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 torqueFlapping torqueVertical rotor damping Horz. flapping forceHorz. 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

 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?