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Fourier-based optimal design of a flexible manipulator path to reduce residual vibration of the endpoint

Published online by Cambridge University Press:  09 March 2009

Kyung-Jo Park  and
Youn-Sik Park
Kyung-Jo Park
Affiliation:
Center for Noise and Vibration ControlDepartment of Mechanical EngineeringKorea Advanced Institute of Science and TechnologyScience TownTaejon305–701 (Korea)
Youn-Sik Park
Affiliation:
Center for Noise and Vibration ControlDepartment of Mechanical EngineeringKorea Advanced Institute of Science and TechnologyScience TownTaejon305–701 (Korea)
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Summary

A method is presented for generating the path which significantly reduces residual vibration. The desired path is optimally designed so that the system completes the required move with minimum residual vibration. The dynamic model and optimal path are effectively formulated and computed by using special moving coordinates, called virtual rigid link coordinates, to represent the link flexibilities. Also joint compliances are included in the model. Characteristics of residual vibration are identified from the linearized equations of motion. From these results, the performance index is selected to reduce residual vibration effectively. The path to be designed is developed by a combined Fourier series and polynomial function to satisfy both the convergence and boundary condition matching problems. The concept of correlation coefficients is used to select the minimum number of design variables, i.e. Fourier coefficients, the only ones which have a considerable effect on the reduction of residual vibration. A two-link manipulator is used to evaluate this method. Results show that residual vibration can be drastically reduced by selecting an appropriate manipulator path.

Keywords

Residual vibrationOptimal pathFourier-based designCorrelation coefficient.
Type
Research Article
Information
Robotica , Volume 11 , Issue 3 , May 1993 , pp. 263 - 272
Copyright
Copyright © Cambridge University Press 1993

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References

1.Aspinwall, D.M., “Acceleration Profiles for Minimizing Residual Response” Transactions of the ASME, JDSMC 102, 3–6 (03., 1980).Google Scholar
2.Makino, H., Furuya, N., Soma, K. and Chin, E., “Research and Development of the SCARA Robot” Proc. 4th Int. Conf. on Production Engineering 885–890 (1980).Google Scholar
3.Sehitoglu, H. and Aristizabal, J.H., “Design of a Trajectory Controller for Industrial Robots Using Bang-Bang and Cycloidal Motion Profiles” ASME Winter Annual Meeting 169–175 (12, 1986).Google Scholar
4.Swigert, C.J., “Shaped Torque Techniques” AlAA J. Guidance and Control 3, 460–467 (09., 1980).CrossRefGoogle Scholar
5.Farrenkopf, R.L., “Optimal Open-Loop Maneuver Profiles for Flexible Spacecraft” AlAA J. Guidance and Control 2, 491–498 (11., 1979).CrossRefGoogle Scholar
6.Turner, J.D. and Junkins, J.L., “Optimal Large-Angle Single-Axis Rotational Maneuvers of Flexible Spacecraft” AlAA J. Guidance and Control 3, 578–585 (11., 1980).CrossRefGoogle Scholar
7.Turner, J.D. and Chun, H.M., “Optimal Distributed Control of a Flexible Spacecraft During a Large-Angle Maneuver” AlAA J. Guidance, Control and Dynamics 7, 257–264 (05, 1984).CrossRefGoogle Scholar
8.Hanafi, A. and Wright, F.W., “Optimal Trajectory Control of Robotic Manipulators” Mechanism and Machine Theory 19, No. 2, 267–273 (1984).CrossRefGoogle Scholar
9.Breakwell, J.A., “Optimal Feedback Slewing of Flexible Spacecraft” AlAA J. Guidance and Control 4, 472–479 (09., 1981).CrossRefGoogle Scholar
10.Juang, J.N., Turner, J.D. and Chun, H.M., “Closed-Form Solutions for Feedback Control with Terminal Con- straints” AlAA J. Guidance, Control and Dynamics 8, 307–320 (01., 1985).Google Scholar
11.Alberts, T.E., Hastings, G.G., Book, W.J. and Dickerson, S.L., “Experiments in Optimal Control of a Flexible Arm with Passive Damping” Proc. Fifth VPl & SU/AIAA Sym. on Dynamics and Control of Large Structures 423–435 (06, 1985).Google Scholar
12.Sliverberg, L.M., “Uniform Damping Control of Space- craft” AlAA J. Guidance, Control and Dynamics 9, 221–227 (05, 1986).CrossRefGoogle Scholar
13.Dougherty, H., Tompetrini, K., Levinthal, J. and Nurre, G., “Space Telescope Pointing Control System” AlAA J. Guidance, Control and Dynamics 5, 403–409 (07, 1982).CrossRefGoogle Scholar
14.Cannon, R.H. and Schmitz, E., “Initial Experiments on the End-Point Control of a Flexible One-Link Robot” Int. J. Robotics Research 3, 62–75 (Fall, 1984).CrossRefGoogle Scholar
15.Meckl, P.H. and Seering, W.P., “Minimizing Residual Vibration for Point-to-Point Motion” Transactions of the ASME J. Vibration, Acoustics, Stress, and Reliability in Design 107, 38–46 (10., 1985).CrossRefGoogle Scholar
16.Onsay, T. and Akay, A., “Vibration Reduction of a Flexible Arm by Time-Optimal Open-loop Control” J. Sound and Vibration 147, No. 2, 283–300 (1991).CrossRefGoogle Scholar
17.Singer, N.C. and Seering, W.P., “Preshaping Command Inputs to Reduce System Vibration” Transactions of the ASME, JDSMC 112, 76–82 (03., 1990).Google Scholar
18.Jayasuriya, S. and Choura, S., “On the Finite Settling Time and Residual Vibration Control of Flexible Structures” J. Sound and Vibration 148, No. 1, 117–136 (1991).CrossRefGoogle Scholar
19.Asada, H., Ma, Z.D. and Tokumaru, H., “Inverse Dynamics of Flexible Robot Arms: Modeling and Computation for Trajectory Control” Transactions of the ASME, JDSMC 112, 177–185 (06, 1990).Google Scholar
20.Fu, K.S., Gonzalez, R.C. and Lee, C.S.G., Robotics: Control, Sensing, Vision, and Intelligence (McGraw-Hill, New York, USA, 1987).Google Scholar