Autonomous Quadrotor Delivery System Modeling and Simulation
Quadrotor Modeling and Control - Carnegie Mellon …€¦ · · 2014-12-01Quadrotor Modeling and...
-
Upload
nguyenthuy -
Category
Documents
-
view
222 -
download
1
Transcript of Quadrotor Modeling and Control - Carnegie Mellon …€¦ · · 2014-12-01Quadrotor Modeling and...
![Page 1: Quadrotor Modeling and Control - Carnegie Mellon …€¦ · · 2014-12-01Quadrotor Modeling and Control 16-311 Introduction to Robotics Guest Lecture on Aerial Robotics February](https://reader034.fdocuments.net/reader034/viewer/2022051601/5ad989187f8b9add658b73e1/html5/thumbnails/1.jpg)
Quadrotor Modeling and Control
16-311 Introduction to RoboticsGuest Lecture on Aerial Robotics
February 05, 2014
Nathan Michael
![Page 2: Quadrotor Modeling and Control - Carnegie Mellon …€¦ · · 2014-12-01Quadrotor Modeling and Control 16-311 Introduction to Robotics Guest Lecture on Aerial Robotics February](https://reader034.fdocuments.net/reader034/viewer/2022051601/5ad989187f8b9add658b73e1/html5/thumbnails/2.jpg)
Lecture Outline
• Modeling:
• Dynamic model from first principles
• Propeller model and force and moments generation
• Control
• Attitude control (inner loop)
• Position control (outer loop)
• Current research challenges
![Page 3: Quadrotor Modeling and Control - Carnegie Mellon …€¦ · · 2014-12-01Quadrotor Modeling and Control 16-311 Introduction to Robotics Guest Lecture on Aerial Robotics February](https://reader034.fdocuments.net/reader034/viewer/2022051601/5ad989187f8b9add658b73e1/html5/thumbnails/3.jpg)
Develop preliminary concepts required to enable autonomous flight:
D. Mellinger, N. Michael, and V. Kumar. Trajectory generation and control for precise aggressive maneuvers with quadrotors. Intl. J. Robot. Research, 31(5):664–674, Apr. 2012.
Lecture Objective
e2e1
e3
1. Vehicle model2. Attitude and position control3. Trajectory generation
![Page 4: Quadrotor Modeling and Control - Carnegie Mellon …€¦ · · 2014-12-01Quadrotor Modeling and Control 16-311 Introduction to Robotics Guest Lecture on Aerial Robotics February](https://reader034.fdocuments.net/reader034/viewer/2022051601/5ad989187f8b9add658b73e1/html5/thumbnails/4.jpg)
Concept Review
Quadrotor Model
Newton-Euler equations:
total force
total torque
mass
F⌧
�=
m13 03
03 I3
� a↵
�+
! ⇥mv! ⇥ I3!
�
moment of inertia
linear acceleration
angular acceleration
angular velocity
linear velocity
![Page 5: Quadrotor Modeling and Control - Carnegie Mellon …€¦ · · 2014-12-01Quadrotor Modeling and Control 16-311 Introduction to Robotics Guest Lecture on Aerial Robotics February](https://reader034.fdocuments.net/reader034/viewer/2022051601/5ad989187f8b9add658b73e1/html5/thumbnails/5.jpg)
Concept Review
Quadrotor Model
Rigid transformation:
rotation translation
Euler angle parameterization of rotation:
Reb
= Rz
( )Ry
(✓)Rx
(�) ZYX (321) form
pe = Rebpb + re
e1
e2
e3b2
b3
re
Reb
pb
b1
![Page 6: Quadrotor Modeling and Control - Carnegie Mellon …€¦ · · 2014-12-01Quadrotor Modeling and Control 16-311 Introduction to Robotics Guest Lecture on Aerial Robotics February](https://reader034.fdocuments.net/reader034/viewer/2022051601/5ad989187f8b9add658b73e1/html5/thumbnails/6.jpg)
Concept Review
Quadrotor Model
Euler angle parameterization of rotation:
Reb
= Rz
( )Ry
(✓)Rx
(�)
yaw pitch roll
Ry(✓) =
2
4c✓ 0 s✓0 1 0
�s✓ 0 c✓
3
5Rx
(�) =
2
41 0 00 c� �s�0 s� c�
3
5 Rz( ) =
2
4c �s 0s c 00 0 1
3
5
e1
e2
e3b2
b3
re
Reb
pb
b1
![Page 7: Quadrotor Modeling and Control - Carnegie Mellon …€¦ · · 2014-12-01Quadrotor Modeling and Control 16-311 Introduction to Robotics Guest Lecture on Aerial Robotics February](https://reader034.fdocuments.net/reader034/viewer/2022051601/5ad989187f8b9add658b73e1/html5/thumbnails/7.jpg)
Quadrotor ModelNewton-Euler equations:
F⌧
�=
m13 03
03 I3
� a↵
�+
! ⇥mv! ⇥ I3!
