speed-induced passive depth stabilization in a biomimetic underwater vehicle with a swim bladder

A nonlinear mathematical model describing the vertical motion of a biomimetic underwater vehicle equipped with a swim bladder is developed. For a passive bladder that changes its volume under hydrostatic pressure, the system can achieve depth stabilization through a speed-induced mechanism when the lever-arm geometry (relative positions of the swim bladder and lifting surfaces) is favorable; otherwise stabilization is not possible. Using the Routh-Hurwitz criterion, analytical stability conditions are obtained in closed form, revealing a lower onset speed that is set by a simple coupling between forward speed and geometry. Numerical simulations confirm the theoretical predictions and reveal the dominant loss-of-stability scenarios: loss of effective stiffness at the onset threshold and oscillatory instability when the mixed speed-geometry factor changes sign. The results demonstrate the feasibility of passive swim-bladder-based depth stabilization and provide practical guidelines for selecting the lever arms of the buoyancy and lift forces and operating speeds in autonomous underwater vehicles.