A comparison of viscous hydrodynamic force models is presented, with application on an autonomous underwater vehicle (AUV). The models considered here are \emph{quasi-steady}, meaning that force is expressed as a function of instantaneous vehicle state. This is in contrast to physical reality, where the force applied to a rigid body moving through a viscous fluid is history-dependent. As a result, the comparison of models is restricted to how well they are able to recreate a force history, rather than how closely they represent the underlying physics. Of the models under consideration, no single model performs significantly better than the others, but several perform worse.

Each viscous hydrodynamic force model presented here is expressed as a linear combination of basis functions, which are nonlinear functions of body-relative velocity. The greater dynamical model is presented in a rigid-body framework with six degrees of freedom, with terms which account for inviscid fluid flow, restoring forces due to gravity, and control forces due to actuator motion. The models are selected from several that have been proposed in the literature, which include empirically-derived and physics-based models. Some models assume that the relationship between force and velocity is fundamentally linear or quadratic in nature, or make assumptions about coupled motion. The models are compared by their relative complexities, and also by their ability to reproduce data sets generated from field experiments. The complete dynamical equations are presented for each model, including coefficients suitable for use with the Virginia Tech 690 AUV.