In an attempt to address the limitations of single function and the poor process flexibility of existing friction stir welding equipment, a new friction stir welding robot has been developed to address practical problems in three-dimensional surface welding. Based on an analysis of the components of the robotic system, a kinematics model was established, and the forward and backward kinematics solutions were derived for the robot. An iterative nearest point algorithm, iterative closest point based on point cloud matching, was used to plan the welding trajectory for the most complex petal welding conditions, and an experimental study was conducted. The results show that the kinematic and dynamic test results were consistent with the acquired simulation curves for specific sizes of the rocket cap flaps under appropriate welding conditions. The normal error of the weld was less than 85 µm, the average tensile strength was 359 MPa, and the elongation was 7.20%, 78.0%, and 72.0% of 2A14-T6 aluminum alloy. The friction stir welding robot exhibited robust performance, and the proposed trajectory planning method is practical and effective. The appearance, geometric dimension, and mechanical properties of the weld achieved the expected criteria, and high-precision welding of large complex thin-walled surfaces is possible.