<p>This paper presents a path planning algorithm for a free-floating robotic satellite system equipped with two robotic arms in 4 degrees of freedom. The proposed approach aims to achieve three main objectives: maintain the satellite’s attitude before and after the task, prevent collisions between the robotic arms and the satellite body, and ensure motion within a fully three-dimensional workspace. Since the path planning problem for free-floating robotic satellites involves multiple objectives, the trajectory planning problem is formulated as a multi-objective optimization problem and addressed using particle swarm optimization (PSO). However, conventional single-step PSO suffers from long computation times and difficulty handling several constraints. To overcome these limitations, two-step path planning approach is proposed. In the first step, the end time posture of the system is determined by maximizing manipulability, ensuring that the robotic arm ends in a configuration that allows greater flexibility for trajectory generation. In the second step, an optimal trajectory is generated using PSO under constraints such as collision avoidance, attitude stabilization, and joint velocity limits. The effectiveness of the proposed method is validated through a series of numerical simulations and compared with conventional single-step PSO.</p>