Air Traffic Complexity: An Input-Output Approach. Amy R Pritchett, Keumjin Lee and Eric JM Feron School of Aerospace Engineering Georgia Tech

Transcription

1 Air Traffic Complexity: An Input-Output Approach Amy R Pritchett, Keumjin Lee and Eric JM Feron School of Aerospace Engineering Georgia Tech

2 Motivation Efforts to balance air traffic demand and airspace capacity Traffic Flow Management (TFM) : Regulate traffic flows based on current and future traffic configuration Dynamic Airspace Configuration (DAC) : Reconfigure the airspace in accordance with the users demands and the traffic complexity Free Flight: While aircraft can go any where, may still need to prevent aircraft from entering any locally complex areas All these methods require ability to assess air traffic complexity in an operationally relevant manner 2

3 Previous Efforts Combination of factors Perceived levels of the complexity Air traffic complexity metric We build upon these methods by examining the control impact required within an airspace configuration 3

4 Input-Output Approach Environment : Weather Sector boundary closure Air route structure Reference Inputs Signal of interest : An additional aircraft Air Air traffic traffic inside inside sector: sector:? No uncertainty No uncertainty? Uncertainty Uncertainty Control activity Control Control architecture: architecture:?minimum control activity Minimum control activity 4

5 Input-Output Approach (2) Model airspace as a closed loop system Build a map of the system s response to all possible instances of the reference signal Describe air traffic complexity from the inputoutput response Extensibile Different airspace models External environmental factors

6 Input-Output Approach (3) Def1: Reference input is any hypothetical aircraft entering the sector of interest at any heading and location Def2: Air traffic complexity is a measure of the control activity required to accept a hypothetical aircraft entering into the sector. Absolute complexity is based on optimal (minimum) control activity Relative complexity specific to a sub-optimal controller denotes the additional complexity 6

7 Input-Output Approach (4) Nominal aircraft Entering aircraft position angle Entering aircraft Entering aircraft bearing angle Sector boundary Def 3: The entering aircraft position angle defines the entry position of the aircraft into the sector as an angle representing its position relative to the sector center Def 4: The entering aircraft bearing defines the relative track of an entering aircraft with respect to the line connecting the aircraft to the center of the sector 7

8 Details Of The System Detail of the plant used in our examples Safety regions around each aircraft Horizontal motion of aircraft Only one impulsive turn Constant velocity Control architecture Ref: Pallottino, L., Feron, E., and Bicchi, A., Conflict resolution problems for air traffic management systems solved with mixed integer programming, IEEE, Trans. Intelligent Transportation System, Vol.3, No.1, 2002 Does not preclude more extensive models 8

9 Conflict geometry Details Of The System (2) Relative velocity vector V 2/1 should point outside forbidden area V 2 /1 V 2 V 1 Safety region Forbidden Area 9

10 Comparing Two Traffic Situations Traffic Situation 1 intruder Traffic position Situation & heading No. 1 angle Traffic Situation 2 intruder Traffic position Situation & heading No. 2 angle y axis (nmi) 0 y axis (nmi) x axis (nmi) x axis (nmi) Both are conflict free airspace right now can measure complexity as result in an entering aircraft 10

11 Complexity Map of Traffic Situation #1 Contours of minimum control activity required to accept entering aircraft Intruder position angle (deg) Entering aircraft position angle (deg) Entering aircraft position angle (deg) 11 Intruder bearing angle (deg) Entering aircraft bearing (deg) (deg)

12 Complexity Map of Traffic Situation #1 (2) Entering aircraft bearing (deg) (deg) Intruder bearing angle (deg) C/0 0/CC 0/C CC/0 Particular entering aircraft (Position=120, Bearing=20 ) Heading change Entry position Uncertainty Special attention on some parts of the sector boundary Intruder position angle (deg) Entering aircraft position angle (deg) Entering aircraft position angle (deg) 12

13 Complexity Map of Traffic Situation #2 Entering Entering aircraft aircraft bearing bearing (deg) (deg) Intruder bearing angle (deg) Minimum heading changes required (deg) Contours of minimum control activity required to accept entering aircraft Intruder position angle (deg) Entering aircraft position angle angle (deg) (deg) 13

14 Scalar Measures of Air Traffic Complexity Many possible scalar measures Worst-case value Sensitivity to inputs Average value Overall input-output response The area enclosed on a complexity map How often aircraft need to be controlled Many other methods are possible 14

15 Comparing Two Complexity Maps Entering aircraft bearing (deg) Intruder bearing angle (deg) Entering aircraft bearing (deg) Entering aircraft bearing bearing (deg) (deg) Intruder bearing angle (deg) Minimum heading changes required (deg) Intruder position angle (deg) Intruder position angle (deg) Entering aircraft position angle (deg) Entering aircraft position angle (deg) Entering aircraft position angle angle (deg) (deg) Traffic situation 1: Larger maximum control activity Traffic situation 2: Larger range of entering aircraft position and bearing angles require control activity of at least 10 degrees

16 Partially Closed Sector Boundary Traffic situation y-axis (nmi) A closed part of the sector boundary x-axis (nmi) Partial closure of sector s boundary due to dynamic airspace management restrictions 16

17 2 2 Complexity Map: No Boundary Closure Required heading changes : nominal case J(sum of heading) vs intruder position & heading angle 80 Entering aircraft bearing (deg) Intruder Entering bearing angle (deg) intruder aircraft heading bearing angle (deg) (deg) intruder position angle (deg) Intruder position Entering angle aircraft (deg) position angle (deg) Entering aircraft position angle (deg) 17

18 Complexity Map: Partially Closed Boundary 80 Required heading changes : Sector closed J(sum of heading) vs intruder position & heading angle Intruder Entering intruder position angle (deg) position aircraft angle position (deg) angle (deg) Intruder Entering bearing angle (deg) intruder aircraft heading bearing angle (deg) (deg) % increase on the average value Entering aircraft bearing (deg) Entering aircraft position angle (deg)

19 Comparing Scalar Measures Across Situations 67% increase Traffic #1 Traffic #2 Traffic #3 (N) Traffic #3 (P) Average (deg) Worstcase(deg) N: Nominal sector with no boundary closure P: Sector with partially closed boundary 39% increase 19

20 Conclusion Proposed input-output approach Define air traffic complexity as the closed-loop response of the airspace against reference inputs Complexity map displays the effective complexity of the traffic situation in a manner suitable for minute-byminute decisions Scalar measures provide succinct measures of traffic situation Can evaluate a number of effects Impact of near-term decisions (e.g., aircraft acceptance) (on-going) Use to evaluate airway structures within airspace (on-going) Use in a predictive manner 20

21 Thank you very much for listening Any questions? 21