Collision Avoidance Trajectory for an Ekranoplan
M. Ciarcià
1
and C. Grillo,
2
Università degli Studi di Palermo, Palermo, Italy, 90128
The risk of collision is one of the crucial aspects for the applications of Ekranoplans in
civil transportation. In fact, the extremely low flight altitude of these aircraft increases
dramatically the chances of interference between their flight path and the multitude of
obstacles populating the surrounding area. In this work we consider the optimal collision
avoidance problem between a cruising Ekranoplan and a steady obstacle located on its flight
path. First we solve the optimal control problem imposing that the collision avoidance
maneuver lies on the longitudinal plane identified by the initial cruising conditions. In the
second part of this work we state the three-dimensional version of the same collision
avoidance problem.
I. Introduction
he risk of collision is one of the crucial aspects for the applications of Ekranoplans in civil transportation. In
fact, the extremely low flight altitude of these aircrafts increases dramatically the chances of interference
between their flight path and the multitude of obstacles populating the surrounding area. Examples of those
potential obstacles are: ships, small boats, and stumbling blocks.
T
In the first part of this work we investigate the bi-dimensional optimal collision avoidance problem between a
cruising Ekranoplan and a steady obstacle located on the ground imposing that the collision avoidance maneuver lies
on the longitudinal plane. The following assumptions are employed: (i) initially the Ekranoplan is moving in a
quasisteady levelled cruise trajectory; (ii) after the avoidance manoeuvre a recovery manoeuvre is executed by the
aircraft to return to the initial cruise path; (iii) both the avoidance manoeuvre and the recovery manoeuvre lie on the
same vertical plane identified by the initial cruise trajectory. The investigation of the collision avoidance
performances on the longitudinal flight is encouraged by the relatively large quasi-flat turn radius of the
Ekranoplans. The second part of this work is dedicated to state the equivalent three-dimensional case of the
collision avoidance problem. In detail we collect the complete set of differential constraints that describe the lateral
motion of the aircraft considering the ground effect.
The approach to the problem considered, is to maximize wrt the controls the timewise minimum distance
between the aircraft and the obstacle. This yields to a maximin problem or Chebyshev problem of optimal control,
which is not solvable in a direct way. Hence, a technique is performed to transform the Chebyshev problem into a
Bolza problem.
1
Once reduced in this form the optimization problem can be solved numerically applying the
multiple-subarc sequential gradient-restoration algorithm.
2,3
The main target of this research is to determine the relationship between the optimal avoidance maneuver and the
control to execute it. In turn, this relationship is basilar to the development of a guidance scheme capable of
approximating the optimal trajectory in real time.
It is worth to notice that the peculiar aerodynamic characteristics of the Ekranoplans joined to their relatively
weak manoeuvrability make this application of optimal control techniques particularly challenging. We believe that
the results of the present approach would lead the future investigations toward a suitable collision avoidance
strategy.
Key Words: Collision avoidance, ekranoplan, optimal control, Chebyshev problems, Bolza problems, multiple-
subarc sequential gradient-restoration algorithm.
American Institute of Aeronautics and Astronautics
1
1
Postdoctoral Research Fellow, Dipartimento di Ingeneria dei Trasporti, Università degli Studi di Palermo, Viale
delle Scienze Ed. 8, Palermo, Italy,90128 , AIAA Member.
2
Associate Professor, Dipartimento di Ingeneria dei Trasporti, Università degli Studi di Palermo, Viale delle
Scienze Ed. 8, Palermo, Italy,90128 , AIAA Member.
AIAA Atmospheric Flight Mechanics Conference
10 - 13 August 2009, Chicago, Illinois
AIAA 2009-5931
Copyright © 2009 by Marco Ciarcià. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.