Download - 2.2.a.lecture Gianluca Antonelli
Introduction to modeling and controlof underwater vehicle-manipulator systems
Gianluca Antonelli
Universita di Cassino e del Lazio Meridionale
http://webuser.unicas.it/lai/robotica
http://www.eng.docente.unicas.it/gianluca antonelli
TRIDENT school
Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Targeted audience and talk’s shape
SAUVIM
50 minutes talk about the mathematical foundations ofUnderwater Vehicle Manipulator Systems (UVMS)
Educational shape (entry level)
knowledge of
mathematics, physicscontrolbasic robotics
equations, equations still equations. . .
Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Outline
ALIVE
UVMSs
Introduction
Mathematical modeling
Two words about dynamic control
Kinematic control
Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
(semi)autonomus UVMSs
PETASUS
Use of a manipulator is common for ROV, mainly in remotelycontrolled or in a master-slave configuration
Among the first autonomus modes:
AMADEUS I & II before 2000, EU
SAUVIM 1997–, USA
PETASUS, Korea
ALIVE 2000-2003, EU
Twin Burger + manipulator, Japan
TRIDENT 2010-2012, EU
Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Notation1
yzb
η1
x
z
θ (pitch)
φ (roll)
ψ (yaw)
ω (heave)
υ (sway)yb
υ (surge)
xb
Forces and ν1,ν2 η1,η
2
momentsMotion along x Surge X u x
Motion along y Sway Y v y
Motion along z Heave Z w z
Rotation about x Roll K p φ
Rotation about y Pitch M q θ
Rotation about z Yaw N r ψ
1[Fossen(1994)]Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Rigid body attitude
Euler angles commonly used
roll
pitch
yaw
ok for the vehicle, designed stable in roll and pitch
For the end-effector possible issues of representation singularities→ non-minimal representations (quaternions)
Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Rigid body kinematics
η =
[
η1
η2
]
∈ R6 ν =
[
ν1
ν2
]
∈ R6
and by defining the matrix Je(RIB) ∈ R
6×6
Je(RIB) =
[
RBI O3×3
O3×3 Jk,o(RIB)
]
it isν = Je(R
IB)η
��
��
��✠
bodyfixed velocities
Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Rigid body dynamics
moving in the free space
MRBν +CRB(ν)ν = τ v
��
��
��✠
MRB =
[
mI3 −mS(rbC)mS(rbC) IOb
]
∈ R6×6
��✒
bodyfixed acceleration
❅❅❅❘
6dof force/moment at the body
Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Added mass and inertia
A body moving in a fluid accelerates it (ρ ≈ 1000 kg/m3)Need to account for an additional inertia(the added mass is not a quantity to be added to the body such that
it has an increased mass)
For submerged bodies, with common AUV shape at low velocities:
MA = − diag {Xu, Yv, Zw,Kp,Mq, Nr}
CA =
0 0 0 0 −Zww Yvv
0 0 0 Zww 0 −Xuu
0 0 0 −Yvv Xuu 00 −Zww Yvv 0 −Nrr Mqq
Zww 0 −Xuu Nrr 0 −Kpp
−Yvv Xuu 0 −Mqq Kpp 0
Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Damping
Viscosity of the fluid causes dissipative drag and lift forces to the body
lift
drag
relative flow
The simplest model is drag-only, diagonal, linear/quadratic in velocity
DRB(ν)ν
DRB(ν) = − diag {Xu, Yv, Zw,Kp,Mq, Nr}+
− diag{
Xu|u| |u| , Yv|v| |v| , Zw|w| |w| ,Kp|p| |p| ,Mq|q| |q| , Nr|r| |r|}
Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Current
Assume a current constant and irrotational in the inertial frame
νIc =
νc,xνc,yνc,z000
νIc = 0
effects added considering the relative velocity in body-fixed frame
νr = ν −RBI ν
Ic
in the Coriolis/centripetal and damping
Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Current
ob
ob
xb
xb
yb
yb
o x
y
νIc
ψ
intuitively, the current is pushing the vehicle
Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Gravity and buoiancy
ob
ob
xb
xb
zb
zb
oxz
rgrg fgfg
rbrbf bf b Mr
gI
θ
fG(RBI ) = RB
I
00W
fB(RBI ) = −RB
I
00B
MR = rBG × fG(RBI ) + rBB × fG(R
BI )
linear in the 3 parameters: WrB
G−BrB
Bconstant in bodyfixed
Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Some dynamic considerations
