1 of 34

Aerial Robotics

Aerodynamics and Propulsion

C. Papachristos

Robotic Workers (RoboWork) Lab

University of Nevada, Reno

CS-491/691

2 of 34

Actuation

Electromechanical Motion

How forces & torques can be generated and controlled, in order to enable flight.

CS491/691 C. Papachristos

3 of 34

Actuation

Different Actuation & Propulsion Designs enable Diversity

CS491/691 C. Papachristos

4 of 34

Aerodynamics

Conservation Laws

  • For any fluid system:

​

    • Mass is neither created nor destroyed: Conservation of Mass - Continuity

​

    • Momentum is neither created nor destroyed: Conservation of Momentum (3D)

​

    • Energy is neither created nor destroyed: Conservation of Energy

​

Mass

 

 

Mass

 

 

CS491/691 C. Papachristos

5 of 34

Aerodynamics

Navier-Stokes Equations

Continuity:

 

 

 

Energy:

  • Describe Unsteady Flow .

​

Note:�Reynolds number is a quantifier of how much the flow is affected by inertia (of the fluid as a whole)

  • Laminar Flow: low Re number
  • Turbulent Flow: high Re number

CS491/691 C. Papachristos

 

 

 

 

 

 

 

 

 

 

6 of 34

Aerodynamics

Euler Equations

Continuity:

 

 

 

 

Incompressible

Form:

 

CS491/691 C. Papachristos

 

 

 

 

 

 

7 of 34

Aerodynamics

Bernoulli Equations

Bernoulli’s Equation:

​

​

​

​

  • Implication:�When the velocity increases, the pressure decreases, and when the velocity decreases, the pressure increases

 

 

 

 

CS491/691 C. Papachristos

8 of 34

Aerodynamics

Aerodynamic Force

  • “Force” generated due to the airflow separation around the airfoil�which causes a difference in upper/lower streamline velocities,�and thus pressures

By J Doug McLean, CC BY-SA 3.0

By Kraaiennest, CC BY-SA 3.0

By רונאלדיניו המלך - , CC BY-SA 4.0

Resultant Force

CS491/691 C. Papachristos

9 of 34

Aerodynamics

Aerodynamic Force & Moment

 

 

v

Note: CoP location changes with AoA

CS491/691 C. Papachristos

10 of 34

Aerodynamics

Aerodynamic Coefficients

 

 

 

 

CS491/691 C. Papachristos

Aerodynamic Lift-Drag “Polar”

11 of 34

Aerodynamics

Laminar / Turbulent Flow

  • Viscous Flow is affected by Conditions at the Boundary Layer
    • Inviscid / Frictionless Flow assumes�that the surface streamline slips over it

​

​

​

​

  • Transition between different Boundary Conditions can take place

​

​

​

​

​

  • Significantly different modes of flow (“smooth” or “swirling/mixing”) can occur around the same profile
    • Laminar Flow (smooth) / Turbulent Flow (swirling/mixing)
  • Whereas real-life flow encompasses friction�with air molecules “sticking” to surface�(and thus having 0 relative velocity):

C. Papachristos

By NASA – Glenn Research Center

Flows over a cylinder profile

12 of 34

Aerodynamics

Separation and Aerodynamic Stall

  • Highly Turbulent Flow can become significantly separated�

​

​

​

​

  • Flow separation results is dramatic increase of Drag�(i.e. resistance to motion through the viscous medium)

CS491/691 C. Papachristos

Flows over circular cylinder, at Re=1.54, 26, 140

13 of 34

Aerodynamics

Separation and Aerodynamic Stall

  • Stall:�Catastrophic and near-sudden loss of Aerodynamic Lift

​

    • Has resulted in multiple aircraft accidents, due to bad operator reaction / perception

CS491/691 C. Papachristos

By DLR, CC-BY 3.0, CC BY 3.0 de

By NASA – Glenn Research Center

Separation points

Turbulent Wake

Separation point moves slightly forward

Maximum Lift

Separation point jumps forward

Separated flow region expands and reduces lift

Large Turbulent Wake�(reduced lift and large pressure drag)

 

 

(Stall angle)

 

 

14 of 34

Aerodynamics

Wingtip Vorticity – “Wake Turbulence”

CS491/691 C. Papachristos

  • Air spillage at the wingtip area reduces aerodynamic efficiency and induces vorticity

​

​

​

​

​

​

​

  • Meta-Aircraft� applications:�

Flow field in the crossflow plane above a wing, showing leading-edge vortices

Spanwise illustration of pressure distribution

15 of 34

Aerodynamics

Rotorcraft

CS491/691 C. Papachristos

16 of 34

Aerodynamics

The Rotor

Video of airflow and vortex patterns with propellers;�tests were conducted at NACA, now NASA Langley Research Center

CS491/691 C. Papachristos

17 of 34

Aerodynamics

  • Rotor modeling is a very complicated process

​

  • A Rotor is different than a propeller
    • Not rigid and contains more motion degrees of freedom
    • Among them blade flapping allows the control of the rotor tip path plane and therefore control the helicopter
  • Used to produce thrust
  • Propeller plane perpendicular to shaft
  • Assumed rigid blades - No flapping
  • Fixed blade pitch angle or collective changes only
  • Used to produce lift and directional control
  • Elastic element between blade and shaft
  • Blade flapping used to change tip path plane
  • Blade pitch angle controlled by swashplate

CS491/691 C. Papachristos

18 of 34

Aerodynamics

The Propeller Blade

 