�
f =4X
i=1
fi
Total force:
along b3
Fb =
2
400f
3
5
COM
f1
f2f3
f4 b2
b3
b1
f1
f2f3
f4b2
b3
b1
Fe = RebFb �mg
Body:
Inertial: gravity
f1
f2f3
f4
e1
e2
e3b2
b3
b1re
![Page 8: Quadrotor Modeling and Control - Carnegie Mellon …€¦ · · 2014-12-01Quadrotor Modeling and Control 16-311 Introduction to Robotics Guest Lecture on Aerial Robotics February](https://reader034.fdocuments.net/reader034/viewer/2022051601/5ad989187f8b9add658b73e1/html5/thumbnails/8.jpg)
Quadrotor ModelNewton-Euler equations:
F⌧
�=
m13 03
03 I3
� a↵
�+
! ⇥mv! ⇥ I3!
�
Total torque:⌧ = r⇥ FRecall:
f1
f2f3
f4 b2
b3
b1
f1
f2f3
f4b2
b3
b1d
⌧b1 = d (f2 � f4)
⌧b2 = d (f3 � f1)b2
b1
⌧+4⌧+2
⌧�3
⌧�1 ⌧b3 = �⌧1 + ⌧2 � ⌧3 + ⌧4
induced moments
propeller direction of rotation
f1
f2f3
f4
e1
e2
e3b2
b3
b1re
![Page 9: Quadrotor Modeling and Control - Carnegie Mellon …€¦ · · 2014-12-01Quadrotor Modeling and Control 16-311 Introduction to Robotics Guest Lecture on Aerial Robotics February](https://reader034.fdocuments.net/reader034/viewer/2022051601/5ad989187f8b9add658b73e1/html5/thumbnails/9.jpg)
Quadrotor ModelEquations of motion:
⌧b1 = d (f2 � f4)
⌧b2 = d (f3 � f1)
⌧b3 = �⌧1 + ⌧2 � ⌧3 + ⌧4
Fe = RebFb �mg
m13 03
03 I3
� a↵
�+
! ⇥mv! ⇥ I3!
