Observer-based hybrid control for global attitude tracking on<i>SO</i>(3) with input quantisation

Hashemi, Seyed Hamed; Pariz, Naser; Sani, Seyed Kamal Hosseini

doi:10.1080/00207179.2022.2043564

Cited by 5 publications

(3 citation statements)

References 39 publications

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“…The proposed hybrid feedback law is developed in this section. In the past decade, hybrid controllers have frequently been used for stabilizing systems evolving in matrix Lie groups [22] since it was proven that continuous and discontinuous feedback laws cannot globally stabilize these systems in the desired set [23]. This is due to the non-contractibility of the configuration space of the attitude and existence of sets that have Lebesgue measure zero [24].…”

Section: Proposed Hybrid Feedback Lawmentioning

confidence: 99%

Task Space Control of Robot Manipulators based on Visual SLAM

Hashemi¹,

Mattila²

2023

Preprint

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This paper aims to address the open problem of designing a globally stable vision-based controller for robot manipulators. Accordingly, based on a hybrid mechanism, this paper proposes a novel task-space control law attained by taking the gradient of a potential function in SE(3). The key idea is to employ the Visual Simultaneous Localization and Mapping (VSLAM) algorithm to estimate a robot pose. The estimated robot pose is then used in the proposed hybrid controller as feedback information. Invoking Barbalat's lemma and Lyapunov's stability theorem, it is guaranteed that the resulting closed-loop system is globally asymptotically stable, which is the main accomplishment of the proposed structure. Simulation studies are conducted on a six degrees of freedom (6-DOF) robot manipulator to demonstrate the effectiveness and validate the performance of the proposed VSLAM-based control scheme.

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Section: Proposed Hybrid Feedback Lawmentioning

confidence: 99%

Task Space Control of Robot Manipulators based on Visual SLAM

Hashemi¹,

Mattila²

2023

Preprint

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“…Hence, there exists a set with Lebesgue measure zero from which the estimation error cannot converge to zero. Hybrid systems have therefore been used to overcome this topological obstruction and to derive observers with global stability on SO(3) [27], SE(3) [28], and SE 2 (3) [29]. For example, two hybrid observers were introduced in [30]; the first observer uses fixed gains, while the second uses variable gains by solving a continuous Riccati equation.…”

Section: B Literature Reviewmentioning

confidence: 99%

Global Asymptotic Convergent Observer for SLAM

Hashemi

Mattila

2022

IEEE Access

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This paper examines the global convergence problem of SLAM algorithms, an issue that faces topological obstructions. This is because the state-space for attitude kinematics is defined on a noncontractible manifold: the special orthogonal group of order three SO(3). Therefore, this paper presents a novel, gradient-based hybrid observer to overcome these topological obstacles. Moreover, the integral action is applied into the proposed observer to estimate unknown constant bias, which results in an increase in bias estimation. Accordingly, a new projection scheme is defined to cope with the integral action. The Lyapunov stability theorem is used to prove the globally asymptotic convergence of the proposed algorithm. Experimental and simulation results are provided to evaluate the performance and to demonstrate the effectiveness and robustness of the proposed scheme.

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“…Hence, there exists a set with Lebesgue measure zero from which the estimation error cannot converge to zero. Hybrid systems have therefore been used to overcome this topological obstruction and to derive observers with global stability on SO(3) [25], SE(3) [26], and SE 2 (3) [27]. For example, two hybrid observers were introduced in [28]; the first observer uses fixed gains, while the second uses variable gains by solving a continuous Riccati equation.…”

Section: Introductionmentioning

confidence: 99%

A Global Asymptotic Convergent Observer for SLAM

Hashemi¹,

Mattila²

2022

Preprint

Self Cite

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This paper examines the global convergence problem of SLAM algorithms, an issue that faces topological obstructions. This is because the state-space of attitude dynamics is defined on a non-contractible manifold: the special orthogonal group of order three SO(3). Therefore, this paper presents a novel, gradient-based hybrid observer to overcome these topological obstacles. The Lyapunov stability theorem is used to prove the globally asymptotic convergence of the proposed algorithm. Finally, comparative analyses of two simulations were conducted to evaluate the performance of the proposed scheme and to demonstrate the superiority of the proposed hybrid observer to a smooth observer.

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Observer-based hybrid control for global attitude tracking onSO(3) with input quantisation

Cited by 5 publications

References 39 publications

Task Space Control of Robot Manipulators based on Visual SLAM

Task Space Control of Robot Manipulators based on Visual SLAM

Global Asymptotic Convergent Observer for SLAM

A Global Asymptotic Convergent Observer for SLAM

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