6 (5..9) 6 An Advanced Manipulation for Space Redundant Macro-Micro Manipulator System Kazuya Yoshida, Hiromitsu Watanabe * *Tohoku University : (Macro-micro manipulator system) (Flexible base), (Vibration suppression) (Reaction null-space), (Singularity-consistent method) : 98-8579 6-6- Tel.: ()795-699 Fax.: ()795-699 E-mail: hiro@astro.mech.tohoku.ac.jp. (ISS) SSRMS (Space Station Remote Manipulator System) ISS 6 (JEM : Japanese Experimental Module) JEMRMS (JEM Remote Manipulator System) (Fig.) ISS JEMRMS )
[ H b H T bm H bm H m ][ ẍb φ ] [ ] [ K b x b [ ] [ F b Jb T = τ J T m c b c m ] ] F h () c b R 6 : c m R 6 : F b R 6 : F h R 6 : fi R n : Fig. Japanese experimental module (JEM) Eq.() Fig. Flexible Base k b. c b M b Micro Manip. Fig. Mechanical model of the macro-micro manipulator system Fig. Link Link Flexible Base. Macro Manip. Micro Manip. Fig. Fig. Model of the macro-micro manipulator system ẋ b φ ). H b R 6 6 : H m R n n : H bm R 6 n : Fig. System configuration
Eq.() M b ẍ b c b ẋ b k b x b = f b () M b : k b : c b : ẍ b, ẋ b, x b : f b :. Fig.5 x b. Eq.() φ ) φ = GH bm x b (E H bm H bm)ζ () G ( ) Macro Arm (Flexible Base) Impedance Model Mbs cbskb Xb ζ n (E H bm H bm) H bm (reaction null-space) Eq.() F/T Sensor Fb Micro Arm Motion Fig. 5 Block diagram of the impedance F/T f b Eq.() ẍ b f b x b Eq.() G(s) = X b F b = M b s c b s k b () ζ ζ Eq.(5) J ẋ d e Fig.6 ζ = {J ( E H bm H bm) ( ) } ẋ d e JGH bm x b (5) f b Eq.()
Vibration suppression )) G Hbm xb d d xe,xe xe xe Kp Kd E-HbmHbm Reaction null-space Reactionless motion Fig. 6 Block diagram of vibration suppression. Eq.() Eq.(5) ζ Eq.(6) ζ = {J ( E H bm H ) bm } ( A b K a ) ( ẋ d e JGH bm x b ) (6) A b K a.5 ) ) Eq.(8) Eq.(7) Eq.(8) φ = GH bm x b (E H bm H bm)ζ (det(j) >.) (7) φ = σb adj(h T bm H bm)u r (det(j) <.) (8) σ : b : u r : detj Eq.(8) adj(h T bmh bm )u r (detj) b.6
Fig.7 w Eq.(9) (Fig.9) Micro arm (Modular arm) Force/Torque sensor w = det (JP rns ))(JP rns )) T (9) Macro arm (PA) P rns = E H bm H bm Fig. 8 Overview of the macro-micro manipulator system k bx Mb c bx k by y Linux, RT-Linux c by x PA Fig. 7 A example of the singular configuration in the reaction null-space Table Experimental condition of the macro part Manipulability Initial configuration (Fig.9).9 Singular configuration (Fig.7).6 6.. Fig.8 Fig. Fig.8 7 PA ) PA F/T. Fig.9 x-y x-y Table, Table 5
, [s] y (Fig.9 ).. Fig., Fig. k bx F M b Joint 5 [deg] Joint [deg] Joint 5 [deg] Joint 5 [deg] y c bxkby c by x.. Fig., Fig. Fig. 9 Experimental model of the macro-micro manipulator system (Joint angles are initial state) Table Experimental condition of the macro part Mass M b Stiffness k b Damping c b. [kg].9 [N/m]. [Ns/m].. Fig. Fig.7 Table Specfication of the micro arm ( link) Mass Length.5 [kg].78 [m] Fig. Fig.5 Fig.6 [s] [deg] Fig.7... Fig. ± [cm]. Table Table [Ns] [s] 6
- - - 5 6 Fig. Motion profile of the flexible base - - - 5 6 Fig. Motion profile of the flexible base with vibration suppression - - - - - - 5 6 Fig. Motion profile of the flexible base with vibration suppression, reactionless endtip position and singularity-consistent method y axis deflection [cm-] - - - 5 6 Fig. 5 Motion profile of the endtip with vibration suppression, reactionless endtip position and singularity-consistent method joint angle [deg] 8 6 - -6 joint joint joint joint 5 6 Fig. Motion profile of the flexible base with vibration suppression and reactionless endtip position - - - VS RNS 5 6 Fig. Motion profile of the endtip with vibration suppression and reactionless endtip position 7-8 5 6 Fig. 6 Motion profile of joint angles with vibration suppression, reactionless endtip position and singularity-consistent method angular velocity [rad/s].6 joint.5 joint joint. joint... -. -. -. -. -.5 -.6 5 6 Fig. 7 Motion profile of angular velocities with vibration suppression, reactionless endtip position and singularity-consistent method
5 5 5 led variable.9.8.7.6.5.. VS RNS 5 5 6 Fig. 8 Motion profile of the endtip with vibration suppression and reactionless endtip position led variable.5.5.5.5 VS RNS 9.5.5 Fig. 9 Profile of led variables of the micro arm with vibration suppression and reactionless endtip position 5 5-5 - -5 5 6 Fig. Motion profile of the flexible base with weighted vibration suppression and reactionless endtip position deflection [cm] 5 5-5 x axis y axis.. 5 6 Fig. Profile of led variables of the micro arm with weighted vibration suppression and reactionless endtip position.. Fig.8 Fig. Fig.8 Fig.9 Eq.(5) [cm] Fig. Fig. ζ 5. - -5 5 6 Fig. Motion profile of the endtip with weighted vibration suppression and reactionless endtip position 7 PA 8
) D.N.Nenchev, K.Yoshida, P.Vichitkulsawat M.Uchiyama, Reaction Null-Space Control of Flexible Structure Mounted Manipulator Systems, IEEE Transactions on Robotics and Automation, vol.5, no.6, December 999. ) D.N.Nenchev, Y.Tsumaki, Motion Analysis of a Kinematically Redundant Seven-DOF Manipulator Under the Singularity-Consistent Method, Proc. of the IEEE International Conference on Robotics and Automation, pp.76-765, September, -9,. ) D.N. 6 vol.6, No., pp.95 998 ) 5 P-S-5, 5 9