Fault-Tolerant Formations of Mobile Robots

1
Fault-Tolerant Formationsof Mobile Robots

• Ross Mead
• CS Dept., University of Southern California, USA
• Rob Long
• Jerry B. Weinberg
• Dept. of CS, Southern Illinois University
  Edwardsville, USA

2
Outline

• Problem Statement
• Considerations
• Approach
• Algorithm
• Implementation
• Evaluation
• Conclusions
• Future Work
• QA

3
Problem Statement

• How can a large collection of robots moving with
  no group organization coordinate to form a global
  structure?

swarm
formation
4
Considerations

• In related work on formations, robotic units
  know
• where they belong in the formation
• who their neighbors are supposed to be
• Criteria of Fredslund Mataric 2002
• generality conforming to a variety of
  formations
• stability maintaining the formation
• dynamic switching capability responding to
  commands for changes in its organization
• robustness/scalability responding to changes in
  group size
• obstacle avoidance dealing with large and small
  obstructions

5
Approach

• Utilize reactive robot control strategies
• closely couple sensor input to actions
• Treat the formation as a cellular automaton
• lattice of computational units (cells)
• each cell is in one of a given set of states
• state transitions governed by a set of rules
• complex emergent behavior from simplicity

6
Robot-Space Cellular Automata

• Each robot in the formation is represented as a
  cell ci in an n-dimensional automaton of N cells

• ci hi, si, F, S

7
Robot-Space Cellular Automata

• Each robot in the formation is represented as a
  cell ci in an n-dimensional automaton of N cells

• ci hi, si, F, S
• neighborhood
• hi ci U n neighbors
• n nmax

• C ? automaton
• C h1 U h2 U U hN
• c1, c2, , cN

8
Robot-Space Cellular Automata

• Each robot in the formation is represented as a
  cell ci in an n-dimensional automaton of N cells

• ci hi, si, F, S
• state
• si pi, ri,des, ri,act, Gi, Ti, ti
• (... described later ...)

• C ? automaton
• C h1 U h2 U U hN
• c1, c2, , cN

9
Robot-Space Cellular Automata

• Each robot in the formation is represented as a
  cell ci in an n-dimensional automaton of N cells

• ci hi, si, F, S
• state transition
• si pi, ri,des, ri,act, Gi, Ti, ti
• (... described later ...)
• sit S(... si-1t-1, sit-1, si1t-1 ...)
• t ? time step (counter)

• C ? automaton
• C h1 U h2 U U hN
• c1, c2, , cN

10
Robot-Space Cellular Automata

• Each robot in the formation is represented as a
  cell ci in an n-dimensional automaton of N cells

• ci hi, si, F, S
• formation
• F f(x), R, F, pseed
• f(x) ? description
• R ? robot separation
• F ? relative heading
• pseed ? start position

• C ? automaton
• C h1 U h2 U U hN
• c1, c2, , cN

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Algorithm Formation Definition

• F is sent to some robot, designating it as the
  seed cell cseed...
• cseed is not a leader, but rather an initiator of
  the coordination process
• For purposes of calculating desired
  relationships, each cell ci considers itself to
  be at some formation-relative position pi
• pi xi f(xi) T
• In the case of cseed, this position pseed is
  given

f(x) a x2
cseed
pseed
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Algorithm Desired Relationships

• The desired relationship ri?j,des from ci to some
  neighbor cj is determined by calculating a vector
  v from pi to the intersection f(vx) and a circle
  centered at pi with radius R
• R2 (vx pi,x)2 (f(vx) pi,y)2 ri?j,des
  vx f(vx) T
• Relationships are rotated by F to account for
  robot heading...

f(x) a x2
R
v
v
pseed
desired relationship with left neighbor ci-1
desired relationship with right neighbor ci1
ri?i-1,des
ri?i1,des
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Algorithm Desired Relationships

• The desired relationship ri?j,des from ci to some
  neighbor cj produces a unique formation-relative
  position pj
• pj pi ri?j,des rj?i,des ri?j,des
• (for stability)

f(x) a x2
pi-1
pi1
pseed
ri?i-1,des
ri?i1,des
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Algorithm Desired Relationships

• ci announces an auction for pjdenoted A(pj)iff
• pi pseed lt pj pseed Gi 0
• (for densest packing) (for stability)

f(x) a x2
pi-1
pi1
pseed
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Algorithm Desired Relationships

• A robot that receives an auction message for pj
  will announce a bid B(pj) iff n 0 (i.e., it has
  no neighborhood and, thus, is not yet part of the
  automaton) or
• n lt nmax pj is closer to pseed
• (for repair) (for densest packing)

f(x) a x2
pi-1
pi1
pseed
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Algorithm Desired Relationships

• A robot that receives an auction message for pj
  will announce a bid B(pj)
• B(pj) E d X n
• d ? distance from robot to pj (weighted by energy
  cost modifier E)
• n ? number of existing neighbors (weighted by
  relation cost modifier X)

f(x) a x2
pi-1
pi1
pseed
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Algorithm Desired Relationships

