Analysis of intrersecting flows of agents - PowerPoint PPT Presentation
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Analysis of intrersecting flows of agents
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Conflict geometry. 2-D. Structured converging flows. pre-determined points of entry ... 3-D geometrical tool may help. MIT-LIDS. MIT-LIDS. Towards Free Flight... – PowerPoint PPT presentation
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Title: 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
3
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 ?
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