IFAC 2005 PragueDongjun Lee and Mark W. Spong, CSL, UIUC
Passive Bilateral Control of Teleoperators under Constant Time-Delay
Dongjun Lee and Mark W. Spong
Coordinated Science LaboratoryUniversity of Illinois at Urbana-Champaign
Research support by NSF IIS 02-33314/CCR 02-09202, ONR N00014-02-1-0011, and College of Engineering at UIUC
IFAC 2005 PragueDongjun Lee and Mark W. Spong, CSL, UIUC
Contributions
1. Novel PD- based control framework for passive bilateral teleoperation with constant time-delays without relying on scattering-based teleoperation
2. Passivity is established using the Parseval’s identity, Lyapunov-Krasovskii technique, and controller passivity concept
3. Master-slave position coordination with explicit position feedback
4. Bilateral force reflection in the static manipulation
Teleoperator with Constant Time-Delays
SlaveRobot
SlaveComm.& Control
SlaveEnviron.
T2 (t)
v2 (t)
F2 (t)
v2 (t)MasterRobot
MasterComm.& Control
HumanOperator
T1 (t)
v1 (t)
F1 (t)
v1 (t)
IFAC 2005 PragueDongjun Lee and Mark W. Spong, CSL, UIUC
Outline
1. Energetic Passivity and Controller Passivity
2. Control Design and Analysis
3. Simulation
4. Conclusion
IFAC 2005 PragueDongjun Lee and Mark W. Spong, CSL, UIUC
Passivity for Interaction Stability and Safety
- Interaction stability: the feedback-interconnection is stable with any passive humans [Hogan89] /environments without relying on their detailed models- Interaction safety: possible damage on human/environment is bounded
Energetic Passivity of the Closed-loop Teleoperator
- maximum extractable energy from the closed-loop teleoperator is bounded- the closed-loop teleoperator does not generate energy by itself
Mechanical power from closed-loop teleoperator
finite constant (depending on initial condition)
Closed-Loop Teleoperator as a Two-Port System
SlaveRobot
SlaveComm.& Control
SlaveEnviron.
T2 (t)
v2 (t)
F2 (t)
v2 (t)MasterRobot
MasterComm.& Control
HumanOperator
T1 (t)
v1 (t)
F1 (t)
v1 (t)
Closed-loop teleoperator
IFAC 2005 PragueDongjun Lee and Mark W. Spong, CSL, UIUC
Controller Passivity and Robust Passivity
SlaveRobot
SlaveComm.& Control
SlaveEnviron.
T2 (t)
v2 (t)
F2 (t)
v2 (t)MasterRobot
MasterComm.& Control
HumanOperator
T1 (t)
v1 (t)
F1 (t)
v1 (t)
Closed-Loop Teleoperator as a Two-Port System
Communication + Control
finite constant
Energetic Passivity
maximum extractable energy from the closed-loop system is bounded
imply1. Simpler passivity analysis
2. Passivity can be ensured regardless of model uncertainty (Robust passivity is achieved)
does not rely on the open-loop dynamics but only on the
controller structure
Controller Passivity [Lee&Li]
combined communication+control block generates only limited amount of energy
Mechanical power generated by the controller
IFAC 2005 PragueDongjun Lee and Mark W. Spong, CSL, UIUC
Outline
1. Energetic Passivity and Controller Passivity
2. Control Design and Analysis
3. Simulation
4. Conclusion
IFAC 2005 PragueDongjun Lee and Mark W. Spong, CSL, UIUC
Control Design
Closed-loop teleoperator is energetically passive if
SlaveRobot
SlaveComm.& Control
SlaveEnviron.
T2 (t)
v2 (t)
F2 (t)
v2 (t)
MasterRobot
MasterComm.& Control
HumanOperator
T1 (t)
v1 (t)
F1 (t)
v1 (t)
local sensing local sensing
Plant Dynamics
Communication
Structure
PD-Based Control
D-controlaction
additional viscousdamping
(e.g. device damping)P-control action w/
passifying dissipation
IFAC 2005 PragueDongjun Lee and Mark W. Spong, CSL, UIUC
Controller Passivity
ControllerPassivity
Controller Power
Decomposition
(i.e. controller generates only bounded amount of energy)
D-actionpower
P-action power
additionalviscous
damping (quadratic in velocity)
- How to ensure that the energy generations by sd(t) and sp(t) be
bounded?
