introduction to multicopter design and...

Introduction to MulticopterDesign and Control

Quan Quan , Associate [email protected]

BUAA Reliable Flight Control Group, http://rfly.buaa.edu.cn/Beihang University, China

Lesson 12 Position Control Based On Semi-Autonomous Autopilot

2016/12/25 2

Howisamulticopter controlledbasedontheSemi‐

AutonomousAutopilotstotrackagiventargetposition?

1. Problem Formulation

2. System Identification

3. Position Controller Design

4. Simulation

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Outline

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Semi-Autonomous Autopilot Based Development

Planning

Position control

Attitude control

Control allocation +Motor control

Position Stabilization

Attitude Stabilization

SAA

FAA

SAA: Semi-Autonomous Autopilot, FAA: Fully-Autonomous Autopilot

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Planning

Position control

内环控制

零散硬件

Commercial Multicopterwith SDK,

Open-Source Multicopter

SAA

FAA

Attitude Stabilization

Position Stabilization

SecondaryD

evelopment

Not only can it avoid the trouble of modifying the low-level source code of autopilots, but also it can utilize commercial reliable autopilots to achieve targets.

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Open-Source Projects Web site URL

Ardupilot http://ardupilot.com

Openpilot http://www.openpilot.org/

Paparazzi http://paparazziuav.org

Pixhawk https://pixhawk.ethz.ch/

Mikrokopter http://www.mikrokopter.de

KKmulticopter http://www.kkmulticopter.kr/

Multiwii http://www.multiwii.com/

Aeroquad http://www.aeroquadstore.com/

Crazyflie https://www.bitcraze.io/category/crazyflie/

CrazePony http://www.crazepony.com/

DR. R&D http://www.etootle.com/

ANO http://www.anotc.com/

Autoquad http://autoquad.org/

MegaPirate http://megapiratex.com/index.php

Erlerobot http://erlerobotics.com/

MegaPirateNG http://code.google.com/p/megapirateng

Open-Source Projects Web site URL

Taulabs http://forum.taulabs.org/

Flexbot http://www.flexbot.cc/

Dronecode https://www.dronecode.org/

Percepto http://www.percepto.co/

Parrot API(SDK) https://projects.ardrone.org/embedded/ardrone-

api/index.html

3DR DRONEKIT(SDK) http://www.dronekit.io/

DJI DEVELOPER(SDK) http://dev.dji.com/cn

DJI MATRICE 100+ DJI

Guidance

https://developer.dji.com/cn/matrice-100/

SDK for XMission(SDK) http://www.xaircraft.cn/en/xmission/developer

EHANG GHOST SDK(SDK) http://dev.ehang.com/

Table 1.1 Major open source Projects



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[1] How J P, et al. Real-time indoor autonomous vehicle test environment. IEEE Transaction on Control Systems, 2008, 28(2): 51-64.

Real-Time Indoor Autonomous Vehicle Test Environment，MIT



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Sem

i-A

uton

omou

s A

utop

ilotStabilize Mode

Altitude Hold Mode

Loiter Mode

……

A position controller is designed based on the stabilize mode, which is the most basic mode among the three commonly-used modes.


Structure of Multicopter with SAA

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Structure of Multicopter with SAA

Tuz

uu u

Figure 12.1 The closed loop diagram based on SAA


Attitude Model+ SAA

(Black Box)

Position Model(Gray Box)

u

u

zu

Tu

bor xv

bor yv

ezv

RC CommandsAttitude Angles

+ Vertical VelocityPosition

+ Yaw Angle

Position Controller

e e e, , ,x y zp p p

bz

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A multicopter is divided into three channels

Altitude Channel Yaw Channel Horizontal position channel


Models of Three Channels

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Parameters depending

on Multicopter and

Autopilot are Unknown.


