Abstract This paper continues the previous effort on the development of a trajectory generation platform that assures minimum-control expenditure and collision-free manoeuvre of a torpedo-shaped autonomous underwater vehicle (AUV) into a funnel-shaped stationary docking station (DS). The earlier-developed guidance system was based on the Inverse Dynamics in the Virtual Domain (IDVD) method accounting for AUV’s dynamics and producing a smooth trackable trajectory, thus guaranteeing safe arrival to DS. The optimality of the real-time generated solutions has been assessed via comparing them with the Legendre–Gauss–Lobatto pseudo-spectral (PS) method solutions that could only be obtained off-line. This paper explores a possibility of employing a more advanced hp-adaptive Radau (hp-AR) PS method for the same Hamiltonian two-point boundary-value problem. The considered approach explicitly encapsulates all realistic vehicular and environmental constraints such as the AUV’s dynamics, ocean current disturbances, no-fly zones, and DS pose while minimizing the vehicle’s controls expenditure and permitting precise manoeuvring into DS. The performance evaluation of the hp-AR PS based optimization routine is carried out through extensive software-in-the-loop simulations. For completeness, computational effectiveness and solution optimality of the trajectory generator engine based on the hp-AR method is compared with two other well-known PS methods based on Legendre and Chebyshev polynomial approximation. The results of this study show the superb performance of the hp-AR method-based trajectory generator among all other PS methods and a possibility of using it along with IDVD in the real-time implementation.

中文翻译：

---

hp-adaptive Radau赝谱方法用于AUV最小努力无碰撞对接操作的可行性分析

摘要 本文延续了之前开发轨迹生成平台的努力，该平台可确保鱼雷形自主水下航行器 (AUV) 进入漏斗形固定坞站 (DS) 的最小控制开销和无碰撞机动。早期开发的制导系统基于虚拟域中的逆动力学 (IDVD) 方法，考虑 AUV 的动力学并产生平滑的可跟踪轨迹，从而保证安全到达 DS。实时生成的解的最优性已通过将它们与只能离线获得的勒让德-高斯-洛巴托伪谱 (PS) 方法解进行比较来评估。本文探讨了对相同的哈密顿两点边值问题采用更先进的 hp 自适应 Radau (hp-AR) PS 方法的可能性。所考虑的方法明确封装了所有现实的车辆和环境约束，例如 AUV 的动力学、洋流扰动、禁飞区和 DS 姿势，同时最大限度地减少车辆的控制支出并允许精确机动进入 DS。基于 hp-AR PS 的优化例程的性能评估是通过广泛的软件在环模拟进行的。为了完整性、计算效率和基于 hp-AR 方法的轨迹生成引擎的最优解，将与基于 Legendre 和 Chebyshev 多项式逼近的另外两种众所周知的 PS 方法进行比较。