Aerospace and Electronic Systems Magazine September 2016 - 43

Fu, Zhang, and Yu

(4)
is the relative velocity of the UAV with respect to the Intruder, which can be derived as:
(5)
where is located at the vector direction of the time to the closest
point t. Due to the relation between
and
can be derived as:
(6)

Figure 4.

Grid-based trajectory representation.

(10)
As can be seen in Figure 3, the miss distance vector
relative velocity vector are orthogonal:

and the

(7)

where Pi is the discrete point of the orderly numbered grid.
To evaluate the performance of collision avoidance, the cost
function F of each step is given in the following equations:

Combining (6) and (7), t can be derived as:

(11)
(12)
(8)

As uncertainties exist in sensing, the conflict detection approach should also consider the sensor measurement errors. A conflict is defined by evaluating the probability P such that at time
instant t the derived miss distance
is less than or equal to the
required minimum separation distance Dsafe:

where sr is the standard deviation of the sensor measurement errors,
is the mean value of the miss distance .
If the following two conditions:
1)
2)

t is positive, and
P(conflict) is greater than 75%,

are both satisfied, a collision will occur between the UAV and Intruder.
After conflicts between multiple intruders are determined, the conflict
resolution is to ensure the flight safety. The collision avoidance for a
UAV is initialized by modeling the flying environment. Considering
the airspace as a rectangular gridding system where each grid point
is viewed as a waypoint, the environment of accommodating UAV
position and predicted collisions is represented as S. All predicted collisions in S are shown as the set Col, which is denoted as follows:

As shown in Figure 4, the trajectory is to connect segments
from a starting point to a destination, which can be described as:
(9)
where is the vector of the ith segment to link with two waypoints. Therefore, the set L can be rewritten as:
SEPTEMBER 2016

If the vector
is far away from the safety zone of Colm, the
cost is derived as (11). If the vector
crosses the safety zone
of Colm, the cost is instead described as (12). w1 is the weighting
factor for threats cost, d(Pi, Pi+1) is Euclidean distance between two
waypoints:
(13)
where (xi, zi) is the current longitudinal position of the UAV, (xi+1,
zi+1) describes the UAV's next position. The pitch angle of UAV is
derived as:
(14)
For the sake of allowing the UAV to safely evade threats, dynamic constraints to prevent the UAV from developing into an irreversible state should be considered. With respect to the studied
UAV, the pitch angle is limited to [-25°, 30°] and the pitch rate
should be within [-5°/s, 5°/s].
The objective of the collision avoidance is to produce a feasible
trajectory with the minimum cost under the dynamic constraints
of the UAV.
Remark 1. The main idea of this article is to integrate a BBObased collision avoidance strategy into the SAA system to ensure
the safe landing. It is assumed that the necessary sensing information for the collision detection algorithm is provided by specific
sensors.

COLLISION AVOIDANCE ALGORITHM
The procedure of collision avoidance can be separated into two
steps, including: 1) BBO-based path planning to produce a set of
waypoints for the flight path with the minimum distance cost; and

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Table of Contents for the Digital Edition of Aerospace and Electronic Systems Magazine September 2016