Aerospace and Electronic Systems Magazine November 2016 Tutorial X - 88

Sense and Avoid for Unmanned Aircraft Systems
In this tutorial paper, both nonfrontal and frontal collision geometries are taken into account. In particular, a general nonfrontal
scenario is described to provide a numerical procedure to calculate
minimum sensing range for any geometry, following [11]. Then,
the frontal case is focused to present a straightforward analytical
approximation.
In general, the avoidance strategy can be based on a horizontal
maneuver, a vertical one, or a combination of both. For fixed wing
aircraft, which represent our main focus in this work, a horizontal maneuver is basically a coordinated turn. For common aircraft
configurations, it is typically easier to gain a desired separation
from the original path by horizontal maneuvering strategies, rather
than by exploiting the maximum achievable rate of climb/descent.
Thus, in the following we assume that the avoidance maneuver is a
coordinated right/left turn at constant velocity and with minimum
turn radius, i.e., which exploits the whole maneuverability of the
aircraft. The assumed geometry is shown in Fig. 8.
Based on the coordinated turn dynamics, the minimum turn radius corresponds to the maximum load factor and to the maximum
bank angle. In fact, the load factor n is related to the bank angle β
by means of the equation

Fig. 8.

Geometry for generic nonfrontal scenario and horizontal avoidance
strategy (adapted from [11]).

(1)

(6)

and is also related to speed VUAV and turn radius R by the equation

(7)

(2)
(8)
where g is the gravity acceleration. In this derivation, we are assuming to use Rmin, βmax, and nmax, and that VUAV is true airspeed with
no wind influence.
The detection range requirement can be computed as follows.
First, the minimum range at which an avoidance maneuver has to
be started in order to keep a minimum separation is calculated. The
minimum separation dmin can be assumed equal to 500 ft. Then, the
time delay between initial sensor detection and avoidance maneuver execution is taken into account.
With reference to Fig. 8, with the aim of calculating the minimum
range requirements as a function of the obstacle azimuth angle φ, problem inputs can be assumed to be VUAV, VOBS (i.e., m), d, and ζ. Then, the
law of cosines can be used to calculate the range from obstacle r.
(3)
and then the obstacle azimuth angle
(4)
Assuming that the obstacle continues on its path and the UAV
maneuvers, in the introduced reference frame the coordinates as a
function of time can be calculated as

where the upper sign within  and  symbols refers to the right
turn.
The separation as a function of time is given by

(9)

We can use the above formulas to calculate numerically the closest
point of approach in each scenario defined by VUAV, VOBS (i.e., m),
d, and ζ. Increasing d, we are thus able to find the value at which
the closest point of approach equals the safety distance. Given this
d, computing r and φ we have the minimum range for avoidance at
each azimuth angle.
As anticipated above, to have the minimum detection range,
we then have to consider the time delay τd, which is needed for all
the phases before avoidance (transition to firm tracking, conflict
detection, avoidance planning).
Given this time delay, the final formula is given by
(10)
and

(5)

IEEE A&E SYSTEMS MAGAZINE

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NOVEMBER 2016, Part II of II

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