Inner–Outer Loop Control for Quadrotor UAVs With Input and State Constraints

Cao, Ning; Lynch, Alan F.

doi:10.1109/tcst.2015.2505642

Cited by 170 publications

(78 citation statements)

References 35 publications

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“…The rotation matrix from

scriptI

scriptB

is denoted by R and parameterized by the so‐called roll‐pitch‐yaw or ZYX Euler angles η =[ ϕ , θ , ψ ] T as

R (η) = [\begin{array}{ccc} c_{ψ} c_{θ} & - s_{ψ} c_{ϕ} + c_{ψ} s_{θ} s_{ϕ} & s_{ϕ} s_{ψ} + c_{ϕ} s_{θ} c_{ψ} \\ s_{ψ} c_{θ} & c_{ψ} c_{ϕ} + s_{ψ} s_{θ} s_{ψ} & - s_{ϕ} c_{ψ} + c_{ϕ} s_{θ} s_{ψ} \\ - s_{θ} & c_{θ} s_{ϕ} & c_{θ} c_{ϕ} \end{array}] .

The control objective is to regulate the vehicle to a desired (constant) position from any initial position, ie, to achieve zero position error

δ_{p}^{i} = p^{i} - p_{d}^{i} = 0

, where p i and

p_{d}^{i}

are the vehicle's current position and desired constant position, respectively, expressed in

scriptI

. As in section 4.4 in the work of Godbolt and the work of Cao and Lynch, we define

δ_{p}^{b} = R^{T} δ_{p}^{}

…”

Section: Nested Saturation Control Of Quadrotor Uavsmentioning

confidence: 99%

“…Therefore, the control objective is equivalent to making

δ_{p}^{b} = 0

, which is to enable p b to track

p_{d}^{b}

. As in the work of Cao and Lynch, the dynamics expressed in

scriptB

{\overset{δ}{true}}_{p}^{b} = - {false[ω^{b} false]}_{\times} δ_{p}^{b} + v^{b}

{\overset{v}{true}}^{b} = - {false[ω^{b} false]}_{\times} v^{b} + g R^{T} E_{3} - \frac{T}{m} e_{3} + d

\overset{R}{true} = R {false[ω^{b} false]}_{\times}

J {\overset{ω}{true}}^{b} = - {false[ω^{b} false]}_{\times} J ω^{b} + τ^{b},

where v b , ω b , and τ b , are the position, translational velocity, angular velocity, and applied torque, expressed in

scriptB

, respectively; d is the external disturbance; T is the sum of all thrusts generated by the propellers; g is the gravity constant; and m and J are the mass and moment of inertia tensor, respectively. The [·] × operator:

{double-struckR}^{3} \to {double-struckR}^{3 \times 3}

is defined as [ x ] × y = x × y .…”

Section: Nested Saturation Control Of Quadrotor Uavsmentioning

confidence: 99%

“…As compared to the work of Cao and Lynch, the boundary gap between neighboring saturation functions is narrowed in this paper, which increases its capability to handle external disturbances. In addition, the effect of bounded disturbance is explicitly considered in this article as compared to existing works, where disturbances are not considered, or only constant disturbances are handled. The second control scheme is motivated by the work of Shreekant et al, which shows that, for multiple scalar integrators, nested saturation without state transformation (as in the work of Teel) is less conservative in terms of the magnitude of the lumped disturbance (due to system uncertainties and external disturbances) that can be handled.…”

Section: Introductionmentioning

confidence: 97%

“…The control law contains the angular velocity term, which is the time derivative of the control input for the outer translational loop. In the work of Cao and Lynch, another 3D vector saturation function, the components of which are modified scalar saturation functions from the work of Teel, is used to develop a nested saturation controller for the outer translation loop of UAVs expressed in the body frame. However, neither the work of Cao and Lynch nor the work of Azinheira and Moutinho explicitly considers external disturbances.…”

Section: Introductionmentioning

confidence: 99%

“…In the work of Cao and Lynch, another 3D vector saturation function, the components of which are modified scalar saturation functions from the work of Teel, is used to develop a nested saturation controller for the outer translation loop of UAVs expressed in the body frame. However, neither the work of Cao and Lynch nor the work of Azinheira and Moutinho explicitly considers external disturbances. In the work of Xie and Lynch, with a backstepping design scheme and a new set of saturation functions, a nested saturation control for visual servoing of UAVs is proposed; however, only a constant disturbance to the vertical motion is considered.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Nested saturation control of multiple vector integrators and its application to motion control of UAVs

Xie

Veitch

2019

Intl J Robust & Nonlinear

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Summary This paper presents two nested input saturation control schemes for a special class of multiple vector integrators with bounded additive disturbances. The considered systems originate from the motion control of rotary‐wing unmanned aerial vehicles (UAVs). The first scheme is based on a feedforward form, which requires state transformation and can be applied to stabilize arbitrary order vector integrator systems. The second scheme is constructed with original state variables using a new approach, applied here to double vector integrator systems. The capability of handling external disturbance using the two schemes is also analyzed. The two schemes are applied to design motion controllers for rotary‐wing UAVs and simulation results are provided to show the performances of two controllers.

