Dynamic modeling and robust control for underwater vehicles by using dual quaternions

A novel representation using dual quaternions for the dynamical model of underwater vehicles is presented. Dual quaternions are developed for terms such as inertia, added mass, Coriolis, damping, gravitational forces, and control inputs. To demonstrate the model's applicability, a particular dynamic model is obtained fora 4DOF underwater vehicle from BlueRobotics. Based on this model, three control strategies were developed: PD control with gravity compensation (PD+G), a robust PD controller with a first-order filter, and an adaptive nonsingular sliding mode control. These control methods were chosen to facilitate a comprehensive comparison and evaluation of their performance across two different scenarios. Additionally, the closed-loop system stability for each control is rigorously analyzed, and three theorems are presented. Numerical examples demonstrate the effectiveness of the control strategies and the dual quaternion-based model. Simulation results showed that the controller based on sliding mode exhibits superior performance compared to the other controllers. Finally, the results showed that the dual quaternion representation eliminates singularities in Euler angles and offers amore compact and general structure for rotations and translations compared to previous methods.