MICRO-502_Aerial_Robotics_Notes

Lecture notes by Yujie He

Last updated on 2021/07/02

All checkpoints summary can be found here!

Intro (week1)

Overview

• Most Civilian Drones are Small

  • flapping wings: operates in small scale; short flight time
  • rotorcraft/multicopters: in medium; could hover in place
  • fixed wings: fixed has longest flight time; cannot hover in place

• but endurance is a challenge

  

Fixed wing Staying in the Air

generate a force Lift L equal and opposite to its own weight W

fixed-wing generates by airflow

• computing lift: $W=\frac{1}{2} C^{l} * \rho {*} V^{2} * S \approx 0.3 * 1.25 * V^2 * S$ (sea level)

  • lift coefficient $C^{l}$: proportional to angle of attack

    at cruise speed $6^{\circ}$, assuming $\frac{1}{2} C^{l}= 0.2$

  • Air density: decreases with the altitude

    1.25 $kg/m^3$ at sea level

  • Air speed V: fly 2x as fast -> 4x lift

  • Wing area S

• compute the required velocity $V = \sqrt{(W / 0.38 * S)}$

• Speed is proportional only to wing loading W/S $W/S = 0.38V^2$

Maintaining constant speed V

• generate a thrust force T equal and opposite to Drag force D

• Drag $D=\frac{1}{2} C^{d} * \rho {*} V^{2} * S = \rm{Lift}/r$

  lift-drag ratio $r = Lift/Drag$

Major Application Fields

• Agriculture
• Energy
• Public safety & security
• Delivery

For Agriculture

• fixed-wing

  inspection: large fields; few lights/value

• quadcopter

  spraying: small fields; high-value crops; difficult terrain

For Energy

• stationary inspection

  fire, related to human safety

• long-range inspection

  frequent, faster inspection to powerline, gasoline

• Power generation

  strong & steady winds

For Public safety & security

• in-vehicle

  policeman

• long-range

  Border patrol, fast intervention

For Delivery

Category

• Long-range: fixed wing; combination of wing and rotors to cover long distance
• Short-range: multicopter

Forcast: parcel delivery > air freight in near future

«Can Drones Deliver?»

• Power requirement: 0.59kW

  deliver 2 kg payload at cruising speed of 45 km/h

• Energy requirement: about 0.39kWh

  deliver 2 kg payload within 10 km radius with 30 km/h headwind

  • power (kW) x distance to speed ratio (d/v) to get energy requirement (kWh)

• Battery & Platform: choose considerations -> cost; weight; energy density; lifetime

• Economics: Electricity/Battery cost per km

Last-cm delivery - Dronistics

• Packdrone + SimplyFly

  Protective foldable cage; Redundant GPS

• Temperature-control box

☑️ Checkpoints

• For a given total mass, what type of small drones (multi-copter, fixed-wing, flapping wing) displays the longest endurance?

  fixed-wing

  fixed-wing drones generate lift with their wings. This means that, unlike a multirotor drone, they don't expend large amounts of energy just to stay in the air and fly more efficiently as a result

• How much faster must an intercontinental airplane fly at cruising altitude compared to sea level?

  $W=\frac{1}{2} C^{l} * \rho {*} V^{2} * S \rightarrow V = \sqrt{\frac{2W}{C^l \rho S}}$

  • sea level: $\rho = 1.25kg/m^3$
  • intercontinental airplane fly ~10000m: $\rho = 0.4135kg/m^3$

  $V \propto \sqrt{1/\rho}$

• What structural factor (i.e. not the engine) affects the cruising speed of fixed-wing drones?

  Speed is only proportional to wing loading (W/S) = Weight/Wing area

  • wing angle -> lift coefficient
  • wing area

• What are the two major drone applications in agriculture?

  Inspection and spraying

• What are the drone applications in the energy sector?

  Stationary inspection; long-range inspection; and power generation

• What are the factors to consider for calculating the cost/km of drone delivery?

  Electricity cost and battery cost

Multicopters (week1)

Introduction

Rotorcrafts (helicopters vs multicopters)

generates lift using high speed rotary blades called rotors

• Features

  • Vertical take-off and landing (VTOL)
  • Very maneuverable
  • Less efficient than fixed wing vehicle

• helicopters-Need complex variable pitch rotors

  • the tail produce a moment to counteract the force generated by main propeller blade when generating main lift
  • change the pitch of the blades (force vector) to produce translation-add complexity

• multicopters-Use multiple fixed-pitch blades

  • each spin in different directions; don't need tails due to balanced moment
  • fix pitch propellers

  overtaken by helicopters due to heavy workload of the pilot

Pros and Cons

Pros-Easy to build and maintain

• Mechanically simple
• Does not require any complex mechanical parts
• Can move around by changing motor speed
• Can hover, takeoff, and land vertically

Cons

• Required energy constantly to hover
• less efficient than helicopters of the same size because the thrust is generated by smaller propellers.

Structure and Physics

Main components

frame; control board; Motors and motor drivers (ESC, electronic speed controller); Propellers; Battery; Receiver

Configuration

• Four propellers generate four lift forces

• Propellers 1& 2 (CCW) have opposite pitch compared to propellers 3 & 4 (CW)

  

Rotation speeds / Forces / Moments

movement are controlled by changing the rotation speed of the propellers

• Force F is proportional to square of propeller speed $F_i \propto w_i^2$
• mg is the weight of the quadrotor
• Moments generated by the forces are $M_i = L \propto F_i$

Hover conditions

1. All forces must be balanced $F_1+ F_2+ F_3+ F_4+ mg = 0$

   move up and down

2. Lift forces must be parallel to gravity $F_i \Vert g$

3. All moments must be balanced $M_1+M_2+M_3+M_4 = 0$

   pitch and roll

4. Rotor speeds must be balanced (torque balanced) $(w1+w3)-(w2+w4) =0$

   yaw

Flight mechanics

How to move a quadrotor around?

• Orientation

  

Violating one or more of these conditions implies that the quadcopter starts to move

Moving Up and Down

• condition1: Forces Not balanced $F_1+ F_2+ F_3+ F_4+ mg \neq 0$

Rotating in Yaw

• Rotor speeds not balanced (torque balanced) $(w1+w3)-(w2+w4) \neq 0$

  $\dot{\psi}=k_{\psi}\left(\left({w}_{2}+{w}_{4}\right)-\left({w}_{1}+{w}_{3}\right)\right)$

• Note: opposite motor pair should increase/decrease motor speeds to keep hovering, or it will keep flying up!

