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Path-Following Control of an Underactuated AUV Using GPS-Based Geometric Error and Threshold-Limited PID

Author(s)

Kai Chen, Shengguo Liang, Xiaoyu Zhao*

Affiliation(s)

Tianjin Hanhai Lanfan Marine Technology Co., Ltd., Tianjin 300457, China *Corresponding Author

Abstract

An underactuated autonomous underwater vehicle (AUV) cannot move laterally under direct control. Its large mass and inertia can lead to overshoot during heading corrections, while GPS positioning noise can cause high-frequency chattering. We propose a PID controller that uses GPS-based geometric error with error thresholding and output limiting, referred to here as threshold-limited PID. Horizontal-plane kinematic and dynamic models were established from the parameters of a 7 m-class vehicle. GPS latitude and longitude were converted to local east-north coordinates. Heron's formula then gave the perpendicular distance to the desired straight-line path, and a vector cross product identified the side of the path occupied by the AUV. The resulting signed error can be calculated without a vehicle model. To reduce unnecessary corrections and chattering caused by small GPS positioning errors, we introduced a 2 m error threshold and reset the stored controller states. Vehicle inertia was addressed by limiting the positional PID heading correction to 30° and adding anti-windup constraints. These constraints work with derivative action, which anticipates error changes and suppresses inertial oscillations, to reduce overshoot and repeated oscillations caused by inertial lag. Comparative MATLAB simulations and lake trials were used to evaluate the controller. In simulation, it eliminated path overshoot relative to conventional PID, improved convergence speed by approximately 43%, and substantially improved steady-state accuracy. For the lake trials, an in-house-developed AUV with X-configured rudders, a length of 7 m, and a mass of 1260 kg followed a four-waypoint piecewise-linear path. Large initial errors decreased rapidly, and the controller accommodated turns between path segments. Errors stayed within the threshold for 86.40% of the operating time. Within this band, the steady-state root mean square error was 0.96 m, indicating submeter steady-state path-following accuracy. Both tests showed rapid convergence and smooth motion with high steady-state accuracy. The controller handles the nonlinear motion and actuation constraints of heavy underactuated AUVs without an accurate dynamic model. This, together with its suitability for real-time embedded implementation, makes it useful for practical path-following tasks.

Keywords

Underactuated AUV; Path Following; GPS-Based Geometric Error; Threshold Filtering; Output-Limited PID

References

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