**2.1.2 Navigation**

The navigation system addresses the task of determining the current state of the vehicle. For surface, land and airborne vehicles, global positioning system (GPS) is readily available and is often used to provide continuous accurate positioning information to the navigation system. However, due to the extremely limited propagation of these signals through water, GPS is largely unavailable for underwater vehicles. The task of the navigation system is then to compute a best estimate of the current state of the vehicle based on multiple measurements from other proprioceptive and exteroceptive sensors, and to use GPS only when it is available. This is completed by using some form of sensor fusion technique, such as Kalman filtering or Particle filtering (Lammas et al., 2010, 2008), to obtain a best estimate of the current operating condition, and allow for inclusion of a correction mechanism when GPS is available, such as when the vehicle is surfaced. Overall, the task of the navigation system is to provide a best estimate of the current state of the vehicle, regardless of what sensor information is available.

Fully Coupled 6 Degree-of-Freedom Control of an Over-Actuated Autonomous Underwater Vehicle 151

these different reference frames for different purposes, the process of transforming

Within the context of control systems, the two main reference frames used are the n-frame and the b-frame. Both contain three translational components and three rotational components, yet the origin of each frame differs. This difference in origin can lead to useful

The n-frame is a co-ordinate space usually defined as a plane oriented at a tangent to the Earth's surface. The most common of these frames for underwater vehicle control design is the North-East-Down (NED) frame. As its name suggests, the three axes of the translational components of this frame have the *x*-axis pointing towards true North, the *y*-axis pointing towards East, and the *z*-axis in the downward direction perpendicular to the Earth's surface. In general, waypoints are defined with reference to a fixed point on the earth, and therefore

The b-frame, also known as the body frame, is a moving reference frame that has its origin fixed to the body of a vehicle. Due to various properties that exist at different points within the body of the vehicle, it is convenient to place the origin of this frame at one of these points to take advantage of, for example, body symmetries, centre of gravity, or centre of buoyancy. As a general rule, the *x*-axis of this frame points from aft to fore along the longitudinal axis of the body, the *y*-axis points from port to starboard, and the *z*-axis points from top to bottom. Due to the orientation of this frame, it is appropriate to express the

As mentioned in 2.3.1, both the NED and body frames have properties that are useful for underwater vehicle control design. Because both are used for different purposes, a means of converting information from one frame to the other is required. The kinematic equation, (1),

Here, the 6 degree-of-freedom (DoF) position and orientation vector in (1), decomposed in

[ ] *<sup>n</sup> <sup>T</sup>*

*<sup>T</sup> <sup>n</sup>*

) (1)

<sup>=</sup> <sup>⎡</sup>*<sup>p</sup>* Θ⎤ <sup>⎣</sup> <sup>⎦</sup> (2)

*n nn p* = *x y z* (3)

η = *J*(η υ

η

and the three orientation components, also known as Euler angles, are given in (4).

Within (2), the three position components are given in (3),

properties which contain certain advantages when designing a control system.

it is convenient to conduct guidance and navigation in this frame.

information from one frame to another must be conducted.

**2.3.1 Frames of reference** 

**2.3.1.1 N-Frame** 

**2.3.1.2 B-Frame** 

velocities of the vehicle in this frame.

achieves this task (Fossen, 1994, 2002).

the NED frame, is denoted by (2).

**2.3.2 Kinematic equation** 
