Modeling with Symmetry Constraints and Symmetry-Breaking Effects on the Vertical and Yaw Dynamics of a Miniature Underwater Vehicle

This paper presents a symmetry-centered analysis of the vertical and yaw dynamics of a low-cost miniature underwater vehicle. Rather than treating the platform only as a control problem, the study formulates the vehicle behavior as a consequence of geometric, hydrostatic and actuation symmetry, as well as of controlled symmetry-breaking effects. A six degrees of freedom (DOF) model is used as the general dynamic description, and reduced subsystems for heave–pitch, yaw and surge are discussed. The proposed contribution is an asymmetry-aware framework that relates ballast imbalance, center-of-gravity displacement, pump mismatch and thruster imbalance to measurable quantities such as vertical positioning error, pitch deviation and yaw drift during immersion. A quantitative geometric-dynamic asymmetry index is proposed to compare nominal symmetric and asymmetric configurations. Experimental information available from the ballast characterization is incorporated. The proposed framework is evaluated through preliminary numerical simulations comparing one nominal symmetric configuration and four controlled symmetry-breaking scenarios. Numerical results demonstrate that structural mass offsets (C1, C2) induce a steady-state attitude error of Δθ=4.2∘ and a parasitic yaw drift of Δψ=2.8∘. Furthermore, transient fluidic ballast imbalances C3 generate a peak asymmetry index of A(t)=0.42, triggering maximum transient tracking deviations up to 8.5∘. These quantitative findings demonstrate that the proposed index provides a highly sensitive and reliable diagnostic indicator. The proposed framework can support symmetry-aware design, calibration and control of small underwater robotic vehicles.