Unmanned Helicopter Control via Visual Servoing with Occlusion Handling - Visual Servoing via Advanced Numerical Methods - page 352

Fig. 19.3 Coordinate
frames. The world reference
frame and the helicopter co-
ordinate frame are denoted
by Σ

Side view Front view

b , respectively.
The origin of the z w

w

and Σ

axis is

set on the ground

19.3 Coordinate Frames

w

be the world reference frame. The z w

Let Σ axis is directed vertically downward.

The origin of the z w

b

axis is set on the ground. A coordinate frame Σ is attached to

the helicopter body as illustrated in Figure 19.3. The ( x b y b z b ) positions of the four

, ,

b

black balls in the frame Σ are given by

⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤

. − . . − .

0 1 0 1 0 1 0 1

⎣ ⎦ , ⎣ ⎦ , ⎣ ⎦ , ⎣ ⎦ .

0 . 1 0 . 1 − 0 . 1 − 0 . 1

(19.1)

0 . 04 0 . 04 0 . 04 0 . 04

Let ξ 4( i − 1)+ j denote the position of ball j in the image plane of camera i .The

helicopter position relative to the world reference frame

w

Σ is denoted by ( x , y , z ).

The roll, pitch and yaw angles are denoted by ψ , θ and φ , respectively. The vector

of generalized coordinates of the helicopter is defined by
q = xyz

φ

. (19.2)

Recall that the helicopter has a horizontal-keeping stabilizer. Both the angles θ and

ψ converge to zero fast enough even when the body is inclined. Thus we may sup-

pose in practice that

θ ( k )=0and ψ ( k )=0 , ∀ k ≥ 0 . (19.3)

The following four variables are individually controlled by control signals sup-
plied to the transmitter (see also Figure 19.3):