�=
Fe
⌧
�=
RebFb �mg
[⌧b1 , ⌧b2 , ⌧b3 ]T
�
Fb =
2
400f
3
5
Motor model:⌧i = ±cQ!̄
2i
fi = cT!̄2i Approximate relationship between propeller
speeds and generated thrusts and moments
2
664
f⌧b1
⌧b2
⌧b3
3
775 =
2
664
cT cT cT cT0 dcT 0 �dcT
�dcT 0 dcT 0�cQ cQ �cQ cQ
3
775
2
664
w̄21
w̄22
w̄23
w̄24
3
775b2
b1
⌧+4⌧+2
⌧�3
⌧�1
![Page 10: Quadrotor Modeling and Control - Carnegie Mellon …€¦ · · 2014-12-01Quadrotor Modeling and Control 16-311 Introduction to Robotics Guest Lecture on Aerial Robotics February](https://reader034.fdocuments.net/reader034/viewer/2022051601/5ad989187f8b9add658b73e1/html5/thumbnails/10.jpg)
Lecture Outline
• Modeling:
• Dynamic model from first principles
• Propeller model and force and moments generation
• Control
• Attitude control (inner loop)
• Position control (outer loop)
• Current research challenges
![Page 11: Quadrotor Modeling and Control - Carnegie Mellon …€¦ · · 2014-12-01Quadrotor Modeling and Control 16-311 Introduction to Robotics Guest Lecture on Aerial Robotics February](https://reader034.fdocuments.net/reader034/viewer/2022051601/5ad989187f8b9add658b73e1/html5/thumbnails/11.jpg)
Control System Diagram
R. Mahony, V. Kumar, and P. Corke. Multirotor aerial vehicles: Modeling, estimation, and control of quadrotor. IEEE Robot. Autom. Mag., 19(3):20–32, Sept. 2012.
Recent tutorial on quadrotor control:
TrajectoryPlanner
Position Controller
Motor Controller
Attitude Controller
Dynamic Model
Attitude Planner d
pd
Rd
u1 = fd
u2 =⇥⌧db1
, ⌧db2, ⌧db3
⇤T
!̄i
![Page 12: Quadrotor Modeling and Control - Carnegie Mellon …€¦ · · 2014-12-01Quadrotor Modeling and Control 16-311 Introduction to Robotics Guest Lecture on Aerial Robotics February](https://reader034.fdocuments.net/reader034/viewer/2022051601/5ad989187f8b9add658b73e1/html5/thumbnails/12.jpg)
Inner Loop
Attitude Control
PD control law:
u2 = �kReR � k!e!
nonlinear e! = ! � !d
Rotation error metric:
eR =1
2
⇣�Rd
�TR�RTRd
⌘_
![Page 13: Quadrotor Modeling and Control - Carnegie Mellon …€¦ · · 2014-12-01Quadrotor Modeling and Control 16-311 Introduction to Robotics Guest Lecture on Aerial Robotics February](https://reader034.fdocuments.net/reader034/viewer/2022051601/5ad989187f8b9add658b73e1/html5/thumbnails/13.jpg)
Inner Loop
Attitude Control
Linearize the nonlinear model about hover:
R0 = R (�0 = 0, ✓0 = 0, 0)
Rotation error metric:
after linearization
eR =1
2
⇣�Rd
�TR0 �RT
0 Rd⌘_
u
2
40 � ��✓
�� 0 ����✓ ��� 0
3
5_
= [��, �✓, � ]T
Rd = Rz
( 0 +� )Ryx
(��,�✓)
![Page 14: Quadrotor Modeling and Control - Carnegie Mellon …€¦ · · 2014-12-01Quadrotor Modeling and Control 16-311 Introduction to Robotics Guest Lecture on Aerial Robotics February](https://reader034.fdocuments.net/reader034/viewer/2022051601/5ad989187f8b9add658b73e1/html5/thumbnails/14.jpg)
Inner Loop
Attitude Control
PD control law:
u2 = �kReR � k!e!
