A note on a motion control problem for a placement machine

Assembling printed circuit boards efficiently using automated placement machines is a challenging task. Here, we focus on a motion control problem for a specific type of placement machines. More specifically, the problem is to establish movement patterns for the robot arm, the feeder rack, and—when appropriate—the worktable, of a sequential pick-and-place machine. In this note we show that a (popular) greedy strategy may not always yield an optimum solution. However, under the relevant Tchebychev metric, we can model the problem as a linear program, thereby establishing the existence of a polynomial time algorithm for this motion control problem. Finally, we give experimental evidence that computing optimal solutions to this motion control problem can yield significantly better solutions than those found by a greedy method.