In this study an innovative parameterized water-bomb wheel modeling method based on recursive solving are introduced, significantly reducing the modeling workload compared to traditional methods. A multi-link supporting structure is designed upon the foundation of the water-bomb wheel model. The effectiveness of the supporting structure is verified through simulations and experiments. For robots equipped with this water-bomb wheel featuring the multi-link support, base on the kinematic model of multi-link structure, a mapping algorithm that incorporates parameterized kinematic solutions and IMU-fused parameterized odometry is proposed. Based on this algorithm, SLAM and autonomous navigation experiments are carried out in simulation environment and real environment respectively. Compared with the traditional algorithm, this algorithm the precision of SLAM is enhanced, achieving high-precision SLAM and autonomous navigation with a robot error rate below 5%.