multirotor

Guidance model for multirotor UAVs

Description

A multirotor object represents a reduced-order guidance model[1] for an unmanned aerial vehicle (UAV). The model approximates the behavior of a closed-loop system consisting of an autopilot controller and a multirotor kinematic model for 3-D motion.

For fixed-wing UAVs, see fixedwing.

Creation

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

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

Properties

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`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 behaviour of the UAV. Specify the proportional (P) and derivative (D) gains for the dynamic model and other UAV parameters. For multirotor UAVs, the structure contains these fields with defaults listed:

'PDRoll'- [3402.97 116.67]
'PDPitch' - [3402.97 116.67]
'PYawRate' - 1950
'PThrust' - 3900
'Mass' - 0.1 (measured in kg)

Example: struct('PDRoll',[3402.97,116.67],'PDPitch',[3402.97, 116.67],'PYawRate',1950,'PThrust',3900,'Mass',0.1)

Data Types: struct

`ModelType` — UAV guidance model type
Read-only: `'MultirotorGuidance'` (default)

This property is read-only.

UAV guidance model type, specified as 'MultirotorGuidance'.

`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. Specify DataType when first creating the object.

Object Functions

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

Examples

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Simulate A Multirotor Control Command

Open Live Script

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

Create the multirotor guidance model.

model = multirotor;

Create a state structure. Specify the location in world coordinates.

s = state(model);
s(1:3) = [3;2;1];

Specify a control command, u, that specified the roll and thrust of the multirotor.

u = control(model);
u.Roll = pi/12;
u.Thrust = 1;

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 multirotor UAV states as a 13-by-n matrix.

simOut = ode45(@(~,x)derivative(model,x,u,e), [0 3], s);
size(simOut.y)

ans = 1×2

          13        3536

Plot the change in roll angle based on the simulation output. The roll angle (the X Euler angle) is the 9th row of the simOut.y output.

plot(simOut.y(9,:))

Figure contains an axes object. The axes object contains an object of type line.

Plot the change in the Y and Z positions. With the specified thrust and roll angle, the multirotor should fly over and lose some altitude. A positive value for Z is expected as positive Z is down.

figure
plot(simOut.y(2,:));
hold on
plot(simOut.y(3,:));
legend('Y-position','Z-position')
hold off

Figure contains an axes object. The axes object contains 2 objects of type line. These objects represent Y-position, Z-position.

You can also plot the multirotor trajectory using plotTransforms. Create the translation and rotation vectors from the simulated state. Downsample (every 300th element) and transpose the simOut elements, and convert the Euler angles to quaternions. Specify the mesh as the multirotor.stl file and the positive Z-direction as "down". The displayed view shows the UAV translating in the Y-direction and losing altitude.

translations = simOut.y(1:3,1:300:end)'; % xyz position
rotations = eul2quat(simOut.y(7:9,1:300:end)'); % ZYX Euler
plotTransforms(translations,rotations,...
    'MeshFilePath','multirotor.stl','InertialZDirection',"down")
view([90.00 -0.60])

Figure contains an axes object. The axes object contains 48 objects of type patch, line.

More About

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UAV Coordinate Systems

The guidance model uses the North-East-Down (NED) coordinate system convention.

The earth frame is assumed to be an inertial frame with an origin that is fixed relative to the earth surface. The frame coordinates are x_e (positive in the direction of north), y_e (positive in the direction of east), and z_e (positive towards the center of the earth). The x_ey_e plane is assumed to be flat.

The UAV body frame is centered on the UAV center of mass. The frame coordinates are x_b (positive towards node of UAV) , y_b (perpendicular to x_b, positive towards right of UAV), and z_b (perpendicular to x_by_b plane, positive downward).

The orientation of the UAV body frame with respect to the earth frame is specified in ZYX Euler angles. 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 Multirotor Guidance Model Equations

These equations define the guidance model for multirotor UAVs.

