Optimal Decision Making in Air Combat: Modeling Flight Trajectories

1. 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

2. 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

3. 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

4. n h v g u m y x c System model - Describes the dynamics of aircraft and missiles - Translational (and rotational) dynamics

5. Dynamic optimization, optimal control • 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 Final state xf Initial state x0

6. Minimum time climb

7. Minimum time flight in 3D

8. Optimal missile avoidance is pursuing • 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

9. B C A D A D C B Family of optimal solutions

10. 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? => ‘Capture zone’ • Game of degree: Saddle point strategies inside the Capture zone • Our research activities: Numerical solution methods, applications

11. Missile-aircraft setting Minimizes flight time Maximizes flight time

12. Maximal shooting range of a missile

13. One-on-one air combat game ¼ t=Dt t=Dt ¼ t=0 t=0 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

14. Orders Commands 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 simulation experiments

15. 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

16. 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.