-
Abstract— This paper presents the design and control of
amultirotor-based aerial manipulator developed for
outdooroperation. The multirotor has eight rotors and large payload
tointegrate a 7-degrees of freedom manipulator arm with enougharm
payload to perform different missions, and to carrysensors and
processing hardware needed for outdoorpositioning. The paper
focuses on the control design andimplementation aspects. A stable
backstepping-based controllerfor the multirotor that uses the
coupled full dynamic model isproposed, and an admittance controller
for the manipulatorarm is outlined. Several experimental tests with
the aerialmanipulator are also presented. In one of the
experiments, theperformance of the pitch attitude controller is
compared to aPID controller. Other experiments of the arm
controllerfollowing an object with the camera are also
presented.
Index Terms—Aerial robotics, aerial manipulation,multirotor
nonlinear control
I. INTRODUCTION
In the last years, robotic research has placed muchemphasis in
the development of autonomous mobile robotsoperating in
unstructured and partially known naturalenvironments [1]. Recently
aerial manipulation has receivedincreasing attention. The use of
aerial mobile manipulatorswould open a range of applications such
as the inspection andmaintenance of aerial power lines, the
building of platformsfor the evacuation of people in rescue
operations or theconstruction in inaccessible sites.
Most of the published work has been devoted to objectgrasping
applications. Several quadrotors and helicopterswith gripping
mechanisms in the belly have been developed[2]. Teams of these
quadrotors have been used forconstruction of cubic structures with
magnetic joints [3], andto build architectural structures with
bricks [4]. In [5]modeling and control of a manipulating UAV is
studied. Alsoan aerial robot with a small arm has been developed
forremote inspection by contact of industrial plants
[6][7].Autonomous helicopter-based aerial manipulators have
alsobeen developed. A small RC helicopter with a gripper hasbeen
used to grasp an object on the ground while in flight [2].[8] and
[9] also present prototypes of helicopters withattached
manipulators.
A problem that arises in aerial manipulation is that thedynamic
behavior of the vehicle changes due to the
*All authors are with the Robotics, Vision and Control group
(GRVC),University of Seville, Spain. E-mail: [email protected].
modification of the aerial mass distribution and dynamics
bygrasping and manipulating objects. The main effects thatappear
and make the dynamic behavior of the multirotor witha manipulator
different from the standard multirotorconfiguration that is usually
considered are the following:
1. Displacement of the center of mass from the verticalaxis at
the geometrical center of the multirotor.
2. Variation of mass distribution: the moments of inertiachange
significantly when the arm moves.
3. The dynamic reaction forces and torques generated bythe
movement of the arm.
These three effects are not usually taken into
accountexplicitly, and are left to the integral term in the
feedbackcontroller for correction. The effects of the displacement
ofthe mass center have been analyzed by some researchers.
Forexample, [11] presents stability limits within which thechanging
mass parameters of the system will not destabilizequadrotors and
helicopters with standard PID controllers. Onthe other hand, [12]
studies the effect of grasping objects at apoint displaced from its
center of mass and develops acontroller that takes it into account
explicitly. In [13], thecenter of mass is also considered, but the
variations of themoments of inertia are discarded. The influence of
the centerof mass being above or below the equatorial multirotor
planeis analyzed in [14]. Adaptive controllers that compensate
theunknown displacement of the center of mass have also
beenpresented [15][16].
Figure 1. AMUSE octoquad aerial manipulator in flight
Backstepping [17] is a controller design methodologywith
guaranteed stability for nonlinear systems which has
Control of a Multirotor Outdoor Aerial Manipulator
G. Heredia, A.E. Jimenez-Cano, I. Sanchez, D. Llorente, V.
Vega,J. Braga, J.A. Acosta and A. Ollero*
-
been applied to VTOL autonomous vehicles [18]. In [19]
theauthors presented a Variable Parameter IntegralBasckstepping
(VPIB) controller for a quadrotor with amanipulator, which took
into account the first two points(variation of center of mass and
moments of inertia with themovement of the arm), but did not
consider the third one(dynamic reaction torques). In this paper, a
controller thatconsider the full dynamic effects and the variation
of themass distribution when the arm moves is presented.