Models of Three Channels (Assumptions)

Altitude Channel

Yaw Channel

Horizontal position channel

e e

e ez T

z z

z v z u T

p v

v k v k u

z zz

z

z z uk k u

b

b h bb

b

b h h b hb

h h

h h h

h h

h h h h

0 11 0

g

v

Θ ω u

p R v

v K v Θ

Θ ω

K Θ K ω K uω

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Objective of Position Control

Given a reference trajectory，it consists two parts:

and

Objective is to design extra position controller satisfying

Is a ball with the center at zero and radius 。

or


d ( )tp d ( )t

4 1( , )0B

d( ) ( ) 0t t x x d 4 1( ) ( ) ( , )t t x x 0BTT

d d d= x pTT= x p

The purpose of the identification is to obtain the parameters of the transfer functions. This will facilitate the controller design.


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Objective

Figure 12.2 System Identification Toolboxof MATLAB.

Figure 12.3 Comprehensive Identification from FrEquency Responses(CIFER) toolbox.

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1. Prior Knowledge. The priorknowledge means the existingknowledge about the characteristicsof the system, the data recordingmethods and other aspects of thesystem. This knowledge is veryhelpful to choose the candidatemodels, design the experiment, anddetermine the calculation methodand the criterion of validation.Because of the different goals ofidentifications, the required priorknowledge may be very different,even for the same system.


Figure 12.4 The procedure of system identification

Procedure

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2. Experiment design. The purposeof the experiment design is to obtainthe input-output data of the system,which can reveal the systemperformance as much as possibleunder known conditions. The input-output data are sometimes recordedduring a specifically designedidentification experiment, where theuser may determine which signals tomeasure and when to measure them.



Procedure

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There are two kinds of experiments for system identification: open-loop experiments and closed-loop experiments, which are shown in Figure 12.3(a)(b), respectively.

• The excitation for open-loop experiments are richerthan that of closed-loop experiments, because any input signal can be selected in open-loop experiments. Obviously, if systems can work without controllers, open-loop experiments are the better choices.

• Some systems are unstable, and they must work with feedback controllers. As a result, the input signals are decided by the controllers.

Figure 12.5 Two kinds of experiments for system identification

Procedure


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3. Data record. Observe the input-output data through the designedexperiment.4. Model selection. Choose a set ofcandidate models and determinewhich one of them is the most suitablemodel through the validation.Through the mathematical modeling,a parametric model with unknownparameters can be obtained. Then, theunknown parameters can becalculated by parametric identificationmethods.



Procedure

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5. Model calculation. The model calculation means that the unknown parameters of the candidate model are determined by appropriate optimization methods.6. Model validation. A criterion is determined to test whether the candidate model with the calculated parameters is valid for the designed purpose. In general, this criterion relies on the observation data, the prior knowledge, and the application of the identified model. If the model with the parameters passes the validation, it will be chosen as the final model. If not, the previous steps need to be revised.

Procedure



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A trade-off open-loop system identification

The modification can be usedfor identification on newsystems. But, the originalsystem is still unknown.

1. Altitude Channel

2. System IdentificationModel used in System Identification

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Unstable

Candidate Model

Controller redesign

Stable


1. Altitude Channel

Model used in System Identification

e e

e ez T

z z

z v z u T

p v

v k v k u

e e

e eT z e z T z

z z

z u p z v z u p

p v

v k k p k v k u

ez zT p z pu k p u

e z p zzz p u pp s G s u s

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Model used in System Identification2. Yaw Channel

Unstable

Stable

Candidate Model


z zz

z

z z uk k u

zu k u

zz z

z

z u z uk k k k u

us G s u s

This channel is harder to control than the other two channels because of the influence of . Thus, the horizontal velocity controller is designed in the following part.

