This paper presents a cross-coupled control approach to the tracking control of parallel manipulators in a synchronous manner. Based on the synchronization goal, the position synchronization error is investigated by considering motion synchronization between each actuator joint and its adjacent ones. A decentralized trajectory tracking controller is then developed with feedback of both position and synchronization errors, formed with a combination of feedforward, feedback and a saturation control. It is proven that this tracking controller can asymptotically stabilize both position and synchronization errors of the system. The proposed controller does not require the explicit use of the system dynamic model. Experiments performed on a 3-DOF parallel manipulator demonstrate improved performance with the proposed synchronous control design.
Amirat, Y. , Francois, G. F. , Pontnau, J. and Dafaoui, M.1996. Design and control of a new six DOF parallel robot: Application to equestrian gait simulation , Mechatronics International Journal of Mechanics, Electronics and Control6(2): 227-239 .
2.
Angeles, J. and Lee, S. K.1989. The modeling of holonomic mechanical systems using a natural orthogonal complement , Transactions CSME13(4): 81-89 .
3.
Begon, P. , Pierrot, F. , and Dauchez, P. 1995. Fuzzy sliding mode control of a fast parallel robot , in Proceedings of IEEE International Conference on. Robotics and Automation., pp. 1178-1183 .
4.
Borenstein, J. and Koren, Y.1987. Motion control analysis of a mobile robot , ASME Journal of Dynamic Systems, Measurement and Control109: 73-79 .
5.
Borenstein, J. Feb. 1995. Control and kinematic design of multi-degree-of freedom mobile robots with compliant linkage , IEEE Transactions on Robotics and Automation11: 21-35 .
6.
Carretero, J. A. , Nahon, M. , and Podhorodeski, R. P. 1998. Workspace analysis of a 3-DOF parallel mechanism , Proceedings of IEEE International Conference on Intelligent Robots and Systems, vol. 2, pp. 1021-1026 .
7.
Chen, N. X. and Song, S.1994. Direct position analysis of 4-6 Stewart Platforms , Journal of Mechanical Design116: 61-66 .
8.
Chiacchio, P. , Pierrot, F. , Sciavicco, L. and Siciliano, B.1993. Robust Design of independent joint controllers with experimentation on a high-speed parallel robot , IEEE Transactions Industrial Electronics, 40(4): 393-403 .
9.
Chiu, T. C. and Tomizuka, M.1998. Coordinated position control of multi-axis mechanical systems . ASME Journal of Dynamic Systems, Measurement, and Control120(3): 389-393 .
10.
Chiu, T. C. , and Tomizuka, M.2001. Contouring control of machine tool feed drive systems: A task coordinate frame approach , IEEE Transactions on Control Systems Technology9(1): 130-139 .
11.
Chuang, H.-Y. and Chang, Y.-C.2000. A novel contour error compensator for 3-PRPS platform , Journal of Robotic Systems17(5): 273-289 .
12.
Clavel, R. 1998. Delta, a fast robot with parallel geometry , Proceedings 18th International Symposium on Industrial Robots, Lausanne, Switzerland, pp. 91-100 .
13.
Fasse, E. D. and Gosselin, C. M.1999. Spatio-geometric impedance control of Gough-Stewart platforms , IEEE Transaction on Robotics and Automation15: 281-288 .
14.
Feng, L. , Koren, Y. and Borenstein, J.1993. Cross-coupling motion controller for mobile robots , IEEE Control Sysems. Magazine13(6): 35-43 .
15.
Filippov, A. F.1988. Differential Equations with Discontinuous Righthand Sides, Kluwer, Dordrecht .
16.
Gauthier, D. , Freeman, P. , Carayannis, G. and Malowany, A.1987. Interprocess communication for distributed robotics . IEEE Transactions on Robotics and Automation3(6): 493-504 .
17.
Heerah, I. and Behabib, B.2003. Architecture selection and singularity analysis of a three-degree-of-freedom planar parallel manipulator , Journal of Intelligent and Robotic Systems37: 355-374 .
18.
Kamano, T. , Suzuki, T. , Iuchi, N. and Tomizuka, M.1993. Adaptive feedforward controller for synchronization of two axes positioning system . Transactions of Society of Instrument and Control Engineers (SICE), Japan , 29(7): 785-791 .
19.
Karkoub, M. , Her, M. G. , Hsu, K. S. and Chen, C. Y.2004. Neural-net tuned PID control of a parallel type mechanism with force feedback for virtual reality applications , Robotica22(3): 319-327 .
20.
Kokkinis, T. and Stoughton, R.1996. Dynamics and control of closed-chain robot arms with application to a new direct-drive robot arm , Inernational Journal of Robotics and Automation, 6(1): 25-34 .
21.
Koren, Y.1980. Cross-coupled biaxial computer controls for manufacturing systems , ASME Journal of Dynamic Systems, Measurement, and Control102(4): 265-272 .
22.
Koren, Y. and Lo, C. C.1991. Variable-gain cross-coupling controller for contouring , Annals of CIRP40(1): 371-374 .
23.
Koren, Y. and Lo, C. C. June 1992. Evaluation of servo-controllers for machine tools , Proceedings of American Control Conference, pp. 370-374 .
