This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Distributed Trajectory Flexibility Preservation for Traffic Complexity Mitigation - ATM 2009Advanced Transportation Research and Engineering 1
Distributed Trajectory Flexibility Preservation for Distributed Trajectory Flexibility Preservation for Traffic Complexity MitigationTraffic Complexity Mitigation
Husni Idris Husni Idris
88thth USA/Europe ATM R&D SeminarUSA/Europe ATM R&D SeminarNapa, CaliforniaNapa, California
June 29 June 29 –– July 2, 2009July 2, 2009
Distributed Trajectory Flexibility Preservation for Traffic Complexity Mitigation - ATM 2009Advanced Transportation Research and Engineering 2
• Authors:
– Husni Idris (L-3 Communications, USA)
– Daniel Delahaye (ENAC, France)
– David Wing (NASA Langley Research Center, USA)
• Thanks to
– Robert Vivona (L-3 Communications)
– Tarek Al-Wakil (L-3 Communications)
– Stephane Peuchmorel (ENAC)
– Danette Allen (NASA Langley Research Center)
• This research was conducted under an NRA contract sponsored by the
NASA NextGen Airspace Project
Authors and Team
Distributed Trajectory Flexibility Preservation for Traffic Complexity Mitigation - ATM 2009Advanced Transportation Research and Engineering 3
• Research Objectives and Questions
• Concept Description
• Trajectory Flexibility Metrics Definition and Estimation
• Trajectory Planning Algorithm and Cost Function
• Traffic Complexity Experiments and Preliminary Results
• Next Steps
Briefing Agenda
Distributed Trajectory Flexibility Preservation for Traffic Complexity Mitigation - ATM 2009Advanced Transportation Research and Engineering 4
• Management of traffic complexity using trajectory-oriented as opposed to airspace-oriented perspective and approach
Research Objectives and Questions
Pilot
Controller
Airspace-Oriented
Pilot
Controller
Trajectory-Oriented
Distributed Trajectory Flexibility Preservation for Traffic Complexity Mitigation - ATM 2009Advanced Transportation Research and Engineering 5
Research Objectives and Questions
• What is impact of trajectory constraint minimization on trajectory ‘flexibility’preservation?
Trajectory Flexibility Preservation- Preserve Ability to Manage Risk Exposure
• What is impact of trajectory ‘flexibility’ preservation on traffic ‘complexity’ prevention and mitigation?
Focus is on flexibility preservation and its impact on traffic complexity
Distributed Trajectory Flexibility Preservation for Traffic Complexity Mitigation - ATM 2009Advanced Transportation Research and Engineering 6
• Research insight applicable to both centralized and
distributed control issues
– Insight into appropriate allocation of air and ground functions, e.g.,
• Trajectory Flexibility Preservation conceived as air-based function
• Constraint Minimization conceived as mostly ground-based function
– What is ‘Traffic Complexity’ in distributed, automated environment?
• Need suitable traffic complexity metric
• Develop concepts, metrics, methods, algorithms, and
experiments, to investigate hypothesized relationships
Research Objectives and Questions
Distributed Trajectory Flexibility Preservation for Traffic Complexity Mitigation - ATM 2009Advanced Transportation Research and Engineering 7
Within conflict resolution look-ahead: e.g. avoid “coincidence” conflict
Concept: Flexibility Preservation
conflict conflict
Non-coordinated coincidental resolutionsready for execution
Active routes
Unrelated conflict pairs
Avoided “coincidence”conflict
Conflict Resolution without Flexibility Preservation
Conflict Resolution with Flexibility Preservation
Ownship
New “coincidence”conflict
Previous conflict
Previous conflict
Implicitly coordinated resolutionsminimizing risk exposure to traffic
Ownship
Look-ahead horizon
Previous Previous
Distributed Trajectory Flexibility Preservation for Traffic Complexity Mitigation - ATM 2009Advanced Transportation Research and Engineering 8
Outside conflict resolution look-ahead: e.g. avoid congestion
Concept: Flexibility Preservation
Hypothesis:If all aircraft apply flexibility preservation function, complexity automatically will be reduced
Airborne flexibility function will question:Do I have enough flexibility to safely proceed?Can I modify my trajectory to increase my flexibility?Do I need to avoid this airspace entirely and replan?
