37 8 Vol. 37, No. 8 2011 8 ACTA AUTOMATICA SINICA August, 2011 1, 2 1 1 1 1 1., ;, ;,,.. DOI,,,, 10.3724/SP.J.1004.2011.01006 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], 2010-12-08 2011-05-17 Manuscript received December 8, 2010; accepted May 17, 2011 (60905047, 61075076, 61075077), (8152500002000003), (201180) Supported by National Natural Science Foundation of China (60905047, 61075076, 61075077), Natural Science Foundation of Guang Dong Province (8152500002000003), and Young Innovative Talent Training Project of Universities in Guangdong (201180) 1. 150001 2. 525000 1. School of Computer Science, Harbin Institute of Technology, Harbin 150001 2. Department of Computer Science, Guangdong University of Petrochemical Technology, Maoming 525000, [5],, [6],, [7],, [8],, ; 2),, [9], [10 11] EDA (Estimation of distribution algorithm), [12], [13],, [14],. ZMP,.,, ZMP ( ) ZMP ( ), ZMP ( ),,.
8 : 1007,,,,. 1 1.1 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,
1008 37 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 0 2.2 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.
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
1010 37, 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 1 1 1 ) 1 2 6 ( 3 1 2 ) 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
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
1012 37 5,,,,,,.. References 1 Ke Wen-De, Cui Gang, Hong Bing-Rong, Cai Ze-Su, Yuan Quan-De. On biped walking of humanoid robot based on movement similarity. Robot, 2010, 32(6): 766 772 (,,,,.., 2010, 32(6): 766 772) 2 Moldenhauer J, Boesnach I, Beth T, Wank V, Bos K. Analysis of human motion for humanoid robots. In: Proceedings of the IEEE International Conference on Robotics and Automation. Barcelona, Spain: IEEE, 2005. 311 316 3 Zhao Xiao-Jun, Huang Qiang, Peng Zhao-Qin, Zhang Li-Ge, Li Ke-Jie. Kinematics mapping of humanoid motion based on human motion. Robot, 2005, 27(4): 358 361 (,,,,.., 2005, 27(4): 358 361) 4 Ruchanurucks M, Nakaoka S, Kudoh S, Ikeuchi K. Generation of humanoid robot motions with physical constraints using hierarchical B-spline. In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems. Edmonton, Canada: IEEE, 2005. 1869 1874 5 Zhang Li-Ge, Huang Qiang, Yang Jie, Shi You, Wang Zhi- Jie, Jafri A R. Design of humanoid complicated dynamic motion with similarity considered. Acta Automatica Sinica, 2007, 33(5): 522 528 (,,,,, Jafri A R.., 2007, 33(5): 522 528) 6 Zhang Li-Ge, Bi Shu-Sheng, Gao Jin-Lei. Human motion data acquiring and analyzing method for humanoid robot motion designing. Acta Automatica Sinica, 2010, 36(1): 107 112 (,,.., 2010, 36(1): 107 112) 7 Takano W, Yamane K, Nakamura Y. Capture database through symbolization, recognition and generation of motion patterns. In: Proceedings of the IEEE International Conference on Robotics and Automation. Roma, Italy: IEEE, 2007. 3092 3097 8 Kim S, Kim C H, Park J H. Human-like arm motion generation for humanoid robots using motion capture database. In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems. Beijing, China: IEEE, 2006. 3486 3491 9 Calderon C A A, Mohan R E, Hu L Y, Zhou C J, Hu H S. Generating human-like soccer primitives from human data. Robotics and Autonomous Systems, 2009, 57(8): 860 869 10 Hu L Y, Zhou C J, Sun Z Q. Biped gait optimization using estimation of distribution algorithm. In: Proceedings of the IEEE-RAS International Conference on Humanoid Robots. Tsukuba, Japan: IEEE, 2005. 283 289 11 Hu L Y, Zhou C J, Sun Z Q. Biped gait optimization using spline function based probability model. In: Proceedings of the IEEE International Conference on Robotics and Automation. Orlando, USA: IEEE, 2006. 830 835 12 Kim J Y, Kim Y S. Walking pattern mapping algorithm using fourier fitting and geometric approach for biped humanoid robots. In: Proceedings of the 9th IEEE-RAS International Conference on Humanoid Robots. Paris, France: IEEE, 2009. 243 249 13 Huang Q, Yokoi K, Kajita S, Kaneko K, Arai H, Koyachi N, Tanie K. Planning walking patterns for a biped robot. IEEE Transactions on Robotics and Automation, 2001, 17(3): 280 289 14 Saidouni T, Bessonnet G. Generating globally optimized sagittal gait cycles of a biped robot. Robotica, 2003,21(2): 199 210 15 Acosta-Calderon C A, Hu H. Robot imitation: Body schema and body percept. Journal Applied Bionics and Biomechanics, 2005,2(3): 131 148 16 Teo K L, Jennings L S, Lee H W, Rehbock V. The Control Parameterization Enhancing Transform for Constrained Optimal Control Problems.The Journal of the Australian Mathematical Society, 1999, 40: 314 335 17 Zhong Qiu-Bo, Pan Qi-Shu, Hong Bing-Rong, Piao Song- Hao. Falling motion control of humanoid robot based on parametric optimum. Robot, 2009, 31(6): 594 598 (,,,.., 2009, 31(6): 594 598),.. E-mail: wendek@163.com (KE Wen-De Associate professor at Guangdong University of Petrochemical Technology, Ph. D. candidate at Harbin Institute of Technology. His research interest covers humanoid robot, motion planning, and intelligent control.)
8 : 1013.. E-mail: 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.).. E-mail: 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.). 2006.. E-mail: 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 2006. His research interest covers mobile robot, simultaneous localization and mapping, and machine vision.). 2004... E-mail: 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 2004. His research interest covers multi-robot system and intelligent control. Corresponding author of this paper.), 2011.. E-mail: zhongqiubo@163.com (ZHONG Qiu-Bo Lecturer. He received his Ph. D. degree from Harbin Institute of Technology in 2010. His research interest covers humanoid robot, motion planning and optimizing.)