Sizing of a fleet of cooperative robots for the transport of homogeneous loads

Abstract

We consider the problem of determining the number of robots necessary to transport a set of homogeneous loads in a given time interval from a zone <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$A$</tex> to a zone <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$B$</tex> , at minimum cost. The cost is function of the number of robots and of the distance travelled by robots. The operations are divided into several phases: loading, loaded travel, unloading, empty travel and battery charging. The case of non-cooperative robots is considered for which we derive a closed-form expression for the optimal number of robots. We then consider the case of cooperative robots where loads can be carried either by a single robot (mono-robot) or by several robots that cooperate (poly-robot). The fleet sizing problem can be formulated as a mathematical programming. We distinguish several scenarios, depending on the respective carrying capacity of mono-robots and poly-robots. Finally, the infinite horizon problem is also addressed, which models a fleet of vehicles and leads to simpler results.