Approximation Algorithms for a Cyclic Routing Problem of Grasp-and-Delivery Robots

抄録

In this paper, we discuss a routing problem of a single grasp-and-delivery robot with unit capacity, which is working at an assembly line of printed circuit boards. The graspand-delivery robot arranges n identical pins from their current configuration to the next required configuration by transferring the pins one by one. We refer to such a transition from a configuration to the next required one as a cycle. The n pins support a printed circuit board from underneath in order to prevent it from overbending, while an automated manipulator embeds a number of electronic parts on to the printed circuit board from above. Each printed circuit board has its own pattern of circuit, and the required configurations for printed circuit boards to be processed are different from each another. Given an initial configuration of the n pins and a sequence of m required configurations for the printed circuit boards, the routing problem asks to find a transfer route of the grasp-and-delivery robot which minimizes the route length over all the m cycles. In this paper, by applying a weighted matroid intersection algorithm, we show that the cyclic routing problem is 2-approximable in polynomial time.