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Multi-Objective Weight Optimization for Trajectory Planning of an Airplane with Structural Damage

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Abstract

This paper presents an integrated approach to determine and apply cost criteria weights for the multi-objective optimization (MOO) problem of emergency landing trajectory generation for an aircraft with structural damage. Cost criteria including terrain avoidance, Safety Value Index (SVI), fire cost, hydraulic and fuel costs and safe landing constraints such as touchdown heading and position, airspeed, and glide slope are defined. A potential field strategy is utilized to rapidly generate solutions based on a library of damaged airplane motion primitives including trim states and transition maneuvers between the trim conditions. As is typical, the diverse metrics compete, preventing simultaneous optimization over all objectives. This paper proposes a novel approach to translate the subjective information provided by Pareto analysis into a weighted cost function using an entropy-based weight selection method. The resultant weights reflect the subjective preferences of a decision maker in the total integrated cost metric. Simulation results demonstrate the effectiveness of weight selection based on the proposed method.

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Abbreviations

Ch :

= hinge moment coefficient

D:

= matrix of variables in data library

DM:

= decision matrix

E:

= entropy

dT :

= airplane distance to terrain

g:

= cost function

h:

= heuristic cost function

I:

= mutual information

J:

= cost function

L:

= subscript for landing condition

M:

= maneuvers

M:

= normalized decision matrix

p, q, r:

= roll, pitch, and yaw rates, respectively, rad/s

P:

= Position of airplane

T:

= trim trajectories

U:

= best solution

V:

= total velocity in body axes, m/s

W:

= weighting factor in heuristic function

W ′ :

= comprehensive weight vector

w j′:

= weights derived from entropy method

α, β, γ :

= angle of attack, sideslip, and flight path angle,

ψ, 𝜃, ϕ :

= yaw, pitch, and roll angles, rad

λ j :

= weights derived from Pareto analysis

ρ :

= correlation

Ω:

= set of cost function

Δx, Δy, Δz:

= variation in airplane position in each trajectory segment, m

Δs:

= length of each trajectory segment

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Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

    D. Asadi

  2. Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI, 48109, USA

    E. M. Atkins

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Asadi, D., Atkins, E.M. Multi-Objective Weight Optimization for Trajectory Planning of an Airplane with Structural Damage. J Intell Robot Syst 91, 667–690 (2018). https://doi.org/10.1007/s10846-017-0753-9

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