Coordination Variables and Consensus for Multiple Vehicle Systems

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Coordination Variables and Consensus for Multiple
Vehicle Systems

• Randy Beard
• Tim McLain
• Brigham Young University

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Outline

• Overview of cooperative control literature.
• Need to move beyond formation control.
• Challenges inherent in cooperation.
• Coordination variables as a method to articulate
  (centralized) team strategies.
• Decentralized algorithms require consensus
  building techniques.
• Examples
• Cooperative timing
• Formation control.

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Literature on Cooperative Control

• Formation Control
• Mobile robots (Wang 91, Balch Arkin 98, Lewis
  Tan 97, Sugar Kumar 98, Fax Murray 02, Eren
  Belhumeur Morse 02, Ogren Egerstedt Hu
  02, Belta Kumar 02, Hong, Shin, Ahn 01,
  Monteiro Bicho 02, Yamaguchi 97, Yamaguchi
  Burdick 98, Desai, Ostrowski Kumar 98, Gentili
  Martinelli 00, Hashimoto 95, Parker 98,
  Pledgie, Hao, Ferreira, Agrawal Murphey 02,
  Sugihara Suzuki 96, Tanner, Kumar Pappas 02)
• Unmanned air vehicles (Giulietti Pollini
  Innocent 00, Proud, Pachter, DAzzo99, Anderson
  Robbins 98, Blake Multhopp 98, Chichka
  Speyer 98, Blake Multhopp 98, Fax Murray 01,
  Schumacher Singh 00)
• Autonomous underwater vehicles (Leonard
  Fiorelli 01, Stilwell Bishop 00)
• Satellites (Kang Yeh 02, Carpenter 02, Kapila,
  Sparks, et. al. 00, Das, Cobb Stallard 98,
  Folta, Bordi Scolese 92, Folta Quinn 98,
  Guinn 98, How, Twiggs, Weidow, Hartman Bauer
  98, McInnes 95, Sedwick, Kong Miller 98)
• Spacecraft (Wang Hadaegh 96, Hadaegh Lu
  Wang 98, Robertson Inalhan How 99, Mesbahi
  Hadaegh 00, Wie Weiss Arapostathis 89, Lau
  96, Joshi 98, Lawton, Beard, Hadaegh 01,
  Mesbahi 02, Ulybyshev 98)
• Automated Highways (Sheikholeslam Desoer 92)

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Literature on Cooperative Control (cont.)

• Non-formation Control
• Task Assignment (Brandt, Brauer, Weiss 00,
  Fontan Mataric 98,)
• Cooperative transport (Chen Luh 94, Hashimoto
  95, Miyata Ota, 00)
• Cooperative Role Assignment (Emery, Sikorski,
  Balch 02)
• Air Traffic Control (Inalhan, Stipanovic, Tomlin
  02, Sastry, Meyer, Tomlin, Lygeros, Godbole,
  Pappas 95)
• Cooperative Timing (McLain, Chandler, Rasmussen,
  Pachter 01, Richards, Bellingham, Tillerson,
  How 02)
• Cooperative Search (Rekleitis, Dudek, Milios
  00, Sweeney, Brunette, Yang, Grupen 02, Wagner,
  Lindenbaum, Bruckstein 99)

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Major focus on formation control

• Why?
• Formation control problem reduces to single agent
  control problems
• Single agent high level decision making and path
  planning for leader.
• Remaining vehicles are controlled using single
  agent tracking strategies.
• Performance metrics are clear.
• Answer We search where the light is the
  brightest.
• It is not because formation problems are the most
  important/relevant cooperation problems.

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Cooperative control problems

• While there are good reasons for formation
  control, it seems that there are many more
  interesting coordination problems
• Search and rescue,
• Cooperative manipulation,
• Task decomposition among heterogeneous vehicles
• Team assignment in robot soccer/capture-the-flag
• Cooperative timing of tasks
• Rendezvous/Join-up
• Simultaneous target intercept
• Task sequencing
• classification/strike/BDA
• multi-target sequence
• etc.

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Inherent Challenges

• Complexity
• Systems of systems.
• Communication
• Limited bandwidth and connectivity.
• What? When? To whom?
• Arbitration
• Team vs. Individual goals.
• Computational resources
• Will always be limited

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Unsolved problem

• We need general theory and approaches to
  cooperative control.
• Current approaches to formation control
  can/should guide our thinking.

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Fundamental Axiom

• Shared knowledge is a necessary condition for
  coordination.

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Focus on Three Examples

• Meet for Dinner Problem
• Cooperative timing problems.
• Required knowledge
• Rendezvous time
• Deep space formation flying.
• Required knowledge
• Configuration of virtual structure.