Rotation in Roll/Pitch

• Forces not parallel to gravity $F_i \nparallel mg$

• moments not balanced $M_1+M_2+M_3+M_4 \neq 0$

  $\dot{\phi}=k_{\phi}\left(\left(w_{1}+w_{4}\right)-\left(w_{2}+w_{3}\right)\right)$

  $\dot{\theta}=k_{\theta}\left(\left(w_{1}+w_{2}\right)-\left(w_{3}+w_{4}\right)\right)$

Summary of equations

• to control the quadrotor state -> setting the rotor speeds for obtaining a desired angular rotation

  inverse operation

Example-Translated flight

Moving Forward

Translated flight requires more thrust than hovering, but not always more power (see section 6)!

• pitch down: decrease F_1 and F_2

• hover: increase F_1 and F_2 to stop rotation

• translate: keep balance between mg and thrust $\mathbf{F} \cos \theta=-m g$

  

• pitch back

Types of Multicopters

main feature; fully actuated multicopters

Configuration

• Tricopter

  • More yaw authority compared to quadcopters

    direct control of yaw

  • More complex mechanical design due to the servo in tail

    need additional servo to roll/pitch the back motor

• Hexacopter/Octacopter

  • More lifting capacity -> more payload
  • Redundancy, so robust to failure
  • Larger size; expensive

• X8 configuration

  • More lifting capacity
  • More efficiency thanks to the coaxial configurations

Fully Actuated Multicopters

underactuated multicopters -> all propellers are rotated in the same plane

Features

• Rotors disks are in different planes
• Fully Actuated to control 6 DoF (heave, roll, pitch and yaw, x and y translation) by using 6 motors

Pros

• Translational and rotational dynamics are decoupled
• improved robustness to disturbances and to perform complex manipulation tasks
• Possibility to plan more complex trajectories

Cons

• Decreased energetic efficiency

Energetics

What is the power consumption of a multicopter during flight?

How to extend multicopters flight time?

• Multicopters have high power requirements

  inefficient compared to fixed-wing or flapping-wing aircraft

  • consume about 200 W/kg on average

  • Centimeter scale quad with LiPo -> 5-7min

  • Decimeter scale quad with LiPo ->20-30min

    changes corresponding to weather conditions and aggressiveness of flight

Energy in hovering

• Power calculation of single motor when drone in hovering

  • Propeller efficiency ranges from 0.85 to about 0.9
  • $r_p \sqrt{\pi}$ is the squire root of the disk area

• Flight time

  • $P_i$ has high variability

Energy in forward flight of quadcopter

• Power consumption during forward flight normalized by the power consumption at hover

  

  • lower power need but higher thrust -> aerodynamics

    tilting the quad to the side -> artificially increase the angle of attack -> generate the increase in thrust in the given power

  • high power ratio again

    drag increases quickly again!

Increase flight time

1. Weight and drag reduction

2. Increase the specific power of the energy source

   switch from LiPo batteries to gasoline (far more energy stored)

3. Docking station for charging/battery swapping

4. Tether for power supply

   reduce battery

5. Improving efficiency via mechanical

6. Energy aware motion planning

   reduce acceleration (aggressive flight)

7. Multi-modal operation

   perching; walking and rolling

☑️ Checkpoints

• What set of conditions corresponds to hovering in a quadcopter?

  Four conditions: balanced weight; parallel to weight; balanced moment (thrust x half frame); balanced rotation speed

• What set of conditions corresponds to a rotation around the yaw axis in a quadcopter?

  imbalanced rotation speed

• How the time of flight of multicopters can be increased?

  1. Weight and drag reduction
  2. Increase the specific power of the energy source
  3. Docking station for charging/battery swapping
  4. Tether for power supply
  5. Improving efficiency via mechanical
  6. Energy aware motion planning
  7. Multi-modal operation

• How the power consumption and total thrust evolve at different forward speeds in multicopters?

  first goes down as thus increases when angle of attack increases

  then goes down because the drag force increases again

Attitude representations (week2)

• how to convert state variables from body frame to earth frame

3D Attitude representation- Euler Angles

• Rotation matrices can be parametrize by Euler Angles

  • Roll $\phi$: rotation around x
  • Pitch $\theta$: rotation around y
  • Yaw $\psi$: rotation around z

  

• Yaw-Pitch-Roll rotation matrix (Z,Y,X) or Heading-Pitch-Roll (h-p-r)

  

  can be summarized as $R=R_{\phi} R_{\theta} R_{\psi}$ （左乘）

• 🚧 Claw Example

  rotation + translation

  补充示例！！！

• Issues: gimbal lock problem

  • sensitive to singularities-when pitch angle is 90 degrees, roll and yaw rotations give the same sensor readings

    lost 1 DoF

    $R=R_{\phi} R_{\frac{\pi}{2}} R_{\psi}=\left[\begin{array}{ccc}0 & 0 & -1 \\ \sin \phi \cos \psi-\cos \phi \sin \psi & \sin \phi \sin \psi+\cos \phi \cos \psi & 0 \\ \cos \phi \cos \psi+\sin \phi \sin \psi & \cos \phi \sin \psi-\sin \phi \cos \psi & 0\end{array}\right]=$ $\left[\begin{array}{ccc}0 & 0 & -1 \\ \sin (\phi-\psi) & \cos (\phi-\psi) & 0 \\ \cos (\phi-\psi) & -\sin (\phi-\psi) & 0\end{array}\right]$

  • fail to produce reliable estimates when the pitch angle approaches 90 degrees.

  • can only be solved by switching to a different representation methods, for example quaternions

Quaternion

the union of scalar and vector

• rotation vector = quet * vector * quet^(-1)

  

  • $p = [0, \mathbf{p}]$ vector in 3-space

  • $q = [s, \lambda \hat{\mathbf{v}}]$ Must meet these requirements

    $\vert \hat{\mathbf{v}} \vert = 1$; $s^2 + \lambda^2 = 1$

• multiplication

  

  $q=\left[\cos \frac{1}{2} \theta, \sin \frac{1}{2} \theta \hat{\mathbf{v}}\right]$ works for relative to x axis ($\theta$)

  week2_quaternion_mat.png

  

🚧 Claw Example

rotation + translation using quaternions

Conversion

• Euler angles to quaternion
• Quaternion to Euler angles (arctan2 is recommended)

Complex examples

frame: image/centered -> camera -> gimbal -> body -> local

$v_{l}=p+R_{p}^{l} v_{p}=p+R_{b}^{l} R_{g}^{b} R_{c}^{g} R_{i}^{c} R_{p}^{i} v_{p}$

🚧 注意谁相对谁！！！​

✖️ Checkpoints

• nothing left in this course

Control (week2&3)

结合exercise进行再次查看

Cascaded control Architecture

• drone architecture

  

• communication: glue to connect different parts (FCU to onboard computer to ground station)

• PID controller

  

  • Open-loop

  • Feedforward control

    • responds to its control signal in a pre-defined way
    • based on a previous knowledge of the system

  • Feedback control

• control example

  Examples	Free-flight glider	Passively stable helicopter	Racing drone	Autonomous Delivery drone
  Sensors	None	None	IMU	IMU + GPS + Vision + Mag
  Controllers	None	None	(Attitude), Rate	Position, Velocity, Attitude, Rate
  Setpoint	None	Manual actuator setpoint	Manual rate setpoint	Autonomous navigation/Manual

• challenges

  • underactuated system for quadcopter
  • approximate aerodynamic model
  • control inputs are idealized (the real model of the motors can be quite hard to model)

• features

  • insert the obstacle avoidance together with velocity setpoint
  • manual commands send thrust and attitude rate commands
  • the lowest level of the controller, the higher bandwidth it needs

• Pros

  • Decouple translational and rotational dynamics

  • Facilitate implementation of the controller

    implement one by one

  • Better failure diagnosis capability

    modular control architecture for debugging them one by one

• Question: why a more advanced controller?

