Haptic human-human interaction: motor learning & haptic communication

Hele tekst

(1)motor learning & haptic communication. Niek Beckers.

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(25) 80 deg. 80 deg. Fi. 80 deg. Fi. |. 80 deg.

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(28) |. 0.3 kg x. y. 0.2 N s m−1.

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(37) 400 N m−1 50 N −3 dB 7.5 Hz. 21 Hz 10 %.

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(40) 350 × 200 mm κ 0.7. 25 N 75 N. P1 P3 Lf. P5 P2 Lu Lb. P4.

(41) Lb x y. P1 q1 Lu. P5 Lu. q5. P4. Ph P2. n Lf. Lf. P3 |. P3. x = [x 3, y3 ]T x = f (q). T. q = [q 1, q 5 ]. P1 = P5 =. ! Lb 2. ! −Lb. !. 2. 0. P1 P2 P4 P5. "T. 0. "T. "T P2 = Lu cos q 1 Lu sin q 1 + P1 ! "T P4 = Lu cos q 5 Lu sin q 5 + P5 Lf. P2 P3 P4. P3 P2. P4. Ph Ph. ∥Ph − P3 ∥ P3 1 (P2 + P4 ) 2 # $ u u = P4 − P2 = x uy # $ 1 uy n= ∥u∥ −u x. Ph =. P2. P4 n.

(42) Ph. P2 Ph P3. % L2f − 14 ∥u∥ 2. P3. P3 &. P3 = Ph + n L2f −. 1 ∥u∥ 2 4 P3. P3. x J(q) = ∂x/∂q. ($x = J(q)$q). 0. κ. 1. 1 κ = ' '' ' 'J−1 ''J'. M (q) q% + C (q, q$ ) q$ + Dc M (q). Dc. Dv Fe. ($q) + Dv q$ =. τq − JT (q) Fe. C (q, q$ ). τq. mf me. P3. 2 3mf. 1 me′ = me + m f 3. 1 3mf. mel 2 ′ mel = mel + m f 3. P2. P4.

(43) ϒq me′ ϒq #. ϒ 0 ϒq = q,1 0 ϒq,5 ϒq,i =. ϒm kr2. +. ϒm. $. ϒs + Lu2. (. 1 ′ mu + mel 3. ). i = 1, 5. kr. ϒs. mu. $q x% = J%q + J$. $q + Dc ϒq q% + me′ JT J%q + me′ JT J$. L b Lu. kr. Lf. ($q) + Dv q$ = τq − JT Fe.

(44) |. 215 mm 0.27 kg. x. Mx. !. = 0, 0.245. "T. 0.55 kg 0.74. 1 m. *. Mq = ϒq + me′ JT J. Mx = J−T Mq J−1 = J−T ϒq J−1 + me′ I2×2. +.

(45) 1 0.8. 0.1 y [m]. κ [−]. 0. 0.6. 0.2. 0.4. 0.3. 0.2. 0.4 0.4 0.3 0.2 0.1. 0. 0 −0.1 −0.2 −0.3 −0.4. 0. 0.8. 0.1. y [m]. 0.6. 0.2 0.4. 0.3 0.4 0.4 0.3 0.2 0.1. 0.2 0 −0.1 −0.2 −0.3 −0.4. x [m] |. 15 mm. 65 g m−1. 1 mm E = 65 GPa. 0.2 mm 75 N. |. Lb Lu Lf kr. 0.07 0.238 0.153 7.3. m m m. [kg]. x [m].

(46) 0.24 N m 1.71 · 10−9 kg m2. 2.9 N m. 8A 20 A. 2.5 s. 48 V. x ≈ 26 m 70 Hz. 100 N. 2Nm. 80 min x. y x. 1.85 · 10−5 N2 1.93 · 10−5 N2 19.8 mN h−1.

(47) < 100 ns. 120 Hz. 50 ms 50 ms.

(48) 2200 W. Fh Ym Cp. xd xd x. Cp Fc. Yr. xd. Fh. |. Ym. xd. e −. Cp. Fc. Ft. Yr. x.

(49) Ya (s). Ya (s) = *. ,. x (s) Fh,x (s). 0. Fh 0 y(s) Fh,y (s) + −1 *. I2×2 + Yr (s)Cp (s). -. x. =. Yr (s) + Yr (s)Cp (s)Ym (s). +. mv = 0.3 kg. bv =. 0.2 N s m−1 60 %. 0.3 kg. Cp. kp. kd. Cp. 18 N s m−1. Fs. 1500 N m−1.

(50) Fh1. Ym1. xd1. −. e1. Cp1. Fc 1. Ft1. Fc 2. Ft2. Yr 1. x1. − Fs. Zs −. Fh2. Ym2. xd2. e2. Cp2. Yr 2. x2. −. |. Zs. 20 N m−1. 400 N m−1. x. y x. y. x 200 N m. y 175 N m (1/1500 + 1/200)−1 =.

(51) |. 0.355 m × 0.215 m. L ×W. 0.74 − 26 m 26 mm s−1 1.05 m s−1 108.4 m s−2 16.7 m s−2 100 N 2 N m 30 N 50 N 0.55 kg 21 Hz 6.5 Hz 1 kHz. ! ! ▽. x x. y y. !. x. y. ! ▽. 0.001 s. 175 N m−1. 50 N. 50 N. xd 30 s.

(52) 400. 300. !. N m−1. ". #. 1 ks. +. 1 kp. $ −1. 200. 100. 0. 0. 100. 200. !. |. 300. N m−1. ". 400. x. 1 kHz. y. x H xd ,x. x. y. 10 Hz −3 dB. √. 17 Hz 0.5. 21 Hz. 100 Hz. Hτc ,qm (jω). τc.

(53) |Hpd ,pr | [−]. 101 100 10−1. ∠Hpd ,pr [deg]. 10−2 90 0 −90. x y. −180 −270. 10−1. 100. 101. 102. f [Hz] |. x. qm fd ≈ 110 Hz. y.

(54) ! ! !Hτ ,q ! − c m. 10−1 10−2 10−3 10−4 10−5 180 0. ∠Hτc ,qm. −180 −360 −540 −720 −900. fd = 111.6 Hz. 101. 102. f | 400 Hz. 90 Hz 0.2 N m. 60 s. Ym x. y. mv = 0.3 kg. R2. > 0.9. 10 Hz 130 Hz.

(55) 0.1. y [m]. 0.2. 0.3 0.1 kg. 0.4 0.2. 0.1. 0. x [m]. −0.1. |. 0.3 kg. −0.2.

