Abstract: The underwater snake robot is a new type of unmanned underwater vehicle inspired by biology. The rigid-soft snake robot is a modular swimming robot driven by rigid propulsions and soft joints. This paper takes the robot as the research object, first, the soft joint is modeled as a flexible universal joint, and then the two types of modules with large physical characteristics differences can be jointly modeled. A rigid-soft unified mathematical model is established, and the static and dynamic characteristics of the robot are evaluated. In addition, snake robot is a typical redundant drive robot, which can use redundant degrees of freedom to complete multi-task control. Therefore, based on the rigid-soft unified model, a task priority control method is established. The trajectory tracking control of both ends of the robot in different situations is simulated with the end position and attitude control as the main task and the base position control as the secondary task. The results show that when the base is fixed and the end moves, the average tracking error of the end is 1.41% in the X direction and 1.02% in the Y direction; When both ends move at the same time, the average tracking error of the end is 0.53% in X direction and 1.64% in Y direction; When the terminal attitude is controlled, the average error of pitch angle is 0.38%, and the average error of yaw angle is 0.14%, which verifies the effectiveness of the controller.