7 0 7 No. 7 Modular Machne Tool & Automatc Manufacturng Technque Jul. 0 00-65 0 07-0033 - 06 *. 0040. 04 PTP s TH6 TP4. A The Moton plannng of Handlng Robot Based on Tme Optmal CAO Bo CAO Q-xn TONG Shang-gao LI Ja-png LUAN Nan LENG Chun-tao LI Zhang-zh. School of Mechancal Engneerng Shangha Jao Tong Unversty Shangha 0040 Chna. Shangha Trown Tech Company Shangha 04 Chna Abstract In order to mprove the speed and statonarty of the Handlng robot when workng the robot s trajectory s planed n jont space usng Cubc splne curve so that the speed and acceleraton s consequent. For the specfc movement and mechancal structure of the robot A Plannng method based on tme optmal s proposed n the tradtonal model based on the PTP movement the trajectory of palletzng process s re-planed. At last t s verfed that the speed of palletzng s greatly mproved by usng the method. Key words moton plannng trajectory plannng handlng robot S-shaped curve 0 3-4 PTP PTP + 0 - - 3 0-0 - 0 * 863 009AA043903 986 E - mal hbwhhk3@ 63. com
34 7 S R θ Z θ Z R A B C D PTP θ t 0 = θ 0 θ t 0 = 0 θ t 0 = 0 θ t = θ θ t = 0 θ t = 0 θ t V max θ t a max 3 θ t A θ t t 0 t / V max a max A = 3 4 S S S 3 5 6 7 3 S 7 5 6 7 θ t = a t 3 + b t + c t + d θ t = a t + b t + c θ t = a 3 t 3 + b 3 t + c 3 t + d 3 4 5 6 t 0 = 0 a = A 6 b = 0 c = 0 d = θ 0 7 S a = a max b = - a max A c = a3 max 6A + θ 0 8
0 7 35 a 3 = A 6 b 3 = - a max + A V max a ) max c 3 = V max + A V max - a max a A max d 3 = θ 0 + a3 max - A V 3 max 6A 6a 3 max t 0 = 0 t = a max + V max A a max - V max a max 9 t = t 3 = V = V 3 = a max + 4 θ - θ 0 - A a a max max A ) a max + 4 θ - θ 0 + a max A a max A ) t V 3 t 3 V max a max θ t = a 4 max + 4a A max θ L - θ 0 - A V max a max t - A ) A a max t - a max 6 + 4 θ L - θ 0 + A a a 3 max max A )) A 4 3 a 4 max A + 4a max θ - θ 0 - a max A a 4 max + 4a A max θ - θ 0 - a max A ) θ t = V 3 t - A 6 t - t 3 3 - θ - θ 0 - θ - θ 0 0 3 S S t = t 3 - θ t = V t - A t V 3 = V + V 6 t - t 3 - θ - θ 0 V = V V t - t = θ - θ 0 4 t 7 V = a = t max V A V 3 V = A t t 3 S t V 3 t + V + V t - t = θ - θ 0 V 3 = V + V t = θ - θ 3 0 A ) t = t 3 - t V = V + a max t - t V = A θ - θ 3 0 A ) 4 S
36 7 θ t = A ) θ - θ 0 A 3 A t - 6 3 ) ) t - θ - θ 0 A 3 - θ - θ 0 P P 3 P 3 P 0 P P P 3 3 3 5 7 5 3 B 8 P 0 θ 0 R 0 Z 0 P θ B 3 6 R Z P θ R Z P 3 θ 3 R 3 Z 3 B P 0 P t P P t P P 3 t 3 t = t + t + t 3 B Z max 6 7 8 9 B B P 0 P t 3 t Z 0 Z Z max 7 t = f Z 0 Z Z max 3 P 0 t 3 Z Z 3 Z max P P P 3 8 P Z max Z max Ztop Z max max Z 0 Z Z Z 3 P A B C D P 0 P t Z max A C D Z top B t 3 = g Z Z 3 Z max 4
0 7 37 t temp max t A t C t D t = t temp t temp max t A t C t D t = max t A t C t D t temp max t A t C t D t = f' Z 0 Z max + g' Z max Z 3 t temp max t A t C t D t = max t A t C t D + f Z 0 Z Z max + g Z Z 3 Z max 6 7 t temp = f' Z 0 Z max + g' Z max Z 3 - t - t 3 5 4 f' Z 0 Z max B Z 0 Z max g' Z max Z 3 B Z max Z 3 00kg 00 0 400 3 600 400 00 0 400 400 5 80 400mm 00mm t t t t 3 Z max 00kg 9 B 3 PTP 0 s s B 07. 854. 997 9. 850 96. 973 4. 50 / 3. 879 / 5 B S PTP B Z max t A t C t D A D.
38 7 J. 004 4 35-38.. B 7. J. 998 3 9-3. J. 003 3. J. 4 85-9. 004 3 80-84. 4. J. 00 3 0 75-77. J. 003 4 3 70-74. 9. 5 GARG D P KUMAR M. Optmzaton technques appled to J. 00 46 5 9-5. multple manpulators for path plannng and torque mnmza- 0. ton J. Engneerng Applcatons of Artfcal Intellgence J. 009 3 5-57. 00 5 3-4 4-5. 6 CAO B DODDS G I IRWIN G W. Constraned tme-effcent and smooth cubc splne trajectory generaton for ndustral robots J. IEE Proceedngs-Control Theory and Applcatons 997 44 5 467-475. 8. Chelmsford Mass. J. 005 34 3 5-7. 3 4 5 4. J. 6 007 7 73-76. 5 Won-Soo Yun Jeong Hoon Ko. Development of a vrtual machnng system J. Internatonal Joural of Machne Tools and Manufacture 00. 6. Qt Lnux M. 006. 6 7 USB NC Qt X. W. Xu and S. T. Newman. Makng CNC machne toolsmore open nteroperable and ntellgent a revew of the technologes J. Computers n Industry 006 57 4-5.. J. 009 84-86. 3. J. 00 5 8-8. 7. Qt J. 009 0 40-4. 8. ARM9 DNC J. 00 6 40-4. 9. Lnux Qt D. 009. 0 Wllam von Hagen Real-Tme and Performance Improve- ARM Lnux ments n the. 6 Lnux Kernel J. Lnux Journal 005 Qt 4-0.