Currently, most wheel-legged robots need to complete the switching of the wheel-and-leg modal in a stationary state, and the existing algorithms of statically switching the wheel-leg modal cannot meet the control requirements of multimodal switching dynamically for robots. In this paper, to achieve efficient switching of the wheel-and-leg modal for a quadruped robot, the novel transformable mechanism is designed. Then, a multimodal coordination operation control framework based on multiple algorithms is presented, incorporating the minimum foot force distribution method (algorithm No.1), the minimum joint torque distribution method (algorithm No.2), and the method of combining the single rigid body dynamic model with quadratic programming (algorithm No.3). In the process of switching wheel-leg modal dynamically, the existing algorithm No.3 is prone to produce the wrong optimal force due to the change of the whole-body rotational inertia. Therefore, an improved algorithm No.1 and algorithm No.2 are proposed, which do not consider the change in the body’s inertia. The control effects of the three algorithms are compared and analyzed by simulation. The results show that algorithm No.3 can maintain a small error in attitude angle and speed tracking regardless of whether the robot is under multilegged support or omnidirectional walking compared to the other two algorithms. However, proposed algorithms No.1 and No.2 can more accurately track the target speed when the robot is walking with wheels raising and falling. Finally, a multi-algorithm combination control scheme formulated based on the above control effects has been demonstrated to be effective for the dynamic switching of the wheel-and-leg modal.