  • linear assumption vs nonlinear system
  • more advanced system can bring optimal performance

Control allocation

convert thrust & torque setpoint into actuator commands

account for different geometries

• from thrust & torque setpoint into actuator

  $\left[\begin{array}{c}u_{0} \\ \vdots \\ u_{N-1}\end{array}\right]=B\left[\begin{array}{l}\tau_{x} \\ \tau_{y} \\ \tau_{z} \\ t_{z}\end{array}\right]$ $u$ : actuator commands (Nx1)

  $\mathcal{T}:$ moment setpoints (3x1)

  $t:$ thrust setpoint $(1 \times 1)$

Method

1. Compute generated force and torque of each actuator

2. Build matrix "Actuator Effectiveness"

3. Compute allocation matrix B as the pseudo-inverse of A

   not always square, so using pseudo-inverse ($B = A^+$)

Remark

• less effective at producing yaw torque

• yaw torque requires more actuator effort than roll and pitch torque

  

Rate control

Input body rate setpoint -> Output torque to each angle rate

Attitude control

Input quaternions setpoint -> Output torque to each angle rate

• How to compute the quaternion error

  $\boldsymbol{q}_{e r r}=\boldsymbol{q}_{\boldsymbol{r e f}} \otimes \boldsymbol{q}_{m}^{*}$

• axis error

  $\left[\begin{array}{c} \Phi_{e} \\ \Theta_{e} \\ \Psi_{e} \end{array}\right] \approx \operatorname{sgn}\left(q_{e}^{0}\right)\left[\begin{array}{l} 2 q_{e}^{1} \\ 2 q_{e}^{2} \\ 2 q_{e}^{3} \end{array}\right]$

Full quaternion based attitude control for a quadrotor

Fresk, E. and Nikolakopoulos, G., 2013, July. Full quaternion based attitude control for a quadrotor. In 2013 European control conference (ECC) (pp. 3864- 3869). IEEE.

• without any transformations and calculations in the Euler’s angle space

• quaternions

  • scalar + vector part

    $\boldsymbol{q}=q_{0}+q_{1} \boldsymbol{i}+q_{2} \boldsymbol{j}+q_{3} \boldsymbol{k} = [q_0, q_1, q_2, q_3]^{\mathsf{T}}$

  • Multiplication of two quaternions p, q is being performed by the Kronecker product

  • $p \otimes q$ represents the combined rotation

  • quaternion multiplication is non-commutative 不遵循交换律

  • All quaternions are assumed to be of unitary length 单位长度

  • The complex conjugate of a quaternion has the same definition as normal complex numbers 复共轭

    $\operatorname{Conj}(\boldsymbol{q})=\boldsymbol{q}^{*}=\left[\begin{array}{llll}q_{0} & -q_{1} & -q_{2} & -q_{3}\end{array}\right]^{T}$

  • if the length of the quaternion is unitary then the inverse is the same as its conjugate 逆即是复共轭

    $\operatorname{Inv}(\boldsymbol{q})=\boldsymbol{q}^{-1}=\frac{\boldsymbol{q}^{*}}{\|\boldsymbol{q}\|^{2}} = {q}^{*}$

• Rotation transformation is built by two quaternion multiplications-the normal and its conjugate

  • rotates the vector v from the fixed frame to the body frame represented by q

    $\boldsymbol{w}=\boldsymbol{q} \otimes\left[\begin{array}{l}0 \\ \mathbf{v}\end{array}\right] \otimes \boldsymbol{q}^{*}$

    where $\textbf{v}$ can be rewritten as location in x, y and z axis. For example,

    $R_{x}(\boldsymbol{q})=\boldsymbol{q} \otimes\left[\begin{array}{l}0 \\ 1 \\ 0 \\ 0\end{array}\right] \otimes \boldsymbol{q}^{*}=\left[\begin{array}{c}q_{0}^{2}+q_{1}^{2}-q_{2}^{2}-q_{3}^{2} \\ 2\left(q_{1} q_{2}+q_{0} q_{3}\right) \\ 2\left(q_{1} q_{3}-q_{0} q_{2}\right)\end{array}\right]$

  • $u$ is the rotation axis (unit vector) and $\alpha$ is the angle of rotation

    $\boldsymbol{q}=\cos \left(\frac{\alpha}{2}\right)+\boldsymbol{u} \sin \left(\frac{\alpha}{2}\right)$

• Calculating quaternions error dynamics

  • desired $\mathbf{q}_{ref}$, measured $\mathbf{q}_{m}$, error $\mathbf{q}_{err}$--multiplying the reference with the conjugate of the estimated quaternion in Kronecker

    $\boldsymbol{q}_{e r r}=\boldsymbol{q}_{\boldsymbol{r e f}} \otimes \boldsymbol{q}_{m}^{*}$

• Angular errors: the reference is demanding a rotation more than π radians, the closest rotation is the inverted direction and this is found by examining q0. If q0 < 0 then the desired orientation is more than π radians away

  $\left[\begin{array}{c} \Phi_{e} \\ \Theta_{e} \\ \Psi_{e} \end{array}\right] \approx \operatorname{sgn}\left(q_{e}^{0}\right)\left[\begin{array}{l} 2 q_{e}^{1} \\ 2 q_{e}^{2} \\ 2 q_{e}^{3} \end{array}\right]$

  其中sgn函数就对应着计算$q_0$的正负

Control strategies for multicopters

• Inner loops for attitude dynamics stabilization
• Outer loops for translational dynamics

Linear

Examples

• Proportional Integral Derivative (PID)
• Linear Quadratic Regulator (LQR)
• LQG

Features

• a linear approximation of the system dynamics
• used when the attitude of the multicopter involves angles that are close to zero

PID controller

• Pros: Easy to design; Intuitive to tune manually (not necessarily easy on a real drone)

• Cons: Imprecise nature of the model due to inaccurate modelling; Limits the performance

• Effects of increasing a parameter independently

  

LQR/LQG

• Features

  • a multirotor (linearized around an equilibrium point) by minimizing a suitable cost function
  • Pros: optimal control method and better than PID (LQR); not need complete knowledge of the state and can rely on estimator/observer (LQG)
  • Cons: requires tuning of Q and R Matrixes

• Practical example-Foldable Drone

  • Attitude control (providing torques) requires adaptation since morphology has an impact on the rotation dynamics
  • should update matrix matrix A during flight

• Effect of Q and R matrixes

  • design parameters to penalize (1) the state variables and (2) the control signals
  • Large value: stabilize the system with less change in State (Q) and Control input (R)
  • Small value: stabilize the system without “caring too much” about ...