(56) Ym Ym Cp. Yr. Ya. Yˆ a Ya (s) =. ,. x (s) Fh,x (s). 0. 0 y(s) Fh,y (s). # $ ˆ 0 ˆYa (s) = Yx (s) 0 Yˆy (s) . . . . .Yˆ a ./.Ya .. -. $ # Yx (s) 0 = 0 Yy (s). 0.9−1. 0.9. Ym 0.2 N s m−1. 0.3 kg Yr x. y Yr Cp Yˆ a 120 s. 0.2 Hz Ym ˆYa. Ya x 6 Hz. 4 Hz Yr. 6 Hz. y 7.5 Hz. 7.5 Hz.

(57) # #! " #Yy # N m−1. " ! |Yx | N m−1. 101 100 10−1 10−2 10−3 10−4 10−5 10−6 90. 101 100 10−1 10−2 10−3 10−4 10−5 10−6 90. ∠Yy [deg]. ∠Yx [deg]. Ym. 0 −90. −180 −270 10−1. 100. 101. Yˆa Ya. 0 −90 −180 −270 10−1. 102. 100. 101. f [Hz]. f [Hz] | x. y. x. 4.8 Hz. y. 102.

(58) 6.5. y [m]. 0.1. 6. 0.2. 5.5. 0.3. 5 0.4 0.2. 0.1. 0. x [m]. −0.1. −0.2. | x. y. Zs. 24.5 ± 2.2. [Hz]. 7. 0.

(59) 48 s. 3s. x(t) = 2.11 sin (0.63t + 4.86) + 2.05 sin (1.10t − 6.88) + 1.91 sin (1.73t + 0.18) + 1.72 sin (2.67t − 8.49). + 1.42 sin (4.24t + 3.75) + 1.31 sin (5.50t − 4.28). + 1.13 sin (6.75t − 9.35) + 0.99 sin (8.01t − 0.54) y(t) = 1.95 sin (0.79t + 4.86) + 1.89 sin (1.26t − 6.88) + 1.77 sin (2.04t + 0.18) + 1.59 sin (2.98t − 8.49). + 1.31 sin (4.56t + 3.75) + 1.21 sin (5.18t − 4.28). + 1.05 sin (6.44t − 9.35) + 0.91 sin (7.70t − 0.55). 18 cm. 13.9 cm s−1. 28.9 cm s−1. ks = 120 N m−1 bs = 2.5 N s m−1. Zs. Fs vo. * + * + Fs = ks pp − po + bs vp − vo. pp. vp. po.

(60) E Es. cm. 1 kHz Ec Ec. I I =1−. Ec Es. Ec. Es R. R =1− Es ,p. 5%. Es ,p Es Es. R.

(61) R > 5% p < 0.01 R<0. I [%]. R = [−17.5, −12.5] %. 30. k s = 120 N m−1. 20. N = 10. 10 0 −10 −20 −40 −30 −20 −10 |. 0. 20 R [%]. R I. 10. 30. 40.

(62) x. y. 70 Hz.

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(71) 0.3 kg. 0.25 N s m−1.

(72) Fi Fi. |. 23 s 20 s T. x. y. mm T (x ) (t) = 28.7 sin (0.94t − 7.77) + 27.1 sin (1.26t − 8.53). + 23.5 sin (1.89t − 4.36) + 18.0 sin (2.83t − 3.79). T (y) (t) = 27.1 sin (1.26t − 0.71) + 25.3 sin (1.57t − 3.45). + 21.6 sin (2.20t + 3.92) + 16.4 sin (3.14t + 4.93) 79 mm s−1. 10 cm 139 mm s−1 (t ∈ [t 0, t 0 + 23] s t 0 ∼ U(0, 20)). !. " 0, 13 π, 23 π, π, 43 π, 35 π rad.

(73) * + * + Fi = ks pp − po + bs vp − vo. ks po. bs. pp. vp. vo. Fi ks = 150 N m−1. bs = 2 N s m−1. Fc ,. -. $ $# # F 0 −15 v (x ) Fc = Dv ≡ (y) = 15 0 v (y) F (x ).

(74) Ft. Fc. Fi. v F 20 mm. Fc. 2N. |. Ft. Fc v. Fi. Fi.

(75) 1 kHz. E 20 s. Es. E. Ec. Es, Es ,0. Es,.

(76) *. Es ,0 − Es,. Es = a + be −λ(t −1) t. λ. a. R2 R2. < 0.25. R2. α. Fc ,a Fc,i. b. +.

(77) Fc,a. Fi = 0 N Fc,a = Ft − (mr x% r + br x$ r ). Ft. mr. br x% r. x$ r. Fc,i. α N 1 / ∥Fc,a ∥ α= N ∥Fc,i ∥ k=1. k. N α. t t. Es,0. 0.05 ±.

(78) t(38) = 0.13 p = 0.90. t(19) = 5.86 p = 1.2 ·. 10−5. t(19) = 6.66 p = 2.3 ·. 10−6. t(38) = −0.72 p = 0.475 t(19) = 7.05 p = 1.0·10−6. t(19) = 5.78 p =. 1.4·10−5 t(38) = −0.20. p = 0.84. t(19) = 0.98 p = 0.338 t(19) = 0.42 p = 0.680. *. Es ,0. +. Es ,0.

(79) E [mm]. 15 (E ). 12.5 10. (E ) (E ). 7.5 5. 0. 10. 20. 30. 40. 50. 60. 70. 80. E s [mm]. 15. !. ". #. $. [mm]. [−] 15. 10. 10. 5. 5. 0. 0. R 2 = 0.783 p < 10−10. 0. 5. 10. 15. 20. 25. E s ,0 [mm]. ! " λ trial−1. 1.5 1 0.5 0. | #. t(38) = 3.05 p = 0.004 $ 10−7 % t(38) = 2.79 p = 0.008 & t(19) = 7.11 p < 10−6. t(19) = 8.65 p <. λ.

(80) β 1 = 0.75 F (1, 76) = 146.19 p < 10−10 ω 2 = 0.78 F (1, 76) = 0.02 p = 0.90. 1.31 N 0.44 N.

(81) 40 mm. |. p=. t(19) = 3.64 p = 1.75 · 10−3. 5.57 · 10−4. t(19) = 4.14. t(38) = 1.41 p = 0.167. 72 %. 77 % 86 %. α F (1, 876) = 123.78 p < 10−16.

(82) α [−]. 1 0.9 0.8 0.7 0.6. 22 25. 30. 35. 40. 45. 50. [−]. |. F (1, 876) = 0.08 p = 0.79. 55. 60 63.

(83) ∼5 mm. α ≈ 72 %. ∼86 %. 80 82 %.

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(92) 80 deg.

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(94) 22.0 ± 2.1 yr. 23 s mm.

