Abstract
During constant-force operations in complex marine environments, underwater manipulators are affected by hydrodynamic disturbances and unknown, time-varying environment stiffness. Under classical impedance control (IC), this often leads to large transient contact forces and steady-state force errors, making high-precision compliant control difficult to achieve. To address this issue, this study proposes a Bayesian recursive least-squares-based fuzzy adaptive impedance control (BRLS-FAIC) strategy with displacement correction for underwater manipulators. Within a position-based impedance-control framework, a Bayesian Recursive Least Squares (BRLS) stiffness identifier is constructed by incorporating process and measurement noise into a stochastic regression model, enabling online estimation of the environment stiffness and its covariance under noisy, time-varying conditions. The identified stiffness is used in a displacement-correction law derived from the contact model to update the reference position, thereby removing dependence on the unknown environment location and reducing steady-state force bias. On this basis, a three-input/two-output fuzzy adaptive impedance tuner, driven by the force error, its rate of change, and a stiffness-perception index, adjusts the desired damping and stiffness online under amplitude limitation and first-order filtering. Using an underwater manipulator dynamic model that includes buoyancy and hydrodynamic effects, MATLAB simulations are carried out for step, ramp, and sinusoidal stiffness variations and for planar, inclined, and curved contact scenarios. The results show that, compared with classical IC and fuzzy adaptive impedance control (FAIC), the proposed BRLS-FAIC strategy reduces steady-state force errors, shortens force and position settling times, and suppresses peak contact forces in variable-stiffness underwater environments.