# 2010 Research Summary

## A Dynamic Programming Approach for Aircraft Conflict Detection

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Jerry Ding and Claire Tomlin

Air Force Office of Scientific Research

This project is concerned with an approach for mid-range conflict detection between two aircraft with intersecting straight line nominal trajectories. By modeling wind disturbances as normally distributed random noise, we compute analytic estimates of the conflict probability for any given conflict scenario. We then formulate the conflict detection problem as a finite horizon decision problem where the decision is whether to allow the aircraft to continue on their nominal trajectories or advise an evasive maneuver that modifies the relative heading between the two aircraft. A dynamic program is proposed to optimize the trade-off between the conflict probability at the time the decision is made and the cost of initiating an evasive maneuver early. The solution of the dynamic program gives the optimal choice of decisions at any discrete time instant over a region of relative coordinates that is predicted to occur with high probability.