## 1 Introduction  
Marine transportation has rapidly grown in recent years, and cross-national trade has become more and more frequent. In this context, the maritime transportation industry has substantially facilitated the development of the global economy, while ship intelligence is widely expected to play a central role in improving efficiency [1, 2]. However, with the increasing demand for maritime traffic, the marine environment has become more complex and crowded, which significantly increases the risk of marine traffic accidents. In the meantime, authoritative maritime accident investigations elaborate that human failures cause about 80% of marine accidents [3, 4]. Most intelligent decision-making tools for ships were designed to limit the occurrence of maritime traffic accidents and ensure navigation safety. In particular, the ability to plan a reasonable path while providing emergency decision making is an essential guarantee in ship driving, which is regarded as a core competency of ship intelligence. On this occasion, collision avoidance is also a critical research field for many maritime experts and scholars [5, 6].  
In this paper, the fast marching (FM) method is chosen due to its good performance in both situation modeling and path planning [7, 8], and the collision avoidance problem for ships in complex restricted waters is considered. In general, both static and dynamic obstacles are included in complex restricted waters, which is significantly different from that in open waters [9, 10]. The presence of static obstacles (such as shorelines, islands, etc.) and the limitation of water depth significantly reduce the navigable area. In this situation,the collision avoidance solutions in open waters may lead to a potential risk of conflicting with shorelines or shallows. Frequently used path planning algorithms generate solutions only according to the current situation, which is quite different from human navigators. An experienced ship navigator always makes appropriate decisions in navigation based on reasonable anticipations and inferences. Therefore, it is vital to consider the evolution of the navigational situation when providing collision avoidance paths. The real challenge is to accurately model such evolution.  
To address these issues, a novel collision avoidance path planning method based on FM was proposed, which considers spatial-temporal interaction effects. At the same time, a novel model was introduced to simulate the situation anticipation of human navigators. The main contribution of the proposed path planning method for autonomous ships are as follows: (1) the FM method is used to create a unified obstacle representation model that is specifically designed to describe the path planning space in complex waters; (2) the spatial-temporal interaction effects of dynamic obstacles are considered and integrated into the construction of planning space; and (3) a path optimization technique based on the trajectory prediction of dynamic objects is put forward for improved flexibility.  
The rest of this paper is organized as follows. In Section 2, typical path planning algorithms are reviewed and analyzed. Section 3 describes the flow chart of the path planning approach and the detail of path planning and optimization. Several simulations are conducted in Section 4 to validate the proposed approach. Section 5 concludes this paper and discusses future research.