Falling Forward of Humanoid Robot Based on Similarity with Parametric Optimum

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1 37 8 Vol. 37, No ACTA AUTOMATICA SINICA August, , , ;, ;,,.. DOI,,,, /SP.J Falling Forward of Humanoid Robot Based on Similarity with Parametric Optimum KE Wen-De 1, 2 CUI Gang 1 HONG Bing-Rong 1 CAI Ze-Su 1 PIAO Song-Hao 1 ZHONG Qiu-Bo 1 Abstract The designing method of falling-forward locomotion of a humanoid robot based on the locomotion similarity is proposed. Firstly, the locomotion similarity is analyzed and the synchronous transition for key postures is proposed. Then, the kinetics constraint equations and the associated physical constraints for the 4-level headstand pendulum of robot s falling-forward locomotion are constituted under the condition of similarity transition. Finally, the method based on the parametric control and enhancing technique is adopted to optimize the parameters in the touching ground process of falling forward. The experiments showed the validity of this designing method. Key words Humanoid robot, similarity, constraint, zero moment point (ZMP), parametric optimum,, [1].,,, [2]., : 1),, [3], [4], Manuscript received December 8, 2010; accepted May 17, 2011 ( , , ), ( ), (201180) Supported by National Natural Science Foundation of China ( , , ), Natural Science Foundation of Guang Dong Province ( ), and Young Innovative Talent Training Project of Universities in Guangdong (201180) School of Computer Science, Harbin Institute of Technology, Harbin Department of Computer Science, Guangdong University of Petrochemical Technology, Maoming , [5],, [6],, [7],, [8],, ; 2),, [9], [10 11] EDA (Estimation of distribution algorithm), [12], [13],, [14],. ZMP,.,, ZMP ( ) ZMP ( ), ZMP ( ),,.

2 8 : 1007,,,, p H ={Φ H (0),, Φ H (t),, Φ H (T )} [ 0, T ],, Φ H (t)=[φ H 1 (t),, φ H i (t),, φ H N(t)] T t, N, p R = {Φ R (0),, Φ R (t),, Φ R (T )}, Φ R (T ) = [φ R 1 (t),, φ R i (t),, φ R N(t)] T, : S H R i (t) = ϖ ( 1 + φr i (t) φ H i (t) φ R i max φ R i min (1 ϖ) S H R (t) = S H R = ) 1 + ( 1 + φ R i (t) φ H i (t) φ R i max φ R i min S H R i (t) N T t=0 SH R (t)dt T ) 1 (1) (2) (3), φ R i max, φ R i min i, (1) t i i, ϖ 0 ϖ 1, ϖ 1,, ϖ 0, ; (2) t, (3) T., 0 < S 1, S 1,. 1.2,,,. [5, 15],,,,., t φ R i (t) = γφ H i (t) + φ i (t) (4), γ, 0 γ 1, φ i (t), γ 1, φ i (t) 0,. t t + t φ R i (t + t) = φ R i (t) + φ R i φ R i (t + t) = φ R i (t) + φ R i φ R i (t + t) = φ R i (t) + φ R i (5), φ R i φ R i φ R i t., t φ R i, φ R i (t + t) = φ R i (t) + φ R i (t) + t+ t t t+ t t+ t t t φ R i (t)dt = φ R i (t)dtdt (6), φ R i (t) Φ R, φ R i (t + t) Φ R, φ R i (t) = d2 (φ R i (t + t) φ R i (t)) dt 2 (7) φ R i (t) < 0, φ R i (t) = 0, φ R i (t) > 0., φ R i (t). 2,,. 2.1,, 1, A, B, C, m 1, m 2, m 3, m 4. S a, S n, S w, S s, S h. θ R (t) = [θ R 1 (t),, θ R 4 (t)] T,

