Lagrangian-based modeling and safety-critical controls for Stewart platforms under marine operations

Abstract

The operation of waves, winds, and ocean currents that affect ships or marine vehicles poses a number of challenges for systems that require balance. To address this issue, this study introduces a 6-degree-of-freedom parallel robot Stewart platform erected on the ship deck to isolate vibrations. First, Lagrangian-based modeling is applied to the ship-mounted Stewart platform. Unlike previous systems that are based on Kane's method or Newtonian mechanics, the Lagrangian-based approach does not require a large number of tedious mathematical transformations; instead, it can be generated by a computer. Because of the complexity of the simulation model, the control design model is simplified from the original. Following that, the Control Lyapunov Function (CLF) is employed to achieve zero convergence and the stabilization of the state errors. To ensure operational safety, the Quadratic Program (QP) problem takes into account the Control Barrier Function (CBF) and Exponential Control Barrier Function (ECBF) constraints. The controllers are equipped with High-Gain Disturbance Observation (DOB). Finally, the Lagrangian-based model is validated by comparison with the MATLAB Simscape Multibody platform. In addition, the performance of the proposed control strategies is analyzed.