Nonlinear

Examples

• Model Predictive Control (MPC)
• Artificial Neural Networks

Features

• The stability domain of a drone controlled with a nonlinear controller can be bigger
• a better model of the drone can lead to better performances
• allows to take explicitly into account aerodynamic effects and forces acting on the drones

An introduction to fully actuated multirotor UAVs

• conventional ones have coupling between the horizontal translational and rotational dynamics

• fully actuated can help decouple translation and rotation; have direct control to corresponding DoF

  key: allocation matrix changes

  • Fixed-tilt

    easier controller; don't need additional motors; lightweight; cannot achieve optimal performance

  • Variable-tilt: change tilt of propellers to achieve desired motion

    can achieve optimal configuration in given task but with complex mechatronics and control

☑️ Checkpoints

• What is the size of the control allocation matrix of an hexacopter with 4 controlled degrees of freedom?

  • hexacopter 六轴，6motors

  • Effectiveness matrix: 4x6

  • Controller allocation: 6x4

    Output: 6 motors; input B x (3torque + 1thrust)

    最底层的控制，就是输入是torque+thrust，输出是n个电机的转速

  • Effectiveness： transformation relationship to torque and thrust for each rotor

• Why do we use the pseudo inverse instead of standard matrix inverse to compute the control allocation matrix from the actuator effectiveness matrix?

  there existing other layout of multicopters except for quadcopters with 4 rotors

• What happens when a rate setpoint [0 0 1] is applied?

  rotate counterclockwise with 1 rad/s in yaw angle

• What are the input and output of the rate controller?

  Input: angle rate setpoint + estimated angle rate

  Output: generated angle torque

• What happens when an attitude setpoint [0 0 pi/2] is applied?

  rotate counterclockwise with pi/2 in yaw angle

• What are the input and output of the attitude controller in a cascaded architecture?

  Input: desired quaternion setpoint + estimated quaternion

  Output: generated angle rotation rate

• How to compute attitude error quaternion from the estimated attitude quaternion and the attitude setpoint quaternion?

  1. compute quaternion error

     $\boldsymbol{q}_{e r r}=\boldsymbol{q}_{\boldsymbol{r e f}} \otimes \boldsymbol{q}_{m}^{*}$

  2. calculate angular errors

     $\left[\begin{array}{c} \Phi_{e} \\ \Theta_{e} \\ \Psi_{e} \end{array}\right] \approx \operatorname{sgn}\left(q_{e}^{0}\right)\left[\begin{array}{l} 2 q_{e}^{1} \\ 2 q_{e}^{2} \\ 2 q_{e}^{3} \end{array}\right]$

State Estimation (week3&4)

Introduction to State Estimation

• STATE: variables used to describe the mathematical state of a dynamical system
• ESTIMATION: finding an approximation of state variables even if the data is incomplete, uncertain, or unstable
• estimate something which you can not see or measure directly

Why State Estimation in Robotics?

• Perfect model & sensor are not available; Errors exist in both sensors & models

  • State of the robot (proprioception)
  • State of the environment (exteroception)

• State Estimation on Aerial Robots

  Height; Attitude; Angular velocity (Most important as they are the primary variables used for the stabilization of the UAV); linear velocity

  • main sensors

    • Inertial Measurement Unit (IMU)
    • Height Measurement (Acoustic, infrared, barometric, laser based)
    • Others: Global Navigation Satellite System (GNSS, outdoor) or VICON (indoor); Camera, Kinect, LIDAR

Estimation for deterministic systems

State Observer (or Luenberger Observer)

• minimize the error between measured and estimated values

• how do we choose the “feedback loop” gain K ?

Dynamical Systems

Estimation error

• observer error

  $\dot{e}_{o b s}=(\boldsymbol{A}-\boldsymbol{K} \boldsymbol{C}) \boldsymbol{e}_{o b s} \rightarrow 0$ => $e_{o b s}(t)=e^{(\boldsymbol{A}-\boldsymbol{K} \boldsymbol{C}) t} e_{o b s}\left(t_{0}\right)$

  • with linear model

    $\dot{x} = Ax + Bu$

    $\dot{\hat{x}} = A\hat{x} + Bu + K (y-\hat{y})$

    $e_{obs} = x - \hat{x}$

• if A-KC <0, the error will lead to 0 when t -> infinity

• How to choose K?

  • gives control on the decay rate of the error function
  • similar to P gain in control (if too big, estimation will oscillate)

State Estimation for stochastic systems

Recap of fundamental concepts

• Mean and variance encode the a‐priori knowledge of the random variable

  • w: Process noise
  • v: Measurement noise

  $\dot{\boldsymbol{x}}=\boldsymbol{A} \boldsymbol{x}+\boldsymbol{B} \boldsymbol{u}+\boldsymbol{w}$ $\boldsymbol{y}=\boldsymbol{C} \boldsymbol{x}+\boldsymbol{D} \boldsymbol{u}+v$

• What is the a‐priori information about uncertainty in our problems?

  W/V are known but w/v are zero-mean

  • W: covariance matrix associated to process noise
  • V: covariance matrix associated to measurement noise

• What is the statistical independence among the values of a random variable in time?

  $E\left[\boldsymbol{w}(k) \boldsymbol{w}^{T}(k+n)\right]=0 \quad \forall n>0$ $E\left[\boldsymbol{v}(k) \boldsymbol{v}^{T}(k+n)\right]=0 \quad \forall n>0$ $+$ $E[\boldsymbol{w}(k)]=E[\boldsymbol{v}(k)]=0$

  white noise stochastic processes -> 期望值都是0

Kalman filter (KF)

• example: estimate drone’s roll angle

  • x: Drone’s roll angle
  • u: Roll Body rate
  • y: Drone’s roll angle (through IMU)
  • $w \sim N (0, Q)$: process error (only in the dynamics not in estimator!)
  • $v \sim N (0, R)$: measurement error (only in the dynamics not in estimator!)

