Kai Virtanen, Tuomas Raivio, and Raimo P. H

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Optimal Pilot Decision and Flight Trajectories in
Air Combat

• Kai Virtanen, Tuomas Raivio, and Raimo P.
  Hämäläinen
• Systems Analysis Laboratory (SAL)
• Helsinki University of Technology (HUT)
• www.sal.hut.fi

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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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Approaches for modeling air combat

• Dynamic optimization
• one active actor
• control the dynamic system in
• the best possible way

• Differential games, game theory
• two actors
• optimization againts the worst
• action of the opponent

• Simulation
• multiple actors
• decision models of pilots

Utilization - Planning of tactics - Pilot
training - Performance evaluation
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System model
- Describes the dynamics of aircraft and
missiles - Translational (and rotational)
dynamics
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Dynamic optimization, optimal control
Final state xf
Initial state x0

• 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

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Minimum time climb
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Minimum time flight in 3D
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Optimal missile avoidance
is pursuing

• Missile assumed to use a known feedback guidance
  law
• One decision maker (aircraft) gt optimal control
  problem
• given vehicle parameters and initial states,
  choose aircraft controls
• Maximization of minimum distance

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Family of optimal solutions
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Pursuit-evasion game
?
?
Evader - Escape if possible - Maximize the cost
of capture
Pursuer - Capture with minimal cost
Fixed roles
Saddle point solution Best possible action
against the worst action of the opponent

• Two-player zero-sum differential game with free
  terminal time
• Game of kind When a capture is possible? gt
  Capture zone
• Game of degree Saddle point strategies inside
  the Capture zone
• Our research activities Numerical solution
  methods, applications

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Missile-aircraft setting
Minimizes flight time
Maximizes flight time
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Maximal shooting range of a missile
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One-on-one air combat game
¼
tDt
tDt
¼
t0
t0
Find the best maneuvering sequence for the
players with respect to the goals 1. Avoid being
captured by the adversary 2. Capture the
adversary by taking into account - Preferences of
a pilot - Uncertainties - Dynamic decision
environment - Behavior of the adversary
Two-target game
Influence diagram game
Influence diagram
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Air combat simulation models

• Multiple aircraft
• More realistic dynamics and uncertainty models
• Discrete-event approach gt Statistical analysis
  of results
• Our research activities
• X-Brawler

Computer generated forces need a model imitating
pilot decision making Influence diagram approach
simulation experiments
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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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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, 2001
• Raivio 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.