We propose integrating the edge-computing paradigm into the multi-robot collaborative scheduling to maximize resource utilization for complex collaborative tasks, which many robots must perform together. Examples include collaborative map-merging to produce a live global map during exploration instead of traditional approaches that schedule tasks on centralized cloud-based systems to facilitate computing. Our decentralized approach to a consensus-based scheduling strategy benefits a multi-robot-edge collaboration system by adapting to dynamic computation needs and communication-changing statistics as the system tries to optimize resources while maintaining overall performance objectives. Before collaborative task offloading, continuous device, and network profiling are performed at the computing resources, and the distributed scheduling scheme then selects the resource with maximum utility derived using a utility maximization approach. Thorough evaluations with and without edge servers on simulation and real-world multi-robot systems demonstrate that a lower task latency, a large throughput gain, and better frame rate processing may be achieved compared to the conventional edge-based systems.