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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.