DIRCOL

A direct collocation method for the numerical solution of optimal control problems

Selected applications of the method

• Robotics: Optimal Path Planning for Industrial Robots

  
  Project on Parameter identification, trajectory optimization, and real time control of industrial robots (only in German)

  Publications:

  • Heim, A.; von Stryk, O.; Pesch, H.J.; Schäffler, H.; Scheuer, K.:
    Parameteridentifikation, Bahnoptimierung und Echtzeitsteuerung von Robotern in der industriellen Anwendung.
    To appear in: Hoffmann, Jäger, Lohmann, Schunck (eds.): Mathematik - Schlüsseltechnologie für die Zukunft (Anwendungsorientierte Verbundprojekte des BMBF auf dem Gebiet der Mathematik), Tagungsband des Statusseminars, 25.-27.10.1995, München (Springer Verlag).
  • von Stryk, O.:
    Optimization of dynamic systems in industrial applications.
    In: H.J. Zimmermann (ed.): Proc. 2nd European Congress on Intelligent Techniques and Soft Computing (EUFIT), Aachen, Germany (Sep. 20-23, 1994) 347-351.
    (please click here for a PostScript version or a gzipped PostScript version of the paper)
  • von Stryk, O.; Schlemmer, M.:
    Optimal control of the industrial robot Manutec r3.
    In: R. Bulirsch, D. Kraft (Hrsg.): Computational Optimal Control, International Series of Numerical Mathematics 115 (Basel: Birkhäuser, 1994) 367-382.
    (please click here for a PostScript version or a gzipped PostScript version of the paper)

• Robotics: Trajectory Optimization for a Shuttle Mounted Robot

  

  Publications:

  • M. Glocker, M. Vögel, O. von Stryk:
    Trajectory optimization of a shuttle mounted robot.
    In: Proc. Workshop on Optimal Control in Hypersonic Flight, Greifswald, 7.-8. Oktober 1999 (TU München, 1999) 71-82.
  • Trajectory Optimization of a Shuttle Mounted Robot (only in German)
  • Optimal paths for a shuttle mounted robotic manipulator with 3 d.o.f. (only in German)

• Flight Mechanics: Trajectory Optimization of an airbreathing lower stage of a two-stage-two-orbit launch vehicle

  Publications:

  • von Stryk, O.:
    Numerical solution of optimal control problems by direct collocation.
    In: R. Bulirsch, A. Miele, J. Stoer, K.-H. Well (eds.): Optimal Control - Calculus of Variations, Optimal Control Theory and Numerical Methods, International Series of Numerical Mathematics 111 (Basel: Birkhäuser, 1993) 129-143.
    Preprint: Schwerpunktprogramm der Deutschen Forschungsgemeinschaft: Anwendungsbezogene Optimierung und Steuerung, Report No. 322, Mathematisches Institut, Technische Universität München (1991).
    PostScript file (618kb), gzipped PostScript file (106kb).

• Flight Mechanics: Range maximization of a hangglider

  Publications:

  • Bulirsch, R.; Nerz, E.; Pesch, H.J.; von Stryk, O.:
    Combining direct and indirect methods in optimal control: range maximization of a hangglider.
    In: R. Bulirsch, A. Miele, J. Stoer, K.-H. Well (eds.): Optimal Control - Calculus of Variations, Optimal Control Theory and Numerical Methods, International Series of Numerical Mathematics 111 (Basel: Birkhäuser, 1993) 273-288.
  • von Stryk, O.:
    Section 8.3 of Numerische Lösung optimaler Steuerungsprobleme: Diskretisierung, Parameteroptimierung und Berechnung der adjungierten Variablen.
    Fortschritt-Berichte VDI, Reihe 8, Nr. 441, VDI-Verlag, Düsseldorf, 158 S., 1995.
    Also: Dissertation (München: Technische Universität, Mathematisches Institut, 1994).

• Flight Mechanics: Optimal control of a passenger aircraft through a downburst windshear

  Publications:

  • von Stryk, O.:
    Section 8.2 of Numerische Lösung optimaler Steuerungsprobleme: Diskretisierung, Parameteroptimierung und Berechnung der adjungierten Variablen.
    Fortschritt-Berichte VDI, Reihe 8, Nr. 441, VDI-Verlag, Düsseldorf, 158 S., 1995.
    Also: Dissertation (München: Technische Universität, Mathematisches Institut, 1994).

