A Six-Degree-of-Freedom Wave Compensation Parallel Robot with Triple-Loop Fractional-Order PI Control Optimized by Tuna Swarm Optimization

For high-precision attitude adjustment tasks of a six-degree-of-freedom (6-DOF) wave-compensation parallel robot in shipborne applications, strong non-stationary wave excitations, abrupt load changes, and broadband disturbances jointly challenge tracking accuracy and smoothness. To address these challenges, this paper proposes a tuna swarm optimization (TSO)-tuned triple-loop Fractional-Order PI control strategy (TSO-FOPI). The proposed approach combines TSO-based offline parameter tuning with a triple-loop FOPI control structure to improve compensation accuracy and robustness, and a closed-loop stability analysis is provided. Power spectral density analysis under swept-frequency excitation indicates that TSO-FOPI effectively suppresses residual vibrations of the robot in the dominant wave-frequency band and achieves better wideband disturbance rejection against injected high-frequency perturbations. Furthermore, under random wave excitation corresponding to sea state 4, the proposed control strategy reduces the overall compensation error by about 59% and 36.4% compared with PI and FOPI controllers, respectively, and improves the overall compensation smoothness by about 65% and 30.25%. In summary, the proposed method shows potential for engineering implementation for high-precision motion control of 6-DOF wave-compensation parallel robots and onboard precision equipment in disturbance-intensive environments.