Journal of Optimization Theory and Applications

, Volume 146, Issue 2, pp 233–254

# Collision Avoidance for an Aircraft in Abort Landing: Trajectory Optimization and Guidance

Article

## Abstract

For a host aircraft in the abort landing mode under emergency conditions, the best strategy for collision avoidance is to maximize wrt to the controls the timewise minimum distance between the host aircraft and an intruder aircraft. This leads to a maximin problem or Chebyshev problem of optimal control. At the maximin point of the encounter, the distance between the two aircraft has a minimum wrt the time; its time derivative vanishes and this occurs when the relative position vector is orthogonal to the relative velocity vector. By using the zero derivative condition as an inner boundary condition, the one-subarc Chebyshev problem can be converted into a two-subarc Bolza-Pontryagin problem, which in turn can be solved via the multiple-subarc sequential gradient-restoration algorithm.

Optimal Trajectory. In the avoidance phase, maximum angle of attack is used by the host aircraft until the minimum distance point is reached. In the recovery phase, the host aircraft completes the transition of the angle of attack from the maximum value to that required for quasisteady ascending flight.

Guidance Trajectory. Because the optimal trajectory is not suitable for real-time implementation, a guidance scheme is developed such that it approximates the optimal trajectory results in real time. In the avoidance phase, the guidance scheme employs the same control history (maximum angle of attack) as that of the optimal trajectory so as to achieve the goal of maximizing wrt the control the timewise minimum distance. In the recovery phase, the guidance scheme employs a time-explicit cubic control law so as to achieve the goal of recovering the quasisteady ascending flight state at the final time.

Numerical results for both the optimal trajectory and the guidance trajectory complete the paper.

## Keywords

Collision avoidance Abort landing Aerospace engineering Optimal control Guidance

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## Authors and Affiliations

• A. Miele
• 1
• T. Wang
• 1
• J. A. Mathwig
• 2
• M. Ciarcià
• 3
1. 1.Aero-Astronautics GroupRice UniversityHoustonUSA
2. 2.PROS Revenue ManagementHoustonUSA
3. 3.Università di PalermoPalermoItaly