954 Vol. 9 No. 10, pp.954 9, 011 Development of Air Hockey Robot tat Makes a Decision based on Game Situation Sakyo Matsusita and Akio Namiki Tis paper proposes a robot wic can play air ockey game wit a uman. Te robot consists of a 4-axis robot arm and a ig-speed vision, and te robot is controlled based on visual information at a rate of 500 [Hz]. Te robot system as te abilities to adjust te strengt level and to cange te strategy based on te game situation. A system designer can easily adjust tese abilities by setting several specified parameters. In tis paper, first, a recursive trajectory generation using continuous images from ig-speed vision is explained. Secondly, te response control to adjust te strengt level of te robot is explained. Tirdly, te decision-making using AHP (Analytic Hierarcy Process) is proposed. Tis ability enable te robot to switc te game plan. Finally, we sow te data of experiments and verify te effectiveness of te system. Key Words: Air Hockey, Response Control, AHP, Hig Speed Vision 1. [1] Bisop [] [3] Bentivegna [4] Wang [5] Nuvation Researc [] 010 8 Ciba University, Graduate Scool of Engineering Fig. 1 Decision making for robot Fig. 1 AHP Analytic Hierarcy Process.. 1 Barrett Arm Barrett Tecnology Inc Barrett Arm 4-DOF [7] JRSJ Vol. 9 No. 10 88 Dec., 011
955 Table 1 Parameters of te air ockey robot system H Heigt of te Hockey Table [m] 0.80 W Widt of te Hockey Table [m] 0.9 D Dept of te Hockey Table [m] 1.99 W g Widt of Goal [m] 0.1 d p Puck Diameter [mm] 81.0 d p Smaser Diameter [mm] 3.0 l 1 Lengt of Link1 [m] 0.55 l Lengt of Link [m] 0.4 Fig. Air ockey robot system Fig. 4 System configuration Fig. 3 Air ockey table and robot CAN Barrett Arm 4. Potron IDP Express [8] 50 10,000 [fps] 500 [fps] 51 5 1. 3 Fig. Barrett Arm Barrett Arm Barrett Arm Fig. 3 Table 1. 4 Fig. 4 Vision PC Vision PC GPU Grapics Processing Unit Geforce GTX 95 CUDA Host PC Barrett Arm MATLAB Real Time Worksop Target PC xpc Target CAN Barrett Arm Vision PC Target PC Barrett Arm 500 [Hz] 3. 3. 1 (i, j) Δf n(i, j) f b (i, j) f(i, j) ˆf(i, j) ˆf(i, j) = ( 1:if f(i, j) <f b (i, j) 1 Δfn(i, j) 0:if f(i, j) f b (i, j) 1 Δfn(i, j) 1 CUDA 1 9 10 89 011 1
95 3. (x p,y p) t x p = a 1t + a 0 y p = b 1t + b 0 3 a 1,a 0,b 1,b 0 3. 1 1 a 1,a 0,b 1,b 0 500 [Hz] a 1,a 0,b 1,b 0 y y p 3 t x x p t = y p b 0 b 1 x p = a 1t + a 0 4 5 (x p,y p ) (x p,y p ) d p d s (x s,y s ) " # " # x s x p = y s y p dp+ds 1 0 x â 1, â 0 â 1 = a 1 â 0 =sgn(a 1)x lim a 0 7 8 x p x lim x lim y 3 500 [fps] 3. 3 (x s,y s ) (ẋ s, ẏ s ) ẏ s =0 ẏ s > 0 (ẋ s, ẏ s ) t q q (x s,y s ) (ẋ s, ẏ s ) )t 0 q 0 q 0 t q q t 3 3 3 q T 3 0 1 t 0 t 0 t 0 α 0 β 0 q T 3 4 q T 7 5 = 1 t t t α 1 β 1 7 7 4 0 0 1 t 0 3t 0 5 4 α β 5 0 1 t 3t α 3 β 3 q T 9 α i β i(i =0 4) q ref 3 " # 1 α 0 α 1 α α 3 t q ref = β 0 β 1 β β 3 4 t 7 10 5 t = t 3. 4 Barrett Arm [9] Fig. 5 M(q) q + (q, q)+g(q) =τ t 3 11 M(q) (q, q) g(q) u q τ = (q, q)+g(q)+m(q)u q q = u q 1 13 u q = q ref + K D( q ref q)+k P (q ref q) 14 4. JRSJ Vol. 9 No. 10 90 Dec., 011
957 Fig. 5 Computed torque metod Fig. 7 Evaluations on te scales wic are different 5. 1 AHP Fig. Bode diagram of transfer function from q ref to q α(0 α 1) 14 α α 0 0 α 1 14 α K 1 K K 3 u q = K 3 q ref + K D(K q ref q)+k P K 1(q ref q) 15 13 15 q ref q Q = K3s + K DK s + K P K 1 1 Q ref s + K Ds + K P K 1 1 K 1(α) =K (α) =K 3(α) =α α Fig. Fig. α 1 K 1 K K 3 α 5. Coice Criterion Fig. 7 AHP Analytic Hierarcy Process: [10] [11] AHP 1 9 10 91 011 1