3 θ R 1 (t), θ R 2 (t), θ R 3 (t), θ R 4 (t) ; φ R (t) = [φ R 1 (t),, φ R 4 (t)] T, φ R 1 (t), φ R 2 (t), φ R 3 (t), φ R 4 (t). V B v(φ(b), φ(b), θ(b), θ(b)) = 2 C(φ(B), θ(b)) φ θ [0 k B y k B z ] φ(b) θ(b) =, k B y 0, k B z 0. C :,, 0, Fig. 1 1 A :, Process of falling forward S A a = [0 0 0] T, S A n = [0 y A n z A n ] T S A w = [0 y A w z A w] T, S A s = [0 y A s z A s ] T S A h = [0 y A h z A h ] T, F (S A a ) e z 0 0 < F (S A n ) e z < F (S A w) e z < F (S A s ) e z V A v(φ(a), φ(a), θ(a), θ(a)) = 2 C(φ(A), θ(a)) φ θ [0 k A y k A z ] φ(a) θ(a) =, C(φ(A), θ(a)) ; F (Sa A ) e z ; V A A ; φ(a), θ(a), φ(a), θ(a) A ; ky A, kz A y, z, ky A 0, kz A 0. (B ):,, S B a = [0 0 0] T, S B n = [0 y B n z B n ] T S B w = [0 y B w z B w ] T, S B s = [0 y B s z B s ] T S B h = [0 y B h z B h ] T, F (S B a ) e z 0 F (S B n ) e z > 0, F (S B w ) e z > 0 F (S B s ) e z > 0, F (S B h ) e z > 0 S C a = [0 0 0] T, S C n = [0 y C n 0] T, S C w = [0 y C w z C w ] T, S C s = [0 y C s z C s ] T, S C h = [0 y C h 0] T, F (S C a ) e z 0, F (S C n ) e z 0, F (S C h ) e z 0, F (S C w ) e z > 0, F (S C s ) e z > 0 V C v(φ(c), φ(c), θ(c), θ(c)) = 2 C(φ(C), θ(c)) φ θ φ(c) θ(c) = 1), [1] D(i, j) = 0 (x i x j ) 2 + (y i y j ) 2 + (z i z j ) 2 (8) (x i, y i, z i ) (x j, y j, z j )., [7] L(φ R (t)) = (exp( µ(φ R i φ R i min)φ R i max φ R i min) + exp( µ(φ R i max φ R i )φ R i max φ R i min)) (9), µ, 0 µ 1. 2) ZMP, ZMP,,, ZMP.

4 8 : 1009 (x zmp, y zmp ) ZMP, [8] x zmp = y zmp = [m i( z i+g)x i m iẍ iz i I iy K iy] m i( z i+g) [m i( z i+g)y i m iÿ iz i I ix K ix] m i( z i+g) (10), m i i, (x i, y i, z i ) i, g, I, K i., ZMP { left max zmp x left max zmp y, left max zmp x (t), right max zmp y. : (t) x zmp right max zmp x (t) (t) y zmp right max zmp y (t) (11) (t), right max zmp x (t), left max zmp y (t) x, y 3) φ R i 4 : φ H i min φ R i min φ R i φ H i min φ R i min φ R i φ R i min φ H i min φ R i φ R i min φ H i min φ R i, φ R i φ H i min φ R i min φ R i φ H i min φ R i min φ R i φ R i min φ H i min φ R i φ R i min φ H i min φ R i φ R i max φ H i max φ H i max φ R i max φ R i max φ H i max φ H i max φ R i max (12) 4 φ R i max φ H i max φ H i max φ R i max φ R i max φ H i max φ H i max φ R i max (13), φ H i min, φ H i max, φ R i min, φ R i max i i, φh i min, φh i max, φr i min, φr i max i i. 3,.,,,,,, [16 17]. [17],,,,,., i P i = m i ċ i,, ċ i i, P = 4 m iċ i,, L i = c i P i + R i I i R T i ω i (14), c i, I i, R i, ω i i. d ( T ) dt φ κ 4 i φ = Φ i i κ 4 (κ 1 sin θ + κ 2 θ + κ3 θ 2 ) η = 0 (15), κ 1, κ 2, κ 3, κ 4, η, η(t) = Σ 4 τ i δ [ti 1,t i)(t), τ i, t [t i 1, t i ), δ [ti 1,t i)(t) = 1, 0. (15), ẏ g(y, η) = 0 (16), ẏ := [θ θ] T, g(y, η) := [ θ (κ 4 η κ θ2 3 κ 1 sin θ)/κ 2 ] T, Q = Q T + T 0 Q t dt (17) Q T = P 1 (P ) 2 + P 2 (L i ) 2 + P 3 (Q E ) 2 + P 4 (Q F ) 2, P 1, P 2, P 3, P 4, Q E /M = diag{sin θ} θ diag{cos θ} θ 2 +g, Q F = y S a +y S n + y S w + y S s + y S h. y S a, y S n, y Sw, y Ss, y Sh y, g. (17), τ i Γ(τ) = Ω 0 (y(t τ)) + tf t p f L 0 (t, y(t τ), τ)dt (18) s.t. f i (τ) = Ω 0 (y(t τ)) + t f L t p 0 (t, y(t τ), τ)dt f 0, i = 1,, 4

