An Influence Diagram Approach to OneonOne Air Combat

An Influence Diagram Approach to One-on-One Air Combat Kai Virtanen, Tuomas Raivio and Raimo P. Hämäläinen Systems Analysis Laboratory Helsinki University of Technology S ystems Analysis Laboratory Helsinki University of Technology 1

Outline • • • Maneuvering decisions in one-on-one air combat Existing modeling approaches Decision analytical maneuvering models Influence diagram One-on-one air combat game Influence diagram for a single maneuvering decision Influence diagram game for a single maneuvering decision Simulation procedure for solving the game Conclusions S ystems Analysis Laboratory Helsinki University of Technology 2

Maneuvering decisions in one-on-one air combat t=Dt t=0 ¼ ¼ t=Dt t=0 Outcome depends on all the maneuvers of both the players Þ Dynamic game problem Objective Find the best maneuvering sequence with respect to the overall goals of a pilot! - Preference model - Uncertainties - Behavior of the adversary - Dynamic decision environment S ystems Analysis Laboratory Helsinki University of Technology 3

Existing modeling approaches • Dynamic game theory – Pursuit-evasion games: - fixed roles of the players - saddle point solution – Two-target games: - qualitative solution, outcome regions in the state space - quantitative solution is intractable – Simple performance criteria – Lack of realistic uncertainty models • Game models emulating the decision making of pilots – Capture the preferences of a pilot – Short planning horizon S ystems => Myopic maneuvering decisions Analysis Laboratory Helsinki University of Technology 4

Decision analytical maneuvering models • Single stage influence diagram model (Virtanen et al. 1999): – Simulates pilot’s short-term decision making in one-on-one air combat • Multistage influence diagram model (Virtanen et al. 2001): – Determines a preference optimal flight path against a given trajectory – A new nonlinear programming -based solution approach Two new models: Contain components representing the behavior of the adversary – stochastically => traditional influence diagram – explicit decision variable => influence diagram game Best myopic controls Simulation procedure for solving one-on-one air combat game S ystems Analysis Laboratory Helsinki University of Technology 5

Influence diagram (ID) (Howard et al. 1984) • Directed acyclic graphs • Describes the major factors of a decision problem • Widely used in decision analytic application areas Time precedence Probabilistic or functional dependence Informational arc Decision Alternatives available to DM Conditional arc Chance Random variables Conditional arc Deterministic Conditional arc Utility Deterministic variables A utility function S ystems Analysis Laboratory Helsinki University of Technology 6

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 S ystems Analysis Laboratory Helsinki University of Technology 7

One-on-one air combat game Black White • Evolution of the player’s states are represented by a set of difference equations, e. g. , point mass model • Goals of the players: 1. Avoid being captured by the adversary 2. Capture the adversary • Four possible outcomes • Maneuvering decisions are represented by an ID The controls of both the players are selected such that the expected utilities at each decision stage are maximized S ystems Analysis Laboratory Helsinki University of Technology 8

ID for a single maneuvering decision Adversary's Present State Present Combat State Present State S ystems Analysis Laboratory Helsinki University of Technology Adversary's Maneuver Adversary’s State Solution: Discrete controls => Rollback procedure Continuous controls => Nonlinera programmings Present Measurement Combat State Measurement Maneuver State Situation Evaluation Present Threat Situation Assessment 9

ID game for a single maneuvering decision Solution: Discrete controls => Matrix game Continuous controls => Nonlinear programmings Black’s comprehension Implies Information Structure Combat state White's comprehension S ystems Analysis Laboratory Helsinki University of Technology 10

Simulation procedure for solving the game t: =t+Dt Black’s Threat Assessment at t Black’s Influence Diagram at t Black’s State at t S ystems Analysis Laboratory Helsinki University of Technology Black’s Control at t Terminate? White’s State at t White’s Threat Assessment at t Black’s Threat Assessment at t+1 White’s Influence Diagram at t Black’s State at t+1 White’s Control at t White’s Threat Assessment at t+1 t: =t+Dt 11

Numerical example • Symmetric initial state • White’s aircraft more agile • Solution generated with the simulation procedure and the ID game • White wins Black Altitude, m White S ystems Y-range , m Analysis Laboratory Helsinki University of Technology , m e g an X-r 12

Conclusions • New influence diagram models: – Model human preferences under uncertainty and multiple competing objectives in one-on-one air combat – Take into account the rational behavior of the adversary – Single stage model => Produce the best myopic controls, can be calculated in real-time – A new way to produce reprisal strategies in a two-target game • Utilization: – Planning fighter maneuvers – Air combat simulators, a good computer guided aircraft • Future research: S ystems – Longer planning horizon => multistage models – Open-loop solutions of the multistage one-on-one air combat game Analysis Laboratory Helsinki University of Technology 13