# Guidance Model

Reduced-order model for UAV

**Libraries:**

UAV Toolbox /
Algorithms

## Description

The Guidance Model block represents a small unmanned aerial vehicle (UAV)
guidance model that estimates the UAV state based on control and environmental inputs. The
model approximates the behavior of a closed-loop system consisting of an autopilot controller
and a fixed-wing or multirotor kinematic model for 3-D motion. Use this block as a
reduced-order guidance model to simulate your fixed-wing or multirotor UAV. Specify the
**ModelType** to select your UAV type. Use the **Initial
State** tab to specify the initial state of the UAV depending on the model type.
The **Configuration** tab defines the control parameters and physical
parameters of the UAV.

## Ports

### Input

**Control** — Control commands

bus

Control commands sent to the UAV model, specified as a bus. The name of the input
bus is specified in **Input/Output Bus Names**.

For multirotor UAVs, the model is approximated as separate PD controllers for each command. The elements of the bus are control command:

`Roll`

- Roll angle in radians.`Pitch`

- Pitch angle in radians.`YawRate`

- Yaw rate in radians per second. (D = 0. P only controller)`Thrust`

- Vertical thrust of the UAV in Newtons. (D = 0. P only controller)

For fixed-wing UAVs, the model assumes the UAV is flying under the coordinated-turn condition. The guidance model equations assume zero side-slip. The elements of the bus are:

`Height`

- Altitude above the ground in meters.`Airspeed`

- UAV speed relative to wind in meters per second.`RollAngle`

- Roll angle along body forward axis in radians. Because of the coordinated-turn condition, the heading angular rate is based on the roll angle.

**Environment** — Environmental inputs

bus

Environmental inputs, specified as a bus. The model compensates for these environmental inputs when trying to achieve the commanded controls.

For fixed-wing UAVs, the elements of the bus are `WindNorth`

,
`WindEast`

,`WindDown`

, and
`Gravity`

. Wind speeds are in meters per second and negative speeds
point in the opposite direction. `Gravity`

is in meters per second
squared.

For multirotor UAVs, the only element of the bus is `Gravity`

in
meters per second squared.

**Data Types: **`bus`

### Output

**State** — Simulated UAV state

bus

Simulated UAV state, returned as a bus. The block uses the
`Control`

and `Environment`

inputs with the
guidance model equations to simulate the UAV state.

For multirotor UAVs, the state is a five-element bus:

**WorldPosition**-`[x y z]`

in meters.**WorldVelocity**-`[vx vy vz]`

in meters per second.**EulerZYX**-`[psi theta phi]`

Euler angles in radians.**BodyAngularRateRPY**-`[r p q]`

in radians per second along the`xyz`

-axes of the UAV.**Thrust**-`F`

in Newtons.

For fixed-wing UAVs, the state is an eight-element bus:

**North**- Position in north direction in meters.**East**- Position in east direction in meters.**Height**- Height above ground in meters.**AirSpeed**- Speed relative to wind in meters per second.**HeadingAngle**- Angle between ground velocity and north direction in radians.**FlightPathAngle**- Angle between ground velocity and north-east plane in radians.**RollAngle**- Angle of rotation along body*x*-axis in radians per second.**RollAngleRate**- Angular velocity of rotation along body*x*-axis in radians per second.

**Data Types: **`bus`

## Parameters

**ModelType** — UAV guidance model type

`MultirotorGuidance`

(default) | `FixedWingGuidance`

UAV guidance model type, specified as `MultirotorGuidance`

or
`FixedWingGuidance`

. The model type determines the elements of the
UAV `State`

and the required `Control`

and
`Environment`

inputs.

**Tunable: **No

**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.

**Tunable: **No

**Simulate using** — Type of simulation to run

`Interpreted execution`

(default) | `Code generation`

`Code generation`

— Simulate model using generated C code. The first time you run a simulation, Simulink^{®}generates C code for the block. The C code is reused for subsequent simulations, as long as the model does not change. This option requires additional startup time, but the speed of the subsequent simulations is comparable to`Interpreted execution`

.`Interpreted execution`

— Simulate model using the MATLAB^{®}interpreter. This option shortens startup time but has a slower simulation speed than`Code generation`

. In this mode, you can debug the source code of the block.

**Tunable: **No

**Initial State** — Initial UAV state tab

multiple table entries

Initial UAV state tab, specified as multiple table entries. All entries on this tab are nontunable.

