Control of Quadrotor with Zero-Dynamics Stabilization

Abhijit Das

1

History of Quadrotor Control• Hauser, Sastry and Meyer, “Nonlinear Control Design for Slightly Non-minimum

Phase Systems” 1992• T. J. Koo, F. Hoffmann, H. Shim, and S. Sastry, “Control Design and Implementation

of Autonomus Helicopter” 1998• R. Mahony, T. Hamel and A. Dzul “Hover Control via Approximate Lyapunov Control

for a Model Helicopter” 1999• R. Olfati-Saber, "Nonlinear Control of Underactuated Mechanical Systems with

Application to Robotics and Aerospace Vehicles," 2001• S. Bouabdallah, A. Noth and R. Siegwart, "PID vs LQ control techniques applied to

an weight augmentation high energy consumption indoor micro quadrotor" 2004• P. Castillo, R. Lozano and A. Dzul, "Stabilization of a Mini Rotorcraft Having Four

Rotors,“ 2005

Dynamic Model

l

1f

1M

2M

2f

3M

3f

4M

4f

x

z

y

Y

X

Z

I

B

State Space Model

0 sin1

0 cos sin

cos cos

x

y um

z g

( , , ) ( , , )f g

sin 0

cos sin 0

cos cos

,

m u A

mg

J C A

1

2

3

4

1 1 1 1

0 0

0 0

fM

u f

fl lMf

fl l

fc c c c

3

3

4

1

( , , )

( , , )

T

T

ii

x y z R

R

u f

LagrangianState space

( , , )

y z p

x x

pz x

y y

x y

z

I I J

I I

JI If

I I

I I

I

0 0

( , , ) 0 0

0 0

x

y

z

l

I

lg

I

l

I

, ,T

2 4 1 3 1 2 3 4u f f f f

Challenges and their probable solution

• Underactuation• Nonlinearity• Coupling

• Backstepping• Dynamic Inversion• Sliding Mode Control

Problems

Solutions

Dynamic Inversion

Sliding Mode Control

Backstepping

Simulations: Position Response

Attitude Response

Control Input

With Input Disturbance: Pos. Response

With Input Dist.: Att. Response

With input Dist.: Control Input

References

1. A. Das, S. Subbarao and F. Lewis, "Dynamic Inversion with Zero-Dynamics Stabilization for Quadrotor Control", IET Control Theory & Applications, 2009, vol. 3, Iss. 3, pp. 303-314.

2. A. Das, F. Lewis and S. Subbarao, "Backstepping Approach for Controlling a Quadrotor using Neural Network", Special Issue of Journal of Intellegent and Robotics Systems, vol 56, Issue 1, pp 127, Springer, April 2009.

3. A. Das, F. Lewis, Kamesh Subbarao, Sliding Mode Approach to Control Quadrotor Using Dynamic Inversion, to appear as book chapter in Robust Control, INTECH, 2011.