When working with quadrotors in most cases theexperiments are
performed in indoor testbeds equipped withmulti-camera real time
motion capture systems (i.e. Vicon orOptitrack systems), which
provide very accurate attitude andposition estimation. Furthermore,
small size quadrotors areused in these indoor testbeds, which have
a limitedworkspace. Therefore, the available quadrotor payload for
themanipulator and the objects is small, limiting the
applicationsrange and the manipulation ability.
In this paper the design and development of a largepayload
outdoors aerial manipulator is presented. It uses anoctoquad aerial
platform with sufficient payload to carry ahigh payload dexterous
manipulator arm for realmanipulation applications, in addition to
sensors for outdoorpositioning and powerful computers for
autonomousoperation.
The work presented here has been done in the frameworkof the
ARCAS FP7 European Project [10], which isdeveloping a cooperative
free-flying robot system forassembly and structure construction.
The ARCAS systemwill use aerial vehicles (helicopters and
quadrotors) withmulti-link manipulators for assembly tasks.
The rest of the paper is organized as follows. Section
IIpresents the AMUSE aerial manipulation system. Section
IIIdescribes the development of the AMUSE controllers andSection IV
include experiments to test the validity of theproposed
approach.
II. THE AMUSE AERIAL MANIPULATION SYSTEM
Figure 1 shows the general configuration of the octoquadAerial
Manipulator developed at University of SEville(AMUSE). It is a
multirotor with a multi-link manipulatorarm that has been specially
designed to operate in outdoorscenarios.
The AMUSE aerial platform is a multirotor with eightrotors
located at the ends of a four-arm planar structure, withtwo rotors
positioned coaxially at the end of each arm, whichis usually known
as “octoquad” configuration. The reason touse eight rotors is to
get enough lift and payload for theapplication. Each pair of
coaxial rotors rotates in oppositedirections to compensate the
torque at each arm. Theoctoquad has been preferred over the
standard octocopterconfiguration (eight rotors distributed in the
same plane)because it is more compact, and it is better suited to
fly closeto objects or other obstacles.
The AMUSE octoquad aerial platform has been designedto get
additional payload so that the sensors and controlcomputer needed
to operate outdoors and a multilinkmanipulator arm with enough
payload can be mounted. TheAMUSE mounts eight 750 W motors with
16’’ rotors, which
are located at 41 cm of the center on each of the four bars.The
AMUSE total payload is 8 kg, which is available forsensors,
processing hardware, the manipulator arm and thearm payload.
Figure 2. Two AMUSE prototypes with different arm
configurations. Asmall quadrotor which is similar in size to the
Pelican quadrotor fromAscending Technologies is included in the
photo for size comparison.
Manipulator arms for aerial robots have strong weightlimitations
given the limited payload of these aerial vehicles.Usually the main
design criteria are to minimize the total armweight, maximize the
load to weight ratio and minimize thedisplacement of the center of
gravity when the arm jointsmove, to facilitate control of the
robot. A lightweight 3-dofarm prototype previously developed was
presented in [19].Another arm prototype with 4 dof developed at
University ofSeville is shown in Figure 2-left. Figure 1 presents
theAMUSE with a 7-dof arm developed by Robai [20]. With 7dof it has
better manipulability than the other configurations,and the maximum
payload is 1.5 kg, which is well suited fora large set of
applications.
The AMUSE control computers and sensors for outdooroperation are
shown in Figure 3. The autopilot is amicrocontroller board to which
are connected the IMU, abarometer and an ultrasonic sensor. A
Novatel Real-Time-Kinematic Differential GPS (RTK-DGPS) is also
connectedto the autopilot. This kind of GPS receivers is able to
getcentimeter-level accuracy, which is very helpful to
achievestable hovering and low speed flight needed for
manipulationoperations.
