The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B5. Beijing 2008 
3. THE SIMULATION ENVIRONMENT 
In order to evaluate in advance the main issues related with the 
development of an autonomous guidance system for our 
unmanned model helicopter, we decided to build a simulation 
software with Simulink, a Matlab programming environment 
based on the block scheme algebra. The main goal of this 
approach was to define and to tune the set of servos needed for 
the helicopter control, avoiding any possible damage of the 
system components caused by a trial and error approach in a 
real environment. In order to reliably simulate the dynamics of 
our small-size helicopter, we took into account the effects of 
following components: main rotor, tail rotor, aerodynamic drag 
(wind effect) generated by the fuselage, horizontal and vertical 
fin. To this aim we considered four main servos: the collective 
pitch control, the cyclic stick, the collective stick and the 
throttle. The whole block scheme implemented in Simulink is 
summarized in figure 4. Here the first block models the 
helicopter servos which are input into the second block, the 
dynamic model. In turn, this block outputs translational 
acceleration and angular velocity, related to the body frame, and 
position and attitude in the inertial frame, which are then fed 
into the measurement sensor block. Here noise is added in order 
to better simulate the real behaviour of the GPS, IMU and earth- 
magnetic sensors. The output of this block represents the (noisy) 
state of the system which is evaluated by an Extended Kalman 
Filter (fourth block). Afterthat, the output of the filter is 
compared with a reference trajectory in order to determine again 
the values fo the servos. This trajectory, acting as the feedback 
loop required in every control system, has been generated using 
position and attitude information derived by taking into account 
helicopter and digital cameras (Field of View) technical 
specifications. Each block of figure 4 will be described in the 
following subsections. 
Reference 
K ——1 
Dynamic 
Measurement 
trajectory 
model 
sensors 
Extended 
Kalman filter 
Figure 4. Block scheme of the simulation environment. 
3.1 The dynamic model 
The Raptor 90 has been modeled as a 6 degree of freedom (dof) 
rigid body (3 rotations and 3 translations), whose state is 
described by following measurements (see figure 5): 
- Center of mass position 
p = (x,y,zf (i) 
- Attitude (euler angles) 
q - (<p,3 y y/f ( 2 ) 
where (j) denotes the roll, 0 the pitch and \\i the yaw angle; 
- Velocity 
v=(w,v.iv) r (3) 
- Angular velocity 
G> = (p,q,r) T (4) 
As regards the dynamic and kinematic equations two different 
reference systems have been considered: the inertial frame (A) 
and the body (5) frame (figure 5). 
Figure 5. The inertial frame (A) and the Body frame (B) 
Basically, the analitical model for the helicopter can be 
summarized in following equation system: 
+BC0 B.A xBlB <°B.A = BM C 
m B v c +m B S B ,x s v c = s F 
q = '¥(q) à 
p=' B R(q)\- 
(5) 
where the first two equations describe the rotational and the 
translational helicopter dynamics respectively, while the latters 
allow to determine respectively the aircraft attitude and position 
in the body frame. Such measurements, derived from angular 
and translational velocity computed in the inertial frame, are 
related to the body frame through rotation matrices 'F(q) and 
R(q). Beside dynamic and kinematic equations, a complete 
analitical modeling of the helicopter requires the knowledge 
about forces and couples acting on it. After exhaustive reading 
of most recent literature on UAV helicopters, we decided to 
take into account following forces and couples (figure 6): 
- Gravity force; 
- Main rotor; 
- Tail rotor; 
- Fuselage; 
- Horizontal fin; 
- Vertical fin. 
For brevity sake, we highlight here that the fuselage has been 
considered as a planar plate subjected to dynamic pressure 
along the three axis directions of the body frame. Values of the 
three corresponding equivalent surfaces are reported in table 3. 
We also took into account wind gust effects (aerodynamic drag), 
which acts on 3 helicopter components: fuselage, tail plane and 
the rudder unit. In this case we did not use any of the existing 
models already implemented in Simulink, but rather we 
employed three small Slider Gain blocks which allows the user 
to directly modify the simulation by introducing wind gusts by 
simply moving three cursors with the mouse. 
The helicopter dynamic model block outputs four different 
measurements, which are used by the subsequent block for 
sensor simulation: translational and angular accelerations in the 
body frame and position and attitude in the inertial frame.