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Design and Hardware Implementation of Autopilot Control Laws for MAV Using Super Twisting Control

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Abstract

In this paper we present the design and implementation of autopilot tracking control law for Micro Aerial Vehicle using the second order sliding mode approach. The inner loop attitude tracking control design is carried out using output feedback based second order sliding mode technique, to ensure finite time convergence of the tracking error dynamics. While addressing tracking control of a time varying reference signal, it is important to investigate the stability characteristics of the internal dynamics to ensure perfect tracking. This paper mainly addresses the output tracking control problem for a MAV and investigate the stability characteristics of the longitudinal zero dynamics during tracking. We have proposed a stability proof based on Lyapunov theory to analyze the stability of the MAV longitudinal zero dynamics during tracking. A nonlinear aircraft model obtained using aerodynamic derivatives of The Blackkite 300 mm wingspan fixed MAV is used for both control design and as well as to verify its performance against the classical control methods. Extensive hardware in-loop simulation results of the proposed control algorithm implemented on the commercially available PX4 based Pixhawk autopilot board are also presented here.

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Abbreviations

V :

Airspeed (m/s)

u :

Velocity in body x axis (m/s)

v :

Velocity in body y axis (m/s)

w :

Velocity in body z axis (m/s)

α :

Angle of Attack (rad)

β :

Sideslip angle (rad)

γ :

Flight path angle (rad)

ϕ :

Bank angle (rad)

𝜃 :

Pitch angle (rad)

ψ :

Yaw angle (rad)

p :

Roll rate (rad/s)

q :

Pitch rate (rad/s)

r :

Yaw rate (rad/s)

h :

Altitude (m)

\(\bar {q}\) :

Dynamic Pressure kg/ms 2

δ e :

Elevator deflection (rad)

δ a :

Aileron deflection (rad)

T :

Thrust (N)

X, Y, Z :

Inertial/NED frame coordinates

x, y, z :

Aircraft body axes coordinates

h des :

Desired altitude

𝜃 cmd :

Commanded pitch angle

ψ des :

Desired heading angle

ϕ cmd :

Commanded bank angle

e :

Error Vector

n :

No of states of a system

r :

Relative degree

σ :

Sliding surface

W :

Lyapunov function

C L :

Coefficient of lift

C D :

Coefficient of Drag

C x :

Coefficient of force in the x direction

C y :

Coefficient of force in the y direction

C z :

Coefficient of force in the z direction

C l :

Rolling moment coefficient

C m :

Pitching moment coefficient

C n :

Yawing moment coefficient

C L0 :

C L at zero degree α

C m0 :

C m at zero degree α

C Lmind :

C L at minimum drag

C Dmin :

Minimum drag coefficient

\(C_{L\alpha , \delta _{e}, q}\) :

Change in C L w.r.t to change in α/δ e /q

\(C_{D\delta _{e}, \delta _{a}}\) :

Change in C D w.r.t to change in δ e /δ a

\(C_{m\alpha , \delta _{e}, q}\) :

Change in C m w.r.t to change in α/δ e /q

\(C_{y\beta , p, r, \delta _{a}}\) :

Change in C y w.r.t to change in β/p/r/δ a

\(C_{l\beta , p, r, \delta _{a}}\) :

Change in C l w.r.t to change in β/p/r/δ a

\(C_{n\beta , p, r, \delta _{a}}\) :

Change in C n w.r.t to change in β/p/r/δ a

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Acknowledgements

Authors would like to acknowledge Mr. Swaroop Hangal and Mr. Dileep Krishnan, for their selfless help in setting up of hardware in-loop simulation. This facility was created by funding support from National Programme on Micro Aerial Vehicle (NPMICAV). Authors also acknowledges Dr. Kamali and team FMCD, CSIR-NAL for the help provided in developing the 6DoF simulation model of the Blackkite MAV.

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Authors and Affiliations

  1. Flight Mechanics and Control Division, CSIR-NAL, Old Airport Road, Bangalore, 560017, India

    R. Guruganesh & G. K. Singh

  2. IDP in Systems and Control Engineering, Indian Institute of Technology Bombay, Powai, Mumbai, 400076, India

    B. Bandyopadhyay

  3. Aerospace Engineering Department, Indian Institute of Technology Bombay, Powai, Mumbai, 400076, India

    Hemendra Arya

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  1. R. Guruganesh
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  3. Hemendra Arya
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Correspondence to R. Guruganesh.

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Guruganesh, R., Bandyopadhyay, B., Arya, H. et al. Design and Hardware Implementation of Autopilot Control Laws for MAV Using Super Twisting Control. J Intell Robot Syst 90, 455–471 (2018). https://doi.org/10.1007/s10846-017-0668-5

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