Combining Moving Mass Actuators and Manoeuvring Models for Underwater Vehicles: A Lagrangian Approach

TL;DR

The paper addresses accurate dynamic modeling of underwater vehicles with internal moving mass actuators. It develops a generalized vectorial Newton–Euler formulation by extending Fossen's manoeuvring model to include moving-mass dynamics, yielding $\mathbf{M}'\dot{\boldsymbol{\nu}}' + \mathbf{C}(\boldsymbol{\nu}')\boldsymbol{\boldsymbol{\nu}}' = \boldsymbol{\tau}'$ with a coupled Coriolis term $\mathbf{C}'(\boldsymbol{\nu}')=\mathbf{C}(\boldsymbol{\nu}')+\mathbf{C}_P(\boldsymbol{\nu}',\boldsymbol{r}_p)$ and hydrostatics $\mathbf{g}$. Key contributions include decomposing rigid-body and moving-mass matrices into $M_S$, $M_P(\boldsymbol{r}_p)$, and $M_A$, incorporating moving mass position $\boldsymbol{r}_p$ into the dynamics, and validating the model against the Hamiltonian formulation in Woo:02 for a Remus 100 AUV. The study demonstrates how lever-arm choices between $\boldsymbol{r}_g$ and $\boldsymbol{r}_s$ affect torque coupling and dynamic predictions, providing insights for control design. Overall, the framework enables more faithful, energetically efficient maneuvering analyses for AUVs with internal actuators and supports future controller development exploiting the symmetry properties of the moving-mass contributions.

Abstract

In this paper, we present a Newton-Euler formulation of the equations of motion for underwater vehicles with an interntal moving mass actuator. Furthermore, the moving mass dynamics are expressed as an extension to the manoeuvring model for underwater vehicles, originally introduced by Fossen (1991). The influence of the moving mass is described in body-frame and included as states in both an additional kinematic equation and as part of the coupled rigid-body kinetics of the underwater vehicle. The Coriolis-centripetal effects are derived from Kirchhoff's equations and the hydrostatics are derived using first principals. The proposed Newton-Euler model is validated through simulation and compared with the traditional Hamiltonian internal moving mass actuator formulation.

Figures (4)

• Figure 1: Kinematics of marine craft with moving mass in relation to earth-fixed inertial frame.
• Figure 2: The Remus 100 vehicle with moving mass $m_p$ moving along the dotted line. Since $m_s$ is located at the CO, the CG will always be directly between the CO and $m_p$.
• Figure 3: Simulation results of the proposed model compared to that of Woo:02.
• Figure 4: Simulation results of the proposed model compared to that of Woo:02. Close-up of the first 12 seconds of simulation. Initial conditions are zero.