## 1 Introduction  
In recent years, Maritime Autonomous Surface Ships (MASS), which have the capabilities of smart sensing, advanced guidance, and autonomous control, have been quickly developed. The advantage of MASS is that they utilize sophisticated sensing, artificial intelligence, and machine learning methods to enable autonomous navigation, which is revolutionizing future maritime transportation [1, 2]. The aim of developing MASS is to relax the toil and pain of sailors and captains, to accomplish autonomous sailing even in hazardous ocean environments. However, currently, sailing safety and efficiency are still critical problems for autonomous control of the MASS. These have attracted great research attention. An MASS is generally equipped with radar, LiDAR, and camera sensors [3], which can detect surrounding mobile objects in real time. It obtains its real-time location and relative location with respect to the shore-side from GPS (Global Positioning System), AIS (Autonomous Identification System) [4], and GIS (Geographical Information Systems) [5]. Based on this information, autonomous motion planning and control are performed by an on-line control and decision system. The autonomous control is a critical problem for an MASS to sail in the dynamic maritime environment. There are two phases of motion plan for an MASS:1. Long-term path planning [6], which considers the optimization of the sailing route or path selection. This long-term route planning is mainly conducted off-line by the ship company, based on the information of the waterway routes and the sailing task information. 2. Short-term motion planning [7], which considers the short-term moving speed and moving direction planning to avoid collisions and to optimize sailing performances. The short-term path planning is mainly conducted by the autonomous ship or by a remote control center in real time based on the on-site situation detected by the MASS's on-board sensing system. The algorithms and methods of long-term motion planning include shortest path algorithms [8] or routing algorithms on graphs [9]. For short-term motion planning, great research attention has been devoted to the investigation of collision avoidance and the navigation of autonomous cars and mobile robots [10; 11]. In this paper, the related works are provided in Section 2, and we focus on the motion planning problem of MASS. There are some differences in short-term motion planning of MASS compared to that of Unmanned Ground Vehicles (UGV). 1. First, the size of MASS is larger, and the hydrodynamic force and the inertia force undertaken by MASS are larger than those of UGVs. The MASS motion cannot respond to the control as agilely as UGVs. This requires the short-term motion planning of MASS to be more predictive to take the latency caused by the inertia and the hydrodynamic forces into consideration. 2. Secondly, AIS (Autonomous Identification System), which provides the location, velocity, size, and type of surrounding ships, has been widely installed on today's vessels. Therefore, the MASS can obtain more information about surrounding agents than UGVs. 3. Thirdly, there is no explicit lane constraint in the waterway; the MASS only needs to guarantee its sailing safety against the shore-side and the other ships. The traffic is also less crowded in waterways than that on roads. As a consequence, the MASS has a larger solution space for sailing speed and direction selection. 4. Fourthly, the MASS must avoid overturning in the water, which requires the MASS to sail smoothly. Due to these differences, an MASS can obtain better surrounding information including information about remote ships. The motion plan has a larger decision space, but needs to be more predictive to tolerate inertia to maintain sailing smoothness. The MASS can conduct both the short-term motion plan and multiple interval motion plan online with more considerations of future impacts, because of the knowledge of remote ships.