  

  • initial state estimate
  • -> predicted state estimate
  • + measurement
  • => Optimal state estimate

  

  Prediction (A-Priori) + Update

use Gaussians to implement a Bayesian filter. That’s all the Kalman filter is - a Bayesian filter that uses Gaussians

PREDICTION

• state $\hat{x}_{k}^{-}=A \hat{x}_{k-1}+B u_{k}$

• error covariance $P_{k}^{-}=A P_{k-1} A^{T}+Q$

  keep track not only the state but also the covariance (will keep increase)

UPDATE

• KF Gain $K_{k}=\dfrac{P_{k}^{-} C^{T}}{C P_{k}^{-} C^{T}+R}$

  • trust more in model y_k

    R-> 0 => K_k = 1/C => x_k = y_k/C

  • trust more in measurement x_k

    P_k -> 0 =>K_k = 0 =>x_k = x_k^{_}

• Update state $\hat{x}_{k}=\hat{x}_{k}^{-}+K_{k}\left(y_{k}-C \hat{x}_{k}^{-}\right)$

• $P_{k}=\left(I-K_{k} C\right) P_{K}^{-}$

  minimize the Covariance

sensor fusion on a quadrotor

use multiply KF to achieve better estimation

$\hat{x}_{k_{1 \times 1}}=\hat{x}_{k_{1 \times 1}}^{-}+K_{k_{1 \times n}}\left(y_{k_{n \times 1}}-C_{n \times 1} \hat{x}_{k_{1 \times 1}}^{-}\right)$

Intro to EKF, UKF and particle filters

EKF

• linearizes the nonlinear function around the mean of the current state estimate

Overview

• applied to nonlinear system
• linearize around the state estimate value by computing Jacobian matrices

Equations

• Predication

  $\hat{\boldsymbol{x}}_{k}^{-}=f\left(\hat{\boldsymbol{x}}_{k-1}^{-}, \boldsymbol{u}_{k}\right)$

  $P_{k}^{-}=F P_{k-1} F^{T}+Q$

  F-Computed Jacobian matrix

  $\boldsymbol{F}=\left.\frac{\partial f}{\partial \boldsymbol{x}}\right|_{\hat{\boldsymbol{x}}_{k-1}, \boldsymbol{u}_{k}}$

• Update

  Near optimal Kalman Filter gain

  $K_{k}=\dfrac{P_{k}^{-} H^{T}}{H P_{k}^{-} H^{T}+R_k}$

UKF

• take several points to compute/approximate probability distribution
• choose sigma points according to algorithms

Particle filters

• Combines the results to estimate the mean and covariance of the state

• !computationally intensive

• Different UKF

  • Not limited to a Gaussian distribution
  • points are chosen randomly

State Estimation in aerial robotics

in lab settings

• use MoCap to estimate position and velocity

Outdoor

• Camera, Depth camera Sensor, ToF Range Sensor to estimate pose and height

☑️ Checkpoints

• What structure does the Luenberger Observer remind you?

  closed-loop estimation for deterministic systems

• What does the Kalman Filter (KF) gain do?

  determine to trust either more on measurement or a-prior/model

• For which kind of dynamical systems the KF is useful?

  linear continuous system

  !cannot work in discontinuous system

• What do we need to know a-priori if we want to apply the KF?

  state mean $x_k$ and error covariance $P_k$

• What are the advantages/disadvantages of the UKF w.r.t an EKF?

  EKF

  • need linearization
  • Not an optimal estimator (especially nonlinear)
  • may quickly diverge (when incorrect model/wrong covariance init)
  • may difficult to compute Jacobians

• What are the advantages/disadvantages of a particle filter w.r.t an UKF?

  PF

  • Not limited to a Gaussian distribution
  • need more points → more computational time
  • More accurate as long as having enough particles

🚧 Navigation (week5)

Velocity control

• 🚧 如果低速飞行，不去调整yaw，不然可能会引起震荡！

Waypoint Navigation

Dubins Paths

Vector fields

☑️ Checkpoints

• Which component of the acceleration setpoint is converted to roll angle? To pitch angle?

  • roll
  • pitch

• Why is navigation based on fixed position setpoint inappropriate for fixed-wing drones?

  • cannot do sharp turning

• What type of segment compose a Dubins path?

  • arcs of a minimal radius
  • straight lines

• In which case can we construct a RLR Dubins path?

  distance of waypoints is less than the minimal diameter

• What happens when centrifugal acceleration is not taken into account in the formulation of a circle following vector field?

  It will not follow the vectors and cross the circle lines

🚧 VIO & SLAM (week5)

VIO

SLAM

☑️ Checkpoints

• What is VIO/SLAM useful for?

  • VIO: Visual inertial odometry

    process of estimating the drone state (position, orientation, and velocity) by using only the inputs from Camera(s) and IMU(s)

  • SLAM: Simultaneous Localization and Mapping

• What are the sensors that can be used to do VIO/SLAM?

  Camera(s) and IMU(s)

• What is loop closure?

  the recognition of when the robot has returned to a previously mapped region and the use of this information to reduce the uncertainty in the map estimate.

• What are the main three VIO paradigms?

  • Filters

    • Restrict inference process to latest state of the system

  • Fixed-lag smoothers

    • Restrict inference process to a given time window

  • Full smoothers

    • Estimate the entire history of the states
    • More accurate
    • Real‐time operation can become unfeasible

• Why do we use a camera and an IMU for VIO?

  • Cheap and complementary to each other

  • Camera: Precise during slow motion and provide rich information

    Limited output rate; Not robust to scenes with low texture, high speed motions

  • IMU: Scene independent and High output rate

    Poor signal-to-noise ratio at low accelerations and angular velocities; Estimated motion tends to accumulate drift quickly

Fixed-wing drones (week6)

Introduction

Structure

Flight Mechanics

Control surface

• Ailerons

  • attached to the outboard trailing edge of both wings
  • rotate the aircraft around the longitudinal axis (roll)

• elevators

  • hinged to the trailing edge of the horizontal stabilizer
  • around the horizontal or lateral axis (pitch)

• rudder

  • hinged to the trailing edge of the vertical stabilizer
  • causes an aircraft to yaw or move about the vertical axis

Stability

longitudinal -> pitching

lateral -> rolling

directional -> yawing

Energetics

Induced power

• Induced drag is the drag on the wing that is due to lift

Profile and parasite power

• The total aerodynamic power is obtained by multiplying the drag force by the forward velocity

☑️ Checkpoints

• What are the main flight control surfaces in fixed-wing aircrafts?

  • Ailerons

    • attached to the outboard trailing edge of both wings
    • rotate the aircraft around the longitudinal axis (roll)

  • elevators

    • hinged to the trailing edge of the horizontal stabilizer
    • around the horizontal or lateral axis (pitch)

  • rudder

    • hinged to the trailing edge of the vertical stabilizer
    • causes an aircraft to yaw or move about the vertical axis

• What are the main stabilization strategies in fixed-wing aircrafts?

