Multivariable finite‐time output feedback trajectory tracking control of quadrotor helicopters

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Summary This paper investigates finite‐time formation tracking control problem for multiple quadrotors with external disturbance. The states of the virtual leader are not available to all the followers and the network topology is described by a directed graph. The model of each quadrotor is divided into position subsystem and attitude subsystem. Firstly, novel distributed finite‐time state observers are designed to estimate the relative state errors between followers and the virtual leader. Secondly, the values of these observers are used to design controllers that achieve finite‐time robust coordinated tracking in the position subsystem. Thirdly, the terminal sliding mode disturbance observers and finite‐time attitude tracking controllers are proposed, respectively, in the attitude subsystem to estimate the external disturbance and achieve attitude tracking control. The finite‐time stability analysis of the control algorithms is carried out using the Lyapunov theory and the homogeneous technique. Finally, the efficiency of the proposed algorithm is illustrated by numerical simulations.

{\overset{P}{true}}_{i} = V_{i}

{\overset{V}{true}}_{i} = - g e_{3} + \frac{1}{m_{i}} R false({normalΘ}_{i} false) u_{T i} e_{3} + d_{V i}

{\overset{normalΘ}{true}}_{i} = normalΠ false({normalΘ}_{i} false) {normalΩ}_{i}

{\overset{normalΩ}{true}}_{i} = - {J_{i}}^{- 1} {normalΩ}_{i} \times J_{i} {normalΩ}_{i} + {J_{i}}^{- 1} τ_{i} + d_{normalΩ i},

Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Distributed finite‐time formation control for multiple quadrotors via local communications

Dou

Yang

Wang

et al. 2019

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“…The aim in this subsection is to obtain the desired attitude angle commands and total thrust T i . To this end, taking into account the definition of R ( Θ i ) and

{bold-italicT}_{bold-italici}^{bold'}

, the commanded roll angle ϕ r i , pitch angle θ r i , and control input T i are calculated by

\begin{matrix} alignleft \\ align-1 T_{i} & align-2 = m_{i} \sqrt{T_{i 1}^{'}^{2} + T_{i 2}^{'}^{2} + {(T_{i 3}^{'} + g)}^{2}} \\ align-1 ϕ_{r i} & align-2 = \arcsin (\frac{m_{i} (T_{i 1}^{'} s_{ψ_{r e f}} - T_{i 2}^{'} c_{ψ_{r e f}})}{T_{i}}) \\ align-1 θ_{r i} & align-2 = \arctan (\frac{T_{i 1}^{'} c_{ψ_{r e f}} + T_{i 2}^{'} s_{ψ_{r e f}}}{T_{i 3}^{'} + g}), \end{matrix}

where

T_{i k}^{'}, false(k = 1, 2, 3 false)

denotes the k th element of the vector

T_{i}^{'}

.…”

Section: Finite‐time Fault‐tolerant Formation Controller Designmentioning

confidence: 99%

Finite‐time fault‐tolerant formation control for multiquadrotor systems with actuator fault

Zhao

Zong

Tian

et al. 2018

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Summary This paper investigates the distributed tracking control of a group of underactuated quadrotors in the presence of actuator faults in three‐dimensional space. Using consensus protocol and sliding mode algorithm, a distributed finite‐time fault‐tolerant formation control scheme is developed. The whole closed‐loop system is composed by position loop, attitude loop, and propeller speed loop. A propeller speed fault‐tolerant controller is developed to deal with the unexpected faults of quadrotors. The finite‐time stability of the closed‐loop system is guaranteed through Lyapunov analysis. Finally, the efficiency of the proposed algorithm is illustrated by some numerical simulations.

“…Many practical systems have been modeled as multiple‐input multiple‐output (MIMO) systems and not necessarily in the standard strict feedback form. Such systems include an important class of dynamic systems, for example, multilink robots and quadrotors . In literature, different procedures have been developed for solving the regulation or tracking problems in MIMO nonlinear systems .…”

Section: Introductionmentioning

confidence: 99%

Sustained oscillations in MIMO nonlinear systems through limit cycle shaping

Hakimi

Binazadeh

2019

Summary This paper studies on generating periodic behaviors through shaping stable limit cycles in multiple‐input‐multiple‐output nonlinear systems. For this purpose, first, limit cycles are shaped with respect to the desired sustained oscillations of the system's outputs. Then, the Lyapunov analyses, which are appropriate for stability analysis of invariant sets, are employed to design the control law and conclude the asymptotic convergence toward the predefined limit cycles. The problem is studied in two cases. In the first case, some assumptions in the mathematical model are assumed that leads to simplification in the design procedure. In the second case, the design procedure is discussed in more general cases. Finally, the validity and performance of the proposed method for shaping limit cycles with different geometric shapes are illustrated by computer simulations for practical and numerical examples.