The model governs the acceleration of the UAV center of mass in inertial coordinates as:

$m [\begin{matrix} {\ddot{x}}_{e} \\ {\ddot{y}}_{e} \\ {\ddot{z}}_{e} \end{matrix}] = [\begin{matrix} 0 \\ 0 \\ m g \end{matrix}] + R_{b}^{e} [\begin{matrix} 0 \\ 0 \\ - F_{t h r u s t} \end{matrix}]$

where:

x_e, y_e, andhare the north position, east position, and height of the UAV in the inertial frame, respectively
m and g are the mass and gravitational acceleration of the UAV, respectively
F_thrust is the total force created by the propellers applied to the multirotor along the –z_b axis.
R^e_b is the rotation matrix that rotates the inertial frame to the body frame:
$R_{b}^{e} = [\begin{matrix} c_{θ} c_{ψ} & c_{ψ} s_{ϕ} s_{θ} - c_{ϕ} s_{ψ} & c_{ϕ} c_{ψ} s_{θ} + s_{ϕ} s_{ψ} \\ c_{θ} s_{ψ} & c_{ϕ} c_{ψ} + s_{ϕ} s_{θ} s_{ψ} & - c_{ψ} s_{ϕ} + c_{ϕ} s_{θ} s_{ψ} \\ - s_{θ} & c_{θ} s_{ϕ} & c_{ϕ} c_{θ} \end{matrix}]$
where ψ, ϴ, and ϕare the yaw, pitch, and roll angles, respectively. c and s are abbreviations for cos and sin, respectively.

The model uses two independent proportional-derivative (PD) controllers to control the roll and pitch angles, and two independent proportional (P) controllers to control the yaw rate and thrust.

These equations determine the angular velocity, angular acceleration, and thrust:

$\begin{array}{l} J = [\begin{matrix} 1 & \sin ϕ \tan θ & \cos ϕ \tan θ \\ 0 & \cos ϕ & - \sin ϕ \\ 0 & \frac{\sin ϕ}{\cos θ} & \frac{\cos ϕ}{\cos θ} \end{matrix}] \\ [\begin{matrix} \dot{ϕ} \\ \dot{θ} \\ \dot{ψ} \end{matrix}] = J [\begin{matrix} p \\ q \\ r \end{matrix}] \\ [\begin{matrix} \dot{p} \\ \dot{q} \\ \dot{r} \end{matrix}] = [\begin{matrix} 1 & 0 & - \sin θ \\ 0 & \cos ϕ & \sin ϕ \cos θ \\ 0 & - \sin ϕ & \cos ϕ \cos θ \end{matrix}] [\begin{matrix} K_{P ϕ} (ϕ^{c} - ϕ) + K_{D ϕ} (- \dot{ϕ}) \\ K_{P θ} (θ^{c} - θ) + K_{D θ} (- \dot{θ}) \\ K_{P ψ} ({\dot{ψ}}^{c} - \dot{ψ}) \end{matrix}] \\ {\dot{F}}_{t h r u s t} = K_{P F} (F_{t h r u s t}^{c} - F_{t h r u s t}) \end{array}$

where:

ψ, ϴ, and ϕ are the yaw, pitch, and roll angles, respectively
p,q, and r are the angular rotation with respect to x_b,y_b, and z_b, respectively.
k_P* and k_D*are the proportional and derivative gains of the controller, respectively.
c is the control input
F_thrust is the thrust of the UAV

These equations result in these state variables:

$[\begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} x_{e} & y_{e} & z_{e} & {\dot{x}}_{e} \end{matrix} & {\dot{y}}_{e} & {\dot{z}}_{e} & ψ \end{matrix} & θ & ϕ & p \end{matrix} & q & r & F_{t h r u s t} \end{matrix}]$

References

[1] 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.

multirotor

Description

Creation

Properties

`Name` — Name of UAV
`"Unnamed"` (default) | string scalar

`Configuration` — UAV controller configuration
structure

`ModelType` — UAV guidance model type
Read-only: `'MultirotorGuidance'` (default)

`DataType` — Input and output numeric data types
`'double'` (default) | `'single'`

Object Functions

Examples

Simulate A Multirotor Control Command

More About

UAV Coordinate Systems

UAV Multirotor Guidance Model Equations

References

Extended Capabilities

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

Version History

See Also

Functions

Objects

Blocks

Topics

multirotor

Description

Creation

Properties

Name — Name of UAV "Unnamed" (default) | string scalar

Configuration — UAV controller configuration structure

ModelType — UAV guidance model type Read-only: 'MultirotorGuidance' (default)

DataType — Input and output numeric data types 'double' (default) | 'single'

Object Functions

Examples

Simulate A Multirotor Control Command

More About

UAV Coordinate Systems

UAV Multirotor Guidance Model Equations

References

Extended Capabilities

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

Version History

See Also

Functions

Objects

Blocks

Topics

`Name` — Name of UAV
`"Unnamed"` (default) | string scalar

`Configuration` — UAV controller configuration
structure

`ModelType` — UAV guidance model type
Read-only: `'MultirotorGuidance'` (default)

`DataType` — Input and output numeric data types
`'double'` (default) | `'single'`

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