Figure 3. AMUSE control computers and sensors for outdoor
operation.
The Autopilot is connected through an Ethernet link tothe High
Level Computer (HLC), which is an Intel i7-basedPC. Furthermore,
several cameras are also connected to theHLC (see Figure 4). One of
the cameras is mounted on theend effector and it is used for visual
servoing and relativepositioning of the objects that are being
manipulated. The
-
second camera shown in Figure 4 is attached to the octoquadframe
pointing down, and it is used for relative positioningand hover
flight stabilization, aiding the RTK-DGPS andcomplementing it when
it is not available in high accuracymode. A third camera for
positioning can be also mounted onthe frame pointing down on the
other side of the frame (notshown in Figure 4). A 6-axis
force/torque sensor can beinstalled at the end effector for contact
force/torquemeasurement.
Figure 4. AMUSE octoquad with two cameras: one on the end
effector forobject recognition and another one mounted on the frame
for positioning
The HLC runs 64 bits Ubuntu server with ROS (RobotOperating
System [21]). It also has installed the ARUCOlibrary [22], which
can detect different markers in real time.Markers can be placed in
objects that are being manipulated,or on ground near interest areas
for aiding in positioning.Figure 5 shows an example of a bar with a
marker at its base(left) and the relative pose recognition
performed by ARUCO(right), including relative position and
orientation.
Figure 5. Left: structure bar with a marker at its base
(indicated in the photowith a yellow arrow). Right: relative pose
recognition performed by
ARUCO, including relative position and orientation.
III. AMUSE CONTROLLERS
A. Mathematical modeling
The full dynamic model of a multirotor with a n-linkmanipulator
arm is very complex since it includes thecoupled dynamics of the
quadrotor aerial vehicle and themanipulator [23]. The mathematical
model can be derivedeither using the Lagrange-Euler or the
Newton-Eulerformalisms. The equations in compact matrix form can
bewritten as:
+̈ߦ(ߦ)ܤ ,ߦ൫ܥ +൯̇ߦ (ߦ)݃ = ݑ + ௫௧ݑ
where ߦ is the generalized state that include the degrees
offreedom of the multirotor plus the corresponding to
themanipulator arm joints. Vector u encompasses actuator forcesand
torques exerted by the octoquad rotors and the servoactuators of
the arm joints, and ௫௧ݑ includes external forces
and torques. The mass matrix (ߦ)ܤ includes all the mass
andinertia terms, the matrix ,ߦ൫ܥ ൯̇ߦ the centrifugal and
Coriolisterms, and the vector (ߦ)݃ the gravity terms. Since the
massmatrix is invertible, the following holds:
=̈ߦ ଵି(ߦ)ܤ +ൣݑ −௫௧ݑ ,ߦ൫ܥ −൯̇ߦ ൧(ߦ)݃
For the AMUSE multirotor, the generalized state ߦ is
thefollowing:
=ߦ ߮ߠݖݕݔ] ߰ ଵߛ ଷߛଶߛ ହߛସߛ ]ߛߛ
where ߰,߮,ߠ are the multirotor attitude Euler angles and ߛare
the joint angles of the 7 degrees-of-freedom manipulator.
B. Octoquad controller
The AMUSE octoquad controller is adapted from theVariable
Parameter Integral Backstepping (VPIB) controllerthat was presented
in [19], but using the full coupled dynamicmodel outlined above
instead of the simplified model usedwhen originally developed. It
is a nonlinear controllerobtained through backstepping with an
added integral term,with guaranteed stability. The multirotor
controller termsdepend on the manipulator arm joints positions
andvelocities, and thus the parameters and gains of the
controllervary when the arm moves.