(95) Fi. 80 deg. Fi. |. 80 deg. x(t) = 28.7 sin (0.94t − 7.77) + 27.1 sin (1.26t − 8.53). +23.5 sin (1.89t − 4.36) + 18.0 sin (2.83t − 3.79). y(t) = 27.1 sin (1.26t − 0.71) + 25.3 sin (1.57t − 3.45). +21.6 sin (2.20t + 3.92) + 16.4 sin (3.14t + 4.93) 10 cm 13.9 cm s−1 23 s. 15 s. 80 deg. 7.9 cm s−1 t0 (t ∈ [t 0, t 0 + 23] s t 0 ∼ U(0, 23)s).

(96) * + * + Fi = ks pp − po + bs vp − vo. ks po. bs. pp. vp. vo. ks = 120 N m−1. bs = 7 N s m−1. N = 20 N = 20 N = 10. N = 10.

(97) Es ,0. ks. 250 N m−1. 1 kHz E mm E. Es. 20 s.

(98) Es , Es,0 *. Es ,0. Es ,0. Es,. *. Es ,. +. Es ,0 − Es ,. Es = a ∞ + as e −λs (t −1) + a f e −λ f (t −1) *. t+ λs < λ f. λs λf a ∞ as. af. R2 R2 Z = 741 p < 1 · 10−7. 0.84. Z = 45 p < 1 · 10−5. 0.95. +.

(99) (Ec ). (Ec ). (Es ). E0. < 10 0.05. ±.

(100) (Es ). 8.0 ± 0.3 mm 8.3 ± 0.2 mm 7.7 ± 0.3 mm 8.2 ± 0.3 mm F (3, 54) = 0.89 p = 0.451 ω 2 = −0.006 Es ,0 46.6 ± 2.9 mm 50.4 ± 4.1 mm 2 ω = −0.044. 48.0 ± 3.0 mm 48.5 ± 4.1 mm F (3, 54) = 0.21 p = 0.89.

(101) E [mm]. |. 0. 10. 20. 30. 40. 50. 60. 0. 5. 10. 15. 20. 25. 30. 35. 40 [−]. 45. 50. ±. 55. 60. 65. 70. 75. 80. 85.

(102) E [mm]. |. 0. 10. 20. 30. 40. 50. 60. 0. 5. ±. 10. E s ,0. 15. 20. 25. 30. Es,0. 35. 40 [−]. 45. 50. 55. 60. 65. 70. 75. 80. 85.

(103) E [mm]. |. 0. 10. 20. 30. 40. 50. 60. 0. 5. 10. 15. 20. 25. 30. 35. 40 [−]. 45. 50. 55. 60. 65. 70. 75. ±. 80. 85.

(104) ±. *. Ec,. 10.7 ± 0.6 mm 11.2 ± 0.8 mm. *. p = 0.647. ω2. Es ,0. +. *. Es ,. +. Es , 10.0 ± 0.6 mm 12.0 ± 0.8 mm F (3, 54) = 1.44 p = 0.242 ω 2 = 0.022. +. Es ,0 β 1 = 0.970 F (7, 50) = 186.10 p < 1 · 10−10 ω 2 = 0.96 = 0.032. F (3, 50) = 0.56.

(105) 25. E s ,c , [mm]. 20 15 10 5. 70 60 50 40. !. E s ,0 − E s ,. ". [mm]. 0. 30 20 10 20. 30. 40. 50. 60. 70. 80. E s ,0 [mm]. |. ±. t(37) = 3.82, p = 0.001 t(37) = 2.69, p = 0.011. F (1, 37) = 36.27 p < 1 · 10−6 1.6 ± 0.4 mm 15 % 1.6 ± 0.6 mm 14 % 2.3 ± 0.6 mm 20 % F (2, 37) = 0.78 p = 0.465. t(37) = 3.95, p = 0.001 Es,0 95 %.

(106) λs. χ 2 (2) = 2.48 p = 0.290. 0.17 p = 0.920. p = 0.805. λf. χ 2 (2) = 5.65 p = 0.059. χ 2 (2) = 0.44. χ 2 (3) = 5.63 p = 0.131. p = 0.459. χ 2 (2) =. χ 2 (3) = 4.78 p = 0.189. F (2, 42) = 2.46 p = 0.097 Es ,0. λs. F (1, 42) = 0.56. F (1, 42) = 4.70 p = 0.036 λs F (2, 42) =.

(107) 6. 0.2. 5 ! " λ f trial−1. ! " λ s trial−1. 0.25. 0.15 0.1. 3 2. 0.05. 1. 0. 0. 0.25. 6 R 2 = 0.22 p = 0.0497 R 2 = 0.003 p = 0.822 R 2 = 0.51 p = 0.021. 5 ! " λ f trial−1. 0.2 ! " λ s trial−1. 4. 0.15 0.1 0.05. 3 2 1. 0 20. 40. 60 E. |. 4. (λs ). ,0. 80. [mm]. 0 20. 40. 60 E. ,0. 80. [mm]. (λ f ). Es,0. 95 %. 3.66 p = 0.034 (β 1 ). F (2, 42) = 4.22. p = 0.021. β1 = 1.41 ± 0.66 t(16) = 2.12 p = 0.0497. R2. = 0.22. β 1 = −0.20 ± 0.86 t(18) = −0.23 p = 0.822 R 2 = 0.003 t(42) = 1.54 p = 0.132 β 1 = −1.94 ± 0.68 t(8) =.

(108) −2.86 p = 0.021 R 2 = 0.51. t(42) = −2.84 p = 0.0069.

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(110) 10 cm. 15 cm.

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(119) 23 N m rad−1 2300 N m−1. 10 deg. 0.1 m. 30 deg. 3s 0.5 s. 900 ms. 1200 ms 800 ms. 900 ms. 1200 ms.

(120) 2×. ms. 1s. |. 0.7 N m 0 deg. 3s.

(121) 3s. 0.7 N m 1s 3s. 100 Hz 0.5 s 5 deg s−1 1.2 s. 6 Hz.

(122) F. F F.

(123) ! $ τ, x = θ, θ,. f. xk+1 = Axk + Buk + C p. xk. 0. "T. p xk. − xk. 1. k ⎡1 ⎢ ⎢0 ⎢ A= ⎢ ⎢0 ⎢ ⎢0 ⎣ 8 B= 0. ks. δ 0 δ 1 I 0 1 − τδu 0 0 0 0. ⎡ 0 ⎢ δ ⎢k C = ⎢⎢ s I ⎢ 0 ⎢ 0 ⎣. δ τu. 0. ⎤ ⎥ ⎥ ⎥ ⎥ δ τu ⎥⎥ 1 − τδu ⎥ ⎦ 0 0. 9T. 0 0 0 0. bs δI 0 0 I. bs. 0⎤⎥ 0⎥⎥ 0⎥⎥ 0⎥⎦. τu = 40 ms. uk = −L (xk − t) t. θt. ! "T t = θ t , 0, 0, 0. δ. C = 04×4 uk.