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Example 1 Cooperative Timing

• Meet for Dinner Suppose that
• We all agree to meet for dinner, but do not
  decide on a time or place.
• Later, in our rooms, we discover the problem and
  start calling each other. Everyone has a phone
  and can call any other person, but must do so one
  at a time.
• Also, suppose that some peoples opinion is valued
  more than others.
• What algorithm should be followed to ensure that
  we all come to consensus on a time and a place.

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Practical Example Coordinated Rendezvous
SAM site
detection region
no-fly
no-fly
vehicles must arrive on these vectors
boundary
loiter penalty
uncertainty 1 sigma
X
boundary
boundary
Wind 25knots
Timing vehicles must arrive within 1 sec of one
another
no-fly
25 miles
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Initial Route Plan
detection region
SAM site
no-fly
no-fly
vehicles must arrive on these vectors
boundary
loiter penalty
X
boundary
boundary
Wind 25knots
Timing vehicles must arrive within 1 sec of one
another
no-fly
25 miles
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Pop-up Threat Replan
SAM site
detection region
no-fly
no-fly
vehicles must arrive on these vectors
boundary
loiter penalty
X
boundary
ETA change -- replan!
boundary
Wind 25knots
no-fly
25 miles
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Rendezvous Synchronized
SAM site
detection region
no-fly
no-fly
boundary
loiter penalty
X
boundary
boundary
Wind 25knots
no-fly
25 miles
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Importance of Cooperative Timing Capability
Key capability for cooperative UAV flight the
ability to adjust mission timing on the move to
compensate for inevitable changes to plans and
still make the time-on-target Brig. Gen.
Daniel P. Leaf Operation Allied Force,
Kosovo DoD UAV Roadmap 2002
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Cooperative Timing Critical Information

• Each member of the group must have a common
  knowledge of the time-on-target.

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Example 2 Formation Control
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Formation Control Critical Information

• Each member of the group must have a common
  knowledge of the configuration of the virtual
  structure.

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Coordination Variable
Individual Agents
situation or environment decisions or influences
How effective is the cooperation?
Is the team cooperating?
cooperation constraint
cooperation objective
Team
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Coordination Variable (cont.)
Individual Agents
coordination variable
decision or influence
individual cost
cooperation objective
cooperation constraint
Team
coordination function
Coordination variable minimum information
needed to coordinated
Coordination function individual cost vs. ?
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Cooperative Control Algorithm
Step 2
Choose
Agent N
Agent 2
Agent 1
Step 1
Step 3
Implement cooperative action
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Example 1 Cooperative Timing
3
2
1
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Searching CFs for Team Optimal CV
tight sequence
loose sequence
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Simultaneous Arrival Results
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Tight Sequencing Results
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Loose Sequencing Results
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Range to Target
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Coordination Functions
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Experimental Platform
System Architecture
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Autopilot Design for Mini-UAVs
RF Link
BYU UAV
BYU Autopilot
Interface Device
RF Link
Laptop
PDA / Voice
Operator
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UAV PDA Control
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UAV Voice Control
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Example 2 Formation Control
Supervisor
Formation control
broadcast
Local Control
Spacecraft
Coordination variable formation state
Coordination function combined tracking error
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Decentralization

• One approach to decentralization is to implement
  the centralized coordination scheme on each
  vehicle.
• If each vehicle has identical world knowledge,
  and implements the same coordination algorithm,
  they will each produce the same coordination
  variable.
• However if the world knowledge on each vehicle is
  different, then vehicles much reach consensus.

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Knowledge Consensus
Consensus can be formed at either the input of
the coordination algorithm, the output, or both.
We will focus on the case where the output data
(coordinationvariable) is to be synchronized.
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Definitions
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Invariant Set for Data Consensus
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Consensus and Spanning Trees
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Consensus Strategy
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Consensus with Dissimilar Agents
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Simulation Results Constant CV
Low gainno noise
High gainno noise
Low gainnoise
High gainnoise
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Time-varying Network
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Simulation Results Formation Control
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Average Coordination Variable Error (Ring
communication topology)
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Spacecraft Formation Error
absolute position and attitude error
relative position and attitude error
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Control Effort for Spacecraft 1, 7
Spacecraft 1
Spacecraft 7
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Summary

• We need to develop strategies that address the
  fundamental difficulties inherent in all
  coordination problems.
• For example Cooperation always requires an
  exchange of information.
• What information needs to be shared?
• Coordination variables
• How should the information be acted upon?
• Need to be robust to dissimilar information.
• Need to ensure that team members have
  sufficiently similar information.
• Consensus building