Fully Actuated Aerial Platforms for Aerial Manipulation: Design and

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Fully Actuated Aerial Platforms for Aerial Manipulation:
Design and Control
Workshop on Aerial Manipulation 2016 IEEE ICRA, Stockholm, Sweden
Antonio Franchi
http://homepages.laas.fr/afranchi/robotics/
LAAS-CNRS, Toulouse, France, Europe, . . .
Friday, May 20th , 2016
funded by
Antonio Franchi, http://homepages.laas.fr/afranchi/robotics/
Fully Actuated Aerial Platforms for Aerial Manipulation: Design and Control
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For more information about the control method presented in this talk please check:
A. Franchi, R. Carli, D. Bicego, and M. Ryll, “Full-pose geometric tracking control on SE(3) for
laterally bounded fully-actuated aerial vehicles”, in ArXiv:1605.06645, 2016. [Online].
Available: http://arxiv.org/abs/1605.06645
For more information about our activity on similar topics, refer to:
http://homepages.laas.fr/afranchi/robotics/
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Table of Contents
1. Motivation and Background
2. Modeling and Designing Fully-actuated Aerial Platforms
3. Controlling Fully-actuated Aerial Platforms
4. Conclusions
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Motivation and Background
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Aerial Robots Physical Interacting with the Environment
Aerial robots for physical interaction
• applications: inspection, maintenance, transportation, manipulation. . .
Some examples in recently EU-funded projects:
Seville Univ. (ARCAS)
DLR (ARCAS)
CATEC (ARCAS)
AEROWORKS concept
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Challenges of Physically Interactive Aerial Robotics (I)
Floating base
• active reaction wrench provided by the thrusters
(grounded manipulators have ‘passive’ ground reaction)
• inaccurate positioning
(because of noisy sensing and external disturbances)
(CATEC/USE, ARCAS)
• dynamic coupling
Actuators of the base
• additional aerodynamic layer
motor torque ∼ propeller acceleration
⇓
propeller speed ∼ thrust force
• unmodeled aerodynamics
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Challenges of Physically Interactive Aerial Robotics (II)
Need for a lightweight payload
• arms with weaker motors
• minimal number of sensors
• flexibility ⇒ vibrations
Need to save energy
• underactuated configurations
(i.e., coplanar propellers)
USE (ARCAS)
CATEC/USE (ARCAS)
CATEC (ARCAS)
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Underactuation vs. Full-actuation in Aerial Robots
This talk will focus on the sole platform modeling and control (without arm)
Underactuated
Fully-actuated
• – position-only control (coupled
position and orientation
• + full-pose control (independent
control of position and orientation)
• – force-only control in interaction
• + full-wrench control in interaction
• + only (low) internal drag (efficient)
• – internal wrench
(wasted energy)
• + lower complexity
• – higher complexity
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Modeling and Designing Fully-actuated Aerial Platforms
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Rigid Body Dynamics and Control Wrench
Multi-rotor aerial platforms are essentially made of two elements:
• a rigid body → rigid body dynamics
mp̈W
mge3
B =−
ωW
ωW
ωW
Jω̇
B
B × Jω
B
fW
τB
| {z }
+
where e3 =
h0i
0
1
(1)
total input wrench
• a set of propellers attached to the body → total input wrench
Wrenches of the single propellers:
0
fBi = RBSi 0 wi |wi |, i = 1, . . . , n
cf | {z }
ui
τ Bi = RBSi
h
0
0
±cτ
i
wi |wi |,
| {z }
i = 1, . . . , n
ui
Total input wrench:
" u1 #
.. = RW F u
(2)
B 1
.
i=1
un
" u1 #
n
n
B
B
B
B
τ = ∑ pB,Si × fi + ∑ τ i = F2 .. = F2 u (3)
.
n
fW =RW
B
∑ fBi = RWB F1
i=1
i=1
un
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Underactuated vs Fully-actuated platforms
Putting (2) and (3) in (1):
W
mp̈W
mge3
R
B =−
+ B
ωW
ωW
ωW
0
Jω̇
B
B × Jω
B
0 F1
u,
I F2

where u = 
w1 |w1 |

..
.