e! = ! � !d
eR = [��, �✓, � ]T
TrajectoryPlanner
Position Controller
Motor Controller
Attitude Controller
Dynamic Model
Attitude Planner d
pd
Rd
u1 = fd
u2 =⇥⌧db1
, ⌧db2, ⌧db3
⇤T
!̄i
![Page 15: Quadrotor Modeling and Control - Carnegie Mellon …€¦ · · 2014-12-01Quadrotor Modeling and Control 16-311 Introduction to Robotics Guest Lecture on Aerial Robotics February](https://reader034.fdocuments.net/reader034/viewer/2022051601/5ad989187f8b9add658b73e1/html5/thumbnails/15.jpg)
Outer Loop
Position Control
PD control law:
ea + kdev + kpep = 0
Linearize the nonlinear model about hover:
Nominal input: u1 = mg
TrajectoryPlanner
Position Controller
Motor Controller
Attitude Controller
Dynamic Model
Attitude Planner d
pd
Rd
u1 = fd
u2 =⇥⌧db1
, ⌧db2, ⌧db3
⇤T
!̄i
u2 = 03⇥1
![Page 16: Quadrotor Modeling and Control - Carnegie Mellon …€¦ · · 2014-12-01Quadrotor Modeling and Control 16-311 Introduction to Robotics Guest Lecture on Aerial Robotics February](https://reader034.fdocuments.net/reader034/viewer/2022051601/5ad989187f8b9add658b73e1/html5/thumbnails/16.jpg)
Outer Loop
Position Control
PD control law:
TrajectoryPlanner
Position Controller
Motor Controller
Attitude Controller
Dynamic Model
Attitude Planner d
pd
Rd
u1 = fd
u2 =⇥⌧db1
, ⌧db2, ⌧db3
⇤T
!̄i
u1 = mbT3
�g + ad +Kdev +Kpep
�
How do we pick the gains?ev = v � vd
ep = p� pd
![Page 17: Quadrotor Modeling and Control - Carnegie Mellon …€¦ · · 2014-12-01Quadrotor Modeling and Control 16-311 Introduction to Robotics Guest Lecture on Aerial Robotics February](https://reader034.fdocuments.net/reader034/viewer/2022051601/5ad989187f8b9add658b73e1/html5/thumbnails/17.jpg)
Lecture Outline
• Modeling:
• Dynamic model from first principles
• Propeller model and force and moments generation
• Control
• Attitude control (inner loop)
• Position control (outer loop)
• Current research challenges
![Page 18: Quadrotor Modeling and Control - Carnegie Mellon …€¦ · · 2014-12-01Quadrotor Modeling and Control 16-311 Introduction to Robotics Guest Lecture on Aerial Robotics February](https://reader034.fdocuments.net/reader034/viewer/2022051601/5ad989187f8b9add658b73e1/html5/thumbnails/18.jpg)
Current Research ChallengesHow should we coordinate multiple robots given network and vehicle limitations?
![Page 19: Quadrotor Modeling and Control - Carnegie Mellon …€¦ · · 2014-12-01Quadrotor Modeling and Control 16-311 Introduction to Robotics Guest Lecture on Aerial Robotics February](https://reader034.fdocuments.net/reader034/viewer/2022051601/5ad989187f8b9add658b73e1/html5/thumbnails/19.jpg)
Current Research ChallengesHow do we estimate the vehicle state and localize in an unknown environment using only onboard sensing?
CameraGPS
Laser
IMU
Barometer
Cameras
IMU
![Page 20: Quadrotor Modeling and Control - Carnegie Mellon …€¦ · · 2014-12-01Quadrotor Modeling and Control 16-311 Introduction to Robotics Guest Lecture on Aerial Robotics February](https://reader034.fdocuments.net/reader034/viewer/2022051601/5ad989187f8b9add658b73e1/html5/thumbnails/20.jpg)
Current Research ChallengesHow do we estimate the vehicle state and localize in an unknown environment using only onboard sensing?
![Page 21: Quadrotor Modeling and Control - Carnegie Mellon …€¦ · · 2014-12-01Quadrotor Modeling and Control 16-311 Introduction to Robotics Guest Lecture on Aerial Robotics February](https://reader034.fdocuments.net/reader034/viewer/2022051601/5ad989187f8b9add658b73e1/html5/thumbnails/21.jpg)
Lecture Summary
• Modeling:
• Dynamic model from first principles
• Propeller model and force and moments generation
• Control
• Attitude control (inner loop)
• Position control (outer loop)
• Current research challenges
e2e1
e3
1. Vehicle model2. Attitude and position control3. Trajectory generation