(124) θ0. ! "T t0 = θ 0, 0, τ0, 0. τ0. L ∞ /. xTk Qxk + uk Ruk. k=0. Q. R. T. S=Q+A. #. 0. T. S − SB R + B SB. 0. T. L = R + B SB. 1 −1. 1 −1. T. $. B S A. BT SA. C. ks = 0.4 N m deg−1 bs = 0.05 N m s deg−1 R = 0.5 δ = 0.01 s I = 0.1 kg m2 ks. bs I. θ 0 = −10 deg θ t = 30 deg τ0 = 0.7 N m. −0.7 N m. R.

(125) Q Q1 (1, 1) Q1 (2, 2) θ t ,1. θ t ,2. L. 12 0 12 ⎤ ⎡0 L ⎢ θ i − θi ⎥ τ − τ / i i 1 ⎢ ⎥ M= + ⎢ ⎥ 2 ⎥ 2L i=0 ⎢ σθ2 σ τ i i ⎢ ⎥ ⎣ ⎦. Q2 (1, 1) Q2 (2, 2). θi. τ. σθ2 θ. στ2 τ. (2, 0.1, 0, 0) θ = 30 deg. Q=. δQ δθ t = 1 deg. Q1 (1, 1) ± δQ. Q1 (2, 2) ± δQ. θ t ,1 ± δθ t. Q2 (1, 1) ± δQ. Q2 (2, 2) ± δQ. θ t ,2 ± δθ t. Q. = 2 δQ. = 0.1.

(126) F p > 0.05. 0.38 s. 0.45 s. F. p < 0.05. 0.5 s.

(127) 40 30 20 10. [deg]. 0 −10 −20 40 30 20 10 0 −10 −20. 0 0.3 0.6 0.9 1.2. 0 0.3 0.6 0.9 1.2. 0 0.3 0.6 0.9 1.2. 0 0.3 0.6 0.9 1.2. [s] 0.8 0.4 0. [N m]. −0.4. −0.8 0.8 0.4 0 −0.4. −0.8. 0 0.3 0.6 0.9 1.2. 0 0.3 0.6 0.9 1.2. 0 0.3 0.6 0.9 1.2. [s] |. 0 0.3 0.6 0.9 1.2.

(128) t t = 1.2 s t(15) = 46.80 p < 0.001. Q. Q(1, 1) Q(2, 2) Q(1, 1). Q(2, 2).

(129) [N m]. 2 1 0 −1 −2 0. 0.3 0.6 0.9 1.2. 0. 0.3 0.6 0.9 1.2 [s]. 0. 0.3 0.6 0.9 1.2. 0. 0.3 0.6 0.9 1.2. 0. 0.3 0.6 0.9 1.2 [s]. 0. 0.3 0.6 0.9 1.2. 0. 0.3 0.6 0.9 1.2. 0. 0.3 0.6 0.9 1.2 [s]. 0. 0.3 0.6 0.9 1.2. 0. 0.3 0.6 0.9 1.2. 0. 0.3 0.6 0.9 1.2 [s]. 0. 0.3 0.6 0.9 1.2. [N m]. 2 1 0 −1 −2. [N m]. 2 1 0 −1 −2. [N m]. 2 1 0 −1 −2. |.

(130) 40. [deg]. 30 20 10 30.5 [deg]. 0 −10. p < 0.002. −20 1. 30 p < 0.006. [N m]. 0.5 0. 29.5. −0.5 −1. 0. 0.3. 0.6 [s]. |. 0.9. 1.2.

(131) t(15) = 3.73 p < 0.002 t(15) = −3.20 p < 0.006. Q.

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(133) 40 [deg]. 30 20 10 0 −10 −20. 0. 0.3 0.6 0.9 1.2. 0. 0.3 0.6 0.9 1.2. 0. 0.3 0.6 0.9 1.2. 0. 0.3 0.6 0.9 1.2. 0. 0.3 0.6 0.9 1.2. 0. 0.3 0.6 0.9 1.2. [N m]. 2 1 0 −1 −2 [s] 40 [deg]. 30 20 10 0 −10 −20. 0. 0.3 0.6 0.9 1.2. 0. 0.3 0.6 0.9 1.2. 0. 0.3 0.6 0.9 1.2. 0. 0.3 0.6 0.9 1.2. 0. 0.3 0.6 0.9 1.2. 0. 0.3 0.6 0.9 1.2. [N m]. 2 1 0 −1 −2 [s]. |.

(134) 40 [deg]. 30 20 10 0 −10 −20. 0. 0.3 0.6 0.9 1.2. 0. 0.3 0.6 0.9 1.2. 0. 0.3 0.6 0.9 1.2. 0. 0.3 0.6 0.9 1.2. 0. 0.3 0.6 0.9 1.2. 0. 0.3 0.6 0.9 1.2. [N m]. 2 1 0 −1 −2 [s] 40 [deg]. 30 20 10 0 −10 −20. 0. 0.3 0.6 0.9 1.2. 0. 0.3 0.6 0.9 1.2. 0. 0.3 0.6 0.9 1.2. 0. 0.3 0.6 0.9 1.2. 0. 0.3 0.6 0.9 1.2. 0. 0.3 0.6 0.9 1.2. [N m]. 2 1 0 −1 −2 [s]. |.

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(143) x. mr = 0.3 kg y. br = 0.25 N s m−1.

(144) y x. Fi Fi. |. ! "T T = T (x ) T (y). 20 s. 23 s cm. T (x ) (t) = 2.87 sin (0.94t − 7.77) + 2.71 sin (1.26t − 8.53). + 2.35 sin (1.89t − 4.36) + 1.80 sin (2.83t − 3.79). T (y) (t) = 2.71 sin (1.26t − 0.71) + 2.53 sin (1.57t − 3.45). + 2.16 sin (2.20t + 3.92) + 1.64 sin (3.14t + 4.93). 20 cm. 7.9 cm s−1.

(145) 13.9 cm s−1 (t ∈ [t 0, t 0 + 20] s t 0 ∼ U(0, 20)) * ! " + φ = 0, 13 π, 23 π, π, 34 π, 53 π rad. * + * + Fi = ks pp − po + bs vp − vo. ks vp po. bs. pp. vo ks = 150 N m−1. bs = 2 N s m−1. Fc ,. - # $# $ F (x ) 0 −15 v (x ) Fc = Dv ≡ (y) = 15 0 v (y) F v.

(146) v. Fi. Fc+i Fc. 2 cm 2N. |. Fc Fc+i Fc. v. Fi. Fc+i Fc. Fi. p. v. Fi. Ft 1 kHz. E. cm. 20 s. E Es Ec.

(147) Σp p ! " Σp = E (p − E [p])2 # 2 $ σx ρσx σy = ρσx σy σy2 x x. y. σx2. ρ=0. σ x2. y. N 1 / 2 = σx ,k N k=1. σx2,k. x. k. N. I R CS I Ec. Es. I = 1 − Ec /Es R R = 1 − Es ,p /Es Es,p. Es.