wn |wn |
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W
mp̈W
mge3
R
B =−
+ B
ωW
ωW
ωW
0
Jω̇
B
B × Jω
B
0 F1
u,
I F2

where u = 
w1 |w1 |

..
.

wn |wn |
• all propellers are coplanar ⇒ F1 is rank deficient


 T
0
0 ··· 0
F1 = cf 0 · · · 0 = cf 0T 
1 ··· 1
1T
• the control force is


0
 0 
cf RW
B
1T u
• it can be arbitrarily oriented only changing the whole-body orientation RW
B
• the propeller speeds u control only the amplitude of the force
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W
mp̈W
mge3
R
B =−
+ B
W
W
W
ωB
ωB
ω B × Jω
0
Jω̇
0 F1
u,
I F2

where u = 
w1 |w1 |

..
.

wn |wn |
• If coplanarity assumption is relaxed then ⇒ F1 can be made full-rank


? ? ··· ?
F1 = cf ? ? · · · ?
? ? ··· ?
• the control force is

?
W
RW
B F1 u = cf RB ?
?
?
?
?
···
···
···

?
? u
?
• using u, both orientation and amplitude of the force can be decided
independently of the whole-body orientation RW
B
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Examples of Fully-actuated platforms (I)
quadrotor + tilting propellers1
1
M. Ryll, H. H. Bülthoff, and P. Robuffo Giordano, “A novel overactuated quadrotor unmanned aerial vehicle:
Modeling, control, and experimental validation”, IEEE Trans. on Control Systems Technology, vol. 23, no. 2,
pp. 540–556, 2015.
2
S. Rajappa, M. Ryll, H. H. Bülthoff, and A. Franchi, “Modeling, control and design optimization for a fullyactuated hexarotor aerial vehicle with tilted propellers”, in 2015 IEEE Int. Conf. on Robotics and Automation,
Seattle, WA, 2015, pp. 4006–4013.
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Examples of Fully-actuated platforms (I)
quadrotor + tilting propellers1
planar hexarotor with tilted propellers2
1
M. Ryll, H. H. Bülthoff, and P. Robuffo Giordano, “A novel overactuated quadrotor unmanned aerial vehicle:
Modeling, control, and experimental validation”, IEEE Trans. on Control Systems Technology, vol. 23, no. 2,
pp. 540–556, 2015.
2
S. Rajappa, M. Ryll, H. H. Bülthoff, and A. Franchi, “Modeling, control and design optimization for a fullyactuated hexarotor aerial vehicle with tilted propellers”, in 2015 IEEE Int. Conf. on Robotics and Automation,
Seattle, WA, 2015, pp. 4006–4013.
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Examples of Fully-actuated platforms (II)
4+4 orthogonal rotors3
3
H. Romero, S. Salazar, A. Sanchez, and R. Lozano, “A new UAV configuration having eight rotors: Dynamical model and real-time control”, in 46th IEEE Conf. on Decision and Control, New Orleans, LA, 2007,
pp. 6418–6423.
4
D. Brescianini and R. D’Andea, “Design, modeling and control of an omni-directional aerial vehicle”, in
2016 IEEE Int. Conf. on Robotics and Automation, Stockholm, Sweden, 2015.
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Examples of Fully-actuated platforms (II)
4+4 orthogonal rotors3
cubic octorotor4
3
H. Romero, S. Salazar, A. Sanchez, and R. Lozano, “A new UAV configuration having eight rotors: Dynamical model and real-time control”, in 46th IEEE Conf. on Decision and Control, New Orleans, LA, 2007,
pp. 6418–6423.
4
D. Brescianini and R. D’Andea, “Design, modeling and control of an omni-directional aerial vehicle”, in
2016 IEEE Int. Conf. on Robotics and Automation, Stockholm, Sweden, 2015.
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Controlling Fully-actuated Aerial Platforms
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Inverse Dynamics Approach
Given a reference pose (6D) trajectory:
• pW
Br (t) (position of the CoM)
• RW
Br (t) (orientation of the main body)
Dynamics:
mI
0
W
mge3
0 p̈W
RB 0 F1
B =−
u,
+
ωW
J ω̇
ωW
ωW
0
I F2
B
B × Jω
B
| {z } | {z }
6×6

where u = 
w1 |w1 |

..
.