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The horizontal position channel is identified after the other twochannels are well controlled. In this situation, under the controllerof the yaw channel, is satisfied. Then, is a constant matrix.The transfer function of horizontal position channel is expressed asfollows


3. Horizontal Position Channel

e h hb

h hb

h h

h

1 1diag ,

1 1diag ,

s s ss s

s ss s

v u

v u

p R G u

R G u

d R

R

b h hb hh s s s

vv u vv G u

2016/12/25 23


3. Horizontal Position ChannelFor the SAA which contains a velocity feedback controller, is reasonable. The transfer function is stable in channel and it can be identified directly. Otherwise

b h bb

b

b h h b hb

h h h

h h

h h h h

0 11 0

g

v

Θ ω u

v K v Θ

Θ = ω

Θ K ω uω K K

h b hbh h v vu K v u

b h bb

b

b h h b h h b h hb b

h h h

h h

h h h h

0 11 0

g

v

u v Θ ω u vω

v K v Θ

Θ = ω

K K v K Θ K ω K u

hvK

b h

svv uG


2016/12/25 24

PID Controllerdy y

ue Multicopter

with SAA

p d d d i d( )z e e z e e z e eT p z z p z z p z zu k p p k p p k p p

p d d d i dz zu k k k

1 1 1h hp h hd hd h hd hi h hd

u K R p p K R p p K R p p

Figure 12.5 PID controller

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Simple, no requiring model

PID Controller


Parameters need to be tunedrepeatedly especially forstrongly coupled channel, andit is difficult to achieve an idealtransient process.

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AOD：Additive Output Decomposition, DIC: Dynamic Inversion Control

Gdy 1dG y

dy1G

1. In practice, is unknown, but it can be identified as approximately

2. There have differences between and . How to deal with?G

G

DIC

1. Idea of DIC

Plant


AOD-Based DIC

G

G

2016/12/25 27

AOD for transfer functions：

[2] Quan Quan, Kai-Yuan Cai. Additive-Output-Decomposition-Based Dynamic Inversion Tracking Control for a Class of Uncertain Linear Time-Invariant Systems. The 51st IEEE Conference on Decision and Control, 2012, Maui, Hawaii, USA, 2866-2871.


AOD-Based DIC[2]

1. Idea of DIC

y Gu d s py y yp p py G u s p py Gu d G u

, ,

,

x f t x u

y h t x

p sy t y t y t

, ,

,

p p p p

p p p

x f t x u

y h t x

, ,

, ,s s s s

s s s p p

x f t x u

y h t x h t x

2016/12/25 28

Identification

AOD：

AOD-Based DIC


2. Altitude channel

el

ˆ ˆ( )z z p zzp z p u pd p s G s u s

e z p zzz p u pp s G s u s

epˆ

z p zzz p u p pp s G s u s

es

ˆz p z z p zz zz p u p p u p pp s G s u s G s u s

ep

ˆz p zzz p u p pp s G s u s

lˆ

z z p z p zz zp p u p u pd G s G s u s

e

e e

p

p l

ˆz p zz

z

z p u p

z z p

p s G s u s

p s p s d s

2016/12/25 29

AOD-Based DIC：

is realizable，and

AOD-Based DIC

Unrealizable ，so a low-pass filter is adopted

2. Altitude channel


z pzp uG s

ˆz pzp uG s

ezp

epzp

lzpd

edzp

z pzp uQ s 1ˆz pzp uG s

Figure 12.6 The closed-loop system based on AOD-based DIC

e

1d l

ˆz z p zzp p u z pu s G s p s d s

e

1d l

ˆz z p z p zz zp p u p u z pu s Q s G s p s d s

z pzp uQ s

1ˆz p z pz zp u p uQ s G s 0 1

z pzp uQ

2016/12/25 30

Stability analysis，theorem：

Suppose (1) is minimum phase；

(2) and are stable, and ；

(3) ;

(4) is constant。

Then is bounded and as ，where

3. Position Controller Design AOD-Based DIC2. Altitude channel

Quan Quan, Kai-Yuan Cai. Additive-Output-Decomposition-Based Dynamic Inversion Tracking Control for a Class of Uncertain Linear Time-Invariant Systems. The 51st IEEE Conference on Decision and Control, 2012, Maui, Hawaii, USA, 2866-2871.

