Uncertainty-Aware Multi-Objective Rendezvous Re-Planning for Marine Vehicles Using a Physics-Based Digital Model

This paper presents a digital-twin-driven methodology for uncertainty-aware rendezvous planning between a mothership and a marine drone operating in time-varying metocean conditions and in the presence of fixed obstacles. The digital twin combines planar maneuvering dynamics, propulsion-efficiency models, and evolving current, wind, and wave fields. Environmental uncertainty is introduced through stochastic perturbations of intensity and direction with respect to nominal forecast values. A multi-objective optimization based on Particle Swarm Optimization (PSO) constructs the Pareto front between mothership energy, drone energy, and rendezvous time, while a visibility-graph-based layer guarantees obstacle avoidance. The work focuses on the two-vehicle problem, regarded as an elementary building block for broader multi-agent recovery missions, so as to analyze in a physically interpretable way the stability of the optimal geometry under uncertainty. On this basis, a periodic re-optimization procedure is introduced, through which open-loop execution is compared with digital-twin-informed replanning under perturbed environmental realizations. The numerical campaign assesses the deterministic advantage with respect to geometric baselines based on centroid and center of mass, as well as the benefit of periodic replanning in terms of energy cost, rendezvous time, and geometric route dispersion, using indicators of homotopy consistency, path dispersion, and rendezvous-point dispersion. The results show that periodic forecast updates preserve the topological congruence of the solutions and, with respect to frozen-plan execution, provide an average reduction of 34% in total energy and 14% in rendezvous time, confirming the potential of the digital twin to support robust and computationally sustainable rendezvous decisions in uncertain marine operations.