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

  • Christof Büskens
  • Helmut Maurer


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.


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

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Christof Büskens
    • 1
  • Helmut Maurer
    • 2
  1. 1.Lehrstuhl für IngenieurmathematikUniversität BayreuthGermany
  2. 2.Institut für numerische MathematikUniversität MünsterGermany

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