For multirotor UAVs, the initial state is:

**World Position**-`[x y z]`

in meters.**World Velocity**-`[vx vy vz]`

in meters per second.**Euler Angles (ZYX)**-`[psi theta phi]`

in radians.**Body Angular Rates**-`[p q r]`

in radians per second.**Thrust**-`F`

in Newtons.

For fixed-wing UAVs, the initial state is:

**North**- Position in north direction in meters.**East**- Position in east direction in meters.**Height**- Height above ground in meters.**Air Speed**- Speed relative to wind in meters per second.**Heading Angle**- Angle between ground velocity and north direction in radians.**Flight Path Angle**- Angle between ground velocity and north-east plane in radians.**Roll Angle**- Angle of rotation along body*x*-axis in radians per second.**Roll Angle Rate**- Angular velocity of rotation along body*x*-axis in radians per second.

**Tunable: **No

**Configuration** — UAV controller configuration tab

multiple table entries

UAV controller configuration tab, specified as multiple table entries. This tab allows you to configure the parameters of the internal control behaviour of the UAV. Specify the proportional (P) and derivative (D) gains for the dynamic model and the UAV mass in kilograms (for multirotor).

For multirotor UAVs, the parameters are:

**PD Roll****PD Pitch****P YawRate****P Thrust****Mass**(kg)

For fixed-wing UAVs, the parameters are:

**P Height****P Flight Path Angle****PD Roll****P Air Speed****Min/Max Flight Path Angle**(`[min max]`

angle in radians)

**Tunable: **No

**Input/Output Bus Names** — Simulink bus signal names tab

multiple entries of character vectors

Simulink bus signal names tab, specified as multiple entries of character vectors. These buses have a default name based on the UAV model and input type. To use multiple guidance models in the same Simulink model, specify different bus names that do not intersect. All entries on this tab are nontunable.

## 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*]. The body frame of the UAV is attached to the center of mass with coordinates [

_{e}*x*,

_{b}*y*,

_{b}*z*].

_{b}*x*is the preferred forward direction of the UAV, and

_{b}*z*is perpendicular to the plane that points downwards when the UAV travels during perfect horizontal flight.

_{b}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*denote the UAV air and ground speeds.

_{g}The wind speed is specified as
[*V _{wn}*,

*V*,

_{we}*V*] for the north, east, and down directions. To generate the structure for these inputs, use the

_{wd}`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.

### UAV Multirotor Guidance Model Equations

For multirotors, the following equations are used to define the guidance
model of the UAV. To calculate the time-derivative of the UAV state using these governing
equations, use the `derivative`

function. Specify the inputs using `state`

,
`control`

,
and `environment`

.

The UAV position in the earth frame is [*x _{e}*,

*y*,

_{e}*z*] with orientation as ZYX Euler angles, [

_{e}*ψ*,

*ϴ*,

*ϕ*] in radians. Angular velocities are [

*p*,

*q*,

*r*] in radians per second.

The UAV body frame uses coordinates as [*x _{b}*,

*y*,

_{b}*z*].

_{b}The rotation matrix that rotates vector from body frame to world frame is:

The cos(*x*) and sin(*x*) are abbreviated as
*c _{x}* and

*s*.

_{x}The acceleration of the UAV center of mass in earth coordinates is governed by:

*m* is the UAV mass, *g* is gravity, and
*F _{thrust}* is the total force created by the
propellers applied to the multirotor along the –

*z*axis (points upwards in a horizontal pose).

_{b}The closed-loop roll-pitch attitude controller is approximated by the behavior of 2 independent PD controllers for the two rotation angles, and 2 independent P controllers for the yaw rate and thrust. The angular velocity, angular acceleration, and thrust are governed by:

This model assumes the autopilot takes in commanded roll, pitch, yaw rate, and a commanded total thrust force,
*F ^{c}_{thrust}*. The
structure to specify these inputs is generated from

`control`

.The P and D gains for the control inputs are specified as
*KP _{α}* and

*KD*, where

_{α}*α*is either the rotation angle or thrust. These gains along with the UAV mass,

*m*, are specified in the

`Configuration`

property of the `multirotor`

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.

[2] Mellinger, Daniel, and Nathan
Michael. "Trajectory Generation and Control for Precise Aggressive Maneuvers with Quadrotors."
*The International Journal of Robotics Research*. 2012, pp.
664-74.

## Extended Capabilities

### C/C++ Code Generation

Generate C and C++ code using Simulink® Coder™.

## Version History

**Introduced in R2018b**

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