show abstract

“…The rotation matrix from

scriptI

scriptB

is denoted by R and parameterized by the so‐called roll‐pitch‐yaw or ZYX Euler angles η =[ ϕ , θ , ψ ] T as

R (η) = [\begin{array}{ccc} c_{ψ} c_{θ} & - s_{ψ} c_{ϕ} + c_{ψ} s_{θ} s_{ϕ} & s_{ϕ} s_{ψ} + c_{ϕ} s_{θ} c_{ψ} \\ s_{ψ} c_{θ} & c_{ψ} c_{ϕ} + s_{ψ} s_{θ} s_{ψ} & - s_{ϕ} c_{ψ} + c_{ϕ} s_{θ} s_{ψ} \\ - s_{θ} & c_{θ} s_{ϕ} & c_{θ} c_{ϕ} \end{array}] .

The control objective is to regulate the vehicle to a desired (constant) position from any initial position, ie, to achieve zero position error

δ_{p}^{i} = p^{i} - p_{d}^{i} = 0

, where p i and

p_{d}^{i}

are the vehicle's current position and desired constant position, respectively, expressed in

scriptI

. As in section 4.4 in the work of Godbolt and the work of Cao and Lynch, we define

δ_{p}^{b} = R^{T} δ_{p}^{}

…”

Section: Nested Saturation Control Of Quadrotor Uavsmentioning

confidence: 99%

“…Therefore, the control objective is equivalent to making

δ_{p}^{b} = 0

, which is to enable p b to track

p_{d}^{b}

. As in the work of Cao and Lynch, the dynamics expressed in

scriptB

{\overset{δ}{true}}_{p}^{b} = - {false[ω^{b} false]}_{\times} δ_{p}^{b} + v^{b}

{\overset{v}{true}}^{b} = - {false[ω^{b} false]}_{\times} v^{b} + g R^{T} E_{3} - \frac{T}{m} e_{3} + d

\overset{R}{true} = R {false[ω^{b} false]}_{\times}

J {\overset{ω}{true}}^{b} = - {false[ω^{b} false]}_{\times} J ω^{b} + τ^{b},

where v b , ω b , and τ b , are the position, translational velocity, angular velocity, and applied torque, expressed in

scriptB

{double-struckR}^{3} \to {double-struckR}^{3 \times 3}

is defined as [ x ] × y = x × y .…”

Section: Nested Saturation Control Of Quadrotor Uavsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Nested saturation control of multiple vector integrators and its application to motion control of UAVs

Xie

Veitch

2019

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

show abstract

Quaternion‐based adaptive control for trajectory tracking of quadrotor unmanned aerial vehicles

Pliego‐Jiménez

2021

Adaptive Control & Signal

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Summary The problem of trajectory tracking of aerial vehicles with four rotors and dynamic parameter uncertainties is addressed in this article. By exploiting the cascade structure of the translational and attitude dynamics of the quadrotor, a nonlinear hierarchical adaptive control is proposed. The attitude control law is designed based on the unit quaternion, therefore, the singularities of the Euler angles and angle‐axis representation are avoided. Instead of relying on the stability properties of time‐varying cascade systems, the stability of the whole closed‐loop system is proven by an appropriate Lyapunov function. In addition, a novel method to compute the desired orientation based on the desired Cartesian trajectories and position control inputs is proposed. A set of simulations results are presented to assess the performance of the proposed adaptive controller.

show abstract

A multilevel sampled‐data approach for resilient navigation and control of autonomous systems

Jafarnejadsani

Wan

Hovakimyan

et al. 2019

Intl J Robust & Nonlinear

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SummaryAutonomous systems are rapidly becoming an integrated part of the modern life. Safe and secure navigation and control of these systems present significant challenges in the presence of uncertainties, physical failures, and cyber attacks. In this paper, we formulate a navigation and control problem for autonomous systems using a multilevel control structure, in which the high‐level reference commands are limited by a saturation function, whereas the low‐level controller tracks the reference by compensating for disturbances and uncertainties. For this purpose, we consider a class of nested, uncertain, multiple‐input–multiple‐output systems subject to reference command saturation, possibly with nonminimum phase zeros. A multirate output‐feedback adaptive controller is developed as the low‐level controller. The sampled‐data (SD) design of this controller facilitates the direct implementation on digital computers, where the input/output signals are available at discrete time instances with different sampling rates. In addition, stealthy zero‐dynamics attacks become detectable by considering a multirate SD formulation. Robust stability and performance of the overall closed‐loop system with command saturation and multirate adaptive control are analyzed. Simulation scenarios for navigation and control of a fixed‐wing drone under failures/attacks are provided to validate the theoretical findings.

show abstract

Inner–Outer Loop Control for Quadrotor UAVs With Input and State Constraints

Cited by 170 publications

References 35 publications

Nested saturation control of multiple vector integrators and its application to motion control of UAVs

Nested saturation control of multiple vector integrators and its application to motion control of UAVs

Quaternion‐based adaptive control for trajectory tracking of quadrotor unmanned aerial vehicles

A multilevel sampled‐data approach for resilient navigation and control of autonomous systems

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