A waypoint system consists of a waypoint generator with a human interface.

Waypoints are usually specified using Cartesian coordinates:

Other waypoint properties one may specify are speed, heading, turning radius, etc.

Several algorithms exist to generate a path that the vessel can follow.

When generating paths using waypoints, one often uses straight lines and circle arcs to connect the waypoints, as seen in [tm-fig-waypoints]. The turning radius may also be given as a function of the vessel speed and a maximum rate of turn.

The Line-Of-Sight concept is a geometric principle to set the desired heading towards the next waypoint. In its simplest form, the desired yaw angle is calculated by the formula:

Where \((x_{\mathrm {los}},y_{\mathrm {los}})\) is the position of the waypoint and \(\mathrm {(x,y)}\) the vessels (or vessel reference ) current position. The disadvantage is that the cross-track error is not reduced to zero before the waypoint is reached. Since the cross track error is often the most important error to minimize, an addition to this simple algorithm is needed. One augmentation is to use a yaw reference equal to the bearing from the current position to the intersection of the desired track and the second line as seen in the Figure 2.

The switching to a new waypoint is done when the ship has entered a circle of acceptance.

Other ways to generate reference paths from waypoints may be to use spline or polynomial interpolation methods. These may be utilized in such a way that all the reference signals are continuous, which they are not when using turning circles.

The goal of this dynamic positioning strategy is to maintain a given distance between the vessel and a point P given in the global coordinate system. The position of P ("circle center position") is given by the user as well as the distance R (circle radius) to be maintained between the vessel and P. The reference circle is defined by its center P and its radius R.

This strategy is particularly suitable for cases where the DP vessel has to maintain a constant distance from a given point while the direction of the weather may change.

At each time step, the algorithm updates the heading reference so that the vessel will be given the order to point its bow towards the circle center P. The coordinates of the reference point are updated so that it lays on the circle’s perimeter, while minimizing the distance to the vessel (or the point on the vessel).

Figure 3 shows some possible commanded positions: