Distributed Cooperative Control of Multiple Vehicle Formations Using Structural Potential Functions

1
Distributed Cooperative Control of Multiple
Vehicle Formations Using Structural Potential
Functions

• Reza Olfati-Saber
• Postdoctoral Scholar
• Control and Dynamical Systems
• California Institute of Technology
• Olfati_at_cds.caltech.edu
• UCLA, March 2nd, 2002

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Outline

• Introduction
• Multi-vehicle Formations
• Past Research
• Coordinated Tasks
• Stabilization/Tracking
• Rejoin/Split/Reconfiguration Maneuvers
• Why Distributed Control?
• Formation Graphs
• Rigidity/Foldability of Graphs
• Potential Functions
• Distributed Control Laws
• Simulation Results
• Conclusions

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Introduction
Definition Multi-agent Systems are systems that
consist of multiple agents or vehicles with
several sensors/actuators and the capability to
communicate with one another to perform
coordinated tasks.

• Applications
• Automated highways
• Air traffic control
• Satellite formations
• Search and rescue operations
• Robots capable of playing games (e.g.
  soccer/capture the flag)
• Formation flight of UAVs (Unmanned Aerial
  Vehicles)

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Multi-Vehicle Formations
A group of vehicles with a specific set of
inter-vehicle distances is called a Multi-Vehicle
Formation.
Formation Stabilization
Dynamics
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Past Research

• Robotics navigation using artificial potential
  functions (Rimon and Koditschek, 1992)
• Multi-vehicle Systems
• Coordinated control of groups using artificial
  potentials (Leonard and Fiorelli, 2001)
• Information flow on graphs associated with
• multi-vehicle systems (Fax and Murray, 2001)

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Why Distributed Control?

• No vehicle knows the state/control of all other
  vehicles

• No vehicle knows its relative configuration/veloc
  ity
• w.r.t. all other vehicles unless n 2,3

• The control law for each vehicle must be
  distributed
• so that the overall computational complexity
  of the
• problem is acceptable for large number of
  vehicles

• A system controlled via a centeralized computer
• does not function if that computer breaks.

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What is a Formation?
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Formation Representation
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Coordinated Tasks
Trajectory
Tracking

attitude
Rejoin
One Formation
Two Formations
Split
Reconfiguration
Diamond Formation
Delta Formation
Switching
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Split/Rejoin Maneuvers
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Operational Graph
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Formation Graphs
1
an Edge means
3
2
i) is a neighbor of
ii) measures
4
iii) knows its desired distance to
must be
Distance Matrix
Formation Graph
Set of Vertices
Connectivity Matrix
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Rigidity
1
a
a
Remark c (or d) is called a single mobility
degree of freedom of the formation graph.
d
2
3
c
c
b
b
Definition A planar formation graph with n
nodes and 2n-3 critical links is called a rigid
formation graph.
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Definition A critical link is a link that
eliminates a mobility degree of freedom of a
multi-body system.
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Foldability
1
Definition The following non-redundant set of
equations are called structural constraints of a
formation graph.
a
a
d
2
3
c
c
b
b
Deviation Variable
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Definition A rigid formation graph is foldable
iff the set of structural constraints
associated with the formation graph does not
have a unique solution.
4
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Node Orientation
3
1
2
2
1
3
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Unambiguous FGs
Definition A formation graph is called
unambiguous if it is both rigid and unfoldable.
1
1
3
2
2
6
5
4
7
6
3
5
4
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Potential Functions
Potential Function
Force
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Distributed Control Laws
Hamiltonian
Potential Function
indices of the neighbors of
Theorem(ROS-RMM-IFAC02) The following state
feedback
is a gradient-based bounded and distributed
control law that achieves collision-free local
asymptotic stabilization of any unambiguous
desired formation graph .
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Operational Graph
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Split Maneuvers
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Rejoin Maneuver
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Reconfiguration I
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Reconfiguration II
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Tracking
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Conclusions

• Introducing a framework for formal specification
  of unambiguous formation graphs of multi-vehicle
  systems that is compatible with formation
  control.
• Providing a Lyapunov function and a bounded and
  distributed state feedback that performs
  coordinated tasks such as formation
  stabilization/tracking, split/rejoin, and
  reconfiguration maneuvers.
• Introducing a Hybrid System that represents
  split, rejoin, and reconfiguration maneuvers in a
  unified framework as a discrete-state transition
  where each discrete-state is an unambiguous
  formation graph.