multirotor
Guidance model for multirotor UAVs
Description
A multirotor 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 multirotor kinematic model for 3-D
motion.
Note
This object requires you to install the UAV Library for Robotics System
Toolbox™. To install add-ons, use roboticsAddons and select the desired add-on.
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
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 Multirotor Control Command
This example shows how to use the multirotor guidance model to simulate the change in state of a UAV due to a command input.
Note: To use UAV algorithms, you must install the UAV Library for Robotics System Toolbox®. To install, use roboticsAddons.
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 fixed-wing 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,:))
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
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])
More About
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 [xe, ye, ze] with orientation as ZYX Euler angles, [ψ, ϴ, ϕ] in radians. Angular velocities are [p, q, r] in radians per second.
The UAV body frame uses coordinates as [xb, yb, zb].
When converting coordinates from the world (earth) frame to the body frame of the UAV, the rotation matrix is:
The cos(x) and sin(x) are abbreviated as cx and sx.
The acceleration of the UAV center of mass in earth coordinates is governed by:
m is the UAV mass, g is gravity, and Fthrust is the total force created by the propellers applied to the multirotor along the –zb axis (points upwards in a horizontal pose).
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 angles,
[ψc,
ϴc,
ϕc] and a commanded total thrust
force, Fcthrust. The
structure to specify these inputs is generated from control.
The P and D gains for the control inputs are specified as
KPα and
KDα, where 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] 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
See Also
Functions
control|derivative|environment|ode45|plotTransforms|roboticsAddons|state