Next, the derivation of the pitch attitude controller will
bepresented. The controllers for the other angles are built in
asimilar way. Consider the tracking error ଵ݁ = ௗߠ − ,ߠ whereௗߠ is
the desired pitch angle, and its dynamics:
ௗభ
ௗ௧= ௗ̇ߠ − ߱
Then a virtual control over the angular speed ߱ can
beformulated, which is not a control input. Therefore, thedesired
angular speed can be defined as follows:
߱ௗ = ଵ݇ ଵ݁ + ௗ̇ߠ + ଵߣ ଵ߯
with ଵ݇and ଵߣ positive constants and ଵ߯ = ∫ ଵ݁( )߬ ఛ݀௧
the
integral of the pitch tracking error. Next, the angular
velocitytracking error ଶ݁ and its dynamics can be defined by:
ଶ݁ = ߱ௗ − ߱
ௗమ
ௗ௧= ଵ݇൫̇ߠௗ − ߱൯+ ௗ̈ߠ + ଵߣ ଵ݁ − ̈ߠ
Using (5) and (6) the attitude tracking error dynamicsequation
(4) can be rewritten as:
ௗభ
ௗ௧= − ଵ݇ ଵ݁ − ଵߣ ଵ߯ + ଶ݁
Now, ̈ߠ in (6) can be replaced by its expression in thedynamic
model (2), and the control input ܷఏ appearsexplicitly. Then,
combining the tracking errors of the position
ଵ݁ and the angular speed ଶ݁, and the integral position
trackingerror ଵ߯ using the above equations the control input ܷఏ can
becalculated as:
ܷఏ = ܻܫ) + )[(1߁ − ଵ݇ଶ + (ଵߣ ଵ݁ + ( ଵ݇ + ଶ݇) ଶ݁ − ଵ݇ߣଵ ଵ߯]
− ,ߦଵ൫ܦ −൯̈ߦ ,ߦଵ൫ܥ −൯̇ߦ (ߦ)ଵܩ
where ଶ݇ is a positive constant which determines theconvergence
speed of the angular speed loop, kଵ, λଵ arepositive parameters, and
χଵ the integral tracking error.
,ߦଵ൫ܦ ൯includes̈ߦ corresponding mass and inertia terms from
-
the full dynamic model equations, ,ߦଵ൫ܥ ൯̇ߦ the Coriolis
andcentrifugal terms, and (ߦ)ଵܩ the gravity terms. ݕܫ is themoment
of inertia about the axis perpendicular to the plane ofeach body
(octoquad and arm links), and ܻܫ = ∑ ݕܫ
ଶୀ is the
total moment of inertia.
In practice, the pitch controller terms can be rearranged inthe
following way:
ܷఏ = ܭ](ߛ)ܭ ଵ݁ + ܭ ଶ݁ + ூ߯ܭ ଵ]
− ,ߦଵ൫ܦ −൯̈ߦ ,ߦଵ൫ܥ −൯̇ߦ (ߦ)ଵܩ
where ܭ,ܭ ூܭ, are the parameters of a standard PIDcontroller,
(ߛ)ܭ is a variable gain that depends on the armjoint angle
positions, and ଵܩ,ଵܥ,ଵܦ are the nonlinear termsdescribed above. The
first part of the controller can be seenas a gain-scheduled PID
with the different positions of thearm, while the nonlinear terms
compensate the other effectsdescribed in Section I. In this way, it
is easier to tune thecontroller parameters starting from the
standard PIDs that areused by many multirotors as base
controllers.
The expression of the other attitude controllers (roll andyaw)
and the position controllers can be derived in a similarway.
Despite theoretical advantages of including
feedbackaccelerations terms according to (9), note that
theirintroduction can be a drawback when using numericalalgorithms
in a real-time embedded system if they are notproperly
processed.
C. Manipulator arm controller
The controller for the manipulator arm joints could bederived in
the same manner than the multirotor controllerfrom the dynamic
equations of motion, thus obtaining therequired torques u to drive
the motors of the arm joints. Thisapproach has been followed in
[23][24], which use a torque-based impedance controller for
interaction with objects in theenvironment.
