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.

.