wn |wn |
6×n
Inverse dynamics:
u=
+ B
F1
RW
F2
0
W p̈Br
mge3
0
+v + W
W
W
ωB
J
ω Br
ω B × Jω
ω̇
mI
0
0
I
W
p̈W
B − p̈Br = v
W
W
ω B − ω̇
ω Br
ω̇
Exactly linearized error system
W
W
W
then use any linear-systems control law for v to steer pW
B → pBr (t) and RB → RBr (t)
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Inverse Dynamics Approach
Given a reference pose (6D) trajectory:
• pW
Br (t) (position of the CoM)
• RW
Br (t) (orientation of the main body)
Dynamics:
mI
0
W
mge3
0 p̈W
RB 0 F1
B =−
u,
+
ωW
J ω̇
ωW
ωW
0
I F2
B
B × Jω
B
| {z } | {z }
6×6

where u = 
w1 |w1 |

..
.

wn |wn |
6×n
Inverse dynamics:
+ B
F
RW
u= 1
F2
0
W p̈Br
mge3
0
+N
+v + W
W
W
ωB
J
ω Br
ω B × Jω
ω̇
mI
0
0
I
+ !
F1
F2
W
p̈W
B − p̈Br = v
W
W
ω B − ω̇
ω Br
ω̇
Exactly linearized error system
W
W
W
then use any linear-systems control law for v to steer pW
B → pBr (t) and RB → RBr (t)
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Applications of the Inverse Dynamics Approach: Quadrotor w/ Tilt. Prop.
quadrotor + tilting propellers
M. Ryll, H. H. Bülthoff, and P. Robuffo Giordano, “A novel overactuated quadrotor unmanned
aerial vehicle: Modeling, control, and experimental validation”, IEEE Trans. on Control
Systems Technology, vol. 23, no. 2, pp. 540–556, 2015
16 of 36
Applications of the Inverse Dynamics Approach: Hexarotor
planar hexarotor with tilted propellers
S. Rajappa, M. Ryll, H. H. Bülthoff, and A. Franchi, “Modeling, control and design
optimization for a fully-actuated hexarotor aerial vehicle with tilted propellers”, in 2015 IEEE
Int. Conf. on Robotics and Automation, Seattle, WA, 2015, pp. 4006–4013
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Applications of the Inverse Dynamics Approach: Cubic Octorotor
cubic octorotor
D. Brescianini and R. D’Andea, “Design, modeling and control of an omni-directional aerial
vehicle”, in 2016 IEEE Int. Conf. on Robotics and Automation, Stockholm, Sweden, 2015
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Actuation Limits and Drawbacks of the Inverse Dynamics Approach
The wrench exerted by the propellers has several limitations
motor torque
• maximum speed ∼ maximum
propeller drag
(considered in this talk)
• only positive speeds due to non-symmetric propeller shape
• maximum/minimum speed rate ∼
(non-considered in this talk)
maximum/minimum motor torque
motor/propeller inertia
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Actuation Limits and Drawbacks of the Inverse Dynamics Approach
The wrench exerted by the propellers has several limitations
motor torque
• maximum speed ∼ maximum
propeller drag
• only positive speeds due to non-symmetric propeller shape
• maximum/minimum speed rate ∼
(non-considered in this talk)
maximum/minimum motor torque
motor/propeller inertia
Inverse dynamics:
• desired wrench obtained by matrix (pseudo)inversion
• set of feasible forces not considered
• the smaller the cant angles the larger the input forces
Inverse dynamics approach may lead to unfeasible propeller speeds (>> 0 or < 0)
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Set of Feasible Forces
How to overcome the drawbacks of the previous approach?
Using a novel method presented here5
W
Let’s look at the dynamics while following any trajectory pW
B (t) with RB (t)
W h0i
p̈W
R F