Considering the sole vehicle two effects affects steady state
current effect, constant in the inertial frame
restoring forces, (depends on) constant in the body-fixed frame
Proper integral/adaptive actions need to be designed for finepositioning to avoid disturbance caused by the controller 2
2[Antonelli(2007)]Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Some dynamic considerations
Considering the sole vehicle two effects affects steady state
current effect, constant in the inertial frame
restoring forces, (depends on) constant in the body-fixed frame
Proper integral/adaptive actions need to be designed for finepositioning to avoid disturbance caused by the controller 2
νIcνI
c
inertial body-fixed
current
compensation
during a 90◦
rotation
2[Antonelli(2007)]Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Thrusters
6 or more for full vehicle control (thrust required also in hovering)force/moment (nonlinear) function of
propeller revolution
fluid speed
input torque
affected by several parameters
fluid density
tunnel cross-sectional area
tunnel length
propeller diameter and input-output volumetric flowrate
main cause of bandwidth constraints and limit cycles
Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Some references
For modeling and control of marine vehicles in a control perspective:
[Fossen(1994)]
[Fossen(2002)]
[Antonelli et al.(2008)Antonelli, Fossen, and Yoerger]
[Fossen(2011)]
Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
UVMS kinematics
Oi
η1
ηee
❅❅❘endeffector velocities
❍❍❍❍❍❍❍❍❍❍❍❍❥Jacobian
system velocitiesηee =
[
ηee1
ηee2
]
= Jw(RIB , q)ζ ζ =
ν1
ν2
q
Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
UVMS dynamics
Dynamics via classical Newton-Euler equations by propagating thevelocities and forces
Bi
Ci
Oi−1
Oiri−1,i
ri−1,C
ri−1,B
ri,C
f i,µi
f i+1,µi+1
−ρ∇ig
migdi
Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
UVMS dynamics in matrix form
M(q)ζ +C(q, ζ)ζ +D(q, ζ)ζ + g(q,RIB) = τ
formally equal to a groundfixed industrial manipulator 3
however. . .
Uncertainty in the model knowledge
Low bandwidth of the sensor’s readings
Difficulty to control the vehicle in hovering
Dynamic coupling between vehicle and manipulator
Kinematic redundancy of the system
3[Siciliano et al.(2008)Siciliano, Sciavicco, Villani, and Oriolo]Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
UVMS dynamics
Movement of vehicle and manipulator coupled
movement of the vehicle carrying the manipulator
law of conservation of momentum
Need to coordinate
at velocity level ⇒ kinematic control
at torque level ⇒ dynamic control 4
4[McLain et al.(1996b)McLain, Rock, and Lee][McLain et al.(1996a)McLain, Rock, and Lee]
Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Need for coordination
Coordination and redundancy exploitation is required5:
Redundancy at torque level?
Need to exactly compensate forthe dynamics, not appropriatefor the underwater environment
Space manipulator literature?
The assumption of themomentum conservation is notvalid
5[Khatib(1987), Sentis(2007),Nenchev et al.(1992)Nenchev, Umetani, and Yoshida]
Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Need for coordination
Coordination and redundancy exploitation is required5:
Redundancy at torque level?
Need to exactly compensate forthe dynamics, not appropriatefor the underwater environment
Space manipulator literature?
The assumption of themomentum conservation is notvalid
5[Khatib(1987), Sentis(2007),Nenchev et al.(1992)Nenchev, Umetani, and Yoshida]
Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Need for coordination
Coordination and redundancy exploitation is required5:
Redundancy at torque level?
Need to exactly compensate forthe dynamics, not appropriatefor the underwater environment
Space manipulator literature?
