 24 Table Table 3.1 [ ] Force-Feedback Fig [ ] 15[ ] Fig Joystick map in polar coordinate Table 3.2.3

31 3 25 Table 3.2 A B C D Force-Feedback

32 [step](16.0[sec]) Fig e-20 Curve model Straight model 1e-40 likelihood 1e-60 1e-80 1e-100 1e step Fig Transition of the likelihood for the curve course 40[step] Fig [cm] 60[cm]

33 3 27 Straight model Corve model Fig Choice of the course Table 3.3 A B C D

34 3 28

35 HMM HMM

36 30 [1] Vol. 13 No pp [2] Hidden Markov Model. MVE, 97(207), , [3] HMM GMM [4] DNA Vol.40 No pp [5] HMM (D-II) vol.j85-d-ii no.7 July 2002 pp [6] Vol.22 No.2 pp [7] vol.27 No.5

37 31 pp [8],, / (C ) (2001-4) No ( ) [9] C.M. : Pattern Recognition and Machine Learning.,pp ,2006 [10] :,,pp ,2007

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