# Robot arm problem

Robot arm problem | |
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State dimension: | 1 |

Differential states: | 3 |

Continuous control functions: | 3 |

Path constraints: | 12 |

Interior point equalities: | 12 |

The robot arm problem focuses on minimizing the time used by a robot arm to move from an origin to a destination.
The arm is a bar of length and sticks out distance from its moving axis, while sticking out distance in the other direction. The problem can be found in [Moessner1995]**Address: ** *Im Neuenheimer Feld 368, 69120 Heidelberg, Germany***Author: ** *M. Moessner-Beigel***Month: ** *November***School: ** *Ruprecht-Karls-Universit\"at Heidelberg***Title: ** *Optimale Steuerung f\"ur Industrieroboter unter Ber\"ucksichtigung der getriebebedingten Elastizit\"at***Type: ** *Diplomarbeit***Year: ** *1995*

or in the COPS library.

## Model formulation

The problem is set up using the length , "the vertical angles from the horizontal plane, the controls and the final time ".

The moving robot is modelled with the following equations:

where characterizes the moment of inertia, i.e.

The path constraints on the states and on the controls as well as the boundary conditions can be seen in the optimization problem further down.

## Optimization problem

where is the moment of inertia as above.

## Source Code

Model descriptions are available in

== References ==

[Moessner1995] | M. Moessner-Beigel: Optimale Steuerung f\"ur Industrieroboter unter Ber\"ucksichtigung der getriebebedingten Elastizit\"at, 1995 |