## 2 Trajectory Tracking  
Precise tracking of the trajectory during maneuvering is very important, especially for an autonomous multi-purpose water platform [22; 23] engaged in hydrographic survey missions of restricted access areas like ports, embankments, anchorages, bays and lakes, and rivers. Generally, in such areas, maneuvering requires execution of precise, previously planned track information. Additionally, in any difficult navigational situation such as caused by recreational boats and other traffic, precise execution of the planned or preplanned track becomes crucial. The evaluated track following method, termed guidance logic, was designed originally for aerial applications [24] and unmanned aerial vehicles (UAVs) and was successfully implemented in many UAV applications [24; 25; 26]. This approach is also used by small unmanned surface vessels [27; 28; 29]; however, the platforms applied in that research are significantly smaller than the platform used in the present work. Studies on autonomous navigation algorithms and navigation strategies have been reported [30; 31; 32] while interesting studies for an adaptive system for steering strategy are available [33; 34; 35]. Aspects on the safety of vehicle navigation have been discussed [36; 37; 38] while actual problems concerning control of trajectory tracking for marine vehicles have also been reported [2; 39; 40; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21]. An outline of the steps and the computer programing methods used for trajectory tracking is given in Figure 1. Implementation follows that of a previous study [41] and where the mission control module is similar to a system described elsewhere [22]. This algorithm requires a frequency of 50 Hz (method name: update), meaning that the update method is used 50 times per second. The method is activated only in automatic mode, meaning that only the automatic modes Auto, Guided, Return to Dock (RTD), and Smart RTD use this method. The automatic modes make use of all navigation sensors, and valid sensors readings are compulsory for automatic mode activation. Any missing sensors' data are unable to activate this function. Moreover, the Auto mode requires a programmed route (route plan), the RTD mode requires a dock (home) position and a saved travelled route to perform smart RTD, and the Guided mode requires a desired point location. All data are provided in the form of geographical waypoints (WPs). The update method uses, in order, the following methods:  
* Steering WP--the basic route plan and vehicle destination. The method provides the location that the vehicle should achieve (destination). * NLG controller--the method where the navigation process is implemented. The method, based on destination and vehicle origin, calculates the lateral acceleration. * Steering LA--the method, based on the PID (proportional-integral-derivative) controller, calculates the steering output. * Set Steering--the method converts the steering output to the appropriate navigation controller output signal. The output signal (PWM: Pulse-Width Modulation) is the electrical signal interpreted by the electric motor's controller and the rudder's linear actuator controller. All the methods enumerated above participate in trajectory tracking and have been tuned separately during the platform development and validation process. The guidance logic [24] selects the desired point on the planned trajectory and generates a lateral acceleration (\(a_{s}\)) using this point, in accordance with following formula:  
\[a_{s}=2\frac{V^{2}}{L_{1}}\sin\eta \tag{1}\]  
Figure 1: Trajectory tracking algorithm scheme. where the desired point is on the planned track at distance \(L_{1}\) from the actual origin of the vehicle (Figure 2).