Teleoperation Research Group

1
Experimental Comparison and Complexity Measure
for Bilateral Internet-Based Teleoperators

• Teleoperation Research Group
• Erick J. Rodríguez-Seda
• Dr. Mark W. Spong
• Dr. Dongjun Lee
• March 3, 2006

2
Outline

• Introduction
• Objectives
• Experimental Setup
• Teleoperation Schemes
• Experimental Comparison
• Measure of Complexity
• Final Remarks
• Acknowledgements
• Questions

3
Introduction

• Expansion of Internet
• World wide, cheap
• Large number of Applications
• Communication Problems
• - Stability
• - Performance
• Solutions
• - haptic, force control, synchronization,
  passive
• decomposition, predictors, etc.
• - lack of comparison information
• Previous Work
• - Invariant-Time Delay
• - No Packet Loss

Taylor K. and Dalton B. IEEE Robot. Auntomat.
7(1), 27-34 (2000) Hirche S. and Buss M. 43rd
IEEE CDC 4010-4016 (2004)
4
Objective

• The present work aims to identify and recognize
  the weakness and strength of several published
  algorithms for motion and force control of
  bilateral internet teleoperators. Different
  control techniques based on wave variable, smith
  predictors, and recent algorithms on
  synchronization are compared under variable time
  delay, packet loss and environmental
  disturbances.

5
Outline

• Introduction
• Objectives
• Experimental Setup
• Teleoperation Schemes
• Experimental Comparison
• Measure of Complexity
• Final Remarks
• Acknowledgements
• Questions

6
Experimental Setup
COMPUTER STATION (Control Scheme, Internet
Simulator)
Aluminum Wall In a Remote Location
Force Sensors Master and Slave
SLAVE ROBOT In a Remote Location
MASTER ROBOT Directly Operated by a Person
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Internet Model

• Markov Chain
• UDP
• Time-variant delay
• One Way
• Minimum 48 ms
• Maximum 144 ms
• Mean 80 ms
• Standard Deviation 22 ms
• Packet Loss Rate
• 40 - 60 of Data
• Comparable with a survey by Oboe and Fiorini
  (1998).

Borisov A. and Miller G. 43rd IEEE CDC,
3726-3131(2004) Oboe R. and Fiorini P. Int.
J. Robot. Res. 17(4), 433-449 (1998)
8
Outline

• Introduction
• Objectives
• Experimental Setup
• Teleoperation Schemes
• Experimental Comparison
• Measure of Complexity
• Final Remarks
• Acknowledgements
• Questions

9
Control Schemes

• Wave Scattering Transformation (WS)
• Digital Data Reconstruction Filter (DD)
• Wave Integral and Reconstruction Filter (WI)
• Proportional (P) and Proportional-Derivative (PD)
  Control
• Redefined Input and Output Mapping (RM)
• Wave Predictor with Energy Regulator (WP)

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Wave Scattering Transformation (WS)

• Scattering Transformation and Passivity
• Anderson and Spong (1989)
• Wave Variables
• Niemeyer and Slotine (1991)
• Asymmetric Configuration
• (Force -Velocity Control)
• Symmetric Configuration
• (Velocity Velocity Control)
• Reduces wave reflection effects (Niemeyer and
  Slotine 1991)
• Breakthrough Passivity guaranteed for any
• arbitrary large constant time delay.

Anderson RJ and Spong MW, IEEE Trans. Automat.
Contr. 34(5), 494-501 (1989) Niemeyer G. and
Slotine JJE, IEEE J. Oceanic. Eng. 16(1), 152-162
(1991)
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Implementation of WS
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Digital Data Reconstruction Filter (DD)

• Berestesky et al. (2004)
• Wave-Based approach.
• The summation over time of the wave variables is
  transmitted.
• Missed and out of sequence packets are
  interpolated, guaranteeing the passivity of the
  teleoperation system for time-varying delays and
  packet losses.
• Tracking error is improved.

Berestesky P. et al. IEEE ICRA 4557-4564 (2004)
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Implementation
Running Sum
Internet Comm.
Packet Reader/ Subtractor
Interpolator
Compressor/ Expander
Buffer
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Wave Integral and Reconstruction Filter (WI)

• Niemeyer and Slotine (2004)
• Wave-Based approach.
• Explicit position feedback information.
• Solution Transmitting the wave integrals.
• where p is the momentum and is computed by,
• However, passivity is still compromised.
• A reconstruction filter keeps track of the net of
  flow of energy in the communication channel,
  enforcing passivity.

,
,
Niemeyer G. and Slotine JJE, Int. J. Robot. Res.
23(9), 873-890 (2004)
15
P and PD Controllers

• Lee and Spong (2006).
• Proportional-Derivative (PD) control scheme with
  damping compensation.
• No guarantee of stability or passivity for time
  varying delays and packet drops.

Lee DJ and Spong MW, IEEE Trans. Robot. (2006)
16
Control Law

• The control law is given by,

where Kp, Kv and Kd are positive symmetric gain
matrices, Pe is a dissipation gain matrix, and
tm, ts, and tmaxrt represents the time delays in
the forward and backward directions, and the
maximum roundtrip delay respectively.
17
Redefined Input and Output Mapping (RM)

• Chopra et al. (2004)
• Wave-Based
• Wave redefined to incorporate position, velocity
  and force information.
• Passive Dynamic control law.
• Passivity of the communication channel is not
  guaranteed under time varying delays.

