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A unified control strategy for autonomous aerial vehicles

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Abstract

Unmanned aerial vehicles (UAVs) have become popular in a wide range of applications, including many military and civilian uses. State-of-the-art control strategies for these vehicles are typically tailored to a specific platform and are often limited to a portion of the vehicle’s flight envelope. This article presents a single physics-based controller capable of aggressive maneuvering for the majority of UAVs. The controller is applicable to UAVs with the ability to apply a force along a body-fixed direction, and a moment about an arbitrary axis, which includes UAVs such as multi-copters, conventional fixed-wing, agile fixed-wing, most flying-wings, most tailsitters, some tilt-rotor/wing platforms, and some flapping-wing vehicles. We describe the implementation of this controller on numerous platforms, and demonstrate autonomous flight in outdoor flight tests for a quadrotor and an agile fixed-wing aircraft. To specifically demonstrate the extreme maneuvering capability of the control logic, we perform a rolling flip with the quadrotor and a rolling Harrier and an aggressive turnaround with the fixed-wing aircraft, all using a single controller.

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Abbreviations

\(\mathbf{A }\) :

Closed-loop position error state transition matrix

\({\mathbf {a}}^{des}\) :

Desired acceleration

\({\mathbf {C}}_{bi}\) :

Direction cosine matrix from \({\mathcal {F}}_i\) to \({\mathcal {F}}_b\)

\({\mathbf {C}}_{ri}\) :

Direction cosine matrix from \({\mathcal {F}}_i\) to \({\mathcal {F}}_r\)

\(c_j\) :

Control surface constant for the jth actuator

\({\hat{\mathbf{d }}}_j\) :

Direction of force for the jth actuator

\({\mathbf {e}}_b\) :

Angular error about the body frame axes

\({\mathbf {f}}^{aero}\) :

Aerodynamic force

\({\mathbf {f}}^{c}\) :

Control force

\(f^c\) :

Magnitude of control force (\(\left\Vert {\mathbf {f}}^{c}\right\Vert \))

\({\mathbf {f}}^{nc}\) :

Non-control force

\({\hat{\mathbf{f }}}\) :

Direction of control force (\(\frac{{\mathbf {f}}^{c}}{f^c}\))

\({\hat{\mathbf{f }}}^{ref}\) :

Direction of control force of the reference aircraft

\({\mathcal {F}}_b\) :

Body frame

\({\mathcal {F}}_i\) :

Inertial frame

\({\mathcal {F}}_r\) :

Reference body frame

\({\mathbf {g}}\) :

Acceleration due to gravity

\(g(u^s_j)\) :

Flapping thrust model

\(\varDelta {\mathbf {h}}\) :

Height error

\({\mathbf {I}}\) :

Moment of inertia with respect to center of mass

\(J_j\) :

Propeller advance ratio for the jth actuator

\(k_t\) :

Propeller thrust coefficient

\(k_q\) :

Propeller torque coefficient

\(\mathbf {K_{a_d}}\) :

Derivative attitude control gain

\(\mathbf {K_{a_p}}\) :

Proportional attitude control gain

\({K_{h_i}}\) :

Integral height control gain

\({K_{h_p}}\) :

Proportional height control gain

\({K_{p_d}}\) :

Derivative position control gain

\({K_{p_p}}\) :

Proportional position control gain

\({K_{v}}\) :

Proportional speed control gain

m :

Mass

\({\mathbf {m}}^{c}\) :

Control moment

\({\mathbf {m}}^{nc}\) :

Non-control moment

\({\mathbf {p}}\) :

Position

\(\mathbf {p}^{ref}\) :

Reference position

\(\varDelta \mathbf {p}\) :

Position error

\(\mathbf {q}\) :

Orientation quaternion

\(\mathbf {q}^{ref}\) :

Reference orientation quaternion

\(\bar{\mathbf {q}}^{ref}\) :

Augmented reference orientation quaternion

\(\mathbf {q}^{x}\) :

Quaternion rotation of \(\theta _x\)

\(\mathbf {q}^{y}\) :

Quaternion rotation of \(\theta _y\)

\(\mathbf {q}^{z}\) :

Quaternion rotation of \(\theta _z\)

\(\varDelta \mathbf {q}\) :

Error quaternion

UAV:

Unmanned Aerial Vehicle

\(\mathbf {r}_j\) :

Position vector from the center of mass to the jth actuator

R :

Propeller radius

t :

Time

\(\mathbf {u}^f_j\) :

Force generated by the jth actuator

\(\mathbf {u}^s\) :

Column matrix of actuator signals

\(u^s_j\) :

Actuator signal for the jth actuator

\(u_j\) :

Normalized actuator signal for the jth actuator

\(\mathbf {u}^\tau _j\) :

Torque generated by the jth actuator

V :

Lyapunov function

\(\mathbf {v}\) :

Velocity

\(\mathbf {v}^{ref}\) :

Reference velocity

\(\varDelta \mathbf {v}\) :

Velocity error

\(v_{s,j}\) :

Slipstream speed over the jth actuator

VTOL:

Vertical Takeoff and Landing Aircraft

x :

x-position in \(\mathcal {F}_i\)

y :

y-position in \(\mathcal {F}_i\)

z :

z-position in \(\mathcal {F}_i\)

\(\mu \) :

Torque cancellation constant

\(\varvec{\omega }\) :

Angular velocity

\(\varvec{\omega }^{ref}\) :

Reference angular velocity

\(\varvec{\theta }\) :

Triad of rotations for position control (\([\theta _x~\theta _y~\theta _z]\))

\(\rho \) :

Air density

\(\phi \) :

Roll

\(\theta \) :

Pitch

\(\psi \) :

Yaw

\(\gamma \) :

Wing tilt angle

\(\Box _b\) :

Resolved in the body frame

\(\Box _i\) :

Resolved in the inertial frame

\(\Box _r\) :

Resolved in the reference body frame

\(\Box _x\) :

The x component of a vector

\(\Box _y\) :

The y component of a vector

\(\Box _z\) :

The z component of a vector

\(\Box _{prev}\) :

Value at the previous time step

\(\Box _0\) :

Scalar part of quaternion

\(\Box _{1:3}\) :

Vector part of quaternion

\(\odot \) :

Hamilton quaternion product

\(\Box ^T\) :

Transpose

\(\Box ^*\) :

Conjugate

\(\dot{\Box }\) :

Time derivative

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Acknowledgements

The authors thank Corey Miles and Walter Jothiraj for assistance during flight testing, and Professor Inna Sharf for the valuable comments and conversations. This work was supported by the Natural Sciences and Engineering Research Council (NSERC) [NSERC Discovery Grant RGPIN-2018-04547], the Fonds de Recherche du Quebec—Nature et technologies (FRQNT) and by a McGill Engineering Doctoral Award (MEDA).

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Correspondence to Eitan Bulka.

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Bulka, E., Nahon, M. A unified control strategy for autonomous aerial vehicles. Auton Robot 45, 859–883 (2021). https://doi.org/10.1007/s10514-021-10015-8

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