CS491/691 C. Papachristos

19 of 34

Aerodynamics

The Propeller Blade

  • Linearize Lift-Drag “Polar” for Reynolds number at 2/3 R

 

 

Remember:�Reynolds number quantifies how much the flow is affected by inertia (of the fluid as a whole)

Note: Numerical solution of the Navier–Stokes equations for turbulent flow is extremely difficult

CS491/691 C. Papachristos

20 of 34

Aerodynamics

The Propeller

  • A “propeller” is assumed to present no blade flapping

​

  • It is approximated as a rotor disc producing thrust and drag forces

​

  • Remember: From Bernoulli’s Equation:

​

​

  • Thrust Force�from Integral Momentum�Theorem Derivations:

​

​

​

​

​

​

​

 

 

 

 

 

 

Thrust:

Power:

CS491/691 C. Papachristos

i.e.,

 

21 of 34

Aerodynamics

The Propeller

  • Simplified model forces and moments:
    • Thrust Force: the resultant of the vertical forces acting on all the blade elements

​

​

    • Hub Force: the resultant of all the horizontal forces acting on all the blade elements

​

​

    • Drag Moment: This moment about the rotor shaft is caused by the aerodynamic forces acting on the blade elements
    • The horizontal forces acting on the rotor are multiplied by the moment arm and integrated over the rotor
    • Drag moment determines the power required to spin the rotor

 

 

 

CS491/691 C. Papachristos

22 of 34

Actuation

  • Miniaturization of motion & propulsion systems –in combination with good efficiency– is among the reasons for the success of small aerial robotics

​

Focus on:

  • DC Motors
  • DC Brushless Motors
  • Propelled-systems
  • Servomotors

​

CS491/691 C. Papachristos

23 of 34

Electromechanical

DC Motors

  • Stationary permanent magnet
  • Electromagnet on axis induces torque
  • Split ring + brushes (commutators) switch�direction of current�
  • Easy to build and control

CS491/691 C. Papachristos

24 of 34

Electromechanical

DC Motors

  • More power means faster rotation�Need a convenient method to control power in a) Analog or b) Digital approach

​

  • How to modulate power using a digital signal?�Digital-equivalent functionality allowing to directly control power at the input

​

  • Fixed voltage input, pulse-modulated

Pulse Width Modulation (PWM)

Duty cycle is the proportion of “ON” time vs. period

​

CS491/691 C. Papachristos

25 of 34

Electromechanical

AC Motors

  • Electromagnets are stationary

​

  • Two or Three coils (or more)

​

  • No brushes /commutators

(less maintenance, higher efficiency)

Understanding RMF | The driving force behind every AC machine�https://www.youtube.com/watch?v=wqrGHeuxUvI&t=3m23s

CS491/691 C. Papachristos

26 of 34

Electromechanical

Brushless Motors

  • Electromagnets are stationary (stator part)

​

  • Permanent magnets on the rotating axis (motor part)

(either inside or outside)

​

  • Three coils (or more)

​

  • No brushes

(less maintenance, higher efficiency)

​

  • Brushless motors come with high torque, eliminating the need for gearboxes in case of multirotor aerial robots

​

4-pole

Inrunner

High-pole

Outrunner

Image Copyright: mpoweruk.com

CS491/691 C. Papachristos

27 of 34

Electromechanical

Brushless Motors

  • Typically one microcontroller per motor
    • Phase-switching handled by high-priority Interrupt Service Routines

​

  • Called Electronic Speed Controller (ESC)

​

  • Generates PWM signal for the three (3) motor phases
  • Switching MOSFETs to convert DC input power

​

  • Phase-switching handled based on rotor position
    • Measured directly (sensored) or estimated using back-EMF (sensorless)

CS491/691 C. Papachristos

28 of 34

Communication Protocols

Analog

  • PWM-based modulation of an analog voltage corresponding to a command signal magnitude

​

Digital

  • PWM-based digital encoding of commands
    • Convention of “counting single/multiple pulse width times” within a given frame period (e.g. 20ms)
  • Serial & I2C
    • More advanced digital protocols used with ESCs, sensors, etc.
      • Communication between motor controller and autopilot
    • I2C allows for multiple devices-per-line or bi-directional communication)
      • Serial data line (SDA) + serial clock line (SCL)
      • Specific encoding/decoding allows master/slave communication
      • Multiple devices connected in parallel
      • 7-10 bit address, 100-3400 kbit/s speed

Image Copyright: Wikipedia

CS491/691 C. Papachristos

29 of 34

Control

DC Motor Modeling

  • Electromechanical Model
  • Frequency Domain modeling

​

 

DC Motor Model

 

(A low-pass filter)

CS491/691 C. Papachristos

30 of 34

Speed Control

Motor Output-Feedback Control for Speed

  • Linearized Model
  • Linear Control
  • Output Feedback - driven

DC Motor

Model

 

Control

 

 

 

 

 

 

CS491/691 C. Papachristos

31 of 34

Position Control

Motor Output-Feedback Control for Position

  • Linearized Model
  • Linear Control
  • Output Feedback - driven

DC Motor

Model

 

Control

 

 

 

 

 

 

 

 

CS491/691 C. Papachristos

32 of 34

Position Control

The Servomotor

  • Position Feedback Control is crucial and widely used in actuation of Micro Aerial Vehicle robots

CS491/691 C. Papachristos

33 of 34

Bioinspired Principles

CS491/691 C. Papachristos

34 of 34

Time for Questions !

CS-491/691

CS491/691 C. Papachristos