OwnshipFlexibility metric
Trajectories Designed to Preserve FlexibilityApplicability of Trajectory Flexibility Prediction
Distributed Trajectory Flexibility Preservation for Traffic Complexity Mitigation - ATM 2009Advanced Transportation Research and Engineering 9
e.g., extending RTA tolerance
Concept: Constraint Minimization
Solution Space before Constraint Relaxation Solution Space after Constraint Relaxation
Ownship aircraft A
Conflict resolution look-ahead horizon
Flexibility planning horizon
ETA at fix
RTA at fixFix
RTA tolerance
Aircraft BAircraft C
Aircraft D
Weather system
Conflict free trajectories meeting RTA for aircraft A
Ownship aircraft A
Fix
Aircraft C
Aircraft D
Extended RTA tolerance
Aircraft B
ETA range for conflict free trajectories meeting RTA
Extended ETA range for conflict free trajectories meeting RTA
ETA at fix
More flexible conflict free trajectories meeting RTA tolerance –Reducing aircraft A contribution to complexity
RTA at fix
Conflict
Distributed Trajectory Flexibility Preservation for Traffic Complexity Mitigation - ATM 2009Advanced Transportation Research and Engineering 10
• Challenge: Lack of accepted metrics in literature for trajectory flexibility
• Starting point: Trajectory flexibility defined as its ‘ability to mitigate exposure to risk’
– Defined more specifically as ability of trajectory to accommodate disturbances while meeting constraints (such as safety constraints or flow management constraints)
• Relevant trajectory characteristics– Robustness: Ability to remain feasible given disturbance
– Adaptability: Ability to regain feasibility if feasibility is lost due to disturbance
• Corresponding metrics defined next
Metrics Definition and Estimation
Distributed Trajectory Flexibility Preservation for Traffic Complexity Mitigation - ATM 2009Advanced Transportation Research and Engineering 11
• Approach: Start by analyzing trajectory solution space given
limited degrees of freedom and in simple constraint
scenarios
– (1) Varying only speed as degree of freedom
– (2) Varying only heading as degree of freedom
– (3) Varying both heading and speed as degrees of freedom
– Single RTA RTA and conflict Multiple RTAs and conflicts
Metrics Definition and Estimation
Distributed Trajectory Flexibility Preservation for Traffic Complexity Mitigation - ATM 2009Advanced Transportation Research and Engineering 12
Metrics Definition and Estimation
• Trajectory solution space for– Single RTA at fix– Vary heading between hmin and hmax
– Fixed speed V D = RTA x V = Constant
Fix
y
x
hmax
hmin
Ellipse boundary for meeting the RTA at the fix
Example path stretch routes
A
Distributed Trajectory Flexibility Preservation for Traffic Complexity Mitigation - ATM 2009Advanced Transportation Research and Engineering 13
Metrics Definition and Estimation
• Trajectory solution space for– Single RTA at fix– Vary heading between hmin and hmax
– Vary speed between Vmin and Vmax
Fix
y
x
hmax
hminEllipse boundary for meeting the RTA at Vmin
Example path stretch routes
A
Ellipse boundary for meeting the RTA at Vmax
Distributed Trajectory Flexibility Preservation for Traffic Complexity Mitigation - ATM 2009Advanced Transportation Research and Engineering 14
Metrics Definition and Estimation
• Discretization of trajectory solution space – Trajectory consists of discrete constant-speed, constant-heading segments– Solution space consists of series of conical shells each with heading range between
hmin and hmax
y
t
x
hmin
hmax
Conical shell corresponding to segment with a heading range and constant speed
Aircraft A Instances of heading change
Distributed Trajectory Flexibility Preservation for Traffic Complexity Mitigation - ATM 2009Advanced Transportation Research and Engineering 15
Metrics Definition and Estimation
• Discretization of trajectory solution space – Trajectory consists of discrete constant-speed, constant-heading segments– Solution space consists of series of conical shells each with heading range between
hmin and hmax and speed range between Vmin and Vmax
y
t
x
hmin
hmax
Conical shell corresponding to segment with a heading range and speed range
Aircraft A Instances of heading change
Distributed Trajectory Flexibility Preservation for Traffic Complexity Mitigation - ATM 2009Advanced Transportation Research and Engineering 16
Metrics Definition and Estimation
• Discretization of trajectory solution space – Trajectory consists of discrete constant-speed, constant-heading segments– Solution space reduced by RTA and separation constraints
y
t
x
hmin
hmax
Aircraft A
Intersection of separation zone with the solution space
Intruder aircraft B
RTA
Fix
Intersection of RTA constraint with the solution space
Distributed Trajectory Flexibility Preservation for Traffic Complexity Mitigation - ATM 2009Advanced Transportation Research and Engineering 17
Metrics Definition and Estimation• Flexibility definition extends to heading and speed: ability of trajectory to
