The study addresses the problems of poor connectivity in region division, unbalanced task allocation, and frequent path steering encountered in multi-robot coverage path planning within complex environments filled with multiple obstacles. It proposes a multi-robot coverage path planning method that actively combines a region division algorithm incorporating robot state parameters with multi-objective initial position optimization. Firstly, it actively combines the adaptation mechanism for different residual power state parameters among multiple robots to ensure balanced task allocation. Secondly, it designs a two-way A* evaluation matrix and a BFS connectivity reward and punishment mechanism to actively improve the traditional regional division method. Finally, it optimizes the initial deployment positions of the robots using the adaptive weighted MOTPE algorithm. By simulating complex environments with varying map sizes, obstacle proportions, and shapes, the results demonstrate that the path planning task allocation ratio can actively reach [0.95, 1.05] under different residual power state parameters. Under identical residual power state parameters, the proposed algorithm actively reduces the maximum task deviation by 80% and the standard deviation by 80.02% compared to the DARP algorithm. In the initial position deployment optimization for multiple robots, the proposed method actively decreases the maximum number of turns by 22.86% compared to random search, significantly reduces the total number of turns, and maintains the standard deviation of the total path cost below 2.53. The algorithm effectively enhances the connectivity of region division and task balance while actively reducing the energy consumption of the multi-robot system.