Chopra N. et al. 43rd IEEE CDC, 4540-4547 (2004)
18
Control Law

• Wave variables are redefined as

where Km and Ks are positive constant gains, b
is the matching impedance, and ? is a positive
constant. Then, the total master and slave
controls, Fm and Fs, are given by
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Wave Predictor with Energy Regulation (WP)

• Munir and Book (2002)
• Use of Smith Predictor and Kalman Filter to
  predict the slaves response.
• Inverse Dynamic Control Law.
• It incorporates and energy regulator to guarantee
  the passivity of the communication channel.
• A position corrector is used to avoid drift
  position errors.

Munir S. and Book WJ, IEEE/ASME Trans. Mechatron.
7(2), 124-133 (2002)
20
Wave Predictor with Energy Regulation (WP)
21
Outline

• Introduction
• Objectives
• Experimental Setup
• Teleoperation Schemes
• Experimental Comparison
• Measure of Complexity
• Final Remarks
• Acknowledgements
• Questions

22
Experimental Comparison

• Criteria
• - stability
• - low tracking error
• - transparency
• Trajectories
• - free motion
• - constrained
• motion

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Free Motion Experiment
WS
3 radians
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Free Motion Experiment
First Link
Second Link
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Constrained Motion Experiment
WS
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Constrained Motion Experiment
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Constrained Motion Experiment
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Outline

• Introduction
• Objectives
• Experimental Setup
• Teleoperation Schemes
• Experimental Comparison
• Measure of Complexity
• Final Remarks
• Acknowledgements
• Questions

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Measure of Complexity

• Usefulness
• Ease of design and implementation
• Sensitivity and Adaptability for workspace
  changes and/or unknown parameters.
• Complexity Casti (1979)
• The Mathematical structure of the irreducible
  component subsystems of the process.
• The manner in which the components are connected
  to form a system.
• Measures
• Structural Complexity
• Computational Complexity

Casti JL, Connectivity, complexity and
catastrophe in large-scale systems (1979)
30
Structural Complexity

• Polyhedral Dynamics (or Q-Analysis)
• Based on algebraic topology for studying the
  inherent structure of a system and the
  relationship of its components.
• Originally developed for the study of social
  network, but expanded later to other fields such
  as transportation, ecology, geography and
  communications.

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Polyhedral Dynamics Procedure
Master P-Control
Slave P-Control
Master
Slave

• Divide the control technique into different
  components or subsystems and establish a relation
  between them.
• 2. Create an incidence matrix A where the ij th
  entry of A is equal to one if the components i
  and j satisfy the relation of 1, and is equal to
  zero otherwise.

Internet
Internet
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Polyhedral Dynamics Procedure

• 3. Compute a new matrix B as
• where E is a matrix of same dimension as A with
  all entries equal to one.
• A structure vector Q is then taken from the
  diagonal of B.
• Once the Q vector is obtained, the complexity of
  the control scheme can be evaluated using the
  measure ? which is given as
• where N is the highest level of connectivity of
  the control scheme and Qq is the corresponding Q
  value for the q-level.

1
0
q-level
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Structural Complexity Results
Relation 1 The ith simplicial receives as input
the output of the jth simplicial. Relation 2 The
jth simplicial receives as input the output of
the ith simplicial.
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Computational Complexity

• Computational complexity
• Refers to the amount of time and memory required
  by the computer to execute the control algorithm.
• Traditionally, the runtime cost and memory size
  are estimated by counting the total number of
  operations and instructions of the algorithm,
  i.e. measuring the code length.
• Assumptions
• The control algorithms are irreducible in size.
• The measures are normalized, such that the
  simplest algorithm has a measure of 1.

Fortnow L. and Homer S. (2003, June).
http//theorie.informatik.uni-ulm.de/Personen/tora
n/beatcs/ Lankford F. IEEE Aerosp. Conf. 8,
3849-3857 (2003)
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Computational Complexity Results
Lower value, lower complexity
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Outline

• Introduction
• Objectives
• Experimental Setup
• Teleoperation Schemes
• Experimental Comparison
• Measure of Complexity
• Final Remarks
• Acknowledgements
• Questions

37
Final Remarks

• Stability was achieved for all configurations.
• Tracking error was highly reduced.
• The WP scheme achieved the fastest response and
  lowest tracking error for transient behavior.
• DD, P and PD architectures reported the highest
  transient tracking error.
• Under steady-state conditions, P and PD
  controllers obtained the lowest position error.
• All control schemes improved the feedback force.
  The best results P, PD, WI, RM and WP.

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Final Remarks

• Complex architectures WP scheme, followed by the
  DD, WI and RM.
• Simplest control schemes P, PD and WS.
• The selection process of a particular control
  scheme is sensitive to the desired performance
  and task.
• There are other considerations which may
  influence the selection of a particular control
  scheme.
• Information available about the systems, the
  communication channel and the work space.

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Acknowledgments

• I would like to thanks Dr. Spong for his
  guideline and advise, and Dr. Lee for his ideas
  and help through this research.

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