accommodate disturbances while meeting constraints
– Constraint disturbances: introduction or modification of constraints
– State disturbances: deviation of state from predicted trajectory
Fix
y
x
Example constraint disturbance (e.g., uncertainty in intruder heading)
RTA with tolerance
Example state (heading) disturbance (e.g., due to turbulence)
A
Distributed Trajectory Flexibility Preservation for Traffic Complexity Mitigation - ATM 2009Advanced Transportation Research and Engineering 18
Metrics Definition and Estimation• Trajectory flexibility metrics:
– Robustness: Ability of trajectory to remain feasible despite disturbance
• Metric: Probability of trajectory feasibility given distributions
• If state disturbance modeled by K possible trajectory instances and constraint disturbance
modeled by C possible constraint instances, then
where
• If K trajectory instances are equally likely, RBT estimated by ratio:
where fc(t,x,y) is number of feasible trajectories and
ic(t,x,y) is number of infeasible trajectories, from (t,x,y) to destination, in situation c
– Adaptability: Ability of trajectory to regain feasibility if lost due to disturbance
• Metric:
C:1c y)x,(t,iy)x,(t,f
y)x,(t,fP y)x,(t,RBTcc
cc +×= ∑
=
)(trajPP (traj)PRBT(traj) ifK:1i
if ×== ∑=
∑∈
=feasible is trajSc
cifi
P)(trajP whereituations
(traj)Pf
y))x,(t,f(P y)x,f(t, y)x,(t,ADPC:1c
cc∑=
×==
Distributed Trajectory Flexibility Preservation for Traffic Complexity Mitigation - ATM 2009Advanced Transportation Research and Engineering 19
Metrics Definition and Estimation
t
y
x
11
1
1
1
01
0
00
0
0
0
1
0
00
0
0
00
Reachability of point k over ε given by gk
Point or cell kTime step ε
Initialization of last time step: f=1 if inside RTA tolerance, f=0 if outside
Blocked cells due to loss of separation
Grid of discrete x-y cells
fc(tj-1,x,y) is derived by convolution of gk(x,y) and fc(tj,x,y), sliding k in plane:
feasiblenotisy)x,,(tif0
or)y,)g(x,,(tfy)x,,(tf
1j
jc1jc
−
−
=
−−= ∑∑τ σ
σσ ττ
Starting from final time step
Distributed Trajectory Flexibility Preservation for Traffic Complexity Mitigation - ATM 2009Advanced Transportation Research and Engineering 20
Metrics Definition and Estimation
• Filtering for conflicts: Given: Intruder speed Vint and heading hint ; ownship speed limits Vmin, Vmax and ownship heading limits hmin and hmax; and minimum separation R
• (1) Find four relative angles where i and j are set to “min” or “max”
• (2) Find eight tangency points, k = 1-8
• (3) Find 8 planes with norms nk and distances dk:
• (4) Center of cell (t,x,y) is in conflict if and only if
Distributed Trajectory Flexibility Preservation for Traffic Complexity Mitigation - ATM 2009Advanced Transportation Research and Engineering 21
• Dynamic programming algorithm selected because– Suitable to decision-tree formulation of the solution space and
flexibility map
– Computational and storage load not an issue for non-real-time application
• Three main steps:– (1) Build the tree of state cells according to reachability
– (2) Starting from the last time step, use backward propagation over time to compute and store the optimal cost and tree path from each cell to the destination
– (3) Starting from the initial state, use forward propagation over time to connect the best cells in each time step to the destination
Trajectory Planning Algorithm
Distributed Trajectory Flexibility Preservation for Traffic Complexity Mitigation - ATM 2009Advanced Transportation Research and Engineering 22
Trajectory Planning Algorithm
• Dynamic program back-propagation (recursion)
y)}x,1,(tq(ky)x,1,{Q(tMiny(k))x(k),Q(t,1y)x,1,(tg :yx, k
+→++==+
t
y
xReachability of point k over εgiven by gk
Time step ε
(1) Initialize cost at final time step
Grid of discrete x-y cells
Point or cell k
(2) Find and store best cost Q over reachable states(3) Repeat (2) for each cell
Distributed Trajectory Flexibility Preservation for Traffic Complexity Mitigation - ATM 2009Advanced Transportation Research and Engineering 23
Trajectory Planning Algorithm
• Dynamic program Forward loop to build trajectory
t
y
xReachability of point k over εgiven by gk
Time step ε
Grid of discrete x-y cells
(1) Start from initial cell
(2) Trace optimal path already stored, breaking ties randomly
Distributed Trajectory Flexibility Preservation for Traffic Complexity Mitigation - ATM 2009Advanced Transportation Research and Engineering 24
Trajectory Planning Algorithm
• Cost function
• Four functions used for q: – Shortest path
– Maximize adaptability
– Maximize robustness
– Tradeoff adaptability, robustness and path length (T = final time step)
y)}x,1,(tq(ky)x,1,{Q(tMiny(k))x(k),Q(t,1y)x,1,(tg :yx, k
+→++==+
dist y))x,1,t(distance(k y))x,1,t(q(k =+→=+→
ADP(k)y))x,1,(tq(k −=+→
dist bRBT(k)aADP(k)y))x,1,(tq(k t-Tt-T +−−=+→
RBT(k)y))x,1,(tq(k −=+→
Distributed Trajectory Flexibility Preservation for Traffic Complexity Mitigation - ATM 2009Advanced Transportation Research and Engineering 25