B + mge3
where e3 = 0 , u ∈ U (admissible inputs)
= B 1 u,
W
W
W
ω B + ω B × Jω
ωB
F2
Jω̇
1
It is interesting to analyze the set of admissible input forces when
• the input torque is constrained, i.e., F2 u = τ for a given τ
• the propeller speeds are feasible, i.e., u ∈ U
U1 (ττ ) = {u1 = F1 u
s.t.
F2 u = τ
and
u∈U}
5
A. Franchi, R. Carli, D. Bicego, and M. Ryll, “Full-pose geometric tracking control on SE(3) for laterally
bounded fully-actuated aerial vehicles”, in ArXiv:1605.06645, 2016. [Online]. Available: http://arxiv.
org/abs/1605.06645.
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Feasible Forces in Body Frame: Coplanar Quadrotor
Set of admissible input forces (in body frame)
U1 (ττ ) = {u1 = F1 u
s.t.
F2 u = τ
and
u∈U}
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Feasible Forces in Body Frame: 4+4 Octorotor
U1 (ττ ) = {u1 = F1 u
s.t.
F2 u = τ
and
u∈U}
Octorotor for τ = 0 (approximation)
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Feasible Forces in Body Frame: Hexarotor
U1 (ττ ) = {u1 = F1 u
s.t.
F2 u = τ
and
u∈U}
Hexarotor for τ = 0 (approximation)
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Feasible Forces in Body Frame: Hexarotor for Different Cant Angles
U1 (ττ ) = {u1 = F1 u
s.t.
F2 u = τ
and
u∈U}
Hexarotor for τ = 0 for different cant angles α
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Hierarchical Approach: Attitude Controller
First building block: consider a standard attitude inner loop control, whose
inputs are:
• desired orientation Rd ∈ SO(3)
• measured attitude state RB , ω B
output is:
• reference control torque τ r ∈ R3
ω B − KR eR − Kω ω B
τ r = ω B × Jω
where eR is the orientation error defined as
1
eR = (RTd RB − RTB Rd )∨
2
(4)
and •∨ is the vee map from so(3) to R3 .
Key point
The desired orientation Rd might differ from reference orientation Rr
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Hierarchical Approach: Position Controller
Position tracking errors
ep = pB − pr ,
and
ev = ṗB − ṗr .
(5)
Reference force vector
fr = mp̈r + mge3 − Kp ep − Kv ev ,
(6)
where Kp and Kv are positive diagonal gain matrixes
Remark
If u could always be chosen such that:
RW
B F1 u = fr = mp̈r + mge3 − Kp ep − Kv ev ,
then ep → 0 and ev → 0 exponentially.
However, this is not always possible, due to the input saturation
Idea
Relax the orientation tracking if the position tracking is not possible
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Position-Tracking-Compatible Orientations
R(fr ) = {R ∈ SO(3) | ∃u ∈ U , RF1 u = fr ∧ F2 u = 0}
(7)
Set of orientations of the main body that allow to exert fr on the CoM while ensuring
• propeller speeds feasibility, i.e., u ∈ U
• a given input torque, e.g., F2 u = 0
Position–orientation compatibility
Simultaneous tracking of both pr (t) and Rr (t) is possible
m
Rr (t) ∈ R(fr (t))
Non-compatibility ⇒ relax the orientation tracking
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Control Algorithm
p, ṗ
R
Force (18) u1
LBFA
Projection
Dyn. p, ṗ
Model R, ω
u
R
d
Des. Ori. (15)
Attitude (19) 2
(1)-(5)
Optimization ωd , ω̇d Controller
ω
R
pr , ṗr , p̈r Reference (13)
Force fr
fr
Rr
fr
Control algorithm in pills
At every t, given pr , Rr :
1. compute fr = mp̈r + mge3 − Kp ep − Kv ev
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Control Algorithm