However, there are practical limitations in themanipulator arm
design that prevent it. As stated above, armsfor aerial
manipulators have strong weight restrictions, due tothe payload
limitations of the aerial platforms. The prototypearms that have
been designed for the AMUSE use standardservos or Robotis Dynamixel
servos to drive the joints. Thisis also the case with arms designed
for aerial manipulation[26]. Although some of the larger Dynamixel
servos have thepossibility of joint torque control, torque sensing
has pooraccuracy, making very difficult if not impossible
toimplement torque control.
The AMUSE manipulator arm implements an admittancecontroller,
which is a position-based Cartesian impedancecontroller. The
admittance controller will command a desiredCartesian position Σௗ
for the end effector Tool Center Point(TCP):
Σௗ = Σ் + Σ௧
where Σ் is the TCP position defined by the manipulationtask and
trajectory interpolation, and Σ௧ is the additionaldisplacement that
would get the desired interaction forcesand torques between the end
effector and the objects or theenvironment, calculated by the
admittance controller. Then,
Σௗ is transformed through the manipulator inversekinematics ଵିܭ
and the desired joint position setpoints aretransmitted to the
local joint embedded controllers.
For the inverse kinematic a jacobian-based first-orderalgorithm
has been used. As it is well-known, this algorithmminimizes the
operational space error between the desiredand the actual
end-effector position and orientation,overcoming drift problems
induced by other differentialkinematics schemes.
Additionally, internal motions have also been generatedthrough
the jacobian null space to force a prescribedconfiguration of the
manipulator for a given end-effectorposition and orientation. Thus,
a strategy to minimize thedistance from mechanical joint limits has
been considered.
Finally, to provide a robust behavior crossing through orclose
to singular configurations a modified pseudoinversewith a variable
damping factor based on gaussian-weightedfunctions of the
manipulability measure has been used.
IV. EXPERIMENTS
Several experiments have been done with the AMUSEprototype to
test experimentally the controllers of the aerialmanipulator. See
the accompanying video for several sampleexperiments.
A set of experiments have been done to test the
attitudecontroller in an outdoor scenario. The experiments have
beendone in challenging conditions for the attitude
controller,since the AMUSE was commanded to hover at a
specificaltitude, and then the arm was commanded to make
widemovements at high speed, to test the performance of theattitude
controller. Figure 6 shows three different instants ofone of the
experiments, with the arm in different positions.During the
experiments there was lateral wind with frequentwind gusts, which
introduced significant perturbations inattitude control.
Figure 6. Flight experiment of AMUSE with the 7-dof manipulator
arm:three different instants when moving the arm.
Several arm joints where moving at the same time inthese
experiments. Figure 7 shows the evolution of theAMUSE multirotor
pitch attitude angle during theexperiments. The X-axis is situated
on the plane of the armand the pitch angle is defined as the
rotation of the multirotorin this plane around the Y-axis, which is
perpendicular to theplane. Thus, the pitch angle is the most
influenced by themovement of the arm in these experiments. The
dashed linesin Figure 7 represent the movement of one of the arm
joints(joint 3, which is moving at 75 degrees/s). Since all the
jointsmove at the same time, the dashed line has been included asan
indication of the movement of the arm.
The experiment has been performed with the proposedcontroller
and with a standard PID controller that does nottake into account
the movement of the arm. In the upper plot
-
of Figure 7 it is shown the evolution of the pitch angle withthe
PID controller. When the arm is not moving and centered,the pitch
angle presents oscilations of about 5-5.5 degrees ofamplitude,
which are due to the atmospheric perturbationsand the action of the
controller (this is common to bothcontrollers). But when the arm
begins to move, theoscilations with the PID controller grow rapidly
to around 12degrees. The lower plot of Figure 7 shows the time
evolutionof the AMUSE multirotor with the proposed controller in
thesame experiment. It can be seen that when the arm moves,the
oscillations increase only slightly to 6-6.5 degrees. Thus,the
porposed controller is able to effectively counteract themovement
of the arm to a large extent.