ˆz pzp uG s

z pzp uQ s

z pzp uG s 0 1z pzp uQ

edzp

zpu t ( ) 0zpe t

e edzp z ze p p

1ˆsup 1 1z p z p z pz z zp u p u p uG j G j Q j

2016/12/25 31

3. Position Controller Design AOD-Based DIC3. Other two channels

and

h h v h v b hb h b h

1h d l

ˆs s s s s v v u v u vu Q G v d

h b h v hb hl h v

ˆs s s s v v ud v G u

1d l

ˆu uu s Q s G s s d s

lˆ

ud s s G s u s

2016/12/25 32

3. Position Controller Design AOD-Based DIC3. Other two channels

The desired horizontal velocity needs to be transformed from the desired horizontal position. First, the transient process is expected as follows

where . If so, then . Since

the desired horizontal velocity should satisfy

Then

hh hd h hd( ) pp p K p p h hdlim ( ) ( ) 0

tt t

p p

bh hp R v

b hh d hd h hd( ). pR v p K p p

b h

1h d h hd( ).

pv R K p p

h

2 2 pK D P

2016/12/25 33

Transient process is nice,the tuned parameters are

less,less experiments

Design is somewhat complicated

AOD-Based DIC


4. Simulation

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Plant

Zander J (2013) AR Drone Simulink. https://github.com/justynazander/AR Drone Simulink. Accessed 20 Jan 2016

2016/12/25 35

System Identification

4. Simulation

Figure 12.7 The simulation for the system identification

hu,

zTu u

b eh , ,zp vh

,zpu uvu

Inputs

Outputs Measured Outputs

Actual Outputs

: AR. Drone with Stabilizing ControllerG

2016/12/25 36

1. Prior Knowledge


4. Simulation

The models of multicopters are established above are the prior knowledge.

Altitude Channel

Yaw Channel

Horizontal position channel

e e

e ez T

z z

z v z u T

p v

v k v k u

z zz

z

z z uk k u

b

b h bb

b

b h h b hb

h h

h h h

h h

h h h h

0 11 0

g

v

Θ ω u

p R v

v K v Θ

Θ ω

K Θ K ω K uω

2016/12/25 37

2. Experiment design

4. Simulation


Before the identification, stabilizing controllers will be employed if needed. The controllers of the altitude channel (also called as z channel) and the yaw channel (also called as ψ channel) are designed as

Here, the desired yaw angle is set to 0, so under the well-designed yaw channel controller and the horizontal position channel is decoupled into x channel and y channel. This means that controls velocity through θ, and controls the velocity through . Then

b h hb hh

( ) ( )( ) G ( ) ( )

( ) ( )x v xx

y v yy

v u v

v u v

G s u ss s s

G s u s

vv u vv u

ez zT p z pu k p u z

u k u

d

eyv exv

yvuxvu

0 5 10 150

0.5

1

1.5

0 5 10 150

0.2

0.4

0.6

0 5 10 150

0.2

0.4

0.6

0 5 10 150

0.5

1

1.5

channelx channely

channelz yaw channelTime (s)

Time (s)

Time (s)

Time (s)

(m/s

)bxv

()

rad

(m)

ezp

(m/s

)byv

Setting Time 3.71s

Setting Time 3.52s Setting Time 2.76s

Setting Time 5.85s

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Settling time is long!


4. Simulation

2. Experiment design

Figure 12.8 The actual step response of each channel under PID controller

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4. Simulation

System Identification3. Data record

Pseudo-Random Binary Signals (PRBS) are generated to stimulate these channels.

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4. Simulation

System Identification3. Data record

Figure 12.9 The input output data of the four channels used in the identification (The output dataare the measured outputs)

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The principle of choosing model is

(1) The identification results can pass the model validation and the fitness is used as the criterion.

(2) The identification results are supposed to be minimum-phase systems, because nonminimum phase systems are hard to tackle for most controller designs.

(3) While the previous two principles are guaranteed, the order of the transfer function needs to be chosen as small as possible.

