1 S ystems Analysis Laboratory Helsinki University of Technology Kai Virtanen, Tuomas Raivio and Raimo P. Hämäläinen Systems Analysis Laboratory Helsinki University of Technology Simulating Pilot’s Decision Making by an Influence Diagram Game

2 S ystems Analysis Laboratory Helsinki University of Technology Outline Air combat simulation models Existing modeling approaches Influence diagram (ID) Control decisions in one-on-one air combat ID for a control decision ID game for a control decision Simulation example Conclusions

3 S ystems Analysis Laboratory Helsinki University of Technology Air combat simulation models Analysis of air combat and pilot training are expensive tasks Every air combat situation cannot be analyzed in practice Real time piloted: –Training in a realistic environment Batch: –Controlled and repeatable environment –Discrete-event approaches Computer generated forces need a model that imitates pilot decision making Orders Commands

4 S ystems Analysis Laboratory Helsinki University of Technology Existing modeling approaches Dynamic optimization and game theory: –Optimal flight paths –Simple performance criteria –Lack of realistic uncertainty models –Non-real-time computation Models emulating the decision making of a pilot: –Computational techniques of AI: Rule-based, Value-Driven –Capture the preferences of a pilot –Real-time computation –Short planning horizon => Not optimal but myopic control commands How to handle uncertainties? Behavior of the opponent?

5 S ystems Analysis Laboratory Helsinki University of Technology Influence diagram (ID) (Howard et al. 1984) Directed acyclic graphs Describes the major factors of a decision problem Widely used in decision analysis application areas Decision Chance Deterministic Informational arc Conditional arc Alternatives available to DM Random variables Deterministic variables Time precedence Probabilistic or functional dependence Utility A utility function Conditional arc

6 S ystems Analysis Laboratory Helsinki University of Technology Influence diagram (continued) State of the world is described by attributes States are associated with –Utility –Probability Utility is a commensurable measure for goodness of attributes Results include probability distributions over utility Decisions based on utility distributions Information gathering and updating using Bayesian reasoning

7 S ystems Analysis Laboratory Helsinki University of Technology Control decisions in one-on-one air combat Find the best maneuvering sequence for the DM with respect to the goals 1. Avoid being captured by the AD 2. Capture the AD by taking into account - Preferences of a pilot - Uncertainties - Dynamic decision environment - Behavior of the AD t=  t t=0  t=  t  Influence diagrams representing the control decision of the DM: Single stage ID (Virtanen et al. 1999), –pilot’s short-term decision making Multistage ID ( Virtanen et al ), − preference optimal flight paths against given trajectories New model: Influence diagram game Decision maker (DM) Adversary (AD)

8 S ystems Analysis Laboratory Helsinki University of Technology ID for a control decision Adversary’s State Maneuver Present Threat Situation Assessment State Combat State Threat Situation Assessment Situation Evaluation Present State Adversary's Present State Present Combat State Measurement Present Measurement Adversary's Maneuver Evolution of the players’ states described by a set of differential equations The behavior of the AD?

9 S ystems Analysis Laboratory Helsinki University of Technology ID game for a control decision The best control of the DM against the worst possible action of the AD DM’s belief about AD’s viewpoint DM's viewpoint Combat state The game: - Non-zero-sum - Payoff = Expected utility Solution: - Discrete controls => Matrix game - Continuous controls => Nonlinear programming - Nash or Stackelberg equilibrium

10 S ystems Analysis Laboratory Helsinki University of Technology Simulation example Initial state advantageous for AD DM’s aircraft more agile Solution generated with the ID game DM wins AD DM y-range, km X-range, km altitude, km

11 S ystems Analysis Laboratory Helsinki University of Technology Conclusions The influence diagram game: –Models preferences under uncertainty and multiple competing objectives in one-on-one air combat –Takes into account Rational behavior of the adversary Dynamics of flight Utilization: –Air combat simulators, a good computer guided aircraft –Contributions to the existing air combat game formulations Several computational difficulties are avoided Roles of the players are varied dynamically Producing reprisal strategies –Other simulation applications