  • Longitudinal stability

    making CoG ahead of the aircraft

  • Lateral stable

    • Dihedral angle 翅膀上扬
    • Keel effect and Weight distribution

  • Vertical stability-pitch

    making the side surface greater than ahead of the center of gravity

• How is a flying wing/Tailless aircraft controlled and stabilized?

  • upward reflex (上扬边缘) or elevons (ailerons+elevator) keeps pitch in equilibrium

• What are the main contributions to power consumption in fixed-wing aircrafts?

  • Pressure drag + Friction drag

  • Induced drag + Profile drag (wing) + Parasite drag (body)

    • Induced drag(powers proportional to 1/v)

      drag on the wing that is due to lift

    • Profile drag, Parasite drag (powers proportional to v^3)

Aerial Swarms (week7)

Intro

• Drone light shows

  Centralized = agents transmit individual position to ground computer and receive next location

• Collective Motion in nature

  Decentralized = agents rely on local information and computation

Reynolds flocking algorithm (Reynolds, 1987)

• radius of communication or neighborhood R

• Separation: avoid collision
• Cohesion: attempt to keep close
• Alignment: attempt to match velocity

Reynolds flocking: model

• Equations

  

  • Set of agents in neighborhood $N$
  • identity of $i$-th agent
  • position ${\mathbf{p}_i}$
  • velocity $\dot{\mathbf{p}}_i$
  • acceleration $\ddot{\mathbf{p}}_i$ = control command
  • acceleration term due to the cohesion/separation/alignment $\mathbf{a}_{coh,i}$, $\mathbf{a}_{sep,i}$, and $\mathbf{a}_{align,i}$
  • constant gains corresponding to the cohesion/separation/alignment $C_c$, $C_s$, and $C_a$

• Equilibrium

  

  • Positions converge to a lattice formation (晶格式)

  • Velocities converge to the average of initial velocities

    $\lim _{t \rightarrow \infty} \dot{\boldsymbol{p}}_{i}=\frac{\sum_{i \in\{1,2, \ldots N\}} \dot{\boldsymbol{p}}_{i}(0)}{N}$

Reynolds flocking with migration

• new migration rule steers the swarm towards a desired direction

  • replaces the alignment rule
  • cohesion and separation rules are kept to regulate the agents distances

  

• Equation

  $\ddot{\mathbf{p}}_{i}=\mathbf{u}_{i}$, $\mathbf{u}_{i}=c_{c} \frac{\sum_{j \in N_{i}}\left(\mathbf{p}_{j}-\mathbf{p}_{i}\right)}{\left|N_{i}\right|}-c_{s} \frac{\sum_{j \in N_{i}} \frac{\mathbf{p}_{j}-p_{i}}{\left\|p_{j}-p_{i}\right\|^{2}}}{\left|N_{i}\right|}+c_m \frac{\mathbf{v}_{mig}-\dot{\mathbf{p}}_i}{1}$

  $\forall i \in\{1,2, \ldots, N\}$

  • parameters

    • migration velocity $\mathbf{v}_{mig}$
    • Denominator = 1 since neighbors are not relevant for migration

Case: Aerial swarms for disaster mitigation

SMAV platform with control electronics

Communication radius and turning angle

• large communication radius -> can make sharp turn together because of knowing the position of other robots
• smaller communication radius -> may separate and gather into a flocking often

Virtual agents for flocking with fixed-wing drones

• Winged drone flies around Virtual Agent which moves according to Reynolds rules

  

• Varga et al., Distributed Formation Control of Fixed Wing Micro Aerial Vehicles for Uniform Area Coverage, IROS 2015

  video: https://youtu.be/FYsd2VckGA0

Reynolds flocking with obstacles (Virtual agents)

• Obstacles are modelled as virtual agents

  • Its position is the obstacle’s closest point to the agent
  • Its velocity is perpendicular to the tangent to the obstacle

  $(\mathbf{p}_k, \dot{\mathbf{p}}_k)$ position and velocity of the virtual agent

• Virtual agents exert separation and alignment effects, but not cohesion (not collide with the agent)

• Visualization

  

• Equation (two extra separation and alignment term regarding obstacles)

  $\ddot{\mathbf{p}}_{i}=\mathbf{u}_{i}$

  $\mathbf{u}_{i}=c_{c} \frac{\sum_{j \in N_{i}}\left(\mathbf{p}_{j}-\mathbf{p}_{i}\right)}{\left|N_{i}\right|}-c_{s} \frac{\sum_{j \in N_{i}} \frac{\mathbf{p}_{j}-p_{i}}{\left\|p_{j}-p_{i}\right\|^{2}}}{\left|N_{i}\right|}+c_a \frac{\mathbf{v}_{mig}-\dot{\mathbf{p}}_i}{1} -\left[c_s \frac{\mathbf{p}_k - \mathbf{p}_i}{\Vert \mathbf{p}_k - \mathbf{p}_i \Vert^2} + c_a (\dot{\mathbf{p}}_k - \dot{\mathbf{p}}_i)\right]$

  $\forall i \in\{1,2, \ldots, N\}$

Other models

Vicsek model: particles in confined environments (密闭环境)

Vasarhelyi et al., Optimized flocking of autonomous drones in confined environments, Science Robotics, 2019

DOI: http://doi.org/10.1126/scirobotics.aat3536

Video: https://youtu.be/E4XpyG4eMKE

Project web: http://hal.elte.hu/drones/scirob2018.html

• Rules

  • Separation
  • Self propulsion: Makes the agent match a preferred speed
  • Friction: Viscosity (internal friction) for alignment and oscillation damping

• Equation

  $\left\{\begin{array}{l}\dot{\boldsymbol{p}}_{i}=\boldsymbol{u}_{i} \\ \boldsymbol{u}_{i}=\boldsymbol{v}_{s e p, i}+\boldsymbol{v}_{s p p, i}+\boldsymbol{v}_{\text {fric }, i}\end{array}\right.$

• The full equation contains 12 parameters and requires heuristic methods for optimization

Olfati-Saber model

R. Olfati-Saber, Flocking for multi-agent dynamic systems: algorithms and theory, IEEE Transactions on Automatic Control, 2006

• Rules

  • Distance matching

    • Makes the agents match a desired inter-agent distance
    • Replaces cohesion and separation rules of Reynolds model
    • Mathematically defined as a potential function

  • Alignment: attempt to match the velocity and direction

  

• Equation

  $\ddot{\mathbf{p}}_{i}=\mathbf{u}_{i}$

  $\mathbf{u}_{i}=c_{d} \frac{\sum_{j \in N_{i}} \nabla \left(\rho(\mathbf{p}_{j}-\mathbf{p}_{i}) V (\Vert \mathbf{p}_{j}-\mathbf{p}_{i}\Vert) \right)}{\left|N_{i}\right|}-c_{a} \frac{\sum_{j \in N_{i}} (\dot{\mathbf{p}}_{j}-\dot{\mathbf{p}}_{i})}{\left|N_{i}\right|}$