• Biomechanics:

  

  Publications:

  • M. Hardt, K. Kreutz-Delgado, J.W. Helton, O. von Stryk:
    Obtaining Minimum Energy Biped Walking Gaits with Symbolic Models and Numerical Optimal Control.
    Workshop - Biomechanics meets Robotics, Modelling and Simulation of Motion. Nov. 8-11, 1999, Heidelberg, Germany.
    PostScript file (728kb), gzipped PostScript file (166kb).
  • M. Hardt, O. von Stryk:
    Towards optimal hybrid control solutions for gait patterns of a quadruped.
    Proc. CLAWAR 2000 - 3rd International Conference on Climbing and Walking Robots, Madrid, October 2-4, 2000.

• Automotive Engineering: Optimal Operation and Components' Coordination of a Hybrid Driveline.

  
  The concept of the hybrid driveline consists of a Diesel motor, an electrical motor (powered by a rechargable battery) and a continuous variable transmission. This research is part of a project of the Sonderforschungsbereich 365 Umweltfreundliche Antriebstechnik für Fahrzeuge (A. Kleimaier, U. Zoelch) (information only in German).

  Publications:

  • U. Zoelch:
    Ein Beitrag zu optimaler Auslegung und Betrieb von Hybridfahrzeugen
    Dissertation, Technische Universität München (1998).
  • U. Zoelch. D. Schröder:
    Dynamic optimization method for design and rating of the components of a hybrid vehicle
    Int. Journal of Vehicle Design 19, 1 (1998) 1-13.

• Electrical Engineering:

  
  Project on computational design of microwave oscillators with minimized phase noise (only in German)

  Publications:

  • Anzill, W.; von Stryk, O.:
    Optimum design of microwave oscillators with minimized phase noise.
    In: H. Neunzert (ed.): Progress in Industrial Mathematics at ECMI 94.
    J. Wiley & Sons Ltd and B. G. Teubner (1996) 301-306.
    (please click here for a PostScript version or a gzipped PostScript version of the paper)
  • Anzill, W.; von Stryk, O.; Bulirsch, R.; Russer, P.:
    Phase noise minimization of microwave oscillators by optimal design.
    IEEE MTT-S Symposium Digest, Orlando, Florida, USA (1995) 1565-1568.
    (please click here for gif files of pages 1565, 1566, 1567, 1568)

• Economics: Optimal Management Strategies of a Firm

  Publications:
  • Koslik, B.; Breitner, M.H.:
    An optimal control problem in Economics with four linear controls.
    J. Optimization Theory and Applications 94, 3 (1997) 619-634.
  • Breitner, M.H.; Koslik, B.; von Stryk, O.; Pesch, H.J.:
    Iterative design of economic models via simulation, optimization and modeling.
    In: I. Troch (Hrsg.): Proc. 1st MathMod (IMACS Symposium on Mathematical Modelling), Vol. 5, Feb. 2-4, Vienna (1994) 816-819.
    Mathematics and Computers in Simulation 39 (1995) 527-532.
    (please click here for a PostScript version or a gzipped PostScript version of the paper)
  • Breitner, M.H.; Koslik, B.; von Stryk, O.; Pesch, H.J.:
    Optimal control of investment, level of employment and stockkeeping.
    In: A. Bachem, U. Derigs, M. Jünger, R. Schrader (Hrsg.): Operations Research '93 (Heidelberg: Physica Verlag, 1994) 60-63.
    (please click here for a PostScript version or a gzipped PostScript version of the paper)

  Economic Studies

  • Thimann, C.:
    A model of investment dynamics in eastern Germany: Gradual climb instead of sudden jump.
    Münchener wirtschaftswissenschaftliche Beiträge Nr. 94-18, Volkswirtschaftliche Fakultät, Ludwig-Maximilians-Universität München (1994), forthcoming in: Journal of International and Comparative Economics (JOICE).
  • Thimann, C.; Breitner, M.H.:
    Eastern Germany and the conflict between wage adjustment, investment and employment: A numerical analysis.
    Economic Studies Working Paper No. 2, American Institute for Contemporary German Studies, The John Hopkins University (1995).