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 thexyz
-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 toInterpreted execution
.Interpreted execution
— Simulate model using the MATLAB® interpreter. This option shortens startup time but has a slower simulation speed thanCode 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 [xe,ye,ze]. The body frame of the UAV is attached to the center of mass with coordinates [xb,yb,zb]. xb is the preferred forward direction of the UAV, and zb 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 ze-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, [xb,yb,zb].
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 [xe, ye, 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:
Va and Vg denote the UAV air and ground speeds.
The wind speed is specified as
[Vwn,Vwe,Vwd]
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.
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].
The rotation matrix that rotates vector from body frame to world frame 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 rate, 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] 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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