Mathematical modelling and simulation of variable morphing multi-body AUVs for underwater structure maintenance

Achieving both stability and adaptability is a central challenge for multibody autonomous underwater vehicles (AUVs) operating in complex marine environments. This paper develops a unified mathematical modelling framework that integrates hydrostatic regulation and morphological reconfiguration. Three mechanisms are formulated: buoyancy adjustment for quasi-static equilibrium control, aperture-angle variation for dynamic angular morphing, and linkage-length modulation for geometric–spatial morphing. Numerical simulations based on the derived nonlinear dynamics evaluate their effects under roll disturbances. Results show that compact morphs yield rapid but oscillatory recovery, extended morphs enhance stability at the cost of slower convergence, and intermediate settings provide balanced performance. Phase-space trajectories and posture recovery diagrams confirm the distinct yet complementary roles of the three mechanisms. The study paves the way for the dynamics analysis and control of variable-morphing multibody systems, offering insights into stability–adaptability trade-offs and providing a foundation for future work on fluid–structure interaction, optimization, and digital-twin applications in underwater robotics. • Developed Variable Morphing Multi-body AUVs (VMMAUVs) with dynamic structural adaptation capabilities. • Integrated three complementary mechanisms: buoyancy adjustment, aperture-angle variation, and linkage-length modulation. • Demonstrated enhanced stability and adaptability through comprehensive numerical simulations. • Established unified framework combining hydrostatic regulation and morphological reconfiguration. • Validated control strategies for underwater structure maintenance applications.