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Real-Time Control of an Industrial Robot under Control and State Constraints

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Abstract

The dynamical model in Otter and Turk [10] for the robot Manutec r3 leads to a highly nonlinear optimal control problem with various control and state constraints. The nonlinear programming (NLP) techniques in [1,2,4] are applied to compute the optimal nominal solution for a fixed set of parameters in the system. We consider perturbations in the model which frequently occur in practice: deviations from the precomputed nominal trajectory or perturbations in the mass load. Since the re-optimization of the system for the perturbed set of parameters largely exceeds the running time of the robot, we apply the real-time control techniques developed in [2,4,5]. These methods require the computation of the parameter sensitivity derivatives and implement the first order Taylor expansion of the perturbed optimal solution with respect to the parameters. Real-time computations for the Manutec r3 robot are presented which demonstrate the quality of the real-time approximations.

Keywords

  • Optimal Control Problem
  • State Constraint
  • Sensitivity Differential
  • Industrial Robot
  • Maximal Relative Error

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. C. Büskens: Direkte Optimierungsmethoden zur numerischen Berechnung optimaler Steuerungen. Diploma thesis, Institut für Numerische Mathematik, Universität Münster, Münster, Germany, (1993)

    Google Scholar 

  2. C. Büskens: Optimierungsmethoden und Sensitivitätsanalyse für optimale Steuerprozesse mit Steuer- und Zustands- Beschränkungen. Dissertation, Institut für Numerische Mathematik, Universität Münster, Münster, Germany, (1998)

    Google Scholar 

  3. C. Büskens: Real-Time Solutions for Perturbed Optimal Control Problems by a Mixed Open- and Closed-Loop Strategy. This volume.

    Google Scholar 

  4. C. Büskens, H. Maurer: Sensitivity Analysis and Real-Time Optimization of Parametric Nonlinear Programming Problems. This volume.

    Google Scholar 

  5. C. Büskens, H. Maurer: Sensitivity Analysis and Real-Time Control of Parametric Optimal Control Problems Using Nonlinear Programming Methods. This volume.

    Google Scholar 

  6. C. Büskens, H. Maurer: Real-Time Control of Robots with Initial Value Perturbations Via Nonlinear Programming Methods. Optimization 47 (2000) 383–405

    MathSciNet  MATH  CrossRef  Google Scholar 

  7. C. Büskens, H. J. Pesch, S. Winderl: Real-Time Solutions of Perturbed Control Problems with Linear Controls. This volume

    Google Scholar 

  8. R. F. Haiti, S. P. Sethi, and R. G. Vickson: A Survey of the Maximum Principle for Optimal Control Problems with State Constraints. SIAM Review 37 (1995) 181–218

    MathSciNet  CrossRef  Google Scholar 

  9. H. Maurer, D. Augustin: Sensitivity Analysis and Real-Time Control of Parametric Optimal Control Problems Using Boundary Value Methods. This volume.

    Google Scholar 

  10. M. Otter, and S. Turk: The DFVLR Models 1 and 2 of the Manutec R3 Robot. DFVLR-Mitteilung 88–13, Institut für Dynamik der Flugsysteme, Oberpfaffenhofen, Germany, (1988)

    Google Scholar 

  11. O. von Stryk: Numerische Lösung optimaler Steuerungsprobleme: Diskretisierung, Parameteroptimierung und Berechnung der adjungierten Variablen. Fortschritt-Berichte VDI, Reihe 8,441, VDI Verlag, Germany, (1995)

    MATH  Google Scholar 

  12. M. Vukobratovic: Introduction to Robotics. Springer-Verlag, Berlin, (1989)

    CrossRef  Google Scholar 

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Büskens, C., Maurer, H. (2001). Real-Time Control of an Industrial Robot under Control and State Constraints. In: Grötschel, M., Krumke, S.O., Rambau, J. (eds) Online Optimization of Large Scale Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04331-8_5

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  • DOI: https://doi.org/10.1007/978-3-662-04331-8_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-07633-6

  • Online ISBN: 978-3-662-04331-8

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