• After a period of time, ci announces the winning
  bidder based on the minimum bid B(pj)
• F and ri?j,des are communicated locally within
  the neighborhood.
• Each neighbor cj repeats the process, but
  considers itself to be at its own unique
  formation-relative position pj.

f(x) a x2
pi-1
pi1
pseed
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Algorithm Desired Relationships

• Propagate changes in neighborhoods in succession.
• Calculated relationships generate a connected
  graph that produces the shape of the formation.

f(x) a x2
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Algorithm Actual Relationships

• Using sensor readings, robots calculate an actual
  relationship ri?j,act with each neighbor cj.
• State of all cells in hi governs robot movement
• rotational error Ti and translational error Gi
• relationships based on relative coordinate systems

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Algorithm Extended Definition
21
Algorithm Extended Definition
22
Implementation
23
Evaluation Generality

• The generality of a system refers to its ability
  to conform to a variety of different formations.
• Analysis from various trials and experiments has
  suggested a classification of the formations that
  can currently be produced

24
Evaluation Generality

1. Non-formation (swarm)
2. Explicit formation
3. Straight line formation

1. Function-based formation
2. Branching formation
3. Lattice formation

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Evaluation Stability

• A systems ability to maintain formation (once
  established) dictates its stability.
• To test the control algorithm against this
  principle, we manipulated one or many robots in a
  variety of different formations, changing both
  position and orientation

26
Evaluation Dynamic Switching

• Dynamic switching capabilities refer to the
  ability of the system to respond to an operators
  commands for changes in formation organization.
• To manipulate the formation, a human operator
  sends one of a variety of commands to any single
  robot
• propagates changes in the automaton
• causes a chain reaction in neighbors
• results in a global transformation

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Evaluation Robustness/Scalability

• Evaluating robustness/scalability considers the
  ability of a system to respond to changes in
  group size.
• Algorithm is independent of the number of robots.
• Robots can be reassigned to new tasks or exhibit
  failure.
• As numbers begin to dwindle or the task changes,
  other robots may join the ranks to increase the
  numbers.

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Evaluation Robustness/Scalability
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Conclusions

• Presented a distributed cellular automata-based
  formation control architecture capable of
  controlling large numbers of robots.
• Discussed a distributed auctioning method to
  allow robot formation to reconfigure
  autonomously.
• Examined the architecture with respect to
  necessary characteristics to handle real-world
  events.

30
Questions?
For more information, please visithttp//roboti.c
s.siue.edu/projects/formations/or see the
following papers

• Mead, R. Weinberg, J.B. (2008). A Distributed
  Control Algorithm for Robots in Grid Formations.
  To appear in the Proceedings of the Robot
  Competition and Exhibition of The 23rd National
  Conference on Artificial Intelligence (AAAI-08),
  Chicago, Illinois.
• Mead, R. Weinberg, J.B. (2008). 2-Dimensional
  Cellular Automata Approach for Robot Grid
  Formations. To appear in Student Abstracts and
  Poster Program of The 23rd National Conference on
  Artificial Intelligence (AAAI-08). Chicago,
  Illinois.

• Mead, R., Weinberg, J.B., Croxell, J.R. (2007).
  A Demonstration of a Robot Formation Control
  Algorithm and Platform. To appear in the
  Proceedings of the Robot Competition and
  Exhibition of The 22nd National Conference on
  Artificial Intelligence (AAAI-07), Vancouver,
  British Columbia.
• Mead, R., Weinberg, J.B., Croxell, J.R. (2007).
  An Implementation of Robot Formations using Local
  Interactions. In the Proceedings of The 22nd
  National Conference on Artificial Intelligence
  (AAAI-07), 1889-1890. Vancouver, British Columbia.

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Motivation

• Space Solar Power (SSP)
• How can a massive collection of robots moving
  with no group organization coordinate to form a
  global structure?

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Related Work Tethered Formations

• Saenz-Otero Miller 2005 SPHERES
• Groß et al. 2006
• swarm-bots

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Related Work Reactive Formations

• Fredslund Mataric 2002
• Balch Arkin 1998
• Reynolds 1987
• Farritor Goddard 2004

34
World-Space Cellular Automata

• Environment is represented topologically as a 2-
  or 3-dimensional lattice of cells

1. robot between grid cells
2. boundary surrounds the automaton
3. automaton wraps along boundaries
4. two robots collide trying to occupy same grid
   cell
5. empty cells are stateless

e
35
Robot-Space Cellular Automata

• Each robot in the formation is represented as a
  cell ci in an n-dimensional automaton of N cells

• ci hi, si, F, S
• hi ? neighborhood
• si ? state
• F ? formation definition
• S ? state transition rules

