A New Framework for Solving En-Route Conflicts

Transcription

1 A New Framework for Solving En-Route Conflicts Cyril Allignol, Nicolas Barnier, Nicolas Durand and Jean-Marc Alliot ATM 2013 Chicago June 12 th, 2013

2 Introduction The conflict resolution problem Make sure than any 2 aircraft do not get closer to each other than a given separation norm (usually 5NM horizontally) ft 5 NM Allignol, Barnier, Durand, Alliot (ÉNAC) Framework for Conflict Resolution ATM / 18

3 Introduction The conflict resolution problem Make sure than any 2 aircraft do not get closer to each other than a given separation norm (usually 5NM horizontally) ft 5 NM Widely studied in the last two decades Relies on a realistic trajectory prediction (handling of uncertainties) Model is (too) often closely linked to the resolution method Allignol, Barnier, Durand, Alliot (ÉNAC) Framework for Conflict Resolution ATM / 18

4 Introduction The conflict resolution problem Make sure than any 2 aircraft do not get closer to each other than a given separation norm (usually 5NM horizontally) ft 5 NM Widely studied in the last two decades Relies on a realistic trajectory prediction (handling of uncertainties) Model is (too) often closely linked to the resolution method We propose... A new framework that separates the model from the resolution A public benchmark Two approaches to the problem resolution Allignol, Barnier, Durand, Alliot (ÉNAC) Framework for Conflict Resolution ATM / 18

5 Contents 1 Trajectory Prediction Scenarios Conflict Detection 2 Resolution Evolutionary Algorithm Constraint Programming Results 3 Conclusion Allignol, Barnier, Durand, Alliot (ÉNAC) Framework for Conflict Resolution ATM / 18

6 Trajectory Prediction Trajectories Trajectories are... defined in the horizontal plane sampled into time steps of duration τ from origin O to destination D O and D can be any 2 successive waypoints in the aircraft route. In the proposed benchmark, τ = 3 s in order to be able to catch even the shortest conflicts (two facing aircraft at maximal speed) Allignol, Barnier, Durand, Alliot (ÉNAC) Framework for Conflict Resolution ATM / 18

7 Trajectory Prediction Maneuver model O d 0 d 1 α D n 0 possible values for d 0 n 1 possible values for d 1 n α possible values for α Possible maneuvers per aircraft: n man = n 0 n 1 (n α 1) + 1 Allignol, Barnier, Durand, Alliot (ÉNAC) Framework for Conflict Resolution ATM / 18

8 Trajectory Prediction Handling Uncertainties Uncertainties on maneuvers and speed Maneuver starts at d o ± ε 0 Maneuver distance is d 1 ± ε 1 Maneuver angle is α ± ε α Speed is s ± ε s Trajectory hull model At each time step τ, aircraft position is a modelled as a convex hull containing all possible positions Red: aircraft did not turn yet Green: aircraft is being maneuvered Blue: aircraft is heading towards destination again Allignol, Barnier, Durand, Alliot (ÉNAC) Framework for Conflict Resolution ATM / 18

9 Trajectory Prediction Model Decision variables M = {m i, i [1, n]} i, m i [1, n man ] size of the search space: nman n Optimization Cost of a single maneuver: { 0 if α = 0 cost man (m i ) = (n 0 k 0 ) 2 + k1 2 + k2 α otherwise where m i is the maneuver described by the tuple k 0, k 1, k α Total cost: cost = n cost man (m i ) i=1 Allignol, Barnier, Durand, Alliot (ÉNAC) Framework for Conflict Resolution ATM / 18

10 Trajectory Prediction Versatility This model can be easily modified and refined with: other trajectory prediction methods other modelings for uncertainties different kinds of maneuvers other cost functions (fuel consumption, CO 2 emission, delay...) Allignol, Barnier, Durand, Alliot (ÉNAC) Framework for Conflict Resolution ATM / 18

11 Scenarios Scenarios D 4 D 2 D 1 Aircraft 1 D 3 20NM O NM Aircraft 2 O 2 Aircraft 3 O 3 O 4 Aircraft 4 Allignol, Barnier, Durand, Alliot (ÉNAC) Framework for Conflict Resolution ATM / 18

12 Scenarios Scenarios D 4 D 2 D 1 Aircraft 1 20NM O 1 Scenario parameters: n NM D 3 n man ε = ε 0, ε 1, ε α, ε s Aircraft 2 O 2 Aircraft 3 O 3 O 4 Aircraft 4 Allignol, Barnier, Durand, Alliot (ÉNAC) Framework for Conflict Resolution ATM / 18

13 Conflict Detection Conflict Detection Conflict between trajectories t i and t j for all time steps τ do if dist(convex_hull(m i, τ), convex_hull(m j, τ)) < 5NM then return true end if end for return false Given n aircraft, a 4D matrix C is built: i, j [1, n], i < j m i, m j [1, n man ] where m i, m j are maneuvers of aircraft i and j respectively C i,j,mi,m j = { true if there is a conflict between those trajectories false otherwise Allignol, Barnier, Durand, Alliot (ÉNAC) Framework for Conflict Resolution ATM / 18

