T

Sensors & Signal Processing

Vessel Hull

Vessel Hull

Fig. 3. The motion control hierarchy of a marine surface vessel 2.5 Preliminaries

In the missile literature, guidance laws are typically synonymous with steering laws, assuming that the speed is constant. In this work, guidance laws are either directly prescribed as velocity assignments or partitioned into separate speed and steering laws. The guidance laws are first introduced in a 2-dimensional framework, where a kinematic vehicle is represented by its planar position p(i) = [x(t), y(t)]T e R2 and velocity

Low Bandwidth Demand

Intermediate Bandwidth Demand

High Bandwidth Demand

Environment

Fig. 3. The motion control hierarchy of a marine surface vessel 2.5 Preliminaries

In the missile literature, guidance laws are typically synonymous with steering laws, assuming that the speed is constant. In this work, guidance laws are either directly prescribed as velocity assignments or partitioned into separate speed and steering laws. The guidance laws are first introduced in a 2-dimensional framework, where a kinematic vehicle is represented by its planar position p(i) = [x(t), y(t)]T e R2 and velocity v(t) = dp(t) / dt = p(t) e R2, stated relative to some stationary reference frame. Since most of the AUVs of today are of the survey type, they do not need to perform spatially coupled maneuvers, but typically execute temporally separated planar maneuvers either in the horizontal plane or the vertical plane. Thus, Section 3 and 4 are relevant for such applications. Similar considerations justify the work reported in (Healey & Lienard 1993), (Caccia et al. 2000), and (Lapierre et al. 2003).

In Section 5, the planar methods are extended to a 3-dimensional framework, where a kinematic vehicle is represented by its spatial position p(t) e R3 and velocity v(t) e R3 . Results on spatially coupled motion control of AUVs can be found in (Encarnagao & Pascoal 2000), (Do & Pan 2003), (Aguiar & Hespanha 2004), (Breivik & Fossen 2005a), (B0rhaug & Pettersen 2006), and (Refsnes et al. 2008).

Finally, note that all the illustrations of guidance principles employ the marine convention of a right-handed coordinate system whose z-axis points down.

3. Guidance laws for target tracking

In this section, guidance laws for target tracking are presented. The material is adapted from (Breivik & Fossen 2007).

Denoting the position of the target by pt(i) = [xt(t), yt(t)]T e R2, the control objective of a target-tracking scenario can be stated as

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