*Article* **An Experimental Study on Trajectory Tracking Control of Torpedo-like AUVs Using Coupled Error Dynamics**

**Gun Rae Cho 1,\*, Hyungjoo Kang 1, Min-Gyu Kim 1, Mun-Jik Lee 1, Ji-Hong Li 1, Hosung Kim 2, Hansol Lee <sup>2</sup> and Gwonsoo Lee <sup>3</sup>**


**Abstract:** In this paper, we propose a trajectory tracking controller with experimental verification for torpedo-like autonomous underwater vehicles (AUVs) with underactuation characteristics. The proposed controller overcomes the underactuation problem by designing the desired error dynamics in a coupled form using state variables in body-fixed and world coordinates. Unlike the back-stepping control requiring high-order derivatives of state variables, the proposed controller only requires the first derivatives of the states, which can alleviate noise magnification issues due to differentiation. We adopt time delay estimation to estimate the dynamics indirectly using control inputs and vehicle outputs, making the proposed controller relatively easy to apply without requiring the all of the vehicle dynamics. We also address some practical issues that commonly arise in experimental environments: handling measurement noises and actuation limits. To mitigate the effects of noise on the controller, a filtering technique using a moving window average is employed. Additionally, to account for the actuation limits, we design an anti-windup structure that takes into consideration the nonlinearity between the thrusting force and rotating speed of the thruster. We verify the tracking performance of the proposed controller through experimentation using an AUV. The experimental results show that the 3D motion control of the proposed controller exhibits an RMS error of 0.3216 m and demonstrate that the proposed controller achieves accurate tracking performance, making it suitable for survey missions that require tracking errors of less than one meter.

**Keywords:** autonomous underwater vehicles; robust trajectory tracking; coupled desired error dynamics; time delay estimation