p, ṗ
R
Force (18) u1
LBFA
Projection
Dyn. p, ṗ
Model R, ω
u
R
d
Des. Ori. (15)
Attitude (19) 2
(1)-(5)
ω
R
Force fr
fr
Rr
fr
2. solve Rd = argmin dist (R, Rr )
R∈R(fr )
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Control Algorithm
p, ṗ
R
Force (18) u1
LBFA
Projection
Dyn. p, ṗ
Model R, ω
u
R
d
Des. Ori. (15)
Attitude (19) 2
(1)-(5)
ω
R
Force fr
fr
Rr
fr
R∈R(fr )
ω B − KR eR − Kω ω B , to track Rd
3. compute τ r = ω B × Jω
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Control Algorithm
p, ṗ
R
Force (18) u1
LBFA
Projection
Dyn. p, ṗ
Model R, ω
u
R
d
Des. Ori. (15)
Attitude (19) 2
(1)-(5)
ω
R
Force fr
fr
Rr
fr
R∈R(fr )
ω B − KR eR − Kω ω B , to track Rd
3. compute τ r = ω B × Jω
4. compute u to implement τ r and fr
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Simulation with a Hexarotor: Increasing Position Acceleration
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Simulations with a Hexarotor: Increasing Cant Angle
desired vs. actual position
increasing cant angle α ∈ [0◦ , 35◦ ]
40
λ
λ
0.8
α
max
0
[deg]
[m]
30
−0.8
pr
−1.6
x
0
5
10
15
pr
y
20
pr
z
25
pB
x
pB
30
x
35
pB
20
10
0
x
Underactuated
40
0
5
10
Transition phase
15
20
Fully actuated
25
30
35
40
time [s]
desired vs. actual pitch
propeller forces
15
15
10
10
0
[N]
[deg]
5
−5
−10
−15
−20
0
θr
θd
5
10
5
0
θB
f1
15
20
25
30
35
40
−5
0
5
10
15
20
f2
f3
25
f4
f5
f6
30
35
40
30
35
40
power efficiency
[N/N]
1
0.9
0.8
0
ηf
5
10
15
20
25
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Conclusions
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Future Work: Physical Interaction with a Rigidly-attached Tool
• physical interaction with a rigidly-attached tool
preliminary experiment
exploit the 6 DoFs for position and orientation independent regulation
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Future Work: Aerial Manipulators with Fully-Actuated Bases
• aerial manipulators with a fully-actuated base
preliminary simulation
control of a ‘truly’ redundant aerial manipulator
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Future Work: Exploit Reversible Propellers
• exploit possibility o reversible propellers
speed reversing
(slow motion)
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Open Problems
Cope with the non-idealities when in aerial physical interaction
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Open Problems
• speed–rate saturation
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Open Problems
• speed–rate saturation
• reversing lag
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Acknowledgements
For related work, visit http://homepages.laas.fr/afranchi/robotics/
For this method: A. Franchi, R. Carli, D. Bicego, and M. Ryll, “Full-pose geometric tracking
control on SE(3) for laterally bounded fully-actuated aerial vehicles”, in ArXiv:1605.06645,
2016. [Online]. Available: http://arxiv.org/abs/1605.06645
Markus Ryll
Davide Bicego
(PostDoc at LAAS-CNRS)
(PhD Student at LAAS-CNRS)
Questions?
Ruggero Carli
Sujit Rajappa
(Prof. at the University of Padova)
(PhD Student at MPI for Biol.
Cybernetics)
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Fully Actuated Aerial Platforms for Aerial Manipulation: Design and

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