24.
Koren, Y. and Lo, C. C. 1992. Advanced controllers for feed drives . Annals of CIRP pp. 689-698 .
25.
Kulkarni P. K. and Srinivasan, K.1990. Cross-coupled control of biaxial feed drive servomechanisms , ASME Journal of Dynamic Systems, Measurement, and Control112(2): 225-232 .
26.
Lee, H. C. and Jeon, G. J.1998. A neuro-controller for synchronization of two motion axes , International Journal of Intelligent Systems13(6): 571-586 .
27.
Li, S. , Feng, Z. and Fang, H. 2002. Variable structure control for 6-6 parallel manipulators based on cascaded CMAC , Proceedings of 4th World Congress on Intelligent Control and Automations, Shanghai, China, pp. 1939-1943 .
28.
Lin, H. M. and McInroy, J. E.2003. Adaptive sinusoidal disturbance cancellation for precise pointing of Stewart platforms , IEEE Transactions on Control Systems Technology11: 267-272 .
29.
Merlet, J. P.2000. Parallel Robots, Kluwer Academic Publishers, Dordrecht , pp. 9-10.
30.
Moore, P. R. and Chen, C. M.1995. Fuzzy logic coupling and synchronized control of multiple independent servo-drives , Control Engineering Practice3(12): 1697-1708 .
31.
McNab, R. and Tsao, T. November 1994. Multiaxis contour tracking: A receding time horizon linear quadratic optimal control approach , Dynamic System and Control2-2 .
32.
McNab, R. J. and Tsao, T. C.2000. Receding horizon linear quadratic optimal control for multi-axis contour tracking . ASME Journal of Dynamic Systems, Measurement, and Control122(2): 375-381 .
33.
Naumovic, M.1999. Cross-coupled motion controller for two cooperating robot arms , in Proceedings of IEEE International Symposium on Industrial Electronics, vol.2, pp. 909-913 .
34.
Nefti, S. , Djouani, K. and Amirat, Y. 2002. Neuro-fuzzy based approach for hybrid force/position robot control , Proceedings of IEEE International Conference on Industrial Technology, Bangkok, Thailand, pp. 376-381 .
35.
Park, M. K. , Lee, M. C. and Go, S. J. 2001. The design of sliding mode controller with perturbation observer for a 6-DOF parallel manipulator , Proceedings of International Symposium on Industrial Engineering, Pusan, Korea, vol. 3, pp. 1502-1507 .
36.
Pernechele, C. , Bortoletto, F. and Giro, E. 2000. Neural network algorithm controlling a hexapod platform , in Proceedings of IEEE-INNS-ENNS International Joint Conference on Neural Networks, pp. 349-352 .
37.
Rodriguez-Angeles, A. and Nijmeijer, H.2004. Mutual synchronization of robots via estimated state feedback: A cooperative approach , IEEE Transactions on Control Systems Technology12: 542-554 .
38.
Sirouspour, M. R. and Salcudean, S. E.2001. Nonlinear control of hydraulic robots , IEEE Transactions on Robotics and Automation17: 173-182 .
39.
Slotine, J. J. E. and Li, W.1987. On the adaptive control of robot manipulators , International Journal of Robotics Research6(3): 49-59 .
40.
Slotine, J. J. E. and Sastry, S.1983. Tracking control of nonlinear systems using sliding surfaces, with application to robot manipulators , International Journal of Control38: 465-492 .
41.
Stauffer, R. N.1984. Flight simulation facility features robot position , Robotics Today6(3): 71-72 .
42.
Su, Y. X. , Sun, D. , Ren, L. and Mills, J. K.2006. Integration of saturated PI synchronous control and PD feedback for control of parallel manipulators , IEEE Transactions on Robotics22(1): 202-207 .
43.
Sun, D.2003. Position synchronization of multiple motion axes with adaptive coupling control . Automatica39(6): 997-1005 .
44.
Sun, D. , Feng, G. , Lam, C. M. and Dong, H. N.2005. Orientation control of a differential mobile robot through wheels’ synchronization , IEEE/ASME Transactions on Mechatronics10(3): 345-351 .
45.
Sun, D. and Mills, J. K.2002. Adaptive synchronized control for coordination of multirobot assembly tasks , IEEE Transactions on Robotics and Automation18: 498-510 .
46.
Tomizuka, M. , Hu, J. S. and Chiu, T. C.1992. Synchronization of two motion control axes under adaptive feedforward control , ASME Journal of Dynamic Systems, Measurement, and Control114(6): 196-203 .
47.
Utkin, V. I.1977. Variable structure systems with sliding modes , IEEE Transactions on Automatic ControlAC- 22(2): 212-222 .
48.
Yang, L. F. and Chang, W. H.1996. Synchronization of twin-gyro precession under cross-coupled adaptive feed-forward control . Journal of Guidance, Control, and Dynamics19(3): 534-539 .
49.
Yeh, S. S. and Hsu, P. L.2003. Analysis and design of integrated control for multi-axis motion systems , IEEE Transactions on. Control Systems Technology11: 375-382 .