4. Simulation

System Identification4. Model selection

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5.Model calculation

Time Domain Data

Remove means

Transfer Function Models

4. Simulation


The math works. System identification toolbox. http://www.mathworks.com/help/ident/index.html. Accessed 20 Jan 2016

2016/12/25 43

5. Model calculation

4. Simulation


The fitness of the four channels are: 98.56%, 98.08%, 95.84%, 90.40%

3 2

2

2

15.48 29.94.642 16.09 10.91

7.086 17.024.742 15.49 7.063

6.257.077 6.249

1.277 3.5064.045 3.522

x vx

y vy

z pz

v u

v u

p u

u

sG ss s s

sG ss s s

G ss s

sG ss s

G

2016/12/25 44

AOD-Based DIC

4. Simulation

h hb 2 2

2

2

1 1( ) diag ,( 1) ( 1)

1( )( 1)

1( 1)

z pz

x y

p uz

u

ss s

Q ss

Qs

v vQ u

0.2, 0.2, 0.3, 0.3x y z

Figure 12.10 The simulation structure for the AOD-based DIC controller

Gˆ -1G Q

G

2016/12/25 45

AOD-Based DIC

Simple P/PD Stabilizing Controller AOD-Based DIC

Tracking performanceis improved

4. Simulation

0 5 10 150

0.5

1

1.5

0 5 10 150

0.2

0.4

0.6

0 5 10 150

0.2

0.4

0.6

0 5 10 150

0.5

1

1.5

channelx channely

channelz yaw channelTime (s)

Time (s)

Time (s)

Time (s)

(m/s

)bxv

()

rad

(m)

ezp

(m/s

)byv

Setting Time 3.71s

Setting Time 3.52s Setting Time 2.76s

Setting Time 5.85s(s)

(m/s

)bxv

()

rad

(m)

ezp

(m/s

)byv

3.71s

3.52s 2.76s

5.85s

0 5 10 150

0.2

0.4

0.6

0 5 10 150

0.2

0.4

0.6

0 5 10 150

0.2

0.4

0.6

0 5 10 150

0.2

0.4

0.6

Settling Time 1.10s Settling Time 1.01s

Settling Time 1.60s Settling Time1.02s

channelx channely

channelz yaw channelTime (s) Time (s)

Time (s) Time (s)

2016/12/25 46

Figure 12.11. The comparison of the horizontal position tracking performance

DIC controller has an excellenttracking performance. However,the tracking trajectories ofthe DIC controller lag behindthose of the PD controller alittle. The reason is the gainKph is not large enough. IfKph increases, the time delay ofthe tracking will decrease, butthe transient process will getworse, vice versa. Thus, usersneed to adjust Kph of the DICcontroller according to actualrequirements.

AOD-Based DIC

4. Simulation

-0.6 -0.4 -0.2 0 0.2 0.4-0.6

-0.4

-0.2

0

0.2

0.4

(m)

eyp

(m)exp

Actual Trajectory (AOD-based DIC)Actual Trajectory (PD Controller)Desired Trajectory

5. Summery

2016/12/25 47

1. More and more multicopter companies open the SDKs of their

autopilots. Based on these autopilots, tasks can be accomplished by

secondary developments.

2. Practice method is proposed for secondary developments.

3. In the future, one possibility of the development on multicopters is

that some companies provide a stable and reliable multicopter platform

or operating systems, based on which new applications can be

developed easily.

2016/12/25 48

Acknowledgement

Deep thanks go to

for material preparation.Jing Zhang Zi-Bo Wei Xunhua Dai

2016/12/25 49

Thank you!All course PPTs and resources can be downloaded at

http://rfly.buaa.edu.cn/course

For more detailed content, please refer to the textbook: Quan, Quan. Introduction to Multicopter Design and Control. Springer,

2017. ISBN: 978-981-10-3382-7.It is available now, please visit http://

www.springer.com/us/book/9789811033810

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