Constraint optimization model of a scheduling problem for a robotic arm in automatic systems

In this paper, we investigate the problem of scheduling a 6 DOF robotic arm to carry out a sequence of spray painting tasks. The duration of any given painting task is process dependent and fixed, but the duration of an ''intertask'', corresponding to the process of relocating and reorienting the robot arm from one painting task to the next one, is influenced by the order of tasks and must be minimized by the scheduler. There are multiple solutions for reaching any given painting task and tasks can be performed in either of two different directions. Further complicating the problem are characteristics of the painting process application itself. Unlike spot-welding, painting tasks require movement of the entire robot arm. In addition to minimizing intertask duration, the scheduler must strive to maximize painting quality and the problem is formulated as a multi-objective optimization problem. The scheduling model is implemented as a stand-alone module using constraint programming, and integrated with a larger automatic system. The results of a number of simulation experiments with simple parts are reported, both to characterize the functionality of the scheduler and to illustrate the operation of the entire software system for automatic generation of robot programs for painting.