Paul Pounds
DERF 08
How to Build Practical
Quadrotor Robot Helicopters
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
Blade Design Modifications
 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
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?
Aside: What is Flapping?
Direction of
motion
 Rotors in horizontal translation experience a thrust
imbalance on advancing and retreating blades
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
Aside: Rotor Motion in Pitch
 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
Increased lift
Decreased lift
Roll motion
.
Linear System Model
Horz. flapping force
Horz. thrust force
Differential rotor torque
Flapping torque
Vertical rotor damping
The longitudinal differential equations produce the following
transfer function between pitch and rotor speed (q/w):
.
Root-Locus in h
Optimising for Sensitivity
 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
 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?