The Specified Finite-Time Distributed Observers-Based Velocity-Free Attitude Synchronization for Rigid Bodies on SO(3)

Peng, Xiuhui; Zhang, Geng; Sun, Jing

doi:10.1109/tsmc.2018.2831778

Cited by 37 publications

(32 citation statements)

References 34 publications

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“…Compared with the existing finite‐time attitude synchronization laws, our finite‐time control law is designed on the rotation matrices SO (3) without singularity and ambiguity. Thirdly, the finite‐time–based specified‐time control law for rigid bodies dynamics is proposed in this paper, which is different from our previous paper focusing on the specified‐time observer for rigid body kinematics . The convergence rate shows that the finite‐time–based specified‐time control law has better performance than the specified‐time control law that comes from the asymptotical control law.…”

Section: Introductionmentioning

confidence: 76%

A specified‐time control framework for control‐affine systems and rigid bodies: A time‐rescaling approach

Peng

Sun

Zhang

2019

Intl J Robust & Nonlinear

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Summary This paper addresses the specified‐time control problem for control‐affine systems and rigid bodies, wherein the specified‐time duration can be designed in advance according to the task requirements. By using the time‐rescaling approach, a novel framework to solve the specified‐time control problem is proposed, and the original systems are converted to the transformation systems based on which the specified‐time control laws for both control‐affine systems and rigid bodies are studied. Compared with the existing approaches, our proposed specified‐time control laws can be derived from the known stabilization control laws. To our best knowledge, it is the first time that transformation system–based specified‐time control framework for control‐affine system and rigid body dynamics is proposed. To further improve the convergence performance of specified‐time control, a finite‐time attitude synchronization control law for rigid bodies on rotation matrices is proposed, and thereby, the finite‐time–based specified‐time control law is designed eventually. In the end, numerical simulations and SimMechanics experiments are provided to illustrate effectiveness of the theoretical results.

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Section: Introductionmentioning

confidence: 76%

A specified‐time control framework for control‐affine systems and rigid bodies: A time‐rescaling approach

Peng

Sun

Zhang

2019

Intl J Robust & Nonlinear

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“…Therefore, many existing attitude control laws for single rigid body on SO (3) can be used directly to design the attitude consensus control law, and this is an advantage over the existing literatures whose distributed attitude observers are defined on

{double-struckR}^{4}

. Different from our previous paper, which focuses on the specified‐time distributed observer under a directed acyclic graph, this paper mainly solves the distributed observer with asymptotic convergence on SO (3) under the undirected graph among followers. Specifically, under the different sensor graphs, a distributed observer with different structures is designed in this paper, with the result that the corresponding proofs are also different from that in our previous paper .…”

Section: Distributed Observer Design On So(3)mentioning

confidence: 99%

“…Different from our previous paper, which focuses on the specified‐time distributed observer under a directed acyclic graph, this paper mainly solves the distributed observer with asymptotic convergence on SO (3) under the undirected graph among followers. Specifically, under the different sensor graphs, a distributed observer with different structures is designed in this paper, with the result that the corresponding proofs are also different from that in our previous paper . In the future, designing the finite time (global, almost global) distributed observer or the distributed observer with general communication topology graphs that can also guarantee that the estimated attitude always evolves on SO (3) is a challenging topic.…”

Section: Distributed Observer Design On So(3)mentioning

confidence: 99%

“…Thus, there exists a positive constant m 1 >0 satisfying

false‖ {false({\overset{E}{true}}_{i} - {\overset{E}{true}}_{i}^{T} false)}^{\lor} + μ_{i} {false‖}_{2} \leq m_{1}

such that

{\overset{W}{true}}_{1} \leq m_{1} \sum_{i = 1}^{n} false‖ {\overset{ω}{true}}_{0 i} {false‖}_{2} \leq m_{2} \sqrt{W_{1}}

, where m 2 >0 is a constant. Invoking the comparison principle, one has that the state

{\overset{ω}{true}}_{0 i}

is bounded by some polynomial function of t . To proceed, the time derivative of W is given as

\overset{W}{true} = true \sum_{i = 1}^{n} {\overset{ω}{true}}_{0 i}^{T} J_{i} {\overset{\overset{ω}{true}}{true}}_{0 i} + k_{5} true \sum_{i = 1}^{n} tr ((), - {\overset{E}{true}}_{i} {\overset{\overset{ω}{true}}{true}}_{0 i}) = true \sum_{i = 1}^{n} ((), - k_{4} false‖ {\overset{ω}{true}}_{0 i} {false‖}_{2}^{2} + {\overset{ω}{true}}_{0 i}^{T} μ_{i}) .

Since

{\overset{ω}{true}}_{0 i}

and μ i are bounded, one can conclude that

\int_{0}

…”

Section: Consensus Control Law Developmentmentioning

confidence: 99%

“…For the constructed physical rigid body, the moment of inertia matrix and mass matrix depends on the size of rigid body and its density . Let

L = {false(L_{1}, L_{2}, L_{3} false)}^{T} \in {double-struckR}^{3}

denote the length of the first, second, third principal axes.…”

Section: Simmechanics Experimentsmentioning

confidence: 99%

See 2 more Smart Citations

Distributed observer‐based leader‐follower attitude consensus control for multiple rigid bodies using rotation matrices

Peng

Zhang

2019

Intl J Robust & Nonlinear

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Summary This paper addresses the distributed observer‐based leader‐follower attitude consensus control problem for multiple rigid bodies. An intrinsic distributed observer is proposed for each follower to estimate the leader's trajectory, which is only available to a subset of followers. The proposed observer can guarantee that the estimated attitude evolves on rotation matrices all the time, and it provides us with a simple way to design the attitude consensus control law. The dynamics of rigid bodies and distributed observer are both modeled directly on rotation matrices, so that the singularity and ambiguity can be avoided. Furthermore, adopting the idea of disturbance observer on vector space, a gyro bias observer on the rotation matrices is proposed. Based on the distributed observer, three types of attitude consensus control law are proposed, which are respectively on the basis of full‐state, biased angular velocity, and external disturbance combined with biased angular velocity. Finally, the SimMechanics experiments are provided to illustrate effectiveness of the proposed theoretical results.

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Finite‐time leader–follower consensus control of multiagent systems with mismatched disturbances

Zhao

Sun

et al. 2021

Asian Journal of Control

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We study the robust finite‐time leader–follower output consensus problems for second‐order multiagent systems (MASs) with mismatched disturbances. For mismatched disturbance, the mismatched disturbance observer is used for each follower to estimate the mismatched disturbance in finite time. Then a backstepping control protocol is constructed via Lyapunov finite‐time stability theorem, and we can prove that the output consensus tracking with strong robustness can be reached for the considered MAS in finite time if the communication topology includes a directed spanning tree, where the leader is the root. Finally, we use two simulation examples to illustrate the correctness of the theoretical results.

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The Specified Finite-Time Distributed Observers-Based Velocity-Free Attitude Synchronization for Rigid Bodies on SO(3)

Cited by 37 publications

References 34 publications

A specified‐time control framework for control‐affine systems and rigid bodies: A time‐rescaling approach

A specified‐time control framework for control‐affine systems and rigid bodies: A time‐rescaling approach

Distributed observer‐based leader‐follower attitude consensus control for multiple rigid bodies using rotation matrices

Finite‐time leader–follower consensus control of multiagent systems with mismatched disturbances

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