The burgeoning complexity of space missions has amplified the research focus on robots that are capable of assisting astronauts in accomplishing tasks within space stations. Nevertheless, these robots grapple with substantial mobility challenges in a weightless environment. This study proposed an omnidirectional continuous movement method for a dual-arm robot, inspired by the movement patterns of astronauts within space stations. On the basis of determining the configuration of the dual-arm robot, the kinematics and dynamics model of the robot during contact and flight phases were established. Thereafter, several constraints are determined, including obstacle constraints, prohibited contact area constraints, and performance constraints. An optimization algorithm based on the artificial bee colony algorithm was proposed to optimize the trunk motion law, contact point positions between the manipulators and the inner wall, as well as the driving torques. Through the real-time control of the two manipulators, the robot is capable of achieving omnidirectional continuous movement across various inner walls with complex structures while maintaining optimal comprehensive performance. Simulation results demonstrate the correctness of this method. The method proposed in this paper provides a theoretical basis for the application of mobile robots within space stations.