Optimal Control of Robot Guided Laser Material Treatment
A. Steinbrecher (Weierstrass Institute for Applied Analysis and Stochastics, Germany)
Laser material treatments such as hardening, remelting or welding have become a basic part of the process chain for sophisticated metal workpieces. They allow for precise process control with reproducible results. Mounted on industrial robots, laser treatment devices become increasingly important in automated manufacturing, especially in automotive industry.
For the employment of single robots a number of planning tools is available, considering issues like path-planning, control, collision detection, etc. but disregarding the specific task the robot has to perform. Up to now it is always assumed that the track along which the laser light impinges on the workpiece surface is precisely known. However, especially in the case of curved workpiece boundaries the real movement of the robot tool center point and thus the laser track as well as the laser velocity may differ considerably from the desired one. On the other hand the most natural criterion to decide whether the employment of a robot has been successful is not the tracking of a prescribed path but the question if the robot has achieved its production goal.
In this talk we will consider the numerical treatment of the optimal control of robot guided laser material treatments, where the discrete multibody system of a robot is coupled with a PDE model of the laser treatment. We will present and discuss a new approach of the optimality criterion that is less restrictive to the motion of the robot than the classical approaches. Furthermore, we will discuss the numerical treatment of such optimal control problems. Finally, we will illustrate that approach at an example for hardening of a workpiece. The optimal control problem in this example is to obtain a certain desired hardening profile on the surface of a solid body along a desired curve which is given depending on its arc length and not depending on time.