The assumption of themomentum conservation is notvalid
5[Khatib(1987), Sentis(2007),Nenchev et al.(1992)Nenchev, Umetani, and Yoshida]
Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Needs for coordination
let us move to the kinematical level
What is coming next
an example
a short review
algorithms & tasks for UVMSs
balance movement between vehicle/manipulator
Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
A first kinematic solution
Hoping the vehicle in hovering is not the best strategy to e.e. finepositioning6, better to kinematically compensate with the manipulator
6[Hildebrandt et al.(2009)Hildebrandt, Christensen, Kerdels, Albiez, and Kirchner]Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Kinematic control in pills
A robotic system is kinematically redundant when it possesses moredegrees of freedom than those required to execute a given task
Redundancy may be used to add additional tasks and to handlesingularities
Example for the sole end-effector trajectory
ηee,d ηd, qd τ η, q
IK control
offline trajectory planning not appropriate underwater
Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Kinematic control in pills -2-
Starting from a generic m-dimensional task
σ = f(η, q) ∈ Rm
it is required to invertσ = J(η, q)ζ
The configurations at which J ∈ Rm×6+n is rank deficient are
kinematic singularities
The mobility of the structure is reduced
Infinite solutions to the inverse kinematics problem might exist
Close to a kinematic singularity at small task velocities cancorrespond large joint velocities
Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Kinematic control in pills -3-
σ = Jζ inverted by solving proper optimization problems
Pseudoinverseζ = J †σ = JT
(
JJT)−1
σ
Transpose-basedζ = JTσ
Weighted pseudoinverse
ζ = J†W
σ = W−1JT(
JW−1JT)−1
σ
Damped Least-Squares
ζ = JT(
JJT + λ2Im
)−1σ
need for closedloop also. . .
Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Kinematic control in pills -4-
Handling several tasks7
Extended JacobianAdd additional (6 + n)−m constraints
h(η, q) = 0 with associated Jh
such that the problem is squared with
[
σ
0
]
=
[
J
Jh
]
ζ
7[Chiaverini et al.(2008)Chiaverini, Oriolo, and Walker]Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Kinematic control in pills -4-
Augmented JacobianAn additional task is given
σh = h(η, q) with associated Jh
such that the problem is squared with
[
σ
σh
]
=
[
J
Jh
]
ζ
Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Kinematic control in pills -4-
✛✚
✘✙
ζ
❘
✛✚
✘✙
σ
A mapping from the controlled variable to the task space
An inverse mapping is required
Additional tasks may be considered (e.g. task priority)
Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Kinematic control in pills -4-
✛✚
✘✙
ζ
❘
✛✚
✘✙
σ
✖✕✗✔
■
A mapping from the controlled variable to the task space
An inverse mapping is required
Additional tasks may be considered (e.g. task priority)
Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Kinematic control in pills -4-
✛✚
✘✙
ζ
❘
✛✚
✘✙
σ
✖✕✗✔
■ σa
✚✙✛✘
σb
✙
✖✕✗✔
✶
A mapping from the controlled variable to the task space
An inverse mapping is required
Additional tasks may be considered (e.g. task priority)
Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Kinematic control in pills -4-
Task priority redundancy resolution
σh = h(η, q) with associated Jh
further projected on the the null space of the higher priority one
ζ = J†σ +[
Jh
(
I − J †J)]† (
σh − JhJ†σ)
Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Kinematic control in pills -4-
Singularity robust task priority redundancy resolution 8
σh = h(η, q) with associated Jh
further projected on the the null space of the higher priority one
ζ = J †σ +(
I − J†J)
J†
hσh
8we are talking about algorithmic singularities here. . .Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Kinematic control in pills -4-
AMADEUS
Agility task priority9
Task priority framework to handle both precision and set tasksEach task is the norm of the corresponding error (i.e., mi = 1)Recursive constrained least-squares within the set satisfyinghigher-priority tasks
9[Casalino et al.(2012)Casalino, Zereik, Simetti, Sperinde, and Turetta]Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Kinematic control in pills -4-
Behavioral algorithms (behavior=task), bioinspired, artifical potentials
sensorsbehavior b
ζ2⊗
α2
behavior a
ζ1
supervisor
⊗
α1
behavior c
ζ3⊗
α3
∑
ζ
Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Tasks to be controlled
Given 6 + n DOFs and m-dimensional tasks: End-effector
position, m = 3
pos./orientation, m = 6
distance from a target, m = 1
alignment with the line of sight, m = 2
Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Tasks to be controlled
Manipulator joint-limits
several approaches proposed, m = 1 to n, e.g.