• C ? automaton
• C h1 U h2 U U hN
• c1, c2, , cN

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Algorithm The Visual Walkthrough
f(x) a x2
cseed
pseed
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Algorithm The Visual Walkthrough
f(x) a x2
R
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Algorithm The Visual Walkthrough
f(x) a x2
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Algorithm The Visual Walkthrough
f(x) a x2
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Algorithm The Visual Walkthrough
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Algorithm The Visual Walkthrough
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Algorithm The Visual Walkthrough
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Implementation Robot Platform

• ZigBee module
• packet communication
• share state information
• within neighborhood

• Color-coding system
• visual identification
• neighbor localization
• (actual relationships)

• Scooterbot II base
• strong, but very light
• differential steering system

• XBCv2 microcontroller
• Interactive C
• back-EMF PID motor control
• color camera

44
Implementation Color-Coding System

• Visual identification
• the color of each robot is assigned based on ID
• orange for odd, green for even
• Neighbor localization (actual relationships)
• ri?j,act di?j ai?j T

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Implementation State Diagram
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Implementation Results

• ... and because embedding Windows own media
  format is a too much for PowerPoint...
• Click Here

47
Extending the Formation Definition

• Consider a set f' of M mathematical functions
• f' f1(x), f2(x), ..., fM(x) F f', R, F,
  pseed
• For desired relationships, each fm(x) is
  considered individually...
• yielding its own 1-dimensional neighborhood mhi
• resulting in M neighborhoods and a 2-dimensional
  cellular automaton (M gt 1)
• Hi 1hi U 2hi U ... U Mhi Mc1-1, , 2c1-1,
  1c1-1, c1, 1c11, 2c11, , Mc11

f2(x) x v3
f3(x) x v3
f1(x) 0
R
1hi 1ci-1, ci, ci1
2hi 2ci-1, ci, ci1
3hi 3ci-1, ci, ci1
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How can this be applied to SSP?

• Reflector viewed as 2-dimensional lattice of
  robots and, thus, a 2-dimensional cellular
  automaton...

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Multi-Function Formations
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Multi-Function Formations

• Desired relationship ri?j,des vx f(vx)
  T
• What
• happened?
• Original R2 (vx pi,x)2 (f(vx) pi,y)2

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Multi-Function Formations

• Desired relationship ri?j,des vx f(vx)
  T
• What
• happened?
• Original R2 (vx pi,x)2 (f(vx) pi,y)2
• Alternative R2 vx2 f(vx)2

52
Multi-Function Formations

• Desired relationship ri?j,des vx f(vx)
  T
• Similarly...
• Original R2 (vx pi,x)2 (f(vx) pi,y)2

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Multi-Function Formations

• Similarly...
• Alternative R2 vx2 f(vx)2

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Implementation Robot Faces

• Visual identification
• each robot has a unique three-color column...
• vertical locations of color bands correspond to
  ID
• green on top for even, magenta on top for odd
• 5 locations 4 locations 20 unique faces

55
Implementation Robot Faces

• All around me are familiar faces...

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Implementation Results

• Click Here

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Conclusions Robot Platform

• Hardware ?

• Software ?

• 19 robots developed.
• Accurate motion control.
• Reasonable execution time.
• Reliable communication.
• Robot faces were excellent!

• Extensive and reusable collection of libraries.
• Greatest implementation hurdleInteractive C...
• most time spent debugging
• workaroundsnot fixes
• serial library deadlock
• bug list is... amusing...
• imposes harsh program size
• ... stay away!

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Conclusions Formation Classification

1. Non-formation (swarm)
2. Explicit formation
3. Straight line formation

1. Function-based formation
2. Branching formation
3. Lattice formation

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Conclusions Erroneous Relationships

• Theoretically possible to calculate more than two
  relationships...
• To alleviate this, solve for two minimums
• e(v) vx pi,x

60
Evaluation Generality

1. Non-formation

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Evaluation Generality

1. Explicit formation

62
Evaluation Generality

1. Straight line formation

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Evaluation Generality

1. Function-based formation

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Evaluation Generality

1. Branching formation

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Evaluation Generality

1. Lattice formation

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Evaluation Stability
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Evaluation Dynamic Switching

• Translate

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Evaluation Dynamic Switching

• Rotate (Formation)

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Evaluation Dynamic Switching

• Rotate (Robot)

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Evaluation Dynamic Switching

• Scale

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Evaluation Dynamic Switching

• Resize

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Evaluation Dynamic Switching

• Change

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Evaluation Obstacle Avoidance

• The ability of a system to deal with both large
  and small-scale obstructions is obstacle
  avoidance.

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Evaluation Obstacle Avoidance

• Phase Transition Metaphor (Spears et al. 2004)
• As individuals encounter an obstacle, bonds are
  loosened.
• Avoidance behavior would mimic ice melting into
  water to flow around an obstacle, then refreezing.

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Future Work

• Dynamic neighborhoods
• Seed election
• Formation repair
• Obstacle avoidance
• Global positioning

• 3-dimensional formations
• Disconnected formations
• Formation classification
• Analysis Click here
• Formation management