(148) Ft Fi Fˆ i Fi Fc. α α ≈ 0.8 Fc,u = (1 − α) Dv Fˆ i = Fi + (1 − α) Dv Fi. α D v α. Fi = 0 N Fc,a Fc,i. Fc,a Fi = 0 N Fc,a = Ft − (mr x% r + br x$ r ) Ft. mr. br.

(149) x% r. x$ r Fc,i. α α=. N 1 / ∥Fc,a ∥ N ∥Fc,i ∥ k=1. k. N α. I = β 0 + β 1R + β 2 F + β 3 (R F ) + ϵ R. F β 0,...,3 R F. (R F ). ϵ.

(150) yk ν k. xˆ k |k uk Lk. ωk Fi ωk. Lk. uk yk. xˆ k |k. |. νk. Fi uk. xˆ k |k. uk. yk Fi. 0.05 ±. f. u f.

(151) δ = 0.01 s 8 9T (x ) (y) (x ) (y) (x ) (y) (x ) (y) (x ) (y) $ (x ) $ (y) xk = pk pk vk vk fk fk дk дk Tk Tk Tk Tk p. v. T k. x. y. f. д. T$ xk +1 = Axk + Buk + ωk. ⎡1 0 δ 0 ⎤ 0 0 0 0 ⎢ ⎥ ⎢0 1 0 δ ⎥ 0 0 0 0 ⎢ ⎥ ⎢ 0 0 1 0 δ /m ⎥ 0 0 0 ⎢ ⎥ 0 δ /m 0 0 ⎢0 0 0 1 ⎥ 08×4 ⎥ ⎢ 0 0 0 0 1 − δ /τ 0 δ /τu 0 A= ⎢ ⎥ u ⎢0 0 0 0 ⎥ 0 1 − δ /τ 0 δ /τ u u ⎢ ⎥ ⎥ ⎢0 0 0 0 0 0 1 − δ /τu 0 ⎢ ⎥ ⎥ ⎢0 0 0 0 0 0 0 1 − δ /τ u ⎥ ⎢ 4×8 4×4 ⎥ ⎢ 0 I ⎦ ⎣ ⎤ ⎡ 06×2 ⎥ ⎢ ⎢δ /τu 0 ⎥⎥ ⎢ B= ⎢ δ /τu ⎥⎥ ⎢ 0 ⎥ ⎢ 04×2 ⎦ ⎣. ωk ∼ N(0, Ωω ) m. 0.04 s Ωω =. 1 kg. ωk * + 0, 0, 0, 0, 0, 0, σu2 , σu2 , 0, 0, 0, 0 yk = Hxk + νk. H=. #. I4×4 04×4 04×4 04×4 04×4 I4×4. νk ∼ N(0, Ων ). $. τu =.

(152) Fi 1 0 νk 2 2 2 2 2 2 2 2 σp , σp , σv , σv , σT , σT , σT$ , σT$. ν. Ω =. xˆ k |k−1. Kk. xˆ k |k. yk. + * xˆ k |k = xˆ k |k−1 + Kk yk − Hˆxk |k−1 ˆ A. xˆ k |k −1 Bˆ uk −1. ˆ xk −1|k −1 + Bu ˆ k−1 xˆ k |k−1 = Aˆ. yk xˆ k |k σT2 ,u. σT2$ ,u. uk uk = −Lk xˆ k |k Lk.

(153) Lk #0 N ( 12 0 1 $ / (y) (y) 2 (x ) (x ) J= wp pk − Tk + pk − Tk + k=1. wp. #0 12 0 12$ (y) (y) (x ) (x ) wv vk − T$k + + vk − T$k #0 1 $) 12 0 (y) 2 (x ) w r uk + uk. wv. ˆ B) ˆ (A,. # 1$ $ ) # 1$ (# # $# $ # 1$ x x A 0 B 0 u1 ω +C + = + 2 2 2 2 x k +1 0 A x k 0 B u k ω k C ks = 150 N m−1. bs = 2 N m−1.

(154) wp. wv. σu 1 0.01 m s−1 0.005 m. 101. σP σT = 0.005 m 0.01 m s−1. σT$ ,u. 106. wp. wv. 0N. wr 0.005 m. σT$ = 0.01 m s−1. 1N. σu. σT ,u. σV.

(155) $. t(19) = 8.65 p <. 10−7. &. t. R. t t(19) = 7.11 p < 10−6 t(19) = −0.44 p = 0.669 F (1, 356) = 270.52 p < 10−12 R < 0% I ≈ 0%. F (2, 784) = 1.95 p = 0.144.

(156) 15. !. 40 30. ". 10. 20. 5. 10. 0. 0. Es. Ec [mm]. I [%]. 50. −10 −20 −75. −50. −25. 0. 25. 50 R [%]. |. 10 %. α = 0.72. α = 0.86. Fc,u = (1 − α)Dv Fi Fˆ i. Fc Fc,u. α = 0.86 Fi Fc = 1.31 N Fi = 0.43 N. 0.86 0.18 N 40 %. 75.

(157) α [−]. Fi ⊥ Fc ,u. Fi ∥ Fc ,u. 1. Fˆ i. Fˆ i. 0.9. θ. Fc ,u. 0.8. Fi Fi Fc ,u. 0.7 0.6. 22. 30 35 40 45 50 55 [−]. |F | [N]. 1.5. 63. Fc Fc ,u. 1 0.5 0. Fc. Fi. | α Fc ,u. Fˆ i Fc Fc,u. Fi. θ ≈ 22 deg.

(158) wp. wv. σu2. x. x. 5. 10−2. ! " |S x x | cm2. 100. x [cm]. 10. 0. 10−4. −5 −10. 10−6. 0. 5. 10. 15. 20. t [s]. 10−8. 100. ! "10 ω rad s−1. [−]. 10 8 6 4 2 0 0.6. 0.8. 1. 1.2. E [cm]. | x x Es. 1.

(159) 97.7 % Es σx2. F (1, 36) = 0.04 p = 0.85. F (1, 796) = 1.73 p = 0.19. 0.4. R 2 = 0.518 p = 0.00035. 0 0.6. 0.7. 0.8. 0.9. ". 0.2. 0.2 0.1. • # !. 1. 1.1. ! " σ 2x cm2. 0.3 ! " σ 2x cm2. 0.25. R 2 = 0.729 p < 10−5. 0.15 0.1 0.05 0. E s [cm]. | σ x2 = β 0 + β 1 E s. 95 %. $ t(19) = −1.78 p = 0.089 % t(19) = −2.68 p = 0.023 # t(19) = 6.05 p = 8.1 · 10−6 • t(19) = 6.21 p = 5.8 · 10−6.

