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Real-time systems are one of the fields of computing where major benefits are expected from the increasing availability of multiprocessor technology. Heterogeneous computing environments, which utilize different high-performance machines interconnected via a high speed communication system, are well suited to the large, computation intensive, real-time or non-real-time applications. Nowadays, many of the systems in these environments are powered by rechargeable batteries. Scheduling real-time tasks on these rechargeable systems is an important issue which has been studied in the literatures. In this paper, we explore the task assignment problem on heterogeneous distributed system with rechargeable batteries. Our techniques to solve the problem are based on four heuristics, namely Minimum Schedule Length (MSL), min-min schedule length (MmSL), genetic algorithm (GA), and ant colony optimization (ACO). While the modifications of the MSL, MmSL and GA approaches from their original implementation are somewhat straight-forward, we design a novel structure using ACO. The performance comparisons of these four techniques are performed and the results are discussed. This paper not only gives a suggestion on which heuristic is best suited for the specific problem, but also provides a new direction to solve similar problems.