Motion Modeling and Path Optimization of Amphibious Spherical Robots Based on Unit Quaternions and Fuzzy Control

This paper proposes a motion modeling and path optimization method based on unit quaternions and fuzzy control for amphibious spherical robots. An adaptive spherical robot capable of walking on land and propelling underwater is designed, with compressed gas used to achieve diving and surfacing. Four OpenMV vision sensors are integrated to construct an underwater target recognition system, and an attitude interpolation algorithm based on unit quaternions is established to overcome the singularity problem inherent in Euler angle descriptions. A quaternion-based trajectory interpolation algorithm is combined with PID control for multi-degree-of-freedom underwater motion tracking. The fuzzy adaptive and PSO multi-objective optimization modules were integrated to enhance the adaptability in multi-constraint scenarios. The pool experiments demonstrated the basic feasibility of circular trajectory tracking and dynamic target recognition under controlled conditions, while robustness against hydrodynamic perturbations is primarily supported by simulation and requires further hardware validation.