Singularity-Free Dynamic Equations of AUV-Manipulator Systems

Abstract

In this paper we derive the singularity-free dynamic equations of AUV-manipulator systems using a minimal representation. Autonomous underwater vehicles (AUVs) are normally modeled using the singularity-prone Euler angles, but introducing quasi-coordinates allows us to derive the dynamics using minimal and globally valid non-Euclidean configuration coordinates. This is a great advantage as the configuration space of an AUV is non-Euclidean. We thus obtain a computationally efficient and singularity-free formulation of the dynamic equations with the same complexity as the conventional Lagrangian approach. The closed form formulation makes the proposed approach well suited for system analysis and model-based control. This paper focuses on the kinematic and dynamic properties of AUV-manipulator systems and we present the explicit matrices needed for implementation together with several mathematical relations that can be used to speed up the algorithms. The hydrodynamic and damping forces are also included in the equations. By presenting the explicit equations needed for implementation, the approach presented becomes more accessible and engineers and programmers can implement the results without extensive knowledge of the mathematical background.