Single-Beam Sonar Motion Deformation Compensation and Localization Method for Underwater Robots in Confined Waters

In confined waters such as cylindrical aquaculture cages and ponds, underwater robots for cleaning, harvesting and other tasks that use single-beam mechanical scanning sonar for positioning and navigation are susceptible to multipath interference in complex water environments. Meanwhile, under extreme sea conditions, the severe attitude swaying of the robot and the slow-scanning characteristic of the sonar superimpose on each other, causing range stretching and helical deformation of the acoustic point cloud. To address these problems, this paper analyzes the deformation mechanism of single-beam sonar and proposes a spatiotemporal joint deformation compensation and localization-mapping method. First, an attitude-derived probabilistic confidence model is introduced as a lightweight robustness safeguard to characterize the geometric reliability of sonar echoes and reduce the contribution of low-confidence measurements during subsequent registration. Second, a beam-level spatiotemporal joint de-deformation algorithm is designed: the slant range in polar coordinates is flattened to eliminate nonlinear swaying deformation, and a beam-level displacement back-estimation based on the beam time offset and feedback velocity is employed to remove helical misalignment, thereby enhancing the underlying correction capability for dynamic deformation processes. Finally, a lightweight SLAM architecture that integrates keyframe-based dynamic sub-maps is constructed, where a confidence-weighted ICP is used to estimate the planar position with the heading provided by the compass and provide velocity-based closed-loop feedback, effectively mitigating the problem of global matching divergence caused by underlying dynamic deformations. Real-data-driven semi-physical disturbance tests based on measured pool data show that, under the injected ±45° roll disturbance and translational drift, the proposed method reduces the maximum point-to-reference error MaxAE from 1.059 m to 0.098 m. The reported mean internal registration residual decreases from 0.275 m for the traditional navigation odometry SLAM to 0.158 m for the proposed method, corresponding to a numerical reduction of approximately 42.5%. Under the evaluated conditions, the proposed method effectively mitigates point-cloud deformation and registration instability caused by robot swaying and slow-scanning sonar, while confidence weighting is retained as an auxiliary robustness mechanism for handling low-confidence correspondences.