Efficient Redundancy Control of Redundant Manipulators.

Abstract

Kinematically redundant manipulators have a number of potential advantages over current manipulator design. For this type of arm, some control methods through pseudoinverse and nullspace of Jacobian matrix had been suggested. Questions associated with them are about the difficulty of real-time control because of voluminous operations for deriving the pseudoinverse matrix by singular value decomposition. In this paper new formulation and control methods for solving redundancy in manipulator arms by locally optimizing a kinematic and/or dynamic criterion are presented. Formulation is performed by means of a joint decomposition technique, resulting in a particularly efficient computational scheme which is feasible for real-time control. Control method based on this formulation is given in low computational cost to compare with conventional control methods. 1.‚Ü ‚¦ ‚ª ‚« ŽY ‹AE-pƒ} ƒj ƒs ƒ…ƒOE•[ ƒ^ ‚Ì ‰ž-p•ª-ì ‚ª •L ‚Ü ‚é ‚É ‚ ‚ê ‚Ä,-] •ª ‚È Ž©-R "x ‚ð Ž• ‚ •ç '· ƒ} ƒj ƒs ƒ…ƒOE•[ ƒ^ ‚ª ŠJ "-‚³ ‚ê ‚é ‚ae ‚¤ ‚É ‚È ‚Á ‚Ä ‚« ‚½[1].‚± ‚Ì ‚ae ‚¤ ‚È ƒ} ƒj ƒs ƒ…ƒOE•[ ƒ^ ‚ð-LOEø "I ‚É-˜-p‚· ‚é ‚½ ‚ß,‚± ‚ê ‚Ü ‚Å '½ ‚-‚Ì OE¤‹ † ‚ª ‚È ‚³ ‚ê ‚Ä ‚¢ ‚é.•]-ˆ ‚Ì OE¤ ‹ † ‚Å ‚Í,•ç '· ƒ} ƒj ƒs ƒ…ƒOE•[ ƒ^ ‚Ì "Á ˆÙ Žp •¨ ‰ñ"ð[2][3]‚â •á ŠQ•¨ ‰ñ"ð[4]•`[7],ŠÖ •ß "® •ì "Í ˆÍ ‚Ì • § OEÀ[8],ŠÖ •ß ‰ñ"] Šp '¬ "x,ŠÖ •ß ƒg ƒ‹ ƒN ‚Ì •] ‰¿ ‚ð •Å "K ‰»‚· ‚é "® •ì ‚Ì ŽÀOE»[9]•`[11]‚È ‚Ç ‚ª OEŸ"¢ ‚³ ‚ê,‚» ‚Ì ‹t ‰^"® Šw ‰ð•Í ‚É ‚Í ƒ" ƒR ƒr •s-ñ‚Ì ‹[ Ž-‹t •s-ñ‚¨‚aeñ‚¨‚ae ‚Ñ ‚» ‚Ì ƒ[ ƒ• ‹ó ŠÔ‚ª-p‚¢ ‚ç ‚ê ‚Ä ‚¢ ‚é.‚µ ‚© ‚µ ‚± ‚ê ‚ç ‚Ì •û-@‚Í,‹t ‰^"® Šw‰‰ ŽZ ‚É-c 'å ‚È OEv ŽZ-Ê‚ð •K-v ‚AE ‚µ,ŽÀ Žž ŠÔ• § OEä ‚É ‚Í •¢ "ï ‚Å ‚ ‚é. ‚» ‚± ‚Å,-{ OE¤ ‹ † ‚Í ‹t ‰^"® Šw ‰‰ ŽZ ‚Ì ‰ß'ö ‚É ‚¨‚¢‚¨‚¢ ‚Ä ‚» ‚Ì OEv ŽZ-Ê‚ð ‚¢ ‚© ‚É OE¸‚çOE¸‚ç ‚· ‚© ‚ð OEŸ"¢ ‚· ‚é.