IEEE Robotics & Automation Magazine - September 2012 - 28

sensors. Once a sufficiently accurate height measurement
is available, it is better to use this directly in the control
than add additional levels of complexity in designing a
height observer, especially since, for a typical system, the
only feedforward information available is the noisy accelerometer readings.
Position in the plane can also be determined in a relative or absolute way. Absolute position can be obtained
from a GPS (few-centimeter accuracy at up to 10 Hz [6])
or an external localization device such as a VICON
motion capture system (50 lm accuracy at 375 Hz). However, a GPS does not work indoors and motion-capture
systems are expensive, and their sensor array has a
limited spatial extent that is impractical to scale up for
large indoor environments.
Relative position can be estimated by measuring the distance to objects in the environment from onboard sensors,
typically small onboard laser range finders (LRFs) or
RGBD camera systems such as the Kinect. Well-known
SLAM techniques, borrowing LRF-based techniques
similar to those developed for mobile ground robots over
the last decade, have been applied to quadrotors [14].
However, LRFs provide only a cross section of the 3-D
environment and this scan plane tilts as the vehicle maneuvers, resulting in apparent changes to the distance of walls,
and, in extreme cases, the scan plane can intersect the floor
or ceiling. LRFs are heavy and power hungry, which prevents their application to the next generation of much
smaller quadcopters.
Vision has the advantage that the sensor is small, lightweight, and low power, which will become increasingly
important as the size of aerial vehicles decreases. Vision
can provide essential navigational competencies such as
odometry, attitude estimation, mapping, place and object
recognition, and collision detection. There is a long history
of applying vision to aerial robotic systems [15]-[19] for
indoor and outdoor environments, and the well-known
Parrot AR.Drone game device makes strong use of vision
for attitude and odometry [20]. Vision can also be used for
object recognition based on color, texture, and shape, as
well as collision avoidance.
Vision is not without its challenges. First, vision is computationally intense and can result in a low sample rate.
Since onboard computational power is limited (by SWAP
consumption), most reported systems transmit the images
wirelessly to a ground station, which increases system

complexity, control latency, and the susceptibility to interference and dropouts. However, processor speed continues
to improve, and we can also utilize the vision and control
techniques used by flying insects that perform complex
tasks with very limited sensing and neural capability [21].
Second, there is an ambiguity between certain rotational
and translational motions, particularly, when a narrow
field of view perspective camera is used. Third, the underactuated quadrotor uses the roll and pitch DoF to point the
thrust vector in the direction of the desired translational
motion. For a camera that is rigidly attached to the quadrotor, this attitude control motion induces a large apparent
motion in the image. It is therefore necessary to estimate
vehicle attitude at the instant the image was captured by
the sensor to eliminate this effect. Biological systems face
similar problems, and interestingly, mammals and insects
have developed similar solutions: gyroscopic sensors
(the vestibular sensors of the inner ear and the halteres,
respectively) [22]. Finally, there exists a problem with
recovering motion scale when using a single camera. Stereo
is possible, but the baseline is constrained, particularly as
vehicles get smaller.
Control
The control problem, to track smooth trajectories
ðRÃ (t), nÃ (t)Þ 2 SE(3), is challenging for several reasons.
First, the system is underactuated: there are four inputs
u ¼ (TR , s> )> , while SE(3) is six dimensional. Second, the
aerodynamic model described above is only approximate.
Finally, the inputs are themselves idealized. In practice, the
motor controllers must overcome the drag moments to
generate the required speeds and realize the input thrust
(TR ) and moments (s). The dynamics of the motors and
their interactions with the drag forces on the propellers
can be difficult to model, although first-order linear models are a useful approximation.
A hierarchical control approach is common for quadrotors. The lowest level, the highest bandwidth, is in control
of the rotor rotational speed. The next level is in control of
vehicle attitude, and the top level is in control of position
along a trajectory. These levels form nested feedback loops,
as shown in Figure 5.

Controlling the Motors
Rotor speed drives the dynamic model of the vehicle
according to (8), so high-quality control of the motor
speed is fundamentally important
for overall control of the vehicle;
u1
high bandwidth control of the
ξ* Position
Motor
Rigid Body
Trajectory
thrust TR , denoted by u1 , and the
Controller
ψ*
Controller
Dynamics
Attitude
Planner
R*
torques (sx , sy , sz ), denoted by u2 ,
Controller u2
Attitude
R,Ω
lead to high performance attitude
Planner
and position control. Most quadroξ,v
tor vehicles are equipped with
brushless dc motors that use back
Figure 5. The innermost motor control loop, the intermediate attitude control loop, and
the outer position control loop.
electromotive force (EMF) sensing

IEEE ROBOTICS & AUTOMATION MAGAZINE

SEPTEMBER 2012

Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - September 2012