An integer linear programming model for fair multitarget tracking in cooperative multirobot systems

Cooperative Multi-Robot Observation of Multiple Moving Targets (CMOMMT) denotes a class of problems in which a set of autonomous mobile robots equipped with limited-range sensors keep under observation a (possibly larger) set of mobile targets. In the existing literature, it is common to let the robots cooperatively plan their motion in order to maximize the average targets' detection rate, defined as the percentage of mission steps in which a target is observed by at least one robot. We present a novel optimization model for CMOMMT scenarios which features fairness of observation among different targets as an additional objective. The proposed integer linear formulation exploits available knowledge about the expected motion patterns of the targets, represented as a probabilistic occupancy maps estimated in a Bayesian framework. An empirical analysis of the model is performed in simulation, considering multiple scenarios to study the effects of the amount of robots and of the prediction accuracy for the mobility of the targets. Both centralized and distributed implementations are presented and compared to each other evaluating the impact of multi-hop communications and limited information sharing. The proposed solutions are also compared to two algorithms selected from the literature. The model is finally validated on a real team of ground robots in a limited set of scenarios.