-{ OE¤ ‹ † ‚Å ‚Í,ƒ" ƒR ƒr •s-ñ‚Ì ‹[ Ž-‹t •s-ñ‚ð-p‚¢ ‚é 'ã ‚í ‚è ‚É,ƒ" ƒR ƒr •s-ñ‚ð "ñ •ç '· Ž©-R "x ‚É 'Î ‰ž‚· ‚é •" •ª ƒ" ƒR ƒr •s-ñ ‚AE•ç '· Ž©-R "x ‚É 'Î ‰ž‚· ‚é •" •ª ƒ" ƒR ƒr •s-ñ ‚É •ª ‰ð ‚µ,"ñ •ç '· Ž©-R "x ‚É 'Î ‰ž‚· ‚é •" •ª ƒ" ƒR ƒr •s-ñ‚Ì ‹t •s-ñ ‚É Šî ‚à ‚-'è Ž® ‰»•û-@‚ð "± "ü ‚· ‚é[17].•]-ˆ•" •ª ƒ" ƒR ƒr •s-ñ ‚É Šî ‚à ‚-•ç '· ƒ} ƒj ƒs ƒ…ƒOE•[ ƒ^ ‚Ì 'è Ž®‰»•û-@‚ª 'ñ ˆÄ ‚³ ‚ê ‚Ä ‚¢ ‚é ‚à ‚Ì ‚Ì[12]•` [16],‚» ‚ê ‚ç ‚Í '¬ "x ƒOEƒx ƒ‹ ‚Å ‚Ì ‰^"® Šw "I ‚È •] ‰¿ ‚ð •Å "K ‰»‚· ‚é ‚à ‚Ì ‚É OEÀ'è ‚³ ‚ê ‚Ä ‚¢ ‚é.‚µ ‚© ‚à,•" •ª ƒ" ƒR ƒr •s-ñ‚É Šî ‚à ‚-Žè-@‚Í •]-ˆ ‚Ì ‹[ Ž-‹t •s-ñ ‚É Šî ‚à ‚-Žè-@ ‚AE"¯-l ‚È OE‹ ‰Ê‚ð "¾ ‚é ‚± ‚AE ‚Ì •Ø-¾ ‚ª ‚È ‚³ ‚ê ‚Ä ‚¢ ‚È ‚¢ ‚µ,OEv ŽZ-Ê‚É ŠÖ ‚· ‚é •Ú •× ‚È OEŸ"¢ ‚à ‚È ‚³ ‚ê ‚Ä ‚¢ ‚È ‚¢.‚Ü ‚½ ‰Á'¬ "x ƒOEƒx ƒ‹ ‚Å ‚Ì "®-ÍŠw "I ‚È •] ‰¿ ‚ð •Å "K ‰»‚· ‚é ‚± ‚AE ‚É ŠÖ ‚µ ‚Ä ‚Í ‚Ü ‚Á ‚½ ‚-OEŸ"¢ ‚³ ‚ê ‚Ä ‚¢ ‚È ‚¢.-{ ˜_ • ¶ ‚Å ‚Í,•" •ª ƒ" ƒR ƒr •s-ñ ‚É Šî ‚à ‚-'è Ž®‰»Žè-@‚ð,'¬ "x ƒOEƒx ƒ‹ ‚Å ‚Ì ‰^"® Šw "I ‚È •] ‰¿ ‚ð •Å "K ‰»‚· ‚é •ê • ‡ ‚Ì ‚Ý ‚È ‚ç ‚¸,‰Á '¬ "x ƒOEƒx ƒ‹ ‚Å ‚Ì "®-ÍŠw "I ‚È •] ‰¿ ‚ð •Å "K ‰»‚· ‚é •ê • ‡ ‚É ‚ ‚¢ ‚Ä ‚à OEŸ"¢ ‚· ‚é.‚» ‚Ì ‰ž-p-á ‚AE ‚µ ‚Ä ‚Í •á ŠQ•¨ ‚Ì ‰ñ"ð ‚AEŠÖ•ß ƒgƒ‹ ƒN ‚Ì2•ae˜a ae˜a ‚Ì •Å •¬ ‰» ‚AE‚¢ ‚¤ "ñ ‚ ‚Ì • § OEä •û-@‚𠎦 ‚·.‚³ ‚ç ‚É ‚± ‚Ì "ñ ‚ ‚Ì-á‚ð-p‚¢ ‚Ä,-{ 'è Ž®‰»Žè-@‚ª •]-ˆ ‚Ì ‹[ Ž-‹t •s-ñ ‚É ‚ae ‚é Žè-@ ‚AE "¯-l ‚È OE‹ ‰Ê‚ð "¾ ‚é ‚± ‚AE ‚Ì •Ø-¾ ‚AE, OEv ŽZ-Ê‚É ŠÖ ‚· ‚é OEŸ"¢ ‚à •s ‚¤. 2.‹[ Ž-‹t •s-ñ‚É Šî ‚à ‚-•ç '· ƒ} ƒj ƒs ƒ…ƒOE•[ ƒ^ ‚Ì • § OEä-@ 'Î •Û ‚AE‚· ‚é ƒ} ƒj ƒs ƒ…ƒOE•[ ƒ^ ‚Í ŠÖ •ß Ž©-R "x ‚ªn,ƒA •[ ƒ€ •ae '[ ‚Ì ˆÊ 'u •EŽp •¨ ‚Ì Ž©-R "x ‚ªm‚Å ‚ ‚è,n>m‚Ì •ç '· ƒ} ƒj ƒs ƒ…ƒOE•[ ƒ^ ‚AE‚· ‚é.‚± ‚Ì ‚ae ‚¤ ‚È •ç '· ƒ} ƒj ƒs ƒ…ƒOE•[ ƒ^ ‚𠕪 ‰ð'¬ "x • § OEä,‚ ‚é ‚¢ ‚Í •ª ‰ð‰Á '¬ "x • § OEä ‚· ‚é ‚½ ‚ß ‚Ì ‰^"® •û 'ö Ž® ‚Í ‚» ‚ê ‚¼ ‚êˆÈ‚êˆÈ ‰º ‚Ì ‚ae ‚¤ ‚É ‚È ‚é.