To circumvent persistent connectivity to the cloud infrastructure, the current emphasis on computing at network edge devices in the multi-robot domain is a promising enabler for delay-sensitive jobs, yet its adoption is rife with challenges. This paper proposes a novel utility-aware dynamic task offloading strategy based on a multi-edge-robot system that takes into account computation, communication, and task execution load to minimize the overall service time for delay-sensitive applications. Prior to task offloading, continuous device, network, and task profiling are performed, and for each task assigned, an edge with maximum utility is derived using a weighted utility maximization technique, and a system reward assignment for task connectivity or sensitivity is performed. A scheduler is in charge of task assignment, whereas an executor is responsible for task offloading on edge devices. Experimental comparisons of the proposed approach with conventional offloading methods indicate better performance in terms of optimizing resource utilization and minimizing task latency.