fixedwing

Guidance model for fixed-wing UAVs

Description

A fixedwing object represents a reduced-order guidance model for an unmanned aerial vehicle (UAV). The model approximates the behavior of a closed-loop system consisting of an autopilot controller and a fixed-wing kinematic model for 3-D motion.

For multirotor UAVs, see multirotor.

Creation

model = fixedwing creates a fixed-wing motion model with double precision values for inputs, outputs, and configuration parameters of the guidance model.

model = fixedwing(DataType) specifies the data type precision (DataType property) for the inputs, outputs, and configurations parameters of the guidance model.

Properties

Name — Name of UAV

"Unnamed" (default) | string scalar

Name of the UAV, used to differentiate it from other models in the workspace, specified as a string scalar.

Example: "myUAV1"

Data Types: string

Configuration — UAV controller configuration

structure

UAV controller configuration, specified as a structure of parameters. Specify these parameters to tune the internal control behavior of the UAV. Specify the proportional (P) and derivative (D) gains for the dynamic model and other UAV parameters. The structure for fixed-wing UAVs contains these fields with defaults listed:

• 'PDRoll' - [3402.97 116.67]

• 'PHeight' - 3.9

• 'PFlightPathAngle' - 39

• 'PAirspeed' - 0.39

• 'FlightPathAngleLimits' - [-pi/2 pi/2] ([min max] angle in radians)

Example: struct('PDRoll',[3402.97,116.67],'PHeight',3.9,'PFlightPathAngle',39,'PAirSpeed',0.39,'FlightPathAngleLimits',[-pi/2 pi/2])

Data Types: struct

ModelType — UAV guidance model type

'FixedWingGuidance' (default)

This property is read-only.

UAV guidance model type, specified as 'FixedWingGuidance'.

DataType — Input and output numeric data types

'double' (default) | 'single'

Input and output numeric data types, specified as either 'double' or 'single'. Choose the data type based on possible software or hardware limitations.

Object Functions

control	Control commands for UAV
derivative	Time derivative of UAV states
environment	Environmental inputs for UAV
state	UAV state vector

Examples

Simulate A Fixed-Wing Control Command

This example shows how to use the fixedwing guidance model to simulate the change in state of a UAV due to a command input.

Create the fixed-wing guidance model.

model = fixedwing;

Set the air speed of the vehicle by modifying the structure from the state function.

s = state(model);
s(4) = 5; % 5 m/s

Specify a control command, u, that maintains the air speed and gives a roll angle of pi/12.

u = control(model);
u.RollAngle = pi/12;
u.AirSpeed = 5;

Create a default environment without wind.

e = environment(model);

Compute the time derivative of the state given the current state, control command, and environment.

sdot = derivative(model,s,u,e);

Simulate the UAV state using ode45 integration. The y field outputs the fixed-wing UAV states based on this simulation.

simOut = ode45(@(~,x)derivative(model,x,u,e), [0 50], s);
size(simOut.y)

ans = 1×2

     8   904

Plot the change in roll angle based on the simulation output. The roll angle is the 7th row of the simOut.y output.

plot(simOut.y(7,:))

You can also plot the fixed-wing trajectory using plotTransforms. Create the translation and rotation vectors from the simulated state. Downsample (every 30th element) and transpose the simOut elements, and convert the Euler angles to quaternions. Specify the mesh as the fixedwing.stl file and the positive Z-direction as "down". The displayed view shows the UAV making a constant turn based on the constant roll angle.

downsample = 1:30:size(simOut.y,2);
translations = simOut.y(1:3,downsample)'; % xyz-position
rotations = eul2quat([simOut.y(5,downsample)',simOut.y(6,downsample)',simOut.y(7,downsample)']); % ZYX Euler
plotTransforms(translations,rotations,...
    'MeshFilePath','fixedwing.stl','InertialZDirection',"down")
hold on
plot3(simOut.y(1,:),-simOut.y(2,:),simOut.y(3,:),'--b') % full path
xlim([-10.0 10.0])
ylim([-20.0 5.0])
zlim([-0.5 4.00])
view([-45 90])
hold off

More About

UAV Coordinate Systems

The UAV Toolbox™ uses the North-East-Down (NED) coordinate system convention, which is also sometimes called the local tangent plane (LTP). The UAV position vector consists of three numbers for position along the northern-axis, eastern-axis, and vertical position. The down element complies with the right-hand rule and results in negative values for altitude gain.

The ground plane, or earth frame (NE plane, D = 0), is assumed to be an inertial plane that is flat based on the operation region for small UAV control. The earth frame coordinates are [x_e,y_e,z_e]. The body frame of the UAV is attached to the center of mass with coordinates [x_b,y_b,z_b]. x_b is the preferred forward direction of the UAV, and z_b is perpendicular to the plane that points downwards when the UAV travels during perfect horizontal flight.

The orientation of the UAV (body frame) is specified in ZYX Euler angles. To convert from the earth frame to the body frame, we first rotate about the z_e-axis by the yaw angle, ψ. Then, rotate about the intermediate y-axis by the pitch angle, ϴ. Then, rotate about the intermediate x-axis by the roll angle, ϕ.

The angular velocity of the UAV is represented by [p,q,r] with respect to the body axes, [x_b,y_b,z_b].

UAV Fixed-Wing Guidance Model Equations

For fixed-wing UAVs, the following equations are used to define the guidance model of the UAV. Use the derivative function to calculate the time-derivative of the UAV state using these governing equations. Specify the inputs using the state, control, and environment functions.

The UAV position in the earth frame is [x_e, y_e, h] with orientation as heading angle, flight path angle, and roll angle, [χ, γ, ϕ] in radians.

The model assumes that the UAV is flying under a coordinated-turn condition, with zero side-slip. The autopilot controls airspeed, altitude, and roll angle. The corresponding equations of motion are:

V_a and V_g denote the UAV air and ground speeds.

The wind speed is specified as [V_wn,V_we,V_wd] for the north, east, and down directions. To generate the structure for these inputs, use the environment function.

k_* are controller gains. To specify these gains, use the Configuration property of the fixedwing object.

From these governing equations, the model gives the following variables:

These variables match the output of the state function.

References

[1] Randal W. Beard and Timothy W. McLain. "Chapter 9." Small Unmanned Aircraft Theory and Practice, NJ: Princeton University Press, 2012.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced in R2018b