Analysis of intrersecting flows of agents

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Analysis of intrersecting flows of agents

• Eric Feron David Dugail
• Mini MURI 03/02/02

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Research motivation goals

• Analyses of conflict resolution usually involve
  pairs or a finite number of aircraft
• Need to address the fear of domino effect
• one conflict resolution triggers a new conflict
  elsewhere possibly leading to divergence in the
  system
• Analysis of aircraft flows
• worst-case standpoint
• Stability performance
• simulations for insight on the system dynamics
• analytical proofs

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Background

• A very rich literature on management of conflicts
  involving 2,3 or more but finite number of
  aircraft - Erzberger, Krozel, Kuchar,
  Niedringhaus, Sastry, Tomlin, Zeghal .
• An equally rich literature on conflict management
  with aircraft flows - eg gas models - Bakker,
  Blom, Simpson Open-loop probabilistic models.
• Very little available from current robotics
  literature
• (Recent research by Ruspini, Devasia,
  Meyer,otherwise computational complexity
  results, eg Reif Sharir)
• How does one prove stability, and bound required
  aircraft deviations, for conflict resolution over
  a class of closed-loop aircraft interactions in a
  deterministic setting?

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A "Control Volume" approach

• Motivation Infinite of aircraft flow in and
  out
• Analysis of completely random aircraft flows is
  difficult
• Need to structure the flows flow behaviors

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A control volume approach

• 2-D
• Structured converging flows
• pre-determined points of entry
• regular or random entry
• Aircraft make 1 maneuver when entering
• maneuver is minimal
• offset, heading change maneuvers

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Heading Change vs. Offset Maneuver Models
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Offset maneuver (2/2) (2 flows, decentralized)

• 2 successive heading changes
• Proof by contradiction
• Upper bound on lateral displacement
• dsep min. separation dist.

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Conflict geometry

• 2-D
• Structured converging flows
• pre-determined points of entry
• regular or random entry
• Aircraft make 1 maneuver when entering
• maneuver is minimal
• offset, heading change maneuvers

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Conflicting flows
Distribution of deviations
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Conflict analysis
Deviation angle is bounded by T
where dDsep/R
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Other results

• Bounds on lateral displacements for arbitrary
  encounter angle, speed, distance to conflict.
  Define
• q Encounter angle, m v2/v1
• Then lateral displacement maneuver amplitude for
  stream 1
• is less than
• with
• Bounds on displacement for longitudinal/lateral
  maneuvers
• (Independent utility functions for each aircraft)

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Three flows (1/4)

• Decentralized resolution
• diverges

• Centralized resolution (using mixed integer
  programming)
• stable
• exhibits particular structure

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Three flows (2/4)

• Idea
• create a control structure
• independent of flow
• optimize it to decrease lateral distance from
  original flight path
• Concept
• three-flow compatible
• aircraft are assigned conflict free spots

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Three flows (3/4)
Structured solution
Mixed Integer Prog. solution
Results

• a systematic way to deal with conflicts
• only 30 higher deviation compared with MIP

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Three flows (4/4)

• Control structure
• flow independent
• optimized

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Flow management a 3-D approach

• How geometry and flow management merge ?

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Analysis of robustness

• Maneuver imprecision
• leads to divergence in some scenarios
• Aircraft position uncertainties
• 3-D geometrical tool may help

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Towards Free Flight...

• Limited information
• Situation is obtained by onboard device (radar)
• control volume is attached to each aircraft
• events happen anytime
• Stability performance ?