Robot arm problem
|Robot arm problem|
|Continuous control functions:||3|
|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
School: Ruprecht-Karls-Universit\"at Heidelberg
Title: Optimale Steuerung f\"ur Industrieroboter unter Ber\"ucksichtigung der getriebebedingten Elastizit\"at
or in the COPS library.
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.
where is the moment of inertia as above.
Model descriptions are available in
== References ==
|[Moessner1995]||M. Moessner-Beigel: Optimale Steuerung f\"ur Industrieroboter unter Ber\"ucksichtigung der getriebebedingten Elastizit\"at, 1995|