1. MIT-LIDS Analysis of intrersecting flows of agents Eric Feron & David Dugail Mini MURI 03/02/02

2. MIT-LIDS 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. MIT-LIDS 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?

4. MIT-LIDS 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

5. MIT-LIDS 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 N

6. MIT-LIDS Heading after conflict resolution Original heading Position after conflict resolution Original position W  w Conflict area Heading Change vs. Offset Maneuver Models

7. MIT-LIDS Offset maneuver (2/2) (2 flows, decentralized) 2 successive heading changes Proof by contradiction Upper bound on lateral displacement d sep : min. separation dist. N

8. MIT-LIDS 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

9. MIT-LIDS Conflicting flows Distribution of deviations

10. MIT-LIDS Conflict analysis Deviation angle is bounded by T: where  =D sep /R

11. MIT-LIDS Other results Bounds on lateral displacements for arbitrary encounter angle, speed, distance to conflict. Define:  : Encounter angle,  v 2/ v 1 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)

12. MIT-LIDS Three flows (1/4) Decentralized resolution –diverges N Centralized resolution (using mixed integer programming) –stable –exhibits particular structure

13. MIT-LIDS 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 Three flows (2/4)

14. MIT-LIDS –a systematic way to deal with conflicts –only 30% higher deviation compared with MIP Three flows (3/4) Structured solutionMixed Integer Prog. solution Results

15. MIT-LIDS Control structure –flow independent –optimized Three flows (4/4)

16. MIT-LIDS Flow management : a 3-D approach How geometry and flow management merge ?

17. MIT-LIDS Analysis of robustness Maneuver imprecision –leads to divergence in some scenarios Aircraft position uncertainties 3-D geometrical tool may help

18. MIT-LIDS Towards Free Flight... Limited information Situation is obtained by onboard device (radar) –control volume is attached to each aircraft –events happen anytime Stability & performance ?