Transcript VIATO - Visual Interactive Aircraft Trajectory Optimization

Influence Diagram Game Modeling of
Maneuvering Decisions in One-on-One Air
Combat
Kai Virtanen, Janne Karelahti,
Tuomas Raivio, and Raimo P. Hämäläinen
Systems Analysis Laboratory
Helsinki University of Technology
S ystems
Analysis Laboratory
Helsinki University of Technology
1
Maneuvering decisions in one-on-one air combat
t=Dt
t=0


t=Dt
t=0
Outcome depends on all the maneuvers of both players 
Dynamic game problem
Objective
Find the best maneuvering sequences 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
2
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
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
3
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
4
Decision theoretical maneuvering models
• Single stage influence diagram (Virtanen et al. 1999):
– Short-sighted decision making
• Multistage influence diagram (Virtanen et al. 2004):
– Long-sighted decision making
– Preference optimal flight path against a given trajectory
• Single stage influence diagram game (Virtanen et al. 2003):
– Short-sighted decision making
– Components representing the behavior of the adversary
New multistage influence diagram game model:
• Long-sighted decision making
• Components representing the behavior of the adversary
• Solution with a moving horizon control approach
S ystems
Analysis Laboratory
Helsinki University of Technology
5
Influence diagram 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
Present
Measurement
Combat
State
Measurement
Maneuver
State
Situation
Evaluation
Present
Threat Situation
Assessment
Threat Situation
Assessment
6
Influence diagram air combat game
Black
White
• Goals of the players:
1. Avoid being captured by the adversary
2. Capture the adversary
• Four possible outcomes
• Evolution of the players’ states described by a set of differential
equations, a point mass model
• Evolution of the probabilities described by Bayes’ theorem
• Resulting game optimal controls
- the cumulative expected utility is maximized
- feedback Nash equilibrium
S ystems
Analysis Laboratory
Helsinki University of Technology
7
Multistage influence diagram game
Black’s
viewpoint
Combat state
White's
viewpoint
Situation
Evaluation
at t-2
stage t-1
Situation
Evaluation
at t-1
stage t
Cumulative
expected utility
Situation
Evaluation
Situation
Evaluation
at t
Situation
Evaluation
at t+1
S ystems
Analysis Laboratory
Helsinki University of Technology
8
Moving horizon control approach
Players’ states
at stage t
Dynamic
programming
Truncated
influence diagram game
lasting stages t, t+Dt,…, t+KDt
KDt = length of the planning horizon
Game optimal
control sequences over
stages t, t+Dt, …, t+KDt
t:=t+Dt
Terminate?
Players’ states
at stage t+Dt
Implement the
controls of stage t
S ystems
Analysis Laboratory
Helsinki University of Technology
9
Numerical example
• Symmetric initial state
• White’s aircraft more agile
• White wins
Altitude,
h m
6000
Black
White
5500
5000
1000
2000
4500
1000
S ystems
3000
1500
2000
Analysis Laboratory
2500
4000
x
10
Helsinki University of Technology
y
Conclusions
• The multistage 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 and decision making
• The moving horizon control approach
=> Game optimal control sequences w.r.t the preference model of the players
• 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
– Planning fighter maneuvers
S ystems
Analysis Laboratory
Helsinki University of Technology
11
References
•
•
•
Virtanen, K., Raivio, T., and Hämäläinen, R.P., "Decision Theoretical
Approach to Pilot Simulation," Journal of Aircraft, Vol. 36, No. 4, 1999.
Virtanen, K., Raivio, T., and Hämäläinen, R.P., "Influence Diagram Modeling
of Decision Making in a Dynamic Game Setting," Proceedings of the 1st
Bayesian Modeling Applications Workshop of the 19th Conference on
Uncertainty in Artificial Intelligence, 2003
Virtanen, K., Raivio, T., and Hämäläinen, R.P., "Modeling Pilot's Sequential
Maneuvering Decisions by a Multistage Influence Diagram," Journal of
Guidance, Control, and Dynamics, Vol. 27, No. 4, 2004.
S ystems
Analysis Laboratory
Helsinki University of Technology
12