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The optimal control of collision avoidance trajectories in air traffic management

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  • Clements, John C.

Abstract

A collision avoidance/conflict resolution model for aircraft traversing planar intersecting trajectories is developed based on the actual flight dynamics of each aircraft and the criteria that a flight regime correction is optimal if it represents a minimum-time safe deviation from a preassigned flight program. The formulation of the model leads to a singular optimal control problem where the control variable constraint is the maximum acceptable aircraft turn rate for passenger comfort and safety and the state variable constraint is defined in terms of the radius of the protected zone about a potentially conflicting aircraft. A robust, accurate real-time solution procedure is derived for computing the steering program for the execution of the optimal safe avoidance maneuver. Several representative examples of pairwise trajectory conflicts are analysed in detail. A brief discussion of how the model might be generalized to incorporate changes in airspeed and altitude as well as more comprehensive dynamics is included.

Suggested Citation

  • Clements, John C., 1999. "The optimal control of collision avoidance trajectories in air traffic management," Transportation Research Part B: Methodological, Elsevier, vol. 33(4), pages 265-280, May.
    • Handle: RePEc:eee:transb:v:33:y:1999:i:4:p:265-280
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    References listed on IDEAS

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    1. Friedman, Moshe F., 1989. "On the exact distribution of the number of perceived conflicts with prescribed duration in air traffic control," Transportation Research Part B: Methodological, Elsevier, vol. 23(4), pages 245-256, August.
    2. Friedman, Moshe F., 1991. "Decision analysis and optimality in air traffic control conflict resolution: II. Optimal heading (vectoring) control in a linear planar configuration," Transportation Research Part B: Methodological, Elsevier, vol. 25(1), pages 39-53, February.
    3. Friedman, Moshe F., 1988. "Decision analysis and optimality in air traffic control conflict resolution I. optimal timing of speed control in a linear planar configuration," Transportation Research Part B: Methodological, Elsevier, vol. 22(3), pages 207-216, June.
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    Cited by:

    1. T. Tarnopolskaya & N. Fulton & H. Maurer, 2012. "Synthesis of Optimal Bang–Bang Control for Cooperative Collision Avoidance for Aircraft (Ships) with Unequal Linear Speeds," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 115-144, October.
    2. T. Tarnopolskaya & N. Fulton, 2010. "Synthesis of Optimal Control for Cooperative Collision Avoidance for Aircraft (Ships) with Unequal Turn Capabilities," Journal of Optimization Theory and Applications, Springer, vol. 144(2), pages 367-390, February.
    3. A. Miele & T. Wang & J. A. Mathwig & M. Ciarcià, 2010. "Collision Avoidance for an Aircraft in Abort Landing: Trajectory Optimization and Guidance," Journal of Optimization Theory and Applications, Springer, vol. 146(2), pages 233-254, August.
    4. T. Tarnopolskaya & N. Fulton, 2009. "Optimal Cooperative Collision Avoidance Strategy for Coplanar Encounter: Merz’s Solution Revisited," Journal of Optimization Theory and Applications, Springer, vol. 140(2), pages 355-375, February.

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