Abstract: 【Objective】 High-precision motion control of unmanned surface vehicles (USVs) during towed-sonar operations is challenging because continuous sonar deployment changes the hydrodynamic characteristics of the vehicle, resulting in time-varying inertia, damping, and maneuvering response. Such variations are particularly detrimental to circular survey missions, which require sustained heading regulation and accurate path tracking. Fixed-gain controllers may therefore become mismatched as the sonar deployment distance and angle vary. To address this problem, an adaptive RBFNN-PID motion-control method is developed by integrating towing-state-dependent hydrodynamic modeling, adaptive circular vector-field guidance, and a two-stage PID tuning architecture combining offline particle swarm optimization (PSO) with online radial basis function neural network (RBFNN) compensation. The method aims to maintain accurate and stable speed, heading, and circular-path tracking under continuously varying towing conditions. 【Methods】 A three-degree-of-freedom MMG-based planar maneuvering model is established for a 6.0-m twin-waterjet catamaran USV. Sonar deployment distance and angle are introduced as quantitative descriptors of the towing condition. Added-mass terms are corrected according to changes in wetted surface area caused by the cylindrical deployment mechanism, while surge, sway, and yaw hydrodynamic derivatives are modified using deployment-dependent correction factors calibrated from computational fluid dynamics simulations. The resulting model describes the principal changes in maneuvering characteristics induced by sonar deployment. It assumes a quasi-static deployment process and neglects transient hydrodynamic effects, towed-body oscillation, fluid-structure interaction, and time-delay effects; consequently, it is primarily applicable to low-speed operation in relatively calm waters.An adaptive circular vector-field guidance law is then developed using an arctangent transition function. When the radial tracking error is large, the commanded direction promotes rapid convergence toward the prescribed circle; as the error decreases, the command smoothly approaches the local path tangent. Because increasing deployment distance and angle degrade turning performance, the convergence gain is designed as a decreasing function of the towing state, thereby reducing aggressive heading commands and suppressing overshoot and oscillation. Lyapunov analysis shows that, under bounded heading-tracking error, the closed-loop path error is uniformly ultimately bounded and converges to a neighborhood of the desired path. Asymptotic stability is obtained when the heading error tends to zero.Separate incremental PID controllers are employed for heading and speed regulation. Representative towing states are defined by deployment distances of 1, 2, and 3 m and deployment angles of 0°, 45°, and 90°. For each operating point, PSO is first used to obtain initial PID parameters by minimizing a performance index incorporating integral time-weighted absolute error, control effort, and overshoot penalties. The resulting parameters are further refined in simulation, and two-dimensional Gaussian surface fitting is subsequently used to construct continuous baseline parameter maps.Online adaptation is performed using a three-layer RBFNN with four inputs—tracking error, error variation, deployment distance, and deployment angle—ten Gaussian hidden neurons, and three outputs corresponding to corrections to K_p, K_i, and K_d. A composite performance index combines the tracking error with an anchoring penalty that restricts excessive deviation from the baseline parameter surfaces. Network weights are updated by gradient descent with momentum. An adaptive learning rate further responds to deployment-state variation and tracking error, enabling faster parameter adjustment when towing conditions change while limiting unnecessary parameter fluctuations. The resulting architecture combines the global operating-condition coverage of offline calibration with local real-time adaptation. 【Results and Discussion】 Comparative simulations are performed under identical vehicle models, disturbances, initial conditions, and a desired speed of 2 m/s. The sonar deployment distance is fixed at 3 m, while the deployment angle varies linearly from 0° to 90°. For a 50-m-radius circular path, the proposed RBFNN-PID method achieves a mean position error of 0.115 m, compared with 1.70 m for fixed-gain PID, 1.10 m for backstepping sliding-mode control, and 0.674 m for PSO-PID. These values correspond to reductions of 93.2%, 87.2%, and 82.9%, respectively. The mean speed and heading errors are 0.0419 m/s and 0.696°, and the steering and propulsion commands exhibit reduced oscillation. Simulations at radii of 30, 80, and 100 m yield mean position errors of 0.19, 0.092, and 0.084 m, respectively, indicating consistent performance over different path curvatures.Field trials are subsequently conducted in open water using the 6.0-m catamaran under sea state 2. The control and data-acquisition frequencies are both 10 Hz, the desired speed is 2 m/s, and the sonar deployment speed is 0.6 m/s. For a 50-m-radius circular path, the steady-state mean position error decreases from 4.603 m with conventional PID to 0.124 m with the proposed method, corresponding to a reduction of 97.3%. The mean heading error decreases from 21.810° to 2.233°, a reduction of 89.8%, while the mean speed error decreases from 0.086 to 0.038 m/s. Additional field trials yield a mean position error of 0.24 m for an 80-m-radius path and no more than 0.46 m for a 30-m-radius path. These results demonstrate that the proposed controller can accommodate deployment-induced variations in maneuvering characteristics and maintain stable circular-path tracking under the tested towing conditions. 【Conclusions】 The proposed method integrates towing-state-dependent hydrodynamic correction, adaptive circular vector-field guidance, and an offline-online PID tuning mechanism to address motion-control degradation caused by continuously varying sonar deployment. Simulation and field results show that the method improves trajectory-tracking accuracy and operating-condition adaptability compared with conventional PID, PSO-PID, and backstepping sliding-mode control, demonstrating its engineering applicability to autonomous circular sonar-survey operations.Two limitations remain. First, the hydrodynamic correction model relies on a quasi-static assumption and does not account for towed-body oscillation or fluid–structure interaction. Second, field trials were limited to sea state 2, and applicability under more severe environmental conditions remains to be validated. Future work will introduce environmental-disturbance observers and extend full-scale validation to a broader range of operating conditions and USV platforms.