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?