h(q) =
n∑
i=1
1
ci
qi,max − qi,min
(qi,max − qi)(qi − qi,min)
Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Tasks to be controlled
Drag minimization, m = 1 10
h(q) = DT(q, ζ)WD(q, ζ)
within a second order solution
ζ = J †(
σ − Jζ)
− k(
I − J†J)
([
∂h∂η∂h∂q
]
+∂h
∂ζ
)
10[Sarkar and Podder(2001)]Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Tasks to be controlled
Manipulability/singularity, m = 1
h(q) =∣
∣det(
JJT)∣
∣
(In 11 priorities dynamically swapped between singularity and e.e.)
joints
inhibited direction
singularitysingularity
setclose to
11[Kim et al.(2002)Kim, Marani, Chung, and Yuh]Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Tasks to be controlled
Restoring moments:
m = 3 keep close gravity-buoyancy of the overall system 12
m = 2 align gravity and buoyancy (SAUVIM is 4 tons) 13
f b
f g
τ 2
12[Han and Chung(2008)]13[Marani et al.(2010)Marani, Choi, and Yuh]
Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Tasks to be controlled
Obstacle avoidance m = 1
Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Tasks to be controlled
Workspace-related variablesVehicle distance from the bottom, m = 1Vehicle distance from the target, m = 1
Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Tasks to be controlled
Sensors configuration variables
Vehicle roll and pitch, m = 2Misalignment between the camera optical axis and the target lineof sight, m = 2
Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
However. . .
End effector going out of the workspace and one (eventually weighted)task always leads to singularity
❅❅❅❘
manipulator stretched
Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Balance movement between vehicle and manipulator
Need to distribute the motion e.g.:
move mainly the manipulator when target in workspace
move the vehicle when approaching the workspace boundaries
move the vehicle for large displacement
Some solutions, among them dynamic programming or fuzzy logic
Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Fuzzy logic to balance the movement14
Within a weighted pseudoinverse framework
J†W
= W−1JT(
JW−1JT)−1
W−1(β) =
[
(1− β)I6 O6×n
On×6 βIn
]
with β ∈ [0, 1] output of a fuzzy inference engineSecondary tasks activated by additional fuzzy variables αi ∈ [0, 1]
ζ = J†W
(xE,d +KEeE) +(
I − J†W
JW
)
(
∑
i
αiJ†s,iws,i
)
Only one αi active at onceNeed to be complete, distinguishable, consistent and compactBeyond the dicotomy fuzzy/probability theory very effective intransferring ideas
14[Antonelli and Chiaverini(2003)]Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Dynamic programming to balance the movement15
Freeze the vehicle velocity and implement the agility task priorityto the sole manipulator
Freeze the manipulator velocity and find the vehicle velocityneeded for the remaining tasks components not satisfied
ν
νe
15[Casalino et al.(2012)Casalino, Zereik, Simetti, Sperinde, and Turetta]Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Dynamic programming to balance the movement15
Freeze the vehicle velocity and implement the agility task priorityto the sole manipulator
Freeze the manipulator velocity and find the vehicle velocityneeded for the remaining tasks components not satisfied
ν
νe
15[Casalino et al.(2012)Casalino, Zereik, Simetti, Sperinde, and Turetta]Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Acknowledge
Several researchers kindly provided the materials/video (or theexplications...) for this talkIn casual order:
ISME (Pino Casalino, . . . )
TRIDENT partners (Pedro Sanz, Pere Ridao, . . . )
SAUVIM partners (Junku Yuh, Giacomo Marani, . . . )
DFKI (Frank Kirchner)
OTTER (Tim McLain)
Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Bibliography I
G. Antonelli.
Underwater robots. Motion and force control of vehicle-manipulator systems.
Springer Tracts in Advanced Robotics, Springer-Verlag, Heidelberg, D, 2ndedition, June 2006.