5 , t f, t p f, L i (t, y(t τ), τ) = Ω i (t, y(t τ i δ [ti 1,t i)), τ i δ [ti 1,t i)) (19), t [t p f, t f] t [0, 1], dt(t ) = 4 ψ dt iδ [ti 1,t i)(t ). (16), θ = [y(1) y(2) y(3) y(4)] T θ = [y(5) y(6) y(7) y(8)] T η = [η(1) η(2) η(3)] T (20) 25, : 2 5 ( ) ( ) 2. 2, 100 ms, 100 /s. 3, PR-S ( ) GA (, 9, 11, 0.7 %, 500 ) 4,, PR-S 250, GA 350. ŷ(t ) = y(t(t )) t(t ), ˆη(t ) = ŷ =g(y(t(t )), η(t(t )), t(t )) ṫ(t ) = τ i δ [ti 1,t i)(t ) η(t(t )) τ i δ [ti 1,t i)(t ) ψ i δ [ti 1,t i)(t ) (21) (21) (18), τ ψ Γ(τ, ψ) =Ω i (ŷ(1 τ, ψ))+ 1 0 ˆL 0 (t(t ), ỹ(t τ, ψ), τ, ψ)dt (22) 1 s.t. f i (τ, ψ) = ˆL i (t(t ), ỹ(t τ, ψ), τ, ψ)dt + 0 Ω 0 (ỹ(1 τ, ψ)) 0, i = 1,, N, N e.,,,,. Fig. 2 2 Falling forward of human body 4 Aldebaran Nao, 58 cm, 4.3 kg, 3 Fig. 3 Controlling variables with time

6 8 : 1011, 5 6, 7 ( ),,,,. Fig. 5 5 Simulating effects of falling-forward actions 4 PR-S GA Fig. 4 Convergences of PR-S and GA Fig. 6 6 Practical effects of falling-forward process (a) (a) Angle changing of right ankle (b) (b) Angle changing of right knee (c) (c) Angle changing of right hip (d) (d) Angle changing of right shoulder (e) (e) Angle changing of right elbow 7 Fig. 7 Angle variations of robot s joints when faling forward

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8 8 : hitcuigang@163.com (CUI Gang Professor at the School of Computer Science, Harbin Institute of Technology. His research interest covers robot technology, intelligent control, and computer architecture.).. hithongbr@163.com (HONG Bing-Rong Professor at the School of Computer Science, Harbin Institute of Technology. His research interest covers artificial intelligence and robot technology.) caizesu@hit.edu.cn (CAI Ze-Su Associate professor at the School of Computer Science, Harbin Institute of Technology. He received his Ph. D. degree from Harbin Institute of Technology in His research interest covers mobile robot, simultaneous localization and mapping, and machine vision.) piaosh@hit.edu.cn (PIAO Song-Hao Associate professor at the School of Computer Science, Harbin Institute of Technology. He received his Ph. D. degree from Harbin Institute of Technology in His research interest covers multi-robot system and intelligent control. Corresponding author of this paper.), zhongqiubo@163.com (ZHONG Qiu-Bo Lecturer. He received his Ph. D. degree from Harbin Institute of Technology in His research interest covers humanoid robot, motion planning and optimizing.)