Figure 7. Evolution of the AMUSE pitch attitude angle during
theexperiments.Upper plot: with a PID standard controller which
does not
consider the arm movement and dynamics. Lower plot: with the
proposedfull dynamics backstepping controller.
Another set of experiments have been done with theAMUSE
manipulator arm following an object that it is goingto grasp. The
object has a label on it (see Figure 5), and acamera placed at the
belly of the AMUSE and pointing downto the workspace of the arm
detects the label as described inSection II, and obtains the
relative position of the object withrespect to the end effector of
the arm. The arm controller usesthe inverse kinematics to compute
the commands that shouldbe sent to the servos of the seven arm
joints. Figure 8 showsthe evolution of the joint angles in an
experiment. The bluelines are the reference commands computed by
the controller,and the green lines are the actual values reached by
the joints.It can be seen that when the change of the reference
values istoo fast (as for example at = 74 .ݏ in several joints),
theservos are not able to follow it and the response lags
thereference for some time. Another important point is that
thereferences are checked against workspace limits prior tosending
them to the servos, so that the arm does not hit theframe or the
rotors.
Figure 8. Time evolution of the joint angles of the 7 dof
manipulator arm inan experiment (blue – control references, green –
actual manipulator joints).
Figure 9. Position and orientation errors of the arm end
effector with respectto the references computed by the vision
system in the same experiment
than Figure 8.
Figure 9 shows the position and orientation errors of theend
effector of the arm with respect to the referencescomputed by the
vision system. It can be seen that theposition errors are less than
+/- 0.5 cm most of the time,
40 50 60 70 80-20
02040
Manipulator´s Joint Angles [deg]
1
40 50 60 70 80
304050
2
40 50 60 70 80-40
-20
0
3
40 50 60 70 80
50
100
4
40 50 60 70 80
02040
540 50 60 70 80
-200
20
6
40 50 60 70 80
20
4060
7
Time [s]
40 50 60 70 80-0.04
-0.02
0
0.02
0.04
Positio
nE
rro
rs[m
]
X error
Y error
Z error
40 50 60 70 80-4
-2
0
2
4
Time [s]
Ori
en
tati
on
Err
ors
[deg] error
error
error
105 110 115 120 125
-5
0
5
10
Time [s]
PIT
CH
[de
g]
ARM MOVING
80 85 90 95
-5
0
5
10
Time [s]
PIT
CH
[deg]
ARM MOVING
-
except when the references computed by the vision systemmove too
fast as can be seen in Figure 8 (this corresponds tothe target
object moving away from the arm tip due tooscillations of the AMUSE
multirotor). The orientation errorsare also shown in Figure 8.
V. CONCLUSION
Aerial robotics is evolving to include not only systemswith
sensing capabilities but also with the possibility to acton the
environment, and particularly with manipulationcapabilities. Aerial
manipulators based on quadrotors ormultirotors are being
increasingly used, but most of them forindoor operation and with
very limited payload, thusrestricting applications. This paper has
presented thedevelopment of one of the first large payload
multirotor-based aerial manipulators for outdoor operation.
Thedynamics and mass distribution of the arm when it is
movingaffects significantly the attitude stability of the
multirotor. Anonlinear controller for the multirotor which takes
intoaccount the full dynamics of the arm has been presented. It
isable to dampen the oscillations caused by the arm movementto a
large extent, compared to a controller that does notconsider the
influence of the arm. Furthermore, an admittancecontroller has been
proposed for the manipulator arm.Several experiments with the AMUSE
multirotor and the armhave also been presented. This is an ongoing
work and moreexperiments are being done to test the controllers in
differentconditions.
ACKNOWLEDGMENT
This work has been supported by the ARCAS Project,funded by the
European Commission under the FP7 ICTProgramme (ICT-2011-287617)
and the CLEAR Project(DPI2011-28937-C02-01), funded by the
SpanishGovernment.
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