Passive Bilateral Control of
Teleoperators under Constant Time-Delay
Dongjun Lee and Mark W. Spong
Coordinated Science Laboratory
University 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
Dongjun Lee and Mark W. Spong, CSL, UIUC
IFAC 2005 Prague
Contributions
Teleoperator with Constant Time-Delays
F1 (t)
Master
Human
Operator v1 (t) Robot
T1 (t)
Master
Comm.&
v1 (t)
Control


T2 (t)
Slave
Slave
Comm.&
v (t) Robot
Control 2
F2 (t)
Slave
v2 (t) Environ.
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
Dongjun Lee and Mark W. Spong, CSL, UIUC
IFAC 2005 Prague
Outline
1. Energetic Passivity and Controller Passivity
2. Control Design and Analysis
3. Simulation
4. Conclusion
Dongjun Lee and Mark W. Spong, CSL, UIUC
IFAC 2005 Prague
Passivity for Interaction Stability and Safety
Closed-Loop Teleoperator as a Two-Port System
F1 (t)
Master
Human
Operator v1 (t) Robot
T1 (t)
Master
Comm.&
v1 (t)
Control


T2 (t)
Slave
Slave
Comm.&
v (t) Robot
Control 2
F2 (t)
Slave
v2 (t) Environ.
Closed-loop teleoperator
Energetic Passivity of the Closed-loop Teleoperator
Mechanical power from
closed-loop teleoperator
finite constant (depending
on initial condition)
- maximum extractable energy from the closed-loop teleoperator is bounded
- the closed-loop teleoperator does not generate energy by itself
- 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
Dongjun Lee and Mark W. Spong, CSL, UIUC
IFAC 2005 Prague
Controller Passivity and Robust Passivity
Closed-Loop Teleoperator as a Two-Port System
T1 (t)
F1 (t)
Master
Human
Operator v1 (t) Robot
T2 (t)

Master
Comm.&
v1 (t)
Control
Slave
Slave
Comm.&
v (t) Robot
Control 2

F2 (t)
Slave
v2 (t) Environ.
Communication + Control
Controller Passivity [Lee&Li]
Mechanical power generated
by the controller
finite constant
does not rely on the open-loop
dynamics but only on the
controller structure
combined communication+control block
generates only limited amount of energy
imply
Energetic Passivity
1. Simpler passivity analysis
2. Passivity can be ensured
regardless of model uncertainty
(Robust passivity is achieved)
maximum extractable energy from
the closed-loop system is bounded
Dongjun Lee and Mark W. Spong, CSL, UIUC
IFAC 2005 Prague
Outline
1. Energetic Passivity and Controller Passivity
2. Control Design and Analysis
3. Simulation
4. Conclusion
Dongjun Lee and Mark W. Spong, CSL, UIUC
IFAC 2005 Prague
Control Design
Plant
Dynamics
Communication
Structure
T1 (t)
F1 (t)
Master
Master
Human
Comm.&
Operator v1 (t) Robot v1 (t)
Control
local sensing


T (t)
F (t)
2
2
Slave
Slave
Slave
Comm.&
v (t) Robot v2 (t) Environ.
Control 2
local sensing
PD-Based Control
D-control
action
P-control action w/
passifying dissipation
additional
viscous
damping
(e.g. device
damping)
Closed-loop teleoperator is
energetically passive if
Dongjun Lee and Mark W. Spong, CSL, UIUC
IFAC 2005 Prague
Controller Passivity
Controller
Passivity
(i.e. controller generates only bounded amount of energy)
Controller Power
Decomposition
D-action
power
P-action
power
additional
viscous
damping
(quadratic
in velocity)
- How to ensure that the energy generations by
sd(t) and sp(t) be bounded?
Dongjun Lee and Mark W. Spong, CSL, UIUC
IFAC 2005 Prague
D-action Passivity: Lyapunov-Krasovskii Functional
Lyapunov-Krasovskii (LK) functional
sum of master and slave velocities
D-action Passivity
energy generation bounded by
Lyapunov-Krasovskii
as a storage function
Dongjun Lee and Mark W. Spong, CSL, UIUC
IFAC 2005 Prague
P-action Passivity: Parseval’s Identity
Spring
Energy
:master-slave
position error
Parseval’s identity
convert integral time-domain passivity condition
into a solvable algebraic condition in frequency domain
dissipating
energy
Passivity
Condition
positive-definite if
P-action Passivity
energy generation bounded by
the spring energy
Dongjun Lee and Mark W. Spong, CSL, UIUC
IFAC 2005 Prague
Energetic Structure
Communication+Control
Lyapunov
-Krasovskii
function
Vd(t)
Spring
energy
Vp(t)
sd(t)
+
+
Closed-loop teleoperator
Control
port
T1v1+T2v2
Environ.
port
Open-Loop
Master +
Slave
Robots
Human
+
F1v1+F2v2 Slave
Environ.
sp(t)
Dissipated via Kd
P(t)
under passivity condition (dissipated)
Energy storage: kinetic energy
- 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 (d12) and the slave environment (d22)
Energy inputs from
huamn/environment
Dongjun Lee and Mark W. Spong, CSL, UIUC
IFAC 2005 Prague
Position Coordination and Force Reflection
1. If the human and slave environment are passive. Then, master-slave velocity
(i.e. coupled stability) and position coordination error are bounded.
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).
1)
2)
: Barbalat’s lemma w/
boundedness assumption
3) Closed-loop dynamics
3. Bilateral force reflection: If master and slave velocity and acceleration are
zero (i.e. static manipulation), F1(t)→ - F2(t).
Dongjun Lee and Mark W. Spong, CSL, UIUC
IFAC 2005 Prague
Simulation Results
slave contacts
with a wall
- 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
Dongjun Lee and Mark W. Spong, CSL, UIUC
IFAC 2005 Prague
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 framework
5. Explicit position feedback would be useful for such an application as Internet
teleoperation with packet-loss
6. The proposed framework has also been extended to the cases where communication
delays are asymmetric and unknown with less required-damping
Dongjun Lee and Mark W. Spong, CSL, UIUC
IFAC 2005 Prague
Parseval’s Identity and L2-Stability
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.
quadratic
in v1,v2
Dongjun Lee and Mark W. Spong, CSL, UIUC
IFAC 2005 Prague