Radial-skeleton shape-changing robots are rough-terrain robots and exhibit many advantages in the aspect of mobility, such as excellent terrain adaptability, light weight, good portability, and stable configuration. However, existing gait generation methods are rough and yield low tracking accuracy because the leg-ground contact friction is difficult to predict and control. In addition, no closed-loop control scheme has been proposed for this type of robot. In this study, we designed a 12-legged radial-skeleton robot with a radial expansion ratio of 2.08. Based on the prototype, we proposed a high-precision gait generation algorithm that can be used to any multi-legged radial-skeleton robot and implemented a closed-loop control scheme for accurate path tracking. Combining the contact friction and multi-body dynamics model, the robot prototype exhibits the advantages of omnidirectional motion, high-precision tracking, and motion robustness. By manufacturing a prototype and conducting comparative experiments, we verified that the proposed method yields good performance in terms of trajectory tracking accuracy and robustness in the cases of unknown terrain and interference.