(160) R ≈ −40 %. t t(19) = −2.68 p = 0.023. R<0. R>0. σu2. I [%]. 40 30. σu2 = 0 N2. 20 10 0 −10 −20 −30 −75. |. −50. −25. 0. 25. 50 R [%]. 75.

(161) wp 0 N2. wv. σu2.

(162) R < 0%. I = 0% ∼5 %. R ≈ −40 %.

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(164) ks. ∼40 % I ≈ 0%. ∆p = Fˆ i /ks. R < 50 %.

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(172) 80 deg.

(173) E [mm]. 15 (E ). 12.5. 10. 7.5. 5. 0. 10. 20. 30. 40. 50. 60. 70. 80. 50. 60. 70. 80. [−]. E [mm]. 60 50 40 30 20 10 0. 0. 10. 20. 30. 40 [−]. |. (E ) (E ).

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(178) ks = 150 N m−1 bs = 2 N s m−1.

(179) I = 0%. F (3, 1413) = 1.57 p = 0.1947.

(180) I [%]. 50 40 30 20 10 0 −10 −20 −100. −75. −50. −25. 0. 25. 75. R [%]. | Es Es ,p. 50. I = 1 − Ec /Es. Ec. R = 1 − Es ,p /Es.

(181) 10 N. 20 N 10 N. ∼100 N m−1.

(182) ∼50 % R < −50 %. 5%. I = β 0 +β 1 e γ R R = −125 %. R < −50 %. −50 % < R < 50 %. I ≈ 0%. R.

(183) 50. I [%]. 40 30 20 10 ! 0. I = −8.0 + 18.8e 0.016R. ". −10 −20 −125. −100. |. R < −50 %. −75. −50. −25. 0 R [%]. 25. 50. 75.

(184) R < −50 % −50 % ≤ R < 0 % R ≥ 0%. R > 40 %. R > 40 %.

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(190) −50 % < R < 50 %.

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(200) x(t), y(t) =. 25 /. (x ,y). Ak. k =1. 0 1 (x ,y) (x ,y) sin 2π fk t + φ k. n(x ,y) Tm. δ f = 1/Tm 30 s. 30 Hz. 21.25 mm2 2.

(201) | n (x ) [−] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25. 5 7 11 13 17 23 29 37 47 61 79 103 131 173 223 293 379 491 631 821 1063 1381 1787 2311 2999. f (x ) [Hz]. A(x ) [m]. 0.167 0.233 0.367 0.433 0.567 0.767 0.967 1.233 1.567 2.033 2.633 3.433 4.367 5.767 7.433 9.767 12.633 16.367 21.033 27.367 35.433 46.033 59.567 77.033 99.967. 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.0025 0.0025 0.0025 0.0025 0.0025. φ (x ) [rad] 1.200 1.063 1.389 −0.191 4.361 3.551 −1.299 −0.010 1.019 0.473 1.168 3.484 3.250 1.941 2.594 1.711 3.758 3.178 −0.845 −0.502 2.412 0.958 4.392 0.447 −1.022. n (y) [−] 3 8 10 14 19 24 31 41 53 67 83 107 137 179 227 307 383 499 641 823 1069 1399 1789 2333 3001. f (y) [Hz] 0.100 0.267 0.333 0.467 0.633 0.800 1.033 1.367 1.767 2.233 2.767 3.567 4.567 5.967 7.567 10.233 12.767 16.633 21.367 27.433 35.633 46.633 59.633 77.767 100.033. A(y) [m] 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.0025 0.0025 0.0025 0.0025 0.0025. φ (y) [rad] 4.613 3.099 −1.336 −0.455 0.316 −1.543 1.923 3.287 −0.551 2.378 1.074 −1.422 2.581 3.603 0.932 0.818 1.500 2.751 −0.286 1.980 2.799 1.804 4.170 1.541 1.189.

(202) f (x ,y) (t) f (x ,y) (t) =. 4 /. (x ,y). Ak. k =1. (x ,y). x. y. 0 1 (x ,y) (x ,y) sin ωk t + φ k. (x ,y). Ak k. ωk. x. (x ,y). φk. y. 0.943 rad s−1 (x ,y) nk ωm = 2π /Tm = 0.3142 rad s−1 Tm = 20 s. T1 = 0.1 s. .( . . 1 + T jω ) 2 . . . 1 |A (jω)| = . . . 1 + T2 jω .. T2 = 0.8 s 12 cm2. x. y. 3.142 rad s−1.

(203) | n(x ) [−]. (x ). ωk [rad s−1 ]. (x ). Ak [cm]. (x ). φ k [rad]. (y). nk [−]. (y). ωk [rad s−1 ]. (y). Ak [cm]. (y). φ k [rad]. −7.77 −8.53 −4.36 −3.79. −0.71 −3.45 3.92 4.93. χ 2 (3) = 9.94 p = 0.019 χ 2 (3) = 0.74 p = 0.86. χ 2 (3) = 0.99 p = 0.803 χ 2 (3) = 0.44 p = 0.9321.

(204) CS I I = 1 − Ec /Es R R = 1 − Es ,p /Es Es ,p. Es 10 % I. R. 40 %. 50 %.

(205) 2.5 ". !. ⋆. 1.5. 6 5 4 3. 1. 2. 0.5. 1. | ' U = 22 p = 0.056 ⋆. Ec Es. ". U = 86 p = 0.006 $ U = 23 p = 0.032. ! I 1−. Es, [cm]. 2. [cm]. 7. 40 % 30 % 20 % 10 % 0%. −10 % −20 % −100 % −75 % −50 % −25 %. |. 0%. 25 % 50 % 75 % ! " E s ,p R 1 − Es.

(206) |. [−]. 0. 80. 0 60. 2. 2. 40. 4. 4. 20. 6. 6. 0. 8. 8. E [cm]. 0. 20. 40. [−]. 60. 80. 0. 2. 4. 6. 8. 0. 20. 40. [−]. 60. 80.

(207) |. [−]. 0. 80. 0 60. 2. 2. 40. 4. 4. 20. 6. 6. 0. 8. 8. [−]. 0. 80. 0 60. 2. 2. 40. 4. 4. 20. 6. 6. 0. 8. 8. E [cm]. E [cm]. 0. 0. 20. 20. 40. 40. [−]. [−]. 60. 60. 80. 80.

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(210) |. 0.68 s. 0.88 s. F. 0.05. 0.38 s. 0.79 s 0.87 s 0.88 s. 1.2 s 1.06 s 1.2 s. 0.78 s 0.81 s. 0.9 s 1.05 s. 0.45 s. 0.7 s 1.2 s 0.74 s 1.2 s 0.68 s 0.88 s 0.57 s 1.04 s 0.5 s 1.2 s 0.56 s 1.08 s 0.69 s 0.86 s. 0. 1 0.5 s 0.8 s 01.03 s 1.2 s1 0.5 s 0.85 s 0.96 s 1.2 s.

