Variable Fractional Network Evolutionary Game for Distributed Resilient Task Allocation in Heterogeneous Multi-Robot Systems

Cooperative multi-robot task allocation is a fundamental aspect of autonomous intelligent systems that has garnered considerable research interest. Nevertheless, given that environments are dynamic and uncertain, resilience mechanisms must be studied further. In this paper, we propose a novel mechanism based on the variable fractional network evolutionary game (FNEG), which provides a new paradigm for heterogeneous multi-robot task allocation. Specifically, given communication and timeliness constraints, the problem of task allocation is formulated as an evolutionary network game model. In particular, a kernel of the integral operator based on the variable function is intended to enhance the nearsightedness and memorylessness of traditional replicator dynamics. Next, long-term payoffs are introduced to analyze the evolutionary process of task allocation. Furthermore, the stability of the evolutionary equilibrium strategy is demonstrated. Experiments and comparisons on different scenarios demonstrate that the proposed model is effective for enhancing load balancing and completion rate. The model is scalable in terms of computation time reduction and is resilient in its ability to adapt to system perturbations.