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.
- hp-adaptive Radau method
- Optimal trajectory generation
- Two-point boundary-value problem
- Underwater docking