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In this paper, the cooperative backoff adaptive scheme (COBOS) is proposed for task allocation amongst a team of heterogeneous robots. The COBOS operates in regions with limited communication ranges, and is robust against robot malfunctions and uncertain task specifications, with each task potentially requiring multiple robots. The portability of tasks across teams (or when team demography changes) is improved by specifying tasks using basis tasks in a matrix framework. The adaptive feature of COBOS further increases the flexibility of robot teams, allowing robots to adjust their actions based on past experience. In addition, we study the properties of COBOS: operation domain; communication requirements; computational complexity; and solution quality; and compare the scheme with other task-allocation mechanisms. Realistic simulations are carried out to verify the effectiveness of the proposed scheme.