1 s ystems analysis laboratory helsinki university of technology kai virtanen, tuomas raivio, and...
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S ystemsAnalysis LaboratoryHelsinki University of Technology
Kai Virtanen, Tuomas Raivio, and Raimo P. Hämäläinen
Systems Analysis Laboratory (SAL)
Helsinki University of Technology (HUT)
www.sal.hut.fi
Optimal Pilot Decision and Flight Trajectories in Air Combat
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S ystemsAnalysis LaboratoryHelsinki University of Technology
The Project ”Dynamics and Strategy of Flight”
• Financed by the Finnish Air Force, initiated in 1993• Research group:
– project leader prof. Raimo P. Hämäläinen– prof. Harri Ehtamo– three full-time researchers
• Research topics: – single aircraft performance optimization– analysis of antagonistic aerospace scenarios using
• differential games• decision theoretical tools• simulation
• Cooperation with Laboratory of Aerodynamics of HUT
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S ystemsAnalysis LaboratoryHelsinki University of Technology
Dynamic optimization• one active actor• control the dynamic system in the best possible wayDifferential games, game theory• two actors• optimization againts the worst action of the opponent
Simulation• multiple actors • decision models of pilots
Approaches for modeling air combat
Utilization:- Planning of tactics- Pilot training- Performance evaluation
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S ystemsAnalysis LaboratoryHelsinki University of Technology
System model
yx
hv
n
u
- Describes the dynamics of aircraft and missiles- Translational (and rotational) dynamics
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S ystemsAnalysis LaboratoryHelsinki University of Technology
• Control the dynamic system in the best possible way:– best = e.g., minimal time– obey given constraints: minimum altitude, stall velocity, g-forces,…
• Our research activities:– numerical solution methods
• time discretization and nonlinear programming– interactive optimization software
Initialstate x0
Finalstate xf
u t x t f x t u t t( ) ( ) ( ( ), ( ), )
Dynamic optimization, optimal control
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S ystemsAnalysis LaboratoryHelsinki University of Technology
Minimum time climb
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S ystemsAnalysis LaboratoryHelsinki University of Technology
Minimum time flight in 3D
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S ystemsAnalysis LaboratoryHelsinki University of Technology
• Missile assumed to use a known feedback guidance law• One decision maker (aircraft) => optimal control problem
– given vehicle parameters and initial states, choose aircraft controls
• Maximization of minimum distance
Optimal missile avoidance
is pursuing
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S ystemsAnalysis LaboratoryHelsinki University of Technology
Family of optimal solutions
A B
CD
A
B
C
D
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S ystemsAnalysis LaboratoryHelsinki University of Technology
Pursuit-evasion game
• Two-player zero-sum differential game with free terminal time• Game of kind: When a capture is possible? => ‘Capture zone’• Game of degree: Saddle point strategies inside the Capture zone• Our research activities: Numerical solution methods, applications
Pursuer- Capture with minimal cost
Evader- Escape if possible- Maximize the cost of capture
Saddle point solution:Best possible action against
the worst action of the opponent
?
?
Fixed roles
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S ystemsAnalysis LaboratoryHelsinki University of Technology
Missile-aircraft setting
Minimizes flight time Maximizes flight time
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S ystemsAnalysis LaboratoryHelsinki University of Technology
Maximal shooting range of a missile
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S ystemsAnalysis LaboratoryHelsinki University of Technology
One-on-one air combat game
Find the best maneuvering sequence for the players with respect to the goals1. Avoid being captured by the adversary2. Capture the adversary
by taking into account- Preferences of a pilot - Uncertainties- Dynamic decision environment- Behavior of the adversary
t=t t=0
t=0
t=t
Two-target game
Influence diagram
Influence diagram game
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S ystemsAnalysis LaboratoryHelsinki University of Technology
Air combat simulation models • Multiple aircraft• More realistic dynamics and uncertainty models• Discrete-event approach => Statistical analysis of results• Our research activities:
– X-Brawler
Computer generated forces need a model imitating pilot decision making: Influence diagram approach
Orders
Command
s
simulation experiments
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S ystemsAnalysis LaboratoryHelsinki University of Technology
Future modeling challenges
• Modeling:– Improved models for flight mechanics
• Optimization, differential games:– Optimal control and games under increased uncertainty– Optimal feedback strategy approximation
• Simulation:– Optimal decisions under uncertainty– Combination of discrete-event simulation and optimization
• Methodological contributions are required
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S ystemsAnalysis LaboratoryHelsinki University of Technology
More information• www.sal.hut.fi• Selected publications:Virtanen, Raivio, and Hämäläinen, "Modeling Pilot's Sequential Maneuvering Decisions by a Multistage Influence Diagram," Journal
of Guidance, Control, and Dynamics, Vol. 27, No. 4, 2004. Virtanen, Hämäläinen, and Mattila, "Team Optimal Signaling Strategies in Air Combat," IEEE Transaction on Systems, Man, and
Cybernetics - Part A: Systems and Humans, accepted for publication, 2004.Ehtamo and Raivio, “On Applied Nonlinear and Bilevel Programming for Pursuit-Evasion Games,” Journal of Optimization Theory
and Applications, Vol. 108, No. 1, 2001.Raivio, “Capture Set Computation of an Optimally Guide Missile,” Journal of Guidance, Control, and Dynamics, Vol. 24, no. 6, 2001Raivio and Ehtamo, “On Numerical Solution of a Class of Pursuit-Evasion Games,” Annals of the International Society of Dynamic
Games, Vol. 5, 2000. Raivio and Ehtamo, “Visual Aircraft Identification as a Pursuit-Evasion Game,” Journal of Guidance, Control and Dynamics, Vol. 23
No. 4, 2000.Virtanen, Raivio, and Hämäläinen, "Decision Theoretical Approach to Pilot Simulation," Journal of Aircraft, Vol. 36, No. 4, 1999.Virtanen, Ehtamo, Raivio, and Hämäläinen, "VIATO - Visual Interactive Aircraft Trajectory Optimization," IEEE Transaction on
Systems, Man, and Cybernetics - Part C: Applications and Reviews, Vol. 29, No. 3, 1999.