Reference frames

Position and velocity

For position and velocity vectors of the model the ENU (East North Up) reference frame is used.

The controller is using the W (Wind) reference frame as shown in the figure below, y-axis downwind and z-axis up.

The orientation of the kite is expressed with respect to the EX (Earth XSense = North East Down) reference frame.

The KS (kite sensor) reference frame is the sensor-fixed reference frame. The origin is defined by the location where the sensor is mounted. This is a rotating reference frame. Currently, in the simulation, this is equal to the K (kite) reference frame, which is defined as follows:

• x: from trailing edge to leading edge
• y: to the right looking in flight direction
• z: down

Other reference frames are the EG (North West Up), and the SE (small earth) reference frames which is defined in the plane tangential to the half-sphere with a unit radius and the origin at the tether exit point of the ground-station.

Wind direction

The upwind_direction is the direction the wind is coming from. Zero is at north; clockwise positive. Default: -pi/2, wind from west.

Elevation and azimuth

The position of the kite can be described with two angles, the azimuth angle φ and the elevation angle β .The elevation angle is zero when the height of the kite is zero, and 90° when it is at Zenith. Three azimuth angles are used, the azimuth angle in the wind reference frame and $\mathrm{azimuth\_east}$ and $\mathrm{azimuth\_north}$. The azimuth angles in wind reference frame and $\mathrm{azimuth\_north}$ are defined positive anti-clockwise when seen from above, $\mathrm{azimuth\_east}$ is defined positive clockwise when seen from above. In the log file and the system state $\mathrm{azimuth}$ in wind reference frame is used (for KiteUtils 0.8.2 and higher).

Orientation of the kite

For the orientation, either a quaternion or roll, pitch and yaw angles are used. The orientation is defined with respect to the NED (North, East, Down) reference frame. The origin of the Kite reference frame around which it rotates is the centre point defined as $0.5 * (C + D)$ as origin, where C and D are positions of the point masses of the model close to the tips of the wing.

• yaw angle: zero north, clockwise positive as seen from above

Control inputs

see: Reference frames and control inputs

Small earth reference frame

To understand how the control system is working it is necessary to introduce the small earth reference frame. This name is chosen as an analogy to the geographic coordinate system, describing a position on planet earth: It makes clear to the reader that navigation methods, used on earth (like great circle navigation to find the shortest way between two points on the sphere) can also be used to navigate kites. The position of the kite and the ground station are measured in the "Earth Centered Earth Fixed" reference frame. The position of the kite relative to the ground station has to be converted into the "Wind Reference Frame" ($x_w , y_w , z_w$) as shown in Fig. 5.1.

The origin of the wind reference frame is placed at the anchor point of the tether and its $x_w$ axis is always pointing in the direction of the averaged wind velocity. To obtain the coordinates of the kite in the small earth reference frame its position is projected on the unit sphere around the origin of the wind reference frame. Now, the position of the kite can be described with two angles, the azimuth angle φ and the elevation angle β . The movement of the kite in the direction of the tether is determined by the winch controller and can be ignored by the kite controller. The objective of the flight path controller as described in this thesis is to fly the kite on a prescribed trajectory that is adapted to the wind conditions.

In Fig. 5.1 the vectors $x_k, y_k$ and $z_k$ define the body-fixed kite reference frame. In this chapter, the combination of the wing and the kite control unit (KCU) is seen as kite. The $y_k$ axis is defined by the vector from the left to the right wing tip, the $z_k$ axis is pointing downwards from the position of the kite parallel to the upper part of the tether, and the $x_k$ axis is orthogonal to $y_k$ and $z_k$ . The heading angle ψ is the angle between the direction towards zenith and the vector $x_k$ as projected on the tangential plane touching the position of the kite on the half sphere. If tether is not straight, $z_k$ and $z_{SE}$ are not aligned.

Fechner U. A Methodology for the Design of Kite-Power Control Systems. 2016. 212 p. https://doi.org/10.4233/uuid:85efaf4c-9dce-4111-bc91-7171b9da4b77