# Estimating Critical Latency Affecting Ship's Collision in Re-Mote Maneuvering of Autonomous Ships
## 4 Results
### Estimated Performance Evaluation of Critical Latency
#### 4.3.1 Evaluation of Estimated Performance  
The evaluation results of the estimated performance were described in the order from Scenario 4 with the largest encounter bearing to Scenario 1 with the smallest encounter bearing. Figure 11 explains the estimated results for Scenario 4 (encountering angle of 135), given the initial conditions as follows; OS-TS initial relative distance of 2925 m, initial speed of both vessels v1 (2.57 m/s). Figure 9: Average value of estimated critical latency for four scenarios: (**a**) Scenario 1; (**b**) Scenario 2; (**c**) Scenario 3; (**d**) Scenario 4. Figure 11a shows the collision points estimated by the OS-TS encounter and critical latency. The solid-black, -blue, and -red lines represent the designed route of the OS (000\({}^{\circ}\) of heading), the designed route of the TS (315\({}^{\circ}\) of heading), and part of the turning circle, respectively. In addition, O, T, M, and C represent OS initial position, TS initial position, OS-TS collision position caused by turning maneuver of OS, and OS-TS collision position caused by designed route, respectively. S\({}_{\text{OS}}\) and S\({}_{\text{TS}}\) represent the turning start positions of the OS and TS, respectively. Figure 11b shows the estimation result of the time of collision point C. If time t = 0 marks the start of the turn, then the relative distance at t = 0 for the DR and TC should be the same. The black and blue lines represent the OS-TS relative distance RD_DR by the designed path and the generated OS-TS relative distance RD\({}_{\text{TC}}\). RD\({}_{\text{TC}}\) seems to converge to 0 at point C (24.38 min). Figure 12 relates to Scenario 3 (encountering angle of 90), given the initial conditions as follows. Figure 10: Estimation error of critical latency for each of six vessel speeds and seven rudder angles: (**a**) error for six vessel speeds in four scenarios; (**b**) error for seven rudder angles in four scenarios. OS-TS initial relative distance of 3095 m, initial speed of both vessels 1 (5 knots). The descriptions and the meaning of the symbols in Figure 12 are the same as in Figure 11. In Figure 12a, two collision points of OS-TS are shown. In Figure 12b, the OS-TS relative distance RD\({}_{\text{TC}}\) appears to converge at points M (11.21 min) and C (18.26 min), and the OS-TC relative distance RD\({}_{\text{DR}}\) appears earlier at point M than point C appears to be. Figure 13 relates to Scenario 2 (encountering angle of 45), given the initial conditions as follows. OS-TS initial relative distance of 33,265 m, initial speed of both vessels v1 (5 knots). The descriptions and the meaning of the symbols in Figure 13 are the same as in Figure 11. In Figure 13a, two collision points of OS-TS are shown. In Figure 13b, OS-TS relative distance RD\({}_{\text{DR}}\) is shown to converge at 0 (zero) at Points M (10.82 min) and C (15.02 min), and it is shown to appear earlier at Point M than at Point C.  
Figure 14 relates to Scenario 1 (1-degree head-on situation), given the initial conditions as follows. Figure 12: Estimation results for Scenario 3 (encountering angle of 90): (**a**) OS-TS encounter and collision points; (**b**) Estimation of the OS-TS relative distance and the time at collision Points C and M over time. Figure 13: Estimation results for Scenario 2 (encountering angle of 45): (**a**) OS-TS encounter and collision points; (**b**) Estimation of the OS-TS relative distance and the time at collision Points C and M over time. OS-TS initial relative distance of 901 m, initial speed of both vessels v1(5 knots). The descriptions of Figure 13(a),b are the same as in Figure 11. In Figure 13(a), two collision points of OS-TS are shown. As the encounter relative bearing in Scenario 1 is 1 degree, which is smaller than the previous three scenarios, the three points (S, M, and C) are shown to assemble near each other.