G. Antonelli.
On the use of adaptive/integral actions for 6-degrees-of-freedom control ofautonomous underwater vehicles.
IEEE Journal of Oceanic Engineering, 32(2):300–312, April 2007.
G. Antonelli and S. Chiaverini.
Fuzzy redundancy resolution and motion coordination for underwatervehicle-manipulator systems.
IEEE Transactions on Fuzzy Systems, 11(1):109–120, 2003.
G. Antonelli, T. Fossen, and D. Yoerger.
Springer Handbook of Robotics, chapter Underwater Robotics, pages 987–1008.
B. Siciliano, O. Khatib, (Eds.), Springer-Verlag, Heidelberg, D, 2008.
Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Bibliography II
G. Casalino, E. Zereik, E. Simetti, S. Torelli A. Sperinde, and A. Turetta.
Agility for underwater floating manipulation: Task & subsystem priority basedcontrol strategy.
In 2012 IEEE/RSJ International Conference on Intelligent Robots andSystems, Vilamoura, PT, october 2012.
S. Chiaverini, G. Oriolo, and I. D. Walker.
Springer Handbook of Robotics, chapter Kinematically RedundantManipulators, pages 245–268.
B. Siciliano, O. Khatib, (Eds.), Springer-Verlag, Heidelberg, D, 2008.
T.I. Fossen.
Guidance and Control of Ocean Vehicles.
Chichester New York, 1994.
Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Bibliography III
T.I. Fossen.
Marine Control Systems: Guidance, Navigation and Control of Ships, Rigs andUnderwater Vehicles.
Marine Cybernetics, Trondheim, Norway, 2002.
T.I. Fossen.
Handbook of marine craft hydrodynamics and motion control.
Wiley, 2011.
J. Han and W.K. Chung.
Coordinated motion control of underwater vehicle-manipulator system withminimizing restoring moments.
In Intelligent Robots and Systems, 2008. IROS 2008. IEEE/RSJ InternationalConference on, pages 3158–3163. IEEE, 2008.
Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Bibliography IV
M. Hildebrandt, L. Christensen, J. Kerdels, J. Albiez, and F. Kirchner.
Realtime motion compensation for ROV-based tele-operated underwatermanipulators.
In IEEE OCEANS 2009-Europe, pages 1–6, 2009.
O. Khatib.
A unified approach for motion and force control of robot manipulators: Theoperational space formulation.
IEEE Journal of Robotics and Automation, 3(1):43–53, 1987.
J. Kim, G. Marani, WK Chung, and J. Yuh.
Kinematic singularity avoidance for autonomous manipulation in underwater.
Proceedings of PACOMS, 2002.
G. Marani, S.K. Choi, and J. Yuh.
Real-time center of buoyancy identification for optimal hovering in autonomousunderwater intervention.
Intelligent Service Robotics, 3(3):175–182, 2010.
Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Bibliography V
T.W. McLain, S.M. Rock, and M.J. Lee.
Coordinated control of an underwater robotic system.
In Video Proceedings of the 1996 IEEE International Conference on Roboticsand Automation, pages 4606–4613, 1996a.
T.W. McLain, S.M. Rock, and M.J. Lee.
Experiments in the coordinated control of an underwater arm/vehicle system.
Autonomous robots, 3(2):213–232, 1996b.
D. Nenchev, Y. Umetani, and K. Yoshida.
Analysis of a redundant free-flying spacecraft/manipulator system.
Robotics and Automation, IEEE Transactions on, 8(1):1–6, 1992.
N. Sarkar and T.K. Podder.
Coordinated motion planning and control of autonomous underwatervehicle-manipulator systems subject to drag optimization.
Oceanic Engineering, IEEE Journal of, 26(2):228–239, 2001.
Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012
Bibliography VI
L. Sentis.
Synthesis and Control of Whole-Body Behaviors in Humanoid Systems.
PhD thesis, Stanford University, 2007.
B. Siciliano, L. Sciavicco, L. Villani, and G. Oriolo.
Robotics: modelling, planning and control.
Springer Verlag, 2008.
Gianluca Antonelli TRIDENT school, Mallorca, 1 october 2012