Altruistic task allocation despite unbalanced relationships within Multi-Robot Communities

Typical multi-robot systems consist of robots cooperating to maximize global fitness functions. However, in some scenarios, the set of interacting robots may not share common goals and thus the concept of a global fitness function becomes invalid. This work examines multi-robot communities (MRC), in which individual robots have independent goals. Within the MRC context, we present a task allocation architecture that optimizes individual robot fitness functions over long time horizons using reciprocal altruism. Previous work has shown that reciprocating altruistic relationships can evolve between two willing robots, using market-based task auctions, while still protecting against selfish robots aiming to exploit altruism. As these relationships grow, robots are increasingly likely to perform tasks for one another without any reward or promise of payback. This work furthers this notion by considering cases where an imbalance exists in the altruistic relationship. The imbalance occurs when one robot can perform another robot´s task, thereby exhibiting altruism, but the other robot cannot reciprocate since it is physically unable (e.g. lack of adequate sensors or actuators). A new altruistic controller to deal with such imbalances is presented. The controller permits a robot to build altruistic relationships with the community as a whole (one-to-many), instead of just with single robots (one-to-one). The controller is proven stable and guarantees altruistic relationships will grow, if robots are willing, while still minimizing the effects of selfish robots. Results indicate that the one-to-many controller performs comparable to the one-to-one on most problems, but excels in the case of an unbalanced altruistic relationship.