958 C C 3 C 4 3 4 Fig. 8 AHP for air ockey Fig. 8 C 5 1/5 C 3 1 5 7 7 C 1 = 4 1/5 1 3 5 17 1/7 1/3 1 1 1,1 1 1 3 λ max(c 1) W C1 4 C.I. C.I. = λmax(c1) m m 1 18 m C.I. 0.1 C 1 C.I. 0.1 5 4 C 1 W C1 W C W C3 W C4 W i W = W C W C3 W C4 W C1 = w 1 w w 3 19 w 1 w w 3 w 1 w w 3 5. AHP AHP Fig. 8 x R x R = R a R b 0 R a R b C 1 x R C 1(x R) x E x E = v p d a d b 1 v p d a d b y s =0.15[m] y s = 0.07 [m] y s C C 3 C 4 x E C (x E) C 3(x E) C 4(x E) 5. 3 C x 3 C(x) = 4 W 11(x) W 1q(x)....... W q1(x) W qq(x) 7 5 (i, j =1,,...,q) 1,Wji(x) =Wij (x) q i <j x n x = x 1 x x n 1 3 JRSJ Vol. 9 No. 10 9 Dec., 011
959 C x n +1 k x (k =1,,...,n +1) k C k n +1 C(x) k C C(x) k W ij W ij(x) k W ij( k x)= k W ij (k =1,,, n +1) 4 W ij(x) AHP W ij(x) > 0 W ij(x) W ij(x) =exp(a T ij x/b T ij x) 5 a ij b ij a ij b ij (i, j) a ij b ij 5 C(x) k 4 5 a ij b ij 5 k x 4 a ij b ij k W ij =exp( k x T a ij/ k x T b ij) k x T a ij =(ln k W ij) k x T b ij 7 k =1,,...,n +1 7 Xa ij = Y b ij 8 X = 1 x x n+1 x 9 Y = y 1 y y n+1 30 y k =(ln k W ij) k x 31 X Y R (n+1) (n+1) a ij b ij R n+1 8 Zc ij = 0 i Z = X Y c ij = a ij T b ij T 3 33 34 Z R (n+1) (n+) c ij R n+ 3 c ij c ij l 1 c ij l ĉ ij R n+1 Z l Ẑ Fig. 9 Flow cart of AHP Table Designed values ( k W 1, k W 13, k W 3 )about k C 1 k k R a k R b k W 1 k W 13 k W 3 1 0.0 0.0 1 1/3 1/3 0.0 1.0 1/3 1 5 3 1.0 0.0 3 5 1 4 1.0 1.0 1 7 7 5 0. 0.8 1/1.3 3 5 Table 3 Calculated coefficient vectors in C 1 (x R ) W 1 (x R ) W 13 (x R ) W 3 (x R ) 1.851 0.1 0.139 a ij 1.851 0.5 0.1 0.000 0.5 0.139 0.84 0.019 0.015 b ij 0.84 0.088 0.19.39 0.33 0.17 R (n+1) (n+1) l z l R n+1 3 Ẑĉ ij = z l 35 Ẑ Ẑ 1 ĉ ij Ẑ k C ĉ ij l 1 34 a ij b ij x AHP AHP Fig. 9 C 1 n = C C 3 C 4 n =3 q =3 C 1 4 Table k W 1 k W 13 k W 3 Table a ij b ij Table 3 C C 3 C 4 3 4 5 Fig. 10 9 10 93 011 1
90 Fig. 10 Block diagram of all of te system.. 1 Fig. 11 Fig. 13 Fig. 14 Fig. 15 Fig. 11 0.1 Fig. 13 Fig. 14 Fig. 15 y 0. α = {1.00, 0.5, 0.0, 0.10} 3 Fig. 1 α =1.00 α Fig.. 3 R a R b 0 1 0.5 100 100 Fig. 1 Fig. 17 Fig. 18 Fig. 1 Fig. 17 Fig. 18 R a R b R a R b 100 R a R b (a) t =0.0[s] (b) t =0.1[s] (c) t =0.[s] (d) t =0.3[s] (e) t =0.4[s] (f) t =0.5[s] (g) t =0.[s] () t =0.7[s] (i) t =0.8[s] Fig. 11 Attack motion Fig. 1 Motion by different value of α R a R b JRSJ Vol. 9 No. 10 94 Dec., 011
91 Fig. 13 Trajectories of te puck and te mallet (Attack motions) Fig. 14 Trajectories of te puck and te mallet (Block motions) Fig. 15 Trajectories of te puck and te mallet (Disregard motions) 9 10 95 011 1
9 Fig. 1 Fig. 17 Frequency istogram (Attack motion) Frequency istogram (Block motion) 7. 1 AHP [1] 003 7 [ ] B.E. Bisop and M.W. Spong: Vision-Based Control of an Air Hockey Playing Robot, IEEE Control Systems Magazine, pp.3 3, 1999. [3] PC 8 SI007 pp.559 50, 007. [ 4 ] D.C. Bentivegna, C.G. Atkeson and G. Ceng: A Framework for Learning from Observation using Primitives, vol., no., pp.17 181, 004. [ 5 ] W.-J. Wang, I. Tsai, Z.-D. Cen and G.-H. Wang: A vision based air ockey system wit fuzzy control, IEEE Int. Conf. on Control Applications, vol., no.4, pp.754 759, 00. [ ] Nuvation Researc Air-HockeyBot 1000: Nuvation introduces a robot tat aims to top umans playing air ockey, Nuvation Current Headlines, 008 19 [ 7 ] Barrett Tecnology URL : ttp://www.barrett.com [8] I.Isii,T.Tatebe,Q.Gu,Y.Moriue,T.TakakiandK.Tajima: 000 fps Real-time Vision System wit Hig-frame-rate Video Recording, Proc. of te 010 IEEE International Conference on Robotics and Automation (ICRA010), pp.153 1541, 010. [9] 1988. [10] AHP 000. [11] AHP 000. Sakyo Matsusita 010 3 4 Fig. 18 Frequency istogram (Disregard motion) Akio Namiki 1994 199 1999 000 004 008 JRSJ Vol. 9 No. 10 9 Dec., 011