*Article* **Spiral Dive Control of Underactuated AUV Based on a Single-Input Fractional-Order Fuzzy Logic Controller**

**Zhiyu Cui 1,2, Lu Liu 1,2,\*, Boyu Zhu 1, Lichuan Zhang 1,2, Yang Yu 1,2, Zhexuan Zhao 1, Shiyuan Li <sup>1</sup> and Mingwei Liu <sup>1</sup>**


**\*** Correspondence: liulu12201220@nwpu.edu.cn

**Abstract:** Autonomous underwater vehicles (AUVs) have broad applications owing to their ability to undertake long voyages, strong concealment, high level of intelligence and ability to replace humans in dangerous operations. AUV motion control systems can ensure stable operation in the complex ocean environment and have attracted significant research attention. In this paper, we propose a single-input fractional-order fuzzy logic controller (SIFOFLC) as an AUV motion control system. First, a single-input fuzzy logic controller (SIFLC) was proposed based on the signed distance method, whose control input is the linear combination of the error signal and its derivative. The SIFLC offers a significant reduction in the controller design and calculation process. Then, a SIFOFLC was obtained with the derivative of the error signal extending to a fractional order and offering greater flexibility and adaptability. Finally, to verify the superiority of the proposed control algorithm, comparative numerical simulations in terms of spiral dive motion control were conducted. Meanwhile, the parameters of different controllers were optimized according to the hybrid particle swarm optimization (HPSO) algorithm. The simulation results illustrate the superior stability and transient performance of the proposed control algorithm.

**Keywords:** fractional calculus; autonomous underwater vehicle; fuzzy logic control; particle swarm optimization algorithm
