If this is to be REF-eligible it needs a full text file attached, this cannot be final published pdf but could be version after review but before publisher formatting applied researcher confirmed item not refabable so happy to process without file 13/5/20

Recent advances in sensor fault diagnosis: a review

Motivated by the challenging formation stabilization problem for mobile robotic teams wherein no distance or relative position measurements are available but each robot can only measure some of relative angles with respect to its neighbors in its local coordinate frame, we develop the notion of “angle rigidity” for a multipoint framework, named “angularity”, consisting of a set of nodes embedded in a Euclidean space, and a set of angle constraints among them. Different from bearings or angles defined in a global frame, the angles we use do not rely on the knowledge of a global frame, and are signed according to the counter-clockwise direction. Here, angle rigidity refers to the property specifying that under proper angle constraints, the angularity can only translate, rotate, or scale as a whole when one or more of its nodes are perturbed locally. We first demonstrate that this angle rigidity property, in sharp comparison to bearing rigidity or other reported rigidity related to angles of frameworks in the literature, is not a global property since an angle rigid angularity may allow flex ambiguity. We then construct necessary and sufficient conditions for infinitesimal angle rigidity by checking the rank of an angularity's rigidity matrix. We develop a combinatorial necessary condition for infinitesimal minimal angle rigidity. Using the developed theories, a formation stabilization algorithm is designed for a robotic team to achieve an angle rigid formation, in which only angle measurements are needed. Simulation examples demonstrate the advantages of the proposed angle-only formation control approach.

Angle Rigidity and Its Usage to Stabilize Multiagent Formations in 2-D

Robust tracking control of bearing-constrained leader–follower formation

This article investigates the localization problem of a network in 2-D and 3-D spaces given the positions of anchor nodes in a global frame and internode relative measurements in local coordinate frames. It is assumed that the local frames of different nodes have different unknown orientations. First, an angle-displacement rigidity theory is developed, which can be used to localize all the free nodes by the known positions of the anchor nodes and local relative measurements (local relative position, distance, local relative bearing, angle, or ratio-of-distance measurements). Then, necessary and sufficient conditions for network localizability are given. Finally, a distributed network localization protocol is proposed, which can globally estimate the locations of all the free nodes of a network if the network is infinitesimally angle-displacement rigid. The proposed method unifies local-relative-position-based, distance-based, local-relative-bearing-based, angle-based, and ratio-of-distance-based distributed network localization approaches. The novelty of this article is that the proposed method can be applied in both generic and nongeneric configurations with an unknown global coordinate frame in both 2-D and 3-D spaces.

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Angle-Displacement Rigidity Theory With Application to Distributed Network Localization

Bearing-ratio-of-distance rigidity theory with application to directly similar formation control

In this paper, new concepts of weak rigidity matrix and infinitesimal weak rigidity for planar frameworks are introduced. The weak rigidity matrix is used to directly check if a framework is infinitesimally weakly rigid while previous work can check a weak rigidity of a framework indirectly. An infinitesimal weak rigidity framework can be uniquely determined up to a translation and a rotation (and a scaling also when the framework does not include any edge) by its inter-neighbor distances and angles. We propose applying the new concepts to a three-agent formation control problem with a gradient control law, and further we finally propose a modified Henneberg construction which is a technique to generate minimally rigid (or weakly rigid) graphs.

Infinitesimal Weak Rigidity and Stability Analysis on Three-Agent Formations

In this paper, we introduce new concepts of weak rigidity matrix and infinitesimal weak rigidity for planar frameworks. The weak rigidity matrix is used to directly check if a framework is infinitesimally weakly rigid while previous work can check a weak rigidity of a framework indirectly. An infinitesimal weak rigidity framework can be uniquely determined up to a translation and a rotation (and a scaling also when the framework does not include any edge) by its inter-neighbor distances and angles. We apply the new concepts to a three-agent formation control problem with a gradient control law, and prove instability of the control system at any incorrect equilibrium point and convergence to a desired target formation. Also, we propose a modified Henneberg construction, which is a technique to generate minimally rigid (or weakly rigid) graphs. Finally, we extend the concept of the weak rigidity in R^2 to the concept in R^3.

Infinitesimal Weak Rigidity, Formation Control of Three Agents, and Extension to 3-dimensional Space.

Generalized weak rigidity: Theory, and local and global convergence of formations

In this paper, we develop a hybrid distance-angle rigidity theory that involves heterogeneous distances (or unsigned angles) and signed constraints for a framework in the 2-D and 3-D space. The new rigidity theory determines a (locally) unique formation shape up to a translation and a rotation by a set of distance and signed constraints, or up to a translation, a rotation and additionally a scaling factor by a set of unsigned angle and signed constraints. Under this new rigidity theory, we have a clue to resolve the flip (or reflection) and flex ambiguity for a target formation with hybrid distance-angle constraints. In particular, we can completely eliminate the ambiguity issues if formations are under a specific construction which is called \myemph{signed Henneberg construction} in this paper. We then apply the rigidity theory to formation shape control and develop a gradient-based control system that guarantees an exponential convergence close to a desired formation by inter-neighbor measurements. Several numerical simulations on formation shape control with hybrid distance-angle constraints are provided to validate the theoretical results.

Hybrid distance-angle rigidity theory with signed constraints and its applications to formation shape control

In this paper, we propose a new concept of a rigidity, i.e. generalized rigidity: a general version over the distance rigidity [1]–[3], bearing rigidity [4]–[6] and weak rigidity [7]–[10]. In contrast with the distance rigidity, bearing rigidity and weak rigidity, the new concept makes use of all of distance, bearing and angle constraints to characterize a unique formation shape. For its application, in the 2- and 3-dimensional spaces, we apply the new concept to formation control problems under a gradient-based control law. Then we analyze the stability of the problems, and consequently provide locally asymptotic stability of desired equilibrium point (desired $n$ -agent formation). Finally, we provide a numerical simulation to show validation on our theories.

Seong-Ho Kwon

Papers

Infinitesimal Weak Rigidity and Stability Analysis on Three-Agent Formations

Infinitesimal Weak Rigidity, Formation Control of Three Agents, and Extension to 3-dimensional Space.

Generalized weak rigidity: Theory, and local and global convergence of formations

Hybrid distance-angle rigidity theory with signed constraints and its applications to formation shape control

Generalized Rigidity and Stability Analysis on Formation Control Systems with Multiple Agents