WOLFRAM SYSTEM MODELER

Quadrotor

Interface for the complete quadrotor model

Diagram

Wolfram Language

In[1]:=

SystemModel["Aircraft.Physical.RotaryWing.MultiRotor.Quadrotor"]

Out[1]:=

Information

The Quadrotor model represents the complete drone model, consisting of the QuadrotorBody (representing mass and inertia of the drone), sensors and propulsion system (including DC motor, gear and propeller). It takes input commands from the controller, and the outputs of the model are the translational and rotational position/angle and velocities.

Parameters

The Quadrotor model declares the primary parameters that significantly influence quadrotor design. This declaration is intended to simplify the process of parameter adjustments, making it easier to modify key aspects of the quadrotor's design.

Propulsion System

The propulsion system consists of an electric motor that generates the required torques mounted on each propulsion system inside the QuadrotorBody model, and each one is connected to a gearbox that scales the torques to the propellers. The propeller produces lift force for each propulsive body and the DC motor generates angular rotation. Force and torque signals are introduced in QuadrotorBody and mounted on each corresponding propulsion system.

System Inputs

The inputs to the system consist of the voltages for the four DC motors, and these voltages are determined by the controllers.

Sensors:

Two Sensors from the Modelica standard library has been used for this model. An AbsoluteVelocity (named gpsVel) and an AbsolutePosition (gpsPos) sensor are connected to the frame of the center of the QuadrotorBody. They measure the linear velocity and position of the quadrotor in the Earth's reference frame. Note that negative gain (zVel and zPos) are used to change the direction of the position and velocity in the z direction to be in accordance with the world reference frame of the Aircraft library. All measurements pass to the output translationalM which is a vector of [ x, y, z, u, v, w].

An AbsoluteAngularVelocity sensor is connected to the same frame and models a gyroscope. It records angular velocities in the quadrotor's body reference frame, denoted as p, q and r, and corresponding to rotations around the x, y and z axes. By applying an integrator, the quadrotor's rotational angles, roll, pitch and yaw can be derived. Taking into account the small angle assumption, these angles are equivalent to the Euler angles, φ, θ and ψ. All measurements pass to the output rotationalM which is a vector of [roll, pitch, yaw, p, q, r].

Connectors

This model contains real inputs for the commanded voltage from the control system, and two real outputs from the translational and rotational sensor measurement, which is used as feedback to the control system. The drone features a frame connector located at its center of mass. This connector enables the attachment of loads for package delivery or the connection of mechanical components, as illustrated in the VerticalMotion example.

Parameters (13)

centralMass	Value: 0.38 Type: Mass (kg) Description: Mass of rigid body (bodyCenter.m) (quadrotorBody.centralMass)
propulsionMass	Value: 0.01 Type: Mass (kg) Description: Mass of each propulsion system (quadrotorBody.propulsionMass)
IxxP	Value: 0.001 Type: Inertia (kg⋅m²) Description: Moment of inertia of each propulsion system around x axis (quadrotorBody.IxxP)
IyyP	Value: 0.001 Type: Inertia (kg⋅m²) Description: Moment of inertia of each propulsion system around y axis (quadrotorBody.IyyP)
IzzP	Value: 0.001 Type: Inertia (kg⋅m²) Description: Moment of inertia of each propulsion system around z axis (quadrotorBody.IzzP)
IxxC	Value: 0.01 Type: Inertia (kg⋅m²) Description: Moment of inertia of the central mass of the quadrotor around x axis (quadrotorBody.IxxC)
IyyC	Value: 0.01 Type: Inertia (kg⋅m²) Description: Moment of inertia of the central mass of the quadrotor around y axis (quadrotorBody.IyyC)
IzzC	Value: 0.01 Type: Inertia (kg⋅m²) Description: Moment of inertia of the central mass of the quadrotor around z axis (quadrotorBody.IzzC)
armLength	Value: 0.192 Type: Real Description: Arm length of the quadrotor (quadrotorBody.armLength)
propellerGain	Value: 0.00045 Type: Real Description: Relation between lift force of propeller and rpm (propeller2.p)
gearRatio	Value: 28000.0 / 3300.0 Type: Real Description: Transmission ratio (flange_a.phi/flange_b.phi) (idealGear2.ratio)
motorResistance	Value: 2.25 Type: Resistance (Ω) Description: Resistance at temperature T_ref (resistor.R) (motor1.resistance)
motorInductance	Value: 0.01 Type: Inductance (H) Description: Inductance (inductor.L) (motor1.inductance)

Connectors (4)

	voltage	Type: RealInput[4] Description: Vector of the voltage input of the electric motors
	center	Type: Frame_b Description: Coordinate system fixed to the component with one cut-force and cut-torque (non-filled rectangular icon)
	translationalM	Type: RealOutput[6] Description: Measured position of the quadrotor
	rotationalM	Type: RealOutput[6] Description: Measured angles and angular rates of the quadrotor

Components (19)

	quadrotorBody	Type: QuadrotorBody Description: 6DOF quadrotor base body
	motor3	Type: Motor Description: Third electric motor
	motor1	Type: Motor Description: First electric motor
	motor2	Type: Motor Description: Second electric motor
	propeller3	Type: Propeller Description: Third propeller generates force and rotor rotation
	propeller2	Type: Propeller Description: Second propeller generates force and rotor rotation
	propeller1	Type: Propeller Description: First propeller generates force and rotor rotation
	idealGear2	Type: IdealGear Description: Second gear
	idealGear3	Type: IdealGear Description: Third gear
	idealGear1	Type: IdealGear Description: First gear
	gpsVel	Type: AbsoluteVelocity Description: Sensor to measure absolute position of the quadrotor
	gyroscope	Type: AbsoluteAngularVelocity Description: Sensor measures the angular velocity of the quadrotor
	idealGear4	Type: IdealGear Description: Fourth gear
	motor4	Type: Motor Description: Fourth electric motor
	propeller4	Type: Propeller Description: Fourth propeller generates force and rotor rotation
	angles	Type: Integrator[3] Description: Output the integral of the input signal with optional reset
	gpsPos	Type: AbsolutePosition Description: Measure absolute position vector of the origin of a frame connector
	zPos	Type: Gain Description: Gain converts the height measurement direction
	zVel	Type: Gain Description: Gain converts the height measurement direction