Transcript VIATO - Visual Interactive Aircraft Trajectory Optimization

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
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Outline
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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
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Maneuvering decisions in one-on-one air combat
t=Dt
t=0
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t=Dt
t=0
Outcome depends on all the maneuvers of both the players
 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
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Helsinki University of Technology
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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
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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
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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
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Influence diagram (continued)
• State of the world is described by attributes
• States are associated with
– Utility
– Probability
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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
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Analysis Laboratory
Helsinki University of Technology
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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
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Analysis Laboratory
Helsinki University of Technology
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ID for a single maneuvering decision
Adversary's
Present
State
Present
Combat State
Present
State
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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
Threat Situation
Assessment
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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
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Simulation procedure for solving the game
t:=t+Dt
Black’s Threat
Assessment at t
Black’s
Influence
Diagram at t
Black’s Threat
Assessment at t+1
Black’s
Control at t
Black’s
State at t
Black’s
State at t+1
Terminate?
White’s
State at t
White’s Threat
Assessment at t
White’s
Influence
Diagram at t
White’s
State at t+1
White’s
Control at t
White’s Threat
Assessment at t+1
t:=t+Dt
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Numerical example
• Symmetric initial state
• White’s aircraft more agile
• Solution generated with the
simulation procedure and the
ID game
• White wins
Altitude,h m
6000
Black
White
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4500
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Analysis Laboratory
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Helsinki University of Technology
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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:
– Longer planning horizon => multistage models
– Open-loop solutions of the multistage one-on-one air combat game
S ystems
Analysis Laboratory
Helsinki University of Technology
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