Optimal Control of the Industrial Robot Manutec r3

  • Oskar von Stryk
  • Maximilian Schlemmer
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 115)


Minimum time and minimum energy point-to-point trajectories for an industrial robot of the type Manutec r3 are computed subject to state constraints on the angular velocities. The numerical solutions of these optimal control problems are obtained in an efficient way by a combination of a direct collocation and an indirect multiple shooting method. This combination links the benefits of both approaches: A large domain of convergence and a highly accurate solution. The numerical results show that the constraints on the angular velocities become active during large parts of the time optimal motion. But the resulting stress on the links can be significantly reduced by a minimum energy trajectory that is only about ten percent slower than the minimum time trajectory. As a by-product, the reliability of the direct collocation method in estimating adjoint variables and the efficiency of the combination of direct collocation and multiple shooting is demonstrated. The highly accurate solutions reported in this paper may also serve as benchmark problems for other methods.


Optimal Control Problem State Constraint Multiple Shooting Sequential Quadratic Programming Switching Point 
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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Copyright information

© Birkhäuser Verlag Basel 1994

Authors and Affiliations

  • Oskar von Stryk
    • 1
  • Maximilian Schlemmer
    • 2
  1. 1.Department of MathematicsMunich University of TechnologyMünchenGermany
  2. 2.Institute for Robotics and System DynamicsGerman Aerospace Research Establishment (DLR)WeßlingGermany

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