Qball-X4 Simulator
Seang Cau
February 16, 2011
Introduction
• Simulator is run under MatLAB and
rendered using Quarc.
• Simulates the behavioral properties of the
Quanser Qball-X4.
Quanser Qball-X4
• Visualization is transfer information to the
3D renderer
Figure 1: Visualization
Figure 2: Qball Simulator
Purpose
• To understand the physics of the Qball
• To understand the capabilities of the Qball
• To utilize the simulator as a preliminary
study for integration of sensors
Qball-X4 Model
• x, y, and z axis are defined as positions in
a 3D space
• Roll, pitch, and yaw are defined as the
angles of rotation about the x, y, and z axis
respectively.
• X, Y, and Z are the global workspace axes
Actuator Dynamics
• Thrust is generated by each propeller using the

first-order system
FK
s 
u
• Where u is the PWM input, w is the actuator
bandwidth and K is the positive gain
• A state variable, v, will be used to represent the
actuator dynamics

v
u
s 
Qball-X4 3D Simulator
• Consists of two part for each axis
• Position Controllers
• Model
• Constants are specified in
Qball_X4_parameters.m
Yaw
• Yaw is a constant in the simulator
• It controls the orientation of the QBall
Figure 3: Yaw Black Box
Figure 4: Yaw Controller/Model
Yaw Controller & Model
• Ky = 4 N*m
• Jy = 0.032
• Torque = Ky * u where u is the PWM input
Figure 5: Yaw Controller
Figure 6: Yaw Model
Height
• K = 120 N
• w (omega) = 15 rad/s
• M = 1.4 kg
Figure 7: Height Controller/Model
Height Controller
• Navigates the height based on previous
value and target value.
Figure 8: Height Controller
Height Model
• The dynamic model of height can be
written as
MZ  4F cos(r ) cos( p)  Mg
• Height is affected by thrust, pitch, and roll
Figure 9: Height Model
XY Model
• Thrust affects the x and y axis of the Qball
• Assuming yaw angle is zero, dynamics of motion
in X and Y axes can be written as MX  4 F sin( p )
MY  4 F sin( r )
Figure 10: XY Model
X axis
• X controller affects the pitch angle
Figure 11: X Controller/Model
X Controller
Figure 12: X Controller
Pitch Controller/Model
Figure 13: Pitch Controller/Model
Pitch Controller & Model
Figure 14: Pitch Controller
Figure 15: Pitch Model
Y axis
• Y Controller affects the roll angle
Figure 16: Y Controller/Model
Y Controller
Figure 17: Y Controller
Roll Controller/Model
Figure 18: Roll Controller/Model
Roll Controller & Model
Figure 19: Roll Controller
Figure 20: Roll Model
Summary
• Qball X4 model uses absolute coordinate
system in the xy and height control
• Converts the xy and height commands into
Pitch and Roll commands
• Yaw is kept constant at an assumed zero
Conclusion
• Useful to understand how the integration
of sensor input will occur
• Will be unable to mimick the Qball in
actual conditions due to assumptions