(211) |. Q(1, 1) Q(2, 2) Q(1, 1) Q(2, 2) Q(1, 1) Q(2, 2) Q(1, 1) Q(2, 2) Q(1, 1) Q(2, 2) Q(1, 1) Q(2, 2) Q(1, 1) Q(2, 2) Q(1, 1) Q(2, 2). 0.54 0.11 1.91 0.13 7.84 0.25 3.16 0.12 11.28 0.01 9.72 0.28 2.55 0.01 4.30 0.23. 2.17 0.05 2.15 0.06 5.56 0.15 5.13 0.22 8.99 0.45 6.55 0.32 1.90 0.19 6.14 0.10. 47.17 1.46 26.11 1.30 29.02 1.46 25.58 1.14 110.79 1.70 57.35 2.21 55.89 1.87 42.24 1.75. 28.48 1.15 26.28 1.33 49.47 1.43 26.47 1.32 59.35 1.82 253.77 2.21 22.38 1.37 59.92 1.74. 0.19 0.15 3.66 0.18 6.84 0.01 0.30 0.23 4.43 0.09 16.77 0.77 0.30 0.01 7.72 0.32. 9.01 0.21 5.69 0.20 0.98 0.40 13.12 0.01 16.11 0.57 1.28 0.13 5.84 0.42 1.04 0.06. 72.24 1.96 41.54 1.58 21.01 1.31 113.60 1.99 1118.81 1.66 30.96 1.17 22.43 1.54 45.77 1.40. 27.13 1.06 64.05 1.89 40.83 1.47 43.74 1.60 152.16 2.09 127.77 2.20 21.88 1.74 213.43 2.20. 2.58 0.05 1.68 0.17 1.60 0.34 2.82 0.67 21.41 0.01 11.12 1.00 7.75 0.35 1.90 0.36. 0.79 0.11 7.50 0.02 11.28 0.30 0.97 1.15 1.45 0.34 2.13 0.01 0.01 0.04 8.76 0.01. 103.58 1.92 43.35 1.35 24.94 1.42 52.63 1.75 58.03 1.80 24.88 1.41 19.27 1.98 75.74 1.63. 23.75 1.22 63.92 1.92 118.23 1.20 27.51 1.04 47.89 1.45 162.88 2.21 26.28 1.16 61.65 1.81.

(212) [N m]. 2 1 0 −1 −2 0 0.3 0.6 0.9 1.2. 0 0.3 0.6 0.9 1.2 [s]. 0 0.3 0.6 0.9 1.2. 0 0.3 0.6 0.9 1.2. 0 0.3 0.6 0.9 1.2 [s]. 0 0.3 0.6 0.9 1.2. 0 0.3 0.6 0.9 1.2. 0 0.3 0.6 0.9 1.2 [s]. 0 0.3 0.6 0.9 1.2. 0 0.3 0.6 0.9 1.2. 0 0.3 0.6 0.9 1.2 [s]. 0 0.3 0.6 0.9 1.2. [N m]. 2 1 0 −1 −2. [N m]. 2 1 0 −1 −2. [N m]. 2 1 0 −1 −2. |.

(213) [deg] [N m]. 40 30 20 10 0 −10 −20. 0 0.3 0.6 0.9 1.2. 0 0.3 0.6 0.9 1.2. 0 0.3 0.6 0.9 1.2. 0 0.3 0.6 0.9 1.2. 0 0.3 0.6 0.9 1.2. 0 0.3 0.6 0.9 1.2. 2 1 0 −1 −2. [N m]. [deg]. [s] 40 30 20 10 0 −10 −20. 0 0.3 0.6 0.9 1.2. 0 0.3 0.6 0.9 1.2. 0 0.3 0.6 0.9 1.2. 0 0.3 0.6 0.9 1.2. 0 0.3 0.6 0.9 1.2. 0 0.3 0.6 0.9 1.2. 2 1 0 −1 −2. [s]. |.

(214) [deg] [N m]. 40 30 20 10 0 −10 −20. 0 0.3 0.6 0.9 1.2. 0 0.3 0.6 0.9 1.2. 0 0.3 0.6 0.9 1.2. 0 0.3 0.6 0.9 1.2. 0 0.3 0.6 0.9 1.2. 0 0.3 0.6 0.9 1.2. 2 1 0 −1 −2. [N m]. [deg]. [s] 40 30 20 10 0 −10 −20. 0 0.3 0.6 0.9 1.2. 0 0.3 0.6 0.9 1.2. 0 0.3 0.6 0.9 1.2. 0 0.3 0.6 0.9 1.2. 0 0.3 0.6 0.9 1.2. 0 0.3 0.6 0.9 1.2. 2 1 0 −1 −2. [s]. |.

(215) t [s]. 1.2. 1 0 −1. 0. 0.6. 1.2. 0. 0.6. 1.2. t [s]. 1 0 −1 1 0 −1. 0. 0.6. 1.2. 0. 0.6. 1.2. 0. 0.6. 1.2. t [s]. 1 0 −1 1 0 −1 1 0 −1 1 0 −1. 0. 0.6. 1.2. 0. 0.6. 1.2. 0. 0.6. 1.2. 0. 0.6. 1.2. ∆τ [N m]. 0.6. 1 0 −1. ∆τ [N m]. ∆τ [N m]. 0. 1 0 −1. ∆τ [N m]. ∆τ [N m]. 1 0 −1. t [s]. 1 0 −1 1 0 −1 1 0 −1 1 0 −1. 1 0 −1. 0. 0.6. 1.2. 0. 0.6. 1.2. 0. 0.6. 1.2. 0. 0.6. 1.2. 0. 0.6. 1.2. t [s]. | ∆τ.

(216) C # 1$ (# $ ) # 1$ $# $ # # 1$ x x A 0 B 0 u1 ω = +C + + 2 x2 k +1 0 A x2 k 0 B u2 k ω k. * + Fi1 = ks p2 − p1 + bs * + Fi2 = ks p1 − p2 + bs #. −Cp C= Cp. *. *. v2 − v1. v1 − v2. Cp −Cp. $. +. +. C. C.

(217) Cp ⎡ 0 0 0 0 ⎢ ⎢ 0 0 0 0 ⎢ 0 ks δ /m 0 ⎢ks δ /m ⎢ 0 bs δ /m 0 bs δ /m Cp = ⎢ ⎢ 0 0 0 0 ⎢ ⎢ 0 0 0 0 ⎢ 6×6 ⎢ 0 ⎣. 0 0 0 0 0 0. ⎤ 0 ⎥ ⎥ 0 ⎥ 0 6×6 ⎥ 0 ⎥ 0 ⎥ ⎥ 0 ⎥ ⎥ 0 ⎥ 06×6 ⎥⎦. w p wv σu2 = 0 N2. Es 0.05. Es σu2. 0 N2. σu.

