Optimal algorithm for trajectory plann ing of the robot

Transcription

1 EL ECTR ICMACH IN ESANDCON TROL Vol113 No11 Jan ( ) : SCARA ADAMS/V ew ADAMS :; ; ; ADAMS : TP242 : A : X (2009) Optmal algorthm for trajectory plann ng of the robot L IDong2je Q IU J ang2yan YOU Bo ( School of Automaton Harbn Unversty of Scence and Technology Harbn Chna) Abstract: In order to make trajectory smooth and workng tme op tmal the robot s trajectory n jont space was p lanned w th SCARA robot as research object whle consderng constrants of velocty accel2 eraton and jerk of each jont. genetc algorthm. The tme ntervals between each key pont n jont space were p lanned wth Sm ulaton of robot knem atcs was based on autom atc dynam c analyss of mechancal system (ADAM S) accordng to smulaton model constructed by ADAM S/V ew and op tm al tme ntervals generated by genetc algorthm. The smulaton results show that the m ethod for robot trajectory p lannng desgned can make the robot s trajectory smooth and workng tm e op tmal. Key words: robot; trajectory p lannng; genetc algorthm; ADAM S 1 [ 1 ] [ 2 3 ] [ 4 ] [ 5 6 ] B : : ( ) : ( ) ; ( ) ; ( ) Chna Academc Journal Electronc Publshng House. All rghts reserved.

2 [ 7 8 ] [ 9 10 ] [ ] SCARA ADAMS ) t n t 1 t n h t t + 1 ( t) ( t) ( t) t[ t t + 1 ] ( t) = ( t t) 3 ( t ) + ( t - t ) 3 ( t + 1 ) + 6h 6h - ( t ) h t ( t + 1 ) h t h + t - t h ( t) = ( t t) 2 ( t ) + ( t - t ) 2 ( t + 1 ) + 2h 2h + 1 h ( t) = t + 1 h - + ( t ) h 2 - ( t + 1 ) h 2 6h - t ( t ) + t - t ( t + 1 ) ( t) = ( t + 1 ) - ( t ) h h (1) ( t ) (1) : H = h = h - 1 n = + h H =B (2) 1 ( t 1 ) 2 ( t 2 ) = h - 1 h - 1 n = 6 a h n - n - n - 1 n - 1 h n - 1 b = h n ( t n ) B = 1 b 2 b n - 1 n 1 = a + h h 1 1 h h h h - 1 (2) ( t ) ( 1 ) 2) m n T = n h =1 3 j ( t) V C j j ( t) A C j j ( t) J C j t[ t t + 1 ] = 1 2 n - 1 j = 1 2 m nm ; V C j A C j J C j j 212 f 1 penalty = f 2 penalty = f 3 penalty = t[ t t + 1 ] 0 ; t[ t t + 1 ] 0 ; t[ t t + 1 ] 0 j ( t) V C j j ( t) A C j j ( t) J C j Chna Academc Journal Electronc Publshng House. All rghts reserved.

3 ) : ( ) 2) (3) Matlab Genetc A lgorthm Tool 3) X X : X = X + r(xu - X ) (1 - g /G) c X - r(x - X l ) (1 - g /G) c (4) X u X l r g G c X [0 1 ] ( ) ; 213 : a) ; b) ; c) ; d). txt ADAMS 3SCARA ADAMS [ 13 ] ADAMS/PostProcessor F ( h) = n [ 14 ] ADAMS h + 1 f 1 penalty + 2 f 2 penalty + 3 f 3 penalty =1 ADAMS/V ew SCARA mm 200 mm 135 mm 0 60 mm 4 1SCARA Chna Academc Journal Electronc Publshng House. All rghts reserved. F g. 1S m ula ton m odel of SCARA robot SCARA 3 3 mm4 50 s 300 s3 s Genetc A lgorthm Tool Fle Import Op tons c

4 Genetc A lgorthm Tool Number of varables s( s s s s s) 412 d) ADAMS 3 5 BRBF [ 8 9 ] Chna Academc Journal Electronc Publshng House. All rghts reserved.

5 1 127 ADAMS 53 F g. 5Angle and accelera ton curves of jo n t 3 5 ADAMS : [ 1 ]. [ J ] (3) : REN Jng2y SUN Han2xu. A novel method of trajectory p lannng n Cartesan space[ J ]. Robot (3) : [ 2 ] L IAN G SUN Z Q MU C D. Op tmal moton p lannng passng through knematc sngulartes for robot arm s[ C ] / / IROS Bejng: IEEE Press 2006: [ 3 ]. [ J ] (20) : YANG G J CU I P Y. The study of tme op tmal trajectory p lan2 nng for robot manpulators[ J ]. Chna M echancal Engneerng (20) : [ 4 ]. [D ]. : [ 5 ] GARG D P KUMAR M. Op tm zaton technques app led to mul2 tple manpulators for path plannng and torque m nmzaton [ J ]. Engneerng Applcatons of A rtfcal Intellgence ( 3-4) : [ 6 ] CAO B DODDS G I IRW IN G W. Constraned tme2effcent and smooth cubc sp lne trajectory generaton for ndustral robots [ J ]. IEE P roceedngs2control Theory and Applcatons (5) : [ 7 ] H IROAKIO KEN H MAKOTO I et al. Imp rovement of trajec2 tory trackng for ndustral robot arms by learnng control wth B2 sp lne[ C ] / / ISATP Pscataway: IEEE 2003: [ 8 ]. B [ J ] (2) : ZHANG H Q ZHANG J WANG Y N et al. Chaos optm zaton of B2sp lnes path plannng for robot n jont space [ J ]. Electrc M achnes and Control (2) : [ 9 ]. RBF [D ]. : [ 10 ] LEE M. Evoluton of behavors n autonomous robot usng artf2 cal neural network and genetc algorthm [ J ]. Inform aton Sc2 ences (2) [ 11 ]. B [D ]. : [ 12 ]. SCARA [ J ] ( 3 ) : WANG Y Y YAN B D YUAN H. Applcaton of genetc algo2 rthm n optmum route p lannng of SCARA model assemble robot [ J ]. Journal of Henan Unversty of Scence and Technology (3) : [ 13 ]. [ J ] (19) : DU Z J ZHANG B SUN L N et al. Research on moton smu2 laton of bped walkng robot based on vrtual prototype technology [ J ]. Journal of System S m ulaton ( 19 ) : [ 14 ]. Adam s6 [ C ] : 2003: WANG H T L IU Z Y PE I R. Study of 62DOF robot smulaton system based on Adam s[ C ] / /2003 N atonal System S m ulaton Academ y AnnualM eetng Sym posum. Bejng: Chna A ssocaton for System Smulaton 2003: ( :) Chna Academc Journal Electronc Publshng House. All rghts reserved.