In this work is considered the problem of rest-to-rest motion in a desired pre-fixed time for planar flexible manipulators. We introduce a simple idea permitting the minimization of end-effector residual vibration when reaching a desired angular equilibrium position, in a pre-fixed desired travelling time. The results hold without considering internal elastic damping effect, using a classical controller with feedforward plus joint feedback terms. The new approach concerns the computation of the feedforward control, which is based on backward integration of the elastic dynamics, starting from a rest position of the flexible arms. This backward integration yields basically elastic trajectories permitting to reach the final desired end-effector position without oscillation. The feedback controller is then used to stabilize locally the actual states along these desired trajectories. However, for fast rest to rest motion, the feedback compensator fails to drive the system states along the desired trajectories, this being due to the relatively large initial elastic error. To overcome this limitation, proper joint motion is planned between the desired initial and final positions through optimization techniques, the goal being the minimization of the initial elastic error associated to these joint trajectories. The optimal planning technique is formulated as a Pontryagin optimal control problem. This scheme is validated via numerical tests as well as experiments on a flexible two-link planar manipulator.
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e-mail: lanari@dis.uniromal1.it
e-mail: deluca@dis.uniroma1.if
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March 2004
Technical Papers
Rest-to-Rest Motion for Planar Multi-Link Flexible Manipulator Through Backward Recursion
M. Benosman,
M. Benosman
LAM, Universite´ de Reims Champagne-Ardenne, BP 1039, 51687 Reims Cedex 2, France
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G. Le Vey,
G. Le Vey
Institut de Recherche en Cyberne´tique de Nantes, UMR 6597-CNRS 1 rue de la Noe¨, BP 92101, 44321 Nantes Cedex 3, France
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L. Lanari,
e-mail: lanari@dis.uniromal1.it
L. Lanari
Universit degli studi di Roma “La Sapienza,” Via Eudossiana 18, 00184 Roma, Italy
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A. De Luca
e-mail: deluca@dis.uniroma1.if
A. De Luca
Universit degli studi di Roma “La Sapienza,” Via Eudossiana 18, 00184 Roma, Italy
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M. Benosman
LAM, Universite´ de Reims Champagne-Ardenne, BP 1039, 51687 Reims Cedex 2, France
G. Le Vey
Institut de Recherche en Cyberne´tique de Nantes, UMR 6597-CNRS 1 rue de la Noe¨, BP 92101, 44321 Nantes Cedex 3, France
L. Lanari
Universit degli studi di Roma “La Sapienza,” Via Eudossiana 18, 00184 Roma, Italy
e-mail: lanari@dis.uniromal1.it
A. De Luca
Universit degli studi di Roma “La Sapienza,” Via Eudossiana 18, 00184 Roma, Italy
e-mail: deluca@dis.uniroma1.if
Contributed by the Dynamic Systems, Measurement, and Control Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received by the ASME Dynamic Systems, and Control Division July 28, 2003. Associate Editor: M. Goldfarb.
J. Dyn. Sys., Meas., Control. Mar 2004, 126(1): 115-123 (9 pages)
Published Online: April 12, 2004
Article history
Received:
July 28, 2003
Online:
April 12, 2004
Citation
Benosman, M., Le Vey, G., Lanari, L., and De Luca, A. (April 12, 2004). "Rest-to-Rest Motion for Planar Multi-Link Flexible Manipulator Through Backward Recursion ." ASME. J. Dyn. Sys., Meas., Control. March 2004; 126(1): 115–123. https://doi.org/10.1115/1.1649976
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