With multi-robot systems being increasingly deployed in logistics, surveillance, exploration, et al., the power constrained multi-robot task assignment (MRTA) problem has emerged as a critical research focus. To address this issue, this study proposes an efficient task assignment method for power constrained multi-robot systems, minimizing the return time of the last robot to the depot after task completion. First, a hierarchical minimum marginal cost algorithm is used to generate an initial task assignment plan for multiple robots. Then, leveraging the multi-dimensional characteristics, the initial solution is improved using a variable neighborhood search algorithm, in which a neighborhood operator for charging piles is designed. The four loop structure of the entire algorithm implements hierarchical optimization, ensuring diversity of solutions and achieving effective convergence. Finally, the results demonstrate that under power constraints, the proposed method can obtain better quality solutions in a shorter time compared with existing heuristic algorithms in multi-robot task assignment.