IFAC 2005 PragueDongjun Lee and Mark W. Spong, CSL, UIUC
D-action Passivity: Lyapunov-Krasovskii Functional
D-action Passivity
energy generation bounded by Lyapunov-Krasovskiias a storage function
Lyapunov-Krasovskii (LK) functional
sum of master and slave velocities
IFAC 2005 PragueDongjun Lee and Mark W. Spong, CSL, UIUC
P-action Passivity: Parseval’s Identity
P-action Passivityenergy generation bounded by
the spring energy
Spring Energy
:master-slave position error
Parseval’s identityconvert integral time-domain passivity condition
into a solvable algebraic condition in frequency domain
Passivity Conditio
n
positive-definite if
dissipatingenergy
IFAC 2005 PragueDongjun Lee and Mark W. Spong, CSL, UIUC
Energetic Structure
Open-LoopMaster +
SlaveRobots
Human +
SlaveEnviron.
Closed-loop teleoperator
++
sd(t)
P(t)(dissipated)
T1v1+T2v2 F1v1+F2
v2
Communication+Control
Vd(t)
Energy storage: kinetic energy
sp(t)
Dissipated via Kd under passivity condition
Vp(t)
Lyapunov-Krasovskii
function
Springenergy
- Controller passivity: comm.+control blocks are passified altogether
- Key relation: total energy in the three energy storages can not increase more than energy inputs from the passive human operator (d1
2) and the slave environment (d22)
Controlport
Environ.port
Energy inputs fromhuamn/environment
IFAC 2005 PragueDongjun Lee and Mark W. Spong, CSL, UIUC
Position Coordination and Force Reflection1. If the human and slave environment are passive. Then, master-slave velocity (i.e. coupled stability) and position coordination error are bounded.
3. Bilateral force reflection: If master and slave velocity and acceleration are zero (i.e. static manipulation), F1(t)→ - F2(t).
1)
2. Master-slave position coordination: Suppose that M1(q1), M2(q2) and their first & second partial-derivatives w.r.t. q1,q2 are bounded for all q1,q2. Then, if F1(t)=F2(t)=0 (i.e. no human/environmental forcing), q1(t) →q2(t).
2)
3) Closed-loop dynamics
: Barbalat’s lemma w/ boundedness assumption
IFAC 2005 PragueDongjun Lee and Mark W. Spong, CSL, UIUC
Simulation Results
- 2-DOF serial-link nonlinear planar master and slave robots - a wall installed in the slave environment with the reaction force only along the x-axis - human as a PD-type position controller- both the forward and backward delays = 2 sec (i.e. round-trip delay = 4sec)- free-motion and contact behavior are stable even with the large time-delay- contact force is faithfully reflected to the human when the slave contacts with the wall - master-slave position coordination achieved whenever the contact is removed
slave contacts with a wall
IFAC 2005 PragueDongjun Lee and Mark W. Spong, CSL, UIUC
Conclusion
1. We propose a novel PD-based control framework for passive bilateral teleoperation with constant time-delays without relying on scattering-based teleoperation
2. Utilizing controller passivity concept, Lyapunov-Krasovskii technique, and the Parseval’s identity, the proposed framework passifies the combination of the control and communication blocks together
3. The proposed framework enforces master-slave position coordination and bilateral force reflection in the static manipulation
4. Simulation results validate the proposed framework5. Explicit position feedback would be useful for such an
application as Internet teleoperation with packet-loss6. The proposed framework has also been extended to the cases
where communication delays are asymmetric and unknown with less required-damping
IFAC 2005 PragueDongjun Lee and Mark W. Spong, CSL, UIUC
Parseval’s Identity and L2-Stability
quadratic in v1,v2
Suppose that the human and slave environment are passive and L-stable impedance maps (i.e. F1,F2 are also bounded). Suppose further that the first partial derivatives of M1(q1), M2(q2) w.r.t. q1,q2 are bounded for all q1,q2. Then, if the v1(0),v2(0) and qE(0) are bounded, v1(t),v2(t)L2. Therefore, qE(t)=v1(t)-v2(t) L2 and the Parseval’s identity holds for all t 0.
.