Formation Control of Rigid Graphs with a Flex Node Addition

This paper examines stability properties of distance-based formation control when the underlying topology consists of a rigid graph and a flex node addition. It is shown that the desired equilibrium set is locally asymptotically stable but there exist undesired equilibria. Specifically, we further consider two cases where the rigid graph is a triangle in 2-D and a tetrahedral in 3-D, and prove that any undesired equilibrium point in these cases is unstable. Thus in these cases, the desired formations are almost globally asymptotically stable.Comment: The full version of this paper with general extensions has been submitted to a journal for publicatio

Distributed stabilization control of rigid formations with prescribed orientation

Most rigid formation controllers reported in the literature aim to only stabilize a rigid formation shape, while the formation orientation is not controlled. This paper studies the problem of controlling rigid formations with prescribed orientations in both 2-D and 3-D spaces. The proposed controllers involve the commonly-used gradient descent control for shape stabilization, and an additional term to control the directions of certain relative position vectors associated with certain chosen agents. In this control framework, we show the minimal number of agents which should have knowledge of a global coordinate system (2 agents for a 2-D rigid formation and 3 agents for a 3-D rigid formation), while all other agents do not require any global coordinate knowledge or any coordinate frame alignment to implement the proposed control. The exponential convergence to the desired rigid shape and formation orientation is also proved. Typical simulation examples are shown to support the analysis and performance of the proposed formation controllers.Comment: This paper was submitted to Automatica for publication. Compared to the submitted version, this arXiv version contains complete proofs, examples and remarks (some of them are removed in the submitted version due to space limit.

Rigid formation control of double-integrator systems

In this paper, we study rigid formation control systems modelled by double integrators. Two kinds of double-integrator formation systems are considered, namely formation stabilisation systems and flocking control systems. Novel observations on the measurement requirement, the null space and eigenvalues of the system Jacobian matrix will be provided, which reveal important properties of system dynamics and the associated convergence results.We also establish some new links between single-integrator formation systems and double-integrator formation systems via a parameterised Hamiltonian system, which, in addition, provide novel stability criteria for different equilibria in double-integrator formation systems by using available results in single-integrator formation systems.This work is supported by NICTA, which is funded by the Australian Government as represented by the Department of Broadband, Communications and the Digital Economy and the Australian Research Council through the ICT Centre of Excellence program. It is also partially supported by National Natural Science Foundation of China [grant number 61501282]. B. D. O. Anderson was supported by the ARC [grant number DP130103610]. H.-S. Ahn is supported by the National Research Foundation of Korea [grant number NRF- 2013R1A2A2A01067449]. Z. Sun is supported by the Prime Minister’s Australia Asia Incoming Endeavour Postgraduate Award from Australian Government

A Study of Additives for Aquagel/Bentonite Based Drilling Fluids in Relation to Filtration and Rheological Properties, Smectite Inhibition and Their Application to Marcellus Shale

Since the dawn of rotary drilling, engineers and scholars have persevered, through study and research, to formulate an optimum inhibitive drilling fluid for the shale formations. Although fluids with acceptable performance in shale have been formulated, one only needs to examine the word acceptable in the context above to realize that the industry has ongoing activities to formulate an optimum inhibitive fluid for the Marcellus Shale. In accordance, this research seeks to fabricate a means of reducing formation damage (permeability reduction), stuck pipe incidences, heaving, sloughing and caving which are all due to the swelling of Smectite clay and shale. The ultimate achievement in reducing formation damage would consequently lead to an augmentation in oil and natural gas production from the Marcellus Shale.;This research paper, in its infinite practicality, illustrates the problems associated with swelling and dispersion of shale. The chemistry behind the swelling/dispersion of shale validates this research with respect to inhibition/swelling. Also, presented are the experimental procedures performed in the formulation of an optimum inhibitive drilling fluid such as rheological, filtration and linear swelling experiments.;Most importantly, this paper introduces a novel approach and experiment towards the development of an optimum inhibitive drilling fluid. The study utilizes a novel chemical in the industry: alpha--o Diamino Alkanes (Diamino Butane and Diamino Hexane) as well as comparing the inhibitive capability of two familiar chemicals in conjunction with Chlorides and Hydroxides of Alkali metals, Alkaline earth metals and Transition metals (K+, Na+, Zn+, Ca2+, Mg2+, Li+ etc) in various concentrations.;The rheological, shale inhibition and filtration effects of the aforementioned Hydroxide and Chloride chemicals were tested and examined which led to the subsequent elimination and selection of certain fluids which this research has recommended for testing in Marcellus Shale in West Virginia and similar shale formations throughout the globe. Universally acceptable filtrate loss correlations have been formulated, during the course of this research, for various base drilling fluids.;API standard procedures were utilized in the evaluation of rheological and filtration properties of base drilling fluids and the results obtained from the rheological and filtration experiments are independent of shale formation characteristics. However, the inhibition/Swelling test was limited to the Marcellus Shale formation in the State of West Virginia and the results obtained for inhibition/swelling may not be universally acceptable in the evaluation of other shale formations

Generalized controllers for rigid formation stabilization with application to event-based controller design

This paper discusses generalized controllers for rigid formation shape stabilization. We provide unified analysis to show convergence using different controllers reported in the literature, and further prove an exponential stability of the formation system when using the general form of shape controllers. We also show that different agents can use different controllers for controlling different distances to achieve a desired rigid formation, which enables the implementation of heterogeneous agents in practice for formation shape control. We further propose an event-triggered rigid formation control scheme based on the generalized controllers. The triggering condition, event function and convergence analysis are discusse

Distributed multi-UAV shield formation based on virtual surface constraints

This paper proposes a method for the deployment of a multi-agent system of unmanned aerial vehicles (UAVs) as a shield with potential applications in the protection of infrastructures. For this purpose, a distributed control law based on the gradient of a potential function is proposed to acquire the desired shield shape, which is modeled as a quadric surface in the 3D space. The graph of the formation is a Delaunay triangulation, which guarantees the formation to be rigid. An algorithm is proposed to design the formation (target distances between agents and interconnections) to distribute the agents over the virtual surface, where the input parameters are just the parametrization of the quadric and the number of agents of the system. Proofs of system stability with the proposed control law are provided, as well as a new method to guarantee that the resulting triangulation over the surface is Delaunay, which can be executed locally. Simulation and experimental results illustrate the effectiveness of the proposed approach

Distance-based Control of Kn Formations in General Space with Almost Global Convergence

In this paper, we propose a distance-based formation control strategy for a group of mobile agents to achieve almost global convergence to a target formation shape provided that the formation is represented by a complete graph, and each agent is governed by a single-integrator model. The undamental idea of achieving almost global convergence is to use a virtual formation of which the dimension is augmented with some virtual coordinates. We define a cost function associated with the virtual formation and apply the gradient-descent algorithm to the cost function so that the function has a global minimum at the target formation shape. We show that all agents finally achieve the target formation shape for almost all initial conditions under the proposed control law.This work was supported in part by the Australian Research Council under Grants DP130103610 and DP160104500, and in part by the National Research Foundation of Korea under Grant NRF-2017R1A2B3007034. The work of Z. Sun was supported by the Prime Minister’s Australia Asia Incoming Endeavour Postgraduate Award