During recent years, unmanned surface vehicles are extensively utilised in a variety of maritime applications such as the exploration of unknown areas, autonomous transportation, offshore patrol and others. In such maritime applications, unmanned surface vehicles executing relevant missions that might collide with potential static obstacles such as islands and reefs and dynamic obstacles such as other moving unmanned surface vehicles. To successfully accomplish these missions, motion planning algorithms that can generate smooth and collision-free trajectories to avoid both these static and dynamic obstacles in an efficient manner are essential. In this article, we propose a novel motion planning algorithm named the Dynamic Gaussian process motion planner 2, which successfully extends the application scope of the Gaussian process motion planner 2 into complex and dynamic environments with both static and dynamic obstacles. First, we introduce an approach to generate safe areas for dynamic obstacles using modified multivariate Gaussian distributions. Second, we introduce an approach to integrate real-time status information of dynamic obstacles into the modified multivariate Gaussian distributions. The multivariate Gaussian distributions with real-time statuses of dynamic obstacles can be innovatively added into the optimisation process of factor graph to generate an optimised trajectory. We also develop a variant of the proposed algorithm that integrates the international regulations for preventing collisions at sea, enhancing its operational effectiveness in maritime environments. The proposed algorithms have been validated in a series of benchmark simulations and a dynamic obstacle avoidance mission in a high-fidelity maritime environment in the Robotic operating system to demonstrate the functionality and practicability.
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