How to Build Practical Quadrotor Robot Helicopters

Paul Pounds

DERF 08

Why Quad-Rotor UAVs?

Quad-rotor UAVs have many benefits: Reliable Compact Low maintenance

But Limited payload Limited flight time Fast unstable dynamics

Most quad-rotors are not practical for real civilian applications

Large Quad-Rotors

Larger (>4 kg) Quad-rotors fix these limitations: More payload and batteries Slower rigid body dynamics Efficient rotors -> same footprint as lighter craft

But Demanding rotor performance specifications Slower rotor acceleration Rotors exhibit flapping in horizontal translation

which lead to… More difficult attitude control problems

Fixed-Pitch Rotors

Small, fixed-pitch rotors: Similar size and speed to model plane propellers Single predetermined blade angle of attack Simpler, more reliable - cheap to make and maintain Compact and unobtrusive

Rotor Design Guidelines

Optimise performance with developed design theory: Maximise rotor radius to reduce power requirement Maximise rotor speed to increase thrust Use ideal blade angle and chord to keep air flow

optimal across the blades Use thin airfoils to slice through air efficiently

The Twist Problem

But, thin blades designed only for aerodynamic performance twist into stall under flight loads

Airfoil design must compromise aerodynamic performance for improved stiffness

Increase blade bulk to improve stiffness

Round leading edge for decreased stall sensitivity

Move the camber rearwards to reduce twist moment

Add negative pre-twist, such that the blade will deform into the correct shape under flight load

Blade Design Modifications

Rotor and Blade Design

Completed composite blade

Drive System Guidelines

Use brushless DC motors for high efficiency, convenience and clean indoor use

Use lithium polymer batteries for high power density and long flight time

Use electronic speed controllers to regulate rotor speed and improve dynamic performance

Motor Dynamics

Quadrotors rely entirely on rotor speed changes for flight stabilisation

High-bandwidth drive systems are necessary for authorative attitude control

Small quadrotors have light rotors with fast acceleration -> larger craft require active control to improve their dynamic response

The Slew Problem

Fast speed changes instantaneously draw very high battery current > internal cell resistance causes the voltage to drop

In extreme cases, the voltage drop will cause the ESC to reset and halt the motor mid-flight (bad)

A slew saturation must be implemented to prevent the controller from demanding dangerously large instantaneous speed changes

The control response must still be fast enough to stabilise the craft and reject disturbances

Design for Performance Bounds

Compensated OL Motor Dynamics Bode Plot

Attitude Control

With fast motor response and efficient rotors, flight control should be straight-forward

But flying craft are dynamically unstable

Unstable systems are hard to control

Can we design a helicopter to be easy to control?

Rotors in horizontal translation experience a thrust imbalance on advancing and retreating blades

Aside: What is Flapping?

Direction of motion

Aside: What is Flapping?

Rotors pivot at the hub, changing the angle of the on-coming airflow, causing forces to balance

Aside: What is Flapping?

The horizontal component of thrust acts against the direction of motion and induces a torque around the vehicle’s centre of mass

A pitching quadrotor causes the rotors to move vertically with respect to the airflow

Upwards motion causes the thrust to reduce, downwards motion causes the thrust to increase

Rotor response resists the pitching motion

.

Aside: Rotor Motion in Pitch

Decreased liftIncreased lift

Roll motion

Linear System Model

Differential rotor torque Flapping torque Vertical rotor damping

Horz. flapping force Horz. thrust force

The longitudinal differential equations produce the following transfer function between pitch and rotor speed ():

.

Root-Locus in h

Conceptually, we know that unstable poles are more difficult to control for than stable poles

The Bode Integral shows that the magnitude of the sensitivity function across all frequencies is proportional to the sum of the unstable poles of the open loop plant:

The sensitivity function magnitude for a plant should be minimised for good disturbance rejection

Optimising for Sensitivity

Optimising for Sensitivity

The bode integral is minimised when the rotors are level with the centre of gravity – h = 0

Putting It All Together

Big, fast rotors with thin blades, with pre-twist to compensate for aeroelasticity

Brushless motors and lithium polymer cells Feedback control for fast rotor dynamics and disturbance

rejection that observes slew saturation bounds Put the centre of gravity coincident with the rotor plane

Questions?