  $\forall i \in\{1,2, \ldots, N\}$

  • radius of influence $R$
  • desired inter-agent distance $d_{ref}$
  • weighting function $\rho$
  • distance matching function $V$
  • gradient, derivative in three dimensions $\nabla=\left(\frac{\partial}{\partial x}, \frac{\partial}{\partial y}, \frac{\partial}{\partial z}\right)$

• distance matching example

  • Components

    • weighting function 越近影响越大
    • distance matching function 越靠近$d_{ref}$越小，线性
    • Result: potential function

  

  • Note

    • Principle of minimum potential: minimum defines the stable equilibrium of the system
    • $d_{ref}$ is a stable equilibrium
    • The force acting on an agent is zero in the minimum of the potential. For $d=d_{ref}$, it holds $\nabla(\rho V)=\mathbf{0}$

Drone Swarms

Coppola et al., A Survey on Swarming With Micro Air Vehicles: Fundamental Challenges and Constraints, Front. Robot. AI, ‘20

The combination of centralized planning/control with external positioning has allowed to fly significantly larger swarms. The numbers are lower for the works featuring decentralized control with external positioning, or centralized control with local sensing

Three categories

1. Centralized with external positioning

   latest: September 20 2020

   3,051 drones

   News: https://www.guinnessworldrecords.com/news/2020/10/3051-drones-create-spectacular-record-breaking-light-show-in-china (Company: https://www.dmduav.com/)

   YouTube: https://youtu.be/44KvHwRHb3A

   Bilibili: https://www.bilibili.com/video/BV1jt4y1q762

2. Decentralized with external positioning or centralized with on-board sensing

   Vasarhelyi et al. (2019)

3. Decentralized with on-board sensing

   Saska et al. (2017)

Visual information in flocking

Soria2019IRC-influence of limited visual sensing using Reynolds

Soria et al., The influence of limited visual sensing on the Reynolds flocking algorithm, 2019

• generate flocks with different fields of view

  

  • azimuth/方位角 $\theta [^{\circ}]$
  • width $\alpha [^{\circ}]$

  

• measure flocking performance (all individuals in the flock have the same visual configuration)

  • Order: measure of alignment
  • Safety: ability to avoid collisions
  • Union: ability to stay informed on neighbors
  • Connectivity: ability to broadcast messages among drones

  

• results

  

  • focus on order and safety (alignment and collision prevention capability)
  • largest azimuth and FoV has best performance
  • increase in either azimuth or FoV only will degrade the performance
  • safety can be achieved even with lower FoV

Schilling2019RAL-Learning to flock in simulation with vision

Schilling et al., Learning Vision-Based Flight in Drone Swarms by Imitation, RAL2019

• use 6 cameras in each side
• training on a dataset to generate the velocity vector for the drone

• Stages

  • Dataset generation: Flocking algorithm as ground truth
  • Training phase: Learn mapping between vision and control output
  • Vision-based control: Neural controller for collision-free and cohesive flight

• Note

  • work well in simulation indoor environment
  • it can be robust when individuals has different migration points
  • cannot generalize well in background clutter and different lighting condition

Schilling2021RAL-Learning to flock outdoor with vision

Schilling et al., Vision-Based Drone Flocking in Outdoor Environments, RAL2021

• Setup

  • Drone with only with 4 cameras in four side
  • RTK GNSS is used to compute performance
  • train YOLOv3 tiny to recognize other drones using YOLO

• Control method

  

  1. Real-time drone detection

     • Input: images from 4 cameras

     • Output: x,y coordinates of perceived drones in image frame coordinates

       known size to compute corresponding distance

  2. Multi-agent state tracking

     • Input: Locations of drones & noise models
     • Output: Range and bearing of all perceived drones with noise

  3. Potential-field-based control

     • Input: Range and bearing of all perceived drones
     • Output: velocity vector resulting from Reynolds algorithm

☑️ Check points

• What information does each agent receive in the Reynolds flocking algorithm?

  position and velocity of self and neighbor agents

• How are obstacles modeled in Reynold’s flocking

  virtual agent; integrate into equations with alignment and separation term (non cohesion)

• How is a migration point incorporated in flocking algorithms

  add a migration velocity term

• What does the Olfati-Saber algorithm ensure?

  No collision. The acting force will be zero when reach the preferred distance $d_{ref}$

• What are the three steps of vision-based drone flocking algorithm?

  1. Real-time drone detection
  2. Multi-agent state tracking
  3. Potential-field-based control

  images from 4 cameras -> x,y coordinates of perceived drones in images -> Range and bearing of all perceived drones -> velocity vector

Flapping-Wing (week8)

Introduction

• lift and thrust generation, and maneuvers mostly obtained by using the wings

• imitate the flapping-wing flight of birds, bats, and insects

• scale down better then rotary crafts and fixed wing UAVs

• Challenges:

  • Increased mechanical and control complexity
  • Complex modelling due to unsteady aerodynamics

Structure

categories were determined to be the tail (1) and wing design (2)

• requires the use of a tail for stability and/or control purposes
• generate the lift and thrust forces necessary for flight using flapping wings

Flight mechanics - Lift generation

• Flapping Wings

  two wings are flapped to produce both lift and thrust, thus overcoming gravity and drag to provide sustained flight

• Clapping

  Increase of lift during the “clapping

  cancels out the vertical oscillations

• Morphing/folding

  flap their wings downward, fold them in toward their body

  minimum wing area during the upward flap -> minimize undesired negative lift

Lift generation in hovering flight

Asymmetric hovering

Symmetric hovering

• produced during the entire wing stroke exploiting different unsteady mechanisms.

  • Leading edge vortex
  • Rotational forces
  • Clap-and-flight motion

Lift generation in forward flight

Downstroke/Upstroke

Flight mechanics - Maneuvering

flapping wing MAVs can use the tail and / or the wings for control.

• ail actuation

  • Aircraft tail
  • Aircraft tail with propeller for yaw and elevator for pitch
  • Inverted V-tail

• Wing actuation

  • Changing the angle of incidence
  • Tensioning the wing (拉紧机翼)

Energetics

☑️ Checkpoints

• What are the main types of tail designs found in flapping wing MAVs?

  • Static
  • Active
  • Tailless

• What are the main types of wings designs found in flapping wing MAVs?

  • Flapping
  • Clapping
  • Morphing/Folding

• What are the main mechanisms for lift generation in symmetric hovering flight?

  • Leading edge vortex
  • Rotational forces
  • Clap-and-flight motion

• What are the main steering strategies in flapping flight MAVs?

