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This study explores an innovative approach to integrating modern technology with traditional culture by replacing human performers with clusters of intelligent unmanned vehicles in the Chinese Lunar New Year bench dragon dance. The primary technical challenge lies in addressing the motion control issues of vehicle clusters moving along and out of an Archimedean spiral trajectory, where the forces and constraints acting on the vehicles during the spiral-in and spiral-out processes are symmetrically distributed. To this end, a geometric–analytical framework is developed to tackle kinematic coordination and collision prediction for connected autonomous vehicle fleets along such paths. A motion control model for the unmanned vehicle fleet, incorporating analytical geometry and recursive relationships, is established, accompanied by the proposal of iterative algorithms and intelligent optimization techniques. These methods are employed to compute the fleet’s positions and velocities, determine the interference moments between the lead and following vehicles, and optimize the minimum pitch for collision avoidance. The simulation results demonstrate that the vehicle fleet maintains a stable formation and trajectory along the Archimedean spiral path with minimal speed variations. The motion control problem of autonomous robots following an Archimedean spiral trajectory addressed in this study exhibits a degree of novelty as no related motion control studies have been identified to date, precluding comparative experiments. This work provides fundamental insights into multi-agent coordination along spiral trajectories, offers practical solutions for spatial optimization in autonomous robotic system operations, and presents a paradigmatic framework for the preservation of intangible cultural heritage through robotic systems equipped with motion planning algorithms. Furthermore, it serves as an inspiration for future research into controlling autonomous robots along complex predetermined trajectories, such as the Archimedean spiral. Full article