With the increasing severity of global warming, there is a growing need for eco-friendly vehicles to reduce greenhouse gas emissions. However, the expansion of charging infrastructure is struggling to keep up with the rising number of electric vehicles due to space constraints and installation costs. This paper aims to address this issue by proposing an autonomous driving algorithm for a mobile robot-based movable charging system for electric vehicles, as an alternative to traditional stationary charging stations. Our paper introduces a rule-based path planning algorithm for autonomous robot-based charging systems. To achieve this, we employ the A^* (A-star) algorithm for global path planning towards the charging request position, while utilizing the Dynamic Window Approach (DWA) algorithm for generating avoidance paths around obstacles in the parking lot. The avoidance path generation algorithm differentiates between dynamic and static obstacles, with specific algorithms formulated for each type of obstacle. Finally, we implement the suggested algorithm and verify its performance through simulation.