(218) | Kp. Kv wp. wp [−]. wv Es wv [−]. Es σu [N]. Kp [N m−1 ]. Kv [N s m−1 ]. E s [cm]. 6400.9 15 298.2. 67.1 53.5. 0.306 0.307. 74.75 114.24. 20.14 25.21. 0.945 0.754. 12 277.4 9086.0. 17.8 48.0. 0.332 0.200. 102.99 88.78. 22.78 21.60. 0.829 0.758. 11 280.6 8158.2. 99.6 44.4. 0.345 0.282. 98.24 84.28. 24.19 20.86. 0.855 0.849. 11 293.7 10 373.1. 15.3 28.6. 0.255 0.372. 98.93 94.83. 22.14 21.92. 0.771 0.909. 6857.1 6181.9. 31.2 1.2. 0.183 0.396. 77.55 73.97. 19.50 17.99. 0.799 1.076. 13 582.2 7689.5. 19.2 91.5. 0.262 0.161. 108.13 81.57. 23.53 21.75. 0.722 0.762. 4529.3 15 668.3. 3.2 12.3. 0.161 0.343. 63.57 115.91. 16.40 24.43. 0.883 0.783. 19 237.9 19 511.9. 6.0 3.5. 0.281 0.355. 128.02 128.92. 25.92 25.98. 0.679 0.748. 10 745.6 9315.6. 97.8 89.5. 0.294 0.236. 95.96 89.57. 23.84 22.79. 0.824 0.789. 9551.7 10 621.4. 12.9 94.4. 0.260 0.264. 91.24 95.44. 20.96 23.69. 0.807 0.779. F (3, 1413) = 1.57 p = 0.195.

(219) " 2 ! σˆ x cm2. 101 100 10−1 10−2 105. 1. 104. w p [−]. |. 103 102. 0. 0.5. 0.25. ! " σu2 N2 2 σˆ x. σu2. wp. 0.75. I [%]. 50 40 30 20 10 0 −10 −20 −75. −50. −25. |. σu2. 0 N2. 0. 25. 50 R [%]. 75.

(220) I [%]. 40 30. σu2 = 0 N2. 20 10 0 −10 −20 −30 −75. −50. −25. 0. 25. 50. 75. R [%]. |. Fˆ i Ft Fi. Fc Ft = Fi + Fc ˆ D ˆ (Fˆ c = Dv). Fˆ c ∼80 %. α.

(221) Fˆ i. αD. Fˆ i = Ft − Fˆ c = Ft − αDv = Fi + (1 − α) Dv Fc,u = (1 − α) Dv. Fi ⊥ Fc ,u. Fi ∥ Fc ,u. Fˆ i. Fˆ i θ. Fc ,u Fi Fi. Fc ,u. Fˆ i Fi Fc ,u Fc. |. θ. ∥ Fˆ i ∥/∥Fi ∥ = 1.27 θ = 3.5 deg σθ = 7.5 deg 86 %. ∥ Fˆ i ∥/∥Fi ∥. α ˆ = D.

(222) [−]. 0.08. θ. 0.06 0.04 0.02 0 0.5. 1. ∥ Fˆ i ∥ ∥Fi ∥. | θ. 1.5 [−]. 2. −20. 0. 20. θ [deg]. ∥ Fˆ i ∥/∥Fi ∥. 40.

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(231) Propositions belonging to the thesis:. Haptic human-human interaction Motor learning & haptic communication Niek Beckers. 1.. People are stubborn, they would rather hold on to their own plan at the cost of expending more energy than collaborating with a partner that they do not fully trust or understand (in haptic interaction and in real life).. 2.. Intuitive physical interaction strategies between human and robot cannot be designed without considering haptics, but truly intuitive and natural humanrobot interaction is impossible to achieve through haptics alone.. 3.. To fully exploit the potential of haptics in promoting motor learning, the trainee and trainer should be aware of what is happening and what is expected of them.. 4.. To understand how humans collaborate, we must construct more complex models, but the more complex the model, the harder it is to understand how humans collaborate (based on Bonini’s paradox).. 5.. Publication pressure and grant competition encourage moonshot research, which does not benefit the overall correctness of scientific output.. 6.. One swallow does not make a summer: if the scientific community was really serious about itself, it should stimulate and reward reproduction studies more.. 7.. People who refuse to accept a scientific consensus (about climate change and vaccination) and hold their own opinion as the truth should not be allowed to make decisions on those matters that affect others or the planet.. 8.. Selecting an optimal strategy requires its own optimal strategy.. 9.. Eight propositions are sufficient.. The propositions are considered to be opposable and defendable and have been approved as such by the promotor prof.dr.ir. H. van der Kooij and co-promotor dr. E. van Asseldonk..

(232) Stellingen behorend bij het proefschrift:. Haptic human-human interaction Motor learning & haptic communication Niek Beckers. 1.. Mensen zijn koppig, ze houden liever vast aan hun eigen plan ten koste van meer verbruikte energie dan samen te werken met een partner die ze niet volledig vertrouwen of begrijpen (in haptische interactie en in het echte leven).. 2.. Intuïtieve fysieke interactiestrategieën tussen mens en robot kunnen niet worden ontworpen zonder rekening te houden met haptics, maar echt intuïtieve en natuurlijke mens-robot interactie is niet haalbaar door alleen op haptics te concentreren.. 3.. Om het potentieel van haptics volledig te benutten voor het bevorderen van motorisch leren moeten de leerling en de leraar op de hoogte zijn van wat er gebeurt en wat van hen wordt verwacht.. 4.. Om te begrijpen hoe mensen samenwerken moeten we complexere modellen bouwen, maar hoe complexer het model, des te moeilijker het wordt om te begrijpen hoe mensen samenwerken (gebaseerd op Bonini's paradox).. 5.. Publicatiedruk en subsidieconcurrentie moedigen ‘moonshot’ onderzoek aan, wat de algehele correctheid van de wetenschap niet ten goede komt.. 6.. Een zwaluw maakt nog geen zomer: als de wetenschappelijke gemeenschap zichzelf echt serieus zou nemen, zou ze reproductiestudies meer moeten stimuleren en belonen.. 7.. Mensen die weigeren een wetenschappelijke consensus (bijvoorbeeld over klimaatverandering en vaccinatie) te accepteren en hun eigen mening als de waarheid zien, zouden geen beslissingen mogen nemen over deze zaken die anderen of de planeet treffen.. 8.. Het selecteren van een optimale strategie vereist een eigen optimale strategie.. 9.. Acht stellingen zijn voldoende.. Deze stellingen worden opponeerbaar en verdedigbaar geacht en zijn als zodanig goedgekeurd door de promotor prof.dr.ir. H. van der Kooij en de co-promotor dr. E. van Asseldonk..

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