Aero.trajectory.expandingSquareTrajectory

R2026b

Generate reference signals for expanding square search trajectory

Since R2026a

Syntax

refSignals = Aero.trajectory.expandingSquareTrajectory(Name=Value)

Description

refSignals = Aero.trajectory.expandingSquareTrajectory(Name=Value) generates reference signals for an expanding square search pattern. Use name-value arguments to define the search pattern. For more information, see Algorithms.

Examples

Generate Reference Signals for Expanding Square Trajectory

This example shows how to generate reference signals for an expanding square trajectory.

refSignals = Aero.trajectory.expandingSquareTrajectory(InitialPosition=[0, 0], ...
Speed=100,InitialHeading=pi/4, ...
DatumPoint = [10, 10], Bearing = pi/2, ...
Altitude= 5000, TrackSpacing=1000, ...
NumberOfLegs= 4, OutputFormat= 'timetable')

refSignals = 10×7 timetable
         timestamps         WaypointIndex    xNorth(m)    yEast(m)    Speed(m/s)    Altitude(m)    Heading(rad)    FlightPathAngle(rad)
    ____________________    _____________    _________    ________    __________    ___________    ____________    ____________________

    06-Jul-2026 10:44:42          1                0           0         100              0           0.7854               0.01        
    06-Jul-2026 10:45:32          2               10          10         100           5000           1.5708               0.01        
    06-Jul-2026 10:45:42          3               10        1010         100           5000           3.1416               0.01        
    06-Jul-2026 10:45:52          4             -990        1010         100           5000           4.7124               0.01        
    06-Jul-2026 10:46:12          5             -990        -990         100           5000                0               0.01        
    06-Jul-2026 10:46:32          6             1010        -990         100           5000           1.5708               0.01        
    06-Jul-2026 10:47:02          7             1010        2010         100           5000           3.1416               0.01        
    06-Jul-2026 10:47:32          8            -1990        2010         100           5000           4.7124               0.01        
    06-Jul-2026 10:48:12          9            -1990       -1990         100           5000                0               0.01        
    06-Jul-2026 10:48:52         10             2010       -1990         100           5000                0               0.01        

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Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Example: InitialPosition = [0,0]

InitialPosition — Initial position

[0,0] (default) | 1-by-2 vector | 2-by-1 vector

Initial position of trajectory, specified as a 1-by-2 or 2-by-1 vector in the units specified in Units.

Example: InitialPosition = [0,0]

Data Types: double

Speed — Speed of trajectory

90 (default) | finite real double scalar

Speed of trajectory, specified as a finite real double scalar in the units specified in Units.

Example: Speed = 10

Data Types: double

Altitude — Altitude of trajectory

finite real scalar double

Altitude of the vehicle trajectory, specified as a finite real scalar double in the units specified in Units. This value is constant throughout the vehicle path.

Example: Altitude = 10

Data Types: double

InitialHeading — Initial heading of trajectory

0 (default) | finite real double scalar between 0 and 2*pi

Initial heading of trajectory, specified as a finite real double scalar between 0 and 2*pi, in radians. Specify one each of InitialHeading and FinalHeading.

Example: InitialHeading = pi

Data Types: double

OutputFormat — Output format

timeseries object (default) | timetable object

Output format of reference signals data, specified as a timeseries or timetable object.

Example: OutputFormat = timeseries

Units — Input and output units

Metric (MKS) (default) | English (Velocity in ft/s) | English (Velocity in kts)

Input and output units, specified as one of these values.

Units	Position	Altitude	Speed
Metric (MKS)	Meters	Meters	Meters per second
English (Velocity in ft/s)	Feet	Feet	Feet per second
English (Velocity in kts)	Nautical miles	Feet	Knots

Example: Units = 'Metric (MKS)'

StartTime — Initial time of trajectory operation

datetime('now') (default) | datetime object

Initial time of trajectory operation, specified as a datetime object.

Example: StartTime = datetime('now')

Bearing — Bearing

finite real scalar double between 0 and 2*pi

Bearing, specified as a finite real scalar double between 0 and 2*pi.

Example: Bearing = pi/4

Data Types: double

DatumPoint — Datum point

1-by-2 vector | 2-by-1 vector | finite real double

Datum point is a positional coordinate, specified as a 1-by-2 or 2-by-1 vector in the range finite real double, in the units specified in Units.

Example: DatumPoint = [10, 10]

Data Types: double

InitialAltitude — Initial altitude of trajectory

0 (default) | scalar

Initial altitude of trajectory, specified as a scalar in the units specified in Units.

Example: InitialAltitude = 10

Data Types: double

NumberOfLegs — Number of legs

5 (default) | scalar | positive doubles.

Number of legs in the expanding square, specified as a positive doubles.

Example: InitialAltitude = 10

Data Types: double

PriorTrajectory — Prior trajectory tracking data

timeseries object | timetable object

Prior trajectory tracking data, specified as a timeseries or timetable object. These objects must contain these fields:

• Altitude

• Heading

• Speed

• WaypointIndex

• xNorth

• yEast

• LateralAcceleraion/Turnrate

TrackSpacing — Spacing between tracks

scalar

Spacing between tracks, specified as a scalar.

Example: TrackSpacing = 10

Data Types: double

SearchDirection — Search direction

Clockwise (default) | Counterclockwise

Search direction, specified as Counterclockwise or Clockwise.

ClimbRate — Vertical velocity component of vehicle during ascent

1 (default) | finite real double scalar less than vehicle speed

Vertical velocity component of vehicle during ascent, specified as a finite real double scalar less than the vehicle speed in the units specified in Units.

Example: ClimbRate = 10

Data Types: double

DescentRate — Vertical speed at which vehicle loses altitude

1 (default) | finite real double scalar

Vertical velocity component of vehicle during ascent, specified as a finite real double scalar less than the vehicle speed in the units specified in Units.

Example: DescentRate = 10

Data Types: double

NFZBoundaryPoints — Coordinates that define vertices of polygonal no-fly zone

[ ] (default) | N-by-2 numeric array

Coordinates that define vertices of polygonal no-fly zone, specified as a N-by-2 numeric array, where N is equal to or greater than 3. Each row of the array contains an [x, y] boundary point. The function computes a closed polygon from the supplied points and uses it to detect and avoid restricted airspace.

Example: DescentRate = 10

Data Types: double

NFZAltitudeBound — Maximum altitude of the no-fly zone

0 (default) | scalar numeric

Maximum altitude of the no-fly zone, specified as a scalar numeric. You use this value with the NFZ boundary to determine whether obstacle avoidance is required. If the aircraft altitude is above the specified no-fly-zone altitude bound, the aircraft is permitted to pass through the NFZ without rerouting.

Example: DescentRate = 10

Data Types: double

Output Arguments

refSignals — Trajectory reference signals

timeseries struct | timetable object

Trajectory reference signals, returned as a timeseries struct or timetable object.

Algorithms

Use Aero.trajectory.expandingSquareTrajectory to define the parameters of an expanding square search trajectory:

where S is specified by TrackSpacing.

Version History

Introduced in R2026a

R2026b: No-Fly Zones and Flight Paths

To specify no-fly zones for trajectories, the Aero.trajectory.expandingSquareTrajectory function accepts NFZBoundaryPoints and NFZAltitudeBound arguments. These arguments let you specify areas that vehicles must circumnavigate during trajectory planning.

To compute flight-path angles, the Aero.trajectory.expandingSquareTrajectory function accepts ClimbRate and DescentRate. Outputs now also report flight paths.