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In this paper, a communication-efficient dynamic task scheduling algorithm for a heterogeneous multi-robot system is proposed. To make this task scheduling algorithm to be scalable for various robot teams, a distributed communication with shared global unit mechanism is applied to reduce the storage cost as well as communication overhead. Each robot makes its own decision through communicating with others as well as checking a global unit. This algorithm improves its efficiency by broadcasting specific information only to those who are capable and have interest in the current tasks. To improve the system robustness, an auction-based fitness function is applied to dynamically allocate the tasks among the robots if the pre-assigned robot can not handle the task or a robot fails under dynamic environment. The proposed approach is robust against communication failures and robot failures. Simulation results demonstrate the efficiency and robustness of the proposed approach.