# Estimating Critical Latency Affecting Ship's Collision in Re-Mote Maneuvering of Autonomous Ships
## 1 Introduction  
Estimation of critical latency that can cause a ship's collision in remote maneuvering of autonomous ships can provide a clue to avoid collisions. The autonomous ship refers to the Maritime Autonomous Surface Ships (MASS) as defined by the International Maritime Organization (IMO) [1, 2]. MASS is divided into four levels, depending on the level of control performance, from Level 1 to Level 4. Level 1 is the control level of the existing ship; Level 2 is the level of the existing ship combined with automatic controls; Level 3 is almost entirely an autonomy degrees; Level 4 is the fully autonomy degrees [3, 4, 5]. Currently, most MASS research is conducted at Levels 2 to 3 [6, 7, 8, 9]. Remote maneuvering is included in the second or third level of MASS, which refers to the remote control of ships by a remote operator using a communication network (i.e., long-term evolution network, very high frequency, or very small aperture terminal (V-SAT)) in locations other than MASS (i.e., other ships/coasts) [3, 4, 5, 6, 7, 8]. In this remote maneuvering, it is known that various types of latency can be caused due to various environments (i.e., loss and delay of communication, failure and delay of control signal processing, and human factors) [4, 5, 6, 7, 8, 9]. In addition, latency is known to affect ship collisions, and latency is required to be minimal [3, 4]. However, the minimum value of the required latency and the effect of the latency on collisions have never been reported [3, 4]. Critical latency refers to a specific latency where if a vessel is remotely maneuvered, it may cause the own ship and target to collide with various latencies. Ship collision avoidance is mainly conducted by turning maneuvers under Convention on the International Regulations for Preventing Collisions at Sea (COLREGs) [10]. COLREGs are a set of rules enacted by the IMO in 1972. The rules were recommended for the operation of marine ships and decisions for the give-way and stand-on vessels in eachencountering situation as well as the desired evading direction to prevent collisions. The collision avoidance action of ships is mainly performed by turning maneuver using the rudder, and the rudder angle applied in turning maneuver is determined by referencing the turning circle [11]. The turning circle refers to the ship's turning maneuver characteristic, which is the trajectory of the own ship formed when the ship turns once with a given rudder angle and is usually in the form of a circle with a certain radius. Ship collisions may be considered to occur in two cases as follows; one is due to failure in performing the turning maneuver based on COLREGs, and the other is due to other causes that occur even though the turning maneuver based on COLREGs was performed. Among the latter causes, the most influential cause is reported to be human errors courtesy of the crew [12; 13; 14; 15], which is mainly affected due to the nonlinear properties of turning circles [16; 17; 18; 19; 20; 21]. The factors for nonlinearity that occur when a ship moves are characterized by the nonlinearity of the free surface and the nonlinearity of the shape of the object. Even when drawing a circle while moving a ship, non-linearity must be considered, and data such as speed and angle such as development or change of turning motion appear. In addition, the latter cause is also due to critical latency when remote maneuvering is considered [22; 23; 24; 25]. In the ship collision situation, the focus is on determining the avoidance action at the minimum distance to avoid collision [26], and the avoidance action to be implemented at the minimum distance is related to the ship domain and situation [27; 28; 29]. Moreover, when OS and TS closely approach each other, the probability of collision is high, and when it invades the other's ship domain, action to avoid collision should be evaluated [15; 30].