  • Tail actuation

    • Aircraft tail
    • Aircraft tail with propeller for yaw and elevator for pitch
    • Inverted V-tail

  • Wing actuation

    • Changing the angle of incidence
    • Tensioning the wing (拉紧机翼)
    • Controlling the stroke (拍打角度)

Drone Regulations (week8)

Author: Markus Farner

https://www.bazl.admin.ch/bazl/en/home/good-to-know/drohnen.html

• Unmanned Aircraft Systems (UAS) >= Drones; UAS = Remotely piolted aircraft systems / autonomous aircraft systems

• Rules in Aviation: Federal Office of Civil Aviation Switzerland

• Everything which is not forbidden is allowed -> Switzerland

  Trust, less difficult for innovation

3 Pillar Concept / Drone Categories

1. Open-Within the legal framework (No Authorization required)
2. Specific-Not sufficiently safe (Authorization required)
3. Certified-Approved to accepted standards

Act

• Ordinance on Special Category Aircraft

  • No authorization required for commercial flights
  • No distinction between Unmanned Aircraft and Model Aircraft

• DETEC Ordinance on Special Category Aircraft

  • No authorization below 30kg
  • Within direct visual contact (VLOS)
  • Not within a distance <=100m around crowds

• ANSP (Skyguide) or Airport responsibility

  • > 5km Distance to civil & military airports/aerodromes
  • < 150m AGL (Above Ground Level) within a CTR

• Act in EU

  • Open/Specific/Certified

  • Difference

    • restrictions: MTOM 25kg
    • maximum flying altitude: 120m

Specific Category

Application for an operating permit on the basis of the SORA (Specific Operations Risk Assessment)

Operational Volume = Flight Geography + Contingency Volume

• ❓ Robustness Levels: Integrity + Assurance

U-Space

The U-space is a collection of decentralized services that collectively aim to safely and efficiently integrate drones into the airspace and enable drone operations alongside manned flight.

https://www.bazl.admin.ch/bazl/en/home/good-to-know/drohnen/wichtigsten-regeln/uspace.html.html

https://www.skyguide.ch/en/events-media-board/u-space-live-demonstration/

airspace in block to avoid collision and report the location for further path calculation

• U-space is capable of ensuring the smooth operation of all categories of drones, all types of missions and all drone users in all operating environment

☑️ Checkpoints

• Federal Office of Civil Aviation FOCA

• What defines the three drone categories?

  1. Open-within the legal framework (No Authorization required)

     low risk; maximum flying altitude: 120m

  2. Specific-Not sufficiently safe (Authorization required)

     enhanced risk

  3. Certified-Approved to accepted standards

     risk comparable to manned aviation

• What is the SORA declaration?

  • stands for Specific Operations Risk Assessment
  • used for Specific Drone Categories
  • assigning to a UAS-operation two classes of risk, i.e., ground risk model and air risk model

  the multi-stage process of risk assessment aiming at risk analysis of certain unmanned aircraft operations, as well as defining necessary mitigations and robustness levels

• Is FOCA authorization sufficient for operating drones in the “Specific” category?

  No. FOCA authorization is required for the "Specific" category, but it is not sufficient because other federal, cantonal, and communal authorities may require additional authorizations

• What is U-space?

  🚧 U-Space provides a framework to facilitate the implementation of all types of operation in all classes of airspace and all types of environment, while ensuring an orderly coexistence with manned aviation and air traffic control.

  from U-Space: The airspace of the future

UAS Hardware (week9)

Introduction

main component required

1. The aerial vehicle

   • Air frame

   • Actuators for propulsion and control

   • Energy source

   • Autopilot

     • Sensors for attitude estimation
     • Electronics for regulation, control and communication
     • Sensor and avoid system

2. Payload

   • Cameras
   • Environmental sensors (wind, temperature, humidity)
   • Robotic arms for manipulation

3. Ground Control Station

   • Communication systems
   • Interface to monitor internal parameters and to send commands to the vehicle

Frame and materials

materials comparison

metric when considering materials

• Young's modulus [wiki]

  弹性模量，正向应力与正向应变的比值

  • measure of stiffness
  • defines the relationship between stress and strain
  • Foam < ABS/PLA/Wood < Carbon fiber

  

• Specific modulus [wiki]

  比模量，单位密度的弹性模量，劲度－质量比，在航天工业中有广泛应用。

  • elastic modulus per mass density of a material
  • stiffness to weight ratio
  • High specific modulus materials find wide application in UAVs where minimum structural weight is required.

  

Energy sources

Goal: power the robots to fly

Metric: energy density, power density, charging time and so on

Category

• Nickel-Cadmium (NiCd) | 镍镉

  • Mature and cheap
  • Low energy and power density -> short flight time

• Nickel-Metal Hydrate (NiMh) | 镍氢电池

  由镍镉电池（NiCd battery）改良而来的，其以能吸收氢的金属代替镉（Cd）。它以相同的价格提供比镍镉电池更高的电容量、较不明显的记忆效应、以及较低的环境污染（不含有毒的镉）

  [wiki-zh]

  • Higher energy density than NiCd

• Lithium-Polymer (Li-Po) | 锂离子聚合物电池

  • rapidly growing market and performance
  • Higher energy and power density compared to NiCd
  • Regular geometry for easy integration, e.g., cuboid or cuboid

• Fuel

  • Highest energy and power density
  • complex and higher weight-requires tank, distribution system and maintenance

• Fuel cell

  • Electrochemical reaction of hydrogen fuel with oxygen

Energy and power density

• energy density

  amount of energy stored per unit volume or mass

• power density

  how fast or quickly to discharge into mechanics

  amount of power (time rate of energy) per unit volume or mass

• Conclusion

  • Fuel has highest energy and power density
  • Fuel cell has highest energy but lower power density
  • LiB has higher energy and power density than NiMH and NiCd

Li-Po batteries

• most commonly-used UAV energy source

• Each battery composed of one or more cells connected in series

  S=series, P=Parallel

• Each cell has

  • nominal voltage of 3.7 V

  • a maximum voltage of 4.2 V

  • a capacity (mAh)

    e.g., 1000 mAh

  • a specific discharge and charge rate (C)

    e.g., Discharge rate with 25-50C = 25-50 A of max continuous discharge current; Charge rate 2C = 2 A

Discharge Curves of Li-Po battery

• not linear of time
• the discharge curve is determined by the amount of current (expressed in “C”) drawn from the battery.
• higher discharge rates -> faster rising temperature -> poses overheating risks.

Book: G. C. H. E. Decroon, M. Perçin, B. D. W. Remes, R. Ruijsink, and C. De Wagter, The delfly: Design, aerodynamics, and artificial intelligence of a flapping wing robot. 2015.

Energy Curve of Li-Po battery

• How much energy the same LiPo battery can provide until its voltage drops below a certain voltage

• 10 times higher battery load (discharge rate) -> 17 times shorter flight time

  nonlinear relationship

Actuators

Actuators for propulsion