14 Conflict Detection For a given set of parameters, matrix C forms the benchmark for the corresponding instance. Allignol, Barnier, Durand, Alliot (ÉNAC) Framework for Conflict Resolution ATM / 18

15 Conflict Detection For a given set of parameters, matrix C forms the benchmark for the corresponding instance. Instance files and current results available at: Allignol, Barnier, Durand, Alliot (ÉNAC) Framework for Conflict Resolution ATM / 18

16 Conflict Detection For a given set of parameters, matrix C forms the benchmark for the corresponding instance. Currently available instances: n {5, 10, 15, 20} n man = 151 Instance files and current results available at: ε {ε low, ε mid, ε high } ε low : ε 0 = 1NM, ε 1 = 1NM, ε α = 1, ε s = 1% ε mid : ε 0 = 2NM, ε 1 = 2NM, ε α = 2, ε s = 2% ε high : ε 0 = 3NM, ε 1 = 3NM, ε α = 3, ε s = 3% More to come... Allignol, Barnier, Durand, Alliot (ÉNAC) Framework for Conflict Resolution ATM / 18

17 Contents Resolution 1 Trajectory Prediction Scenarios Conflict Detection 2 Resolution Evolutionary Algorithm Constraint Programming Results 3 Conclusion Allignol, Barnier, Durand, Alliot (ÉNAC) Framework for Conflict Resolution ATM / 18

18 Evolutionary Algorithm Resolution Evolutionary Algorithm Inspired by natural evolution: manipulation of a population of candidate solutions with selection, crossover and mutation operators Fitness function if (i, j), i < j, C i,j,mi,m j 0 C i,j,mi,m j F = i<j if (i, j), i < j, C i,j,mi,m 1 + cost j = 0 Using a sharing process to avoid premature convergence towards local optima Taking advantage of partial separability of the cost function to build adapted crossover and mutation operators Allignol, Barnier, Durand, Alliot (ÉNAC) Framework for Conflict Resolution ATM / 18

19 Resolution Constraint Programming Constraint Programming CSP Model Variables: M = {m i, i [1, n]} Domains: i, m i [1, n man ] Constraints: (i, j), c i,j = {(k, l) C i,j,k,l = 1} We note c i,j the cardinality of the constraint c i,j Solution search and Optimization Branch and Bound Weighted degree adaptative heuristic Optimality proof obtained for most instances Allignol, Barnier, Durand, Alliot (ÉNAC) Framework for Conflict Resolution ATM / 18

20 Resolution Results A solution to a 10-aircraft conflict Allignol, Barnier, Durand, Alliot (ÉNAC) Framework for Conflict Resolution ATM / 18

21 Resolution Results Cost of solutions Average on 10 instances with the same parameters. n CP EA CP EA CP EA CP EA ε low ε med ε high Each maneuver has a cost in the interval [0, 50] CP and EA equivalently efficient Allignol, Barnier, Durand, Alliot (ÉNAC) Framework for Conflict Resolution ATM / 18

22 Cost of solutions Resolution Results The cost is closely related to the number of forbidden maneuver pairs. We define the intrinsic difficulty of an instance by: ρ = c ij i<j Allignol, Barnier, Durand, Alliot (ÉNAC) Framework for Conflict Resolution ATM / 18

23 Resolution Results Cost of solutions The cost is closely related to the number of forbidden maneuver pairs. We define the intrinsic difficulty of an instance by: ρ = c ij i<j Cost e+05 2e+05 3e+05 4e+05 5e+05 6e+05 7e+05 ρ Allignol, Barnier, Durand, Alliot (ÉNAC) Framework for Conflict Resolution ATM / 18

24 Resolution Results Computing times for finding best solution All runs were limited to 5 minutes. Average on 10 instances with the same parameters. n CP EA CP EA CP EA CP EA ε low ε med ε high Unfeasible instances are proved inconsistent (CP only) within 1 second possibility to generate a new instance with more maneuvers allowed A first solution is found within seconds for almost all instances Allignol, Barnier, Durand, Alliot (ÉNAC) Framework for Conflict Resolution ATM / 18

25 Conclusion Conclusions A new framework for conflict resolution Separation of the model from its resolution Many configuration opportunities available at: Two possible approaches for the resolution: Constraint Programming and Evolutionary Algorithm Optimality proof obtained for most instances with CP Further Work Vertical maneuvers Scenarios issued from real data (simulated flight plans) Embedded resolution (i.e. integration into fast-time simulator) Tabu Search algorithm, hybridization Allignol, Barnier, Durand, Alliot (ÉNAC) Framework for Conflict Resolution ATM / 18