IEEE Robotics & Automation Magazine - December 2013 - 28

High-Level Control
The high-level teleoperation controller consists of two parts:
the master system and the virtual slave system, which are coupled by means of the communication channel. The high-level
controller is responsible for the high-level commands coming
from the human operator, for the generation of the reference
control inputs for the low-level controller and for the generation of the force-feedback.

The feedback force applied to the haptic device is proportional to the error between the position of the master p m and
the velocity of the virtual slave v v as it is mapped to the master position, i.e., p *m = ^1/ah v v . This implies that

The Master System
The human operator uses a master haptic device, characterized
by a finite stroke p m ! W H , where W H is the finite hapticdevice workspace, and a limited force f f , with < f f < ! [ f f , f f ] .
In steady state, a constant value of the position of the tip
of the master is mapped
to a constant reference
speed for the aerial vehiThe virtual slave is the
cle. This choice is due to
the fact that the master
real-time simulation of
has a finite configuration
space, i.e., a finite range of
a fully actuated aerial
motion, while the aircraft
has an infinite configuravehicle, for which it is
tion space [28].
The master controller
possible to measure all the
is responsible of two main
information about its state. tasks: to generate a
desired velocity set-point,
v *v , for the virtual slave
and a feedback signal, f f , for the haptic device. The desired
velocity, v *v , is obtained as follows:

The Virtual Slave
The virtual slave is made of two main blocks: the virtual slave
controller and the virtual slave [28], [29].
The virtual slave is the real-time simulation of a fully actuated aerial vehicle, for which it is possible to measure all the
information about its state, i.e., its velocity v v . The virtual slave
is moving in a gravityless and frictionless space and its dynamics are influenced by a viscoelastic coupling Fc to the real vehicle, the virtual vision force FV in (1), and the force f vm
impressed by the master's movement and computed in the virtual slave controller as

v *v = v v p m =: a p m,
ff

200
Attractive
Area

100
Start

50
0

End

-50
-100
-150
-200
-200 -150 -100 -50

0
x

100

150

200

Figure 8. A force field generated from the map of Figure 6 during a
trajectory motion.

IEEE ROBOTICS & AUTOMATION MAGAZINE

DECEMBER 2013

where k f is a proportional gain in units of a spring.

f vm = b v (v *v - v v),

(2)

where b v is a proportional gain in units of a viscous damper.
For simplicity, the vehicle is modeled as point mass dynamics
m v vo v = Fc + FV + f vm =: Fv,
where m v is the mass of the virtual slave, vo v ! R 3 is the virtual slave acceleration. Note that, according to the scheme in
Figure 9, the position of the virtual slave is assumed as the
desired position for the real vehicle.
Low-Level Control
The low-level control is the controller of the real vehicle. Its
main goal is to effectively track the desired state of the virtual
slave by generating the proper actuation input for the real vehicle to solve the underactuation of the real slave. The real slave
controller takes into account the possible intervention of the
vision-based controller that modifies the desired reference to
avoid a detected obstacle. Moreover, this controller yields the
coupling force Fc to the high-level controller to provide information on the state of the real vehicle and the environment.

where v v is the maximum velocity imposed by the user.

150

f f = k f ^ p *m - p mh,

Vision-Based Control
The vision-based controller is responsible for the generation
of the vision-based force, built as explained before. This force
counteracts the force provided by the master through the virtual slave. Hence, the resultant force is applied to the real vehicle. When the distance between the vehicle and the obstacle is
less than a certain threshold, the vision-based controller is
applying a force, as defined in (1).
Passivity
To guarantee the stability of the overall system, a passivitybased approach is adopted [30]. More precisely, by assuring

Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - December 2013