Rigid formation construction from non-rigid components

This paper discusses the construction of rigid formation from arbitrary non-rigid components in two-dimensional space. Specifically, we focus on developing strategies for the construction sequences under the premise of building minimum number of links between the non-rigid components. Three operations, namely spindle splitting, rigid component shrink and edge floating, are proposed. The scenarios of acquiring a rigid formation from different kinds of non-rigid components are discussed respectively. It is proved that our strategy will guarantee the rigidity of the obtained formation with minimum number of inserted links, and will cover all the possible solutions during the construction process

Frequency-limited H∞ model reduction for positive systems

In this paper, the problem of frequency-limited H∞ model reduction for positive linear time-invariant systems is investigated. Specifically, our goal is to find a stable positive reduced-order model for a given positive system such that the H∞ norm of the error system is bounded over a frequency interval of interest. A new condition in terms of matrix inequality is developed for characterizing the frequency-limited H∞ performance. Then an equivalent parametrization of a positive reduced-order model is derived, based on which, an iterative algorithm is constructed for optimizing the reduced-order model. The algorithm utilizes coarse reduced-order models resulting from (generalized) balanced truncation as the initial value. Both continuous- and discrete-time systems are considered in the same framework. Numerical examples clearly show the effectiveness and advantages of the proposed model reduction method

Reach almost sure consensus with only group information

This brief presents a new distributed scheme to solve the consensus problem for a group of agents if neither their absolute states nor inter-agent relative states are available. The new scheme considers a random partition of agents into two subgroups at each step and then uses the relative group representative state as feedback information for the consensus purpose. It is then shown that almost sure consensus can be achieved under the proposed scheme in both discrete time and continuous time. For the discrete time case, almost sure consensus is achieved if and only if the weighting parameter for state update is greater than one. For the continuous time case, almost sure consensus is realized when the weighting parameter is positive. Moreover, it is shown that if a uniform probability is considered for group selection, then the group of agents can reach average consensus in mean.The work of Lin was supported by Zhejiang Provincial Natural Science Foundation of ChinaLR13F030002. The work of Yu was supported in part by the Australian Research Council through Discovery Project DP-130103610, a Queen Elizabeth II Fellowship under Grant DP-110100538, the National Natural Science Foundation of China (61375072), and the Open Research Project (No. ICT1427) of the State Key Laboratory of Industrial Control Technology, Zhejiang University, China

A distributed control law with guaranteed convergence rate for identically coupled linear systems

This paper investigates the stabilization and optimization problems for a group of identically linear agents with undirected interaction topology. It is shown that a distributed control law based on local measurements and relative information exchanged f

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 attitude and translation consensus for networked rigid bodies based on unit dual quaternion

This paper provides unified solutions for distributed attitude and translation consensus problems for networked fully actuated rigid bodies under the fixed and undirected communication topology with the tool of unit dual quaternion. We investigate two kinds of consensus, that is, leaderless consensus and leader-following consensus with a static leader. Firstly, the dynamics of rigid bodies are presented by unit dual quaternion. The control inputs of rigid bodies are also obtained from unit dual quaternion. Secondly, we propose a distributed consensus law in the form of dual quaternion to guarantee that the attitudes and translations of all rigid bodies reach consensus, respectively, without a leader. Thirdly, the leader-following consensus problem with a static leader is studied. With the proposed leader-following consensus law, the states of all rigid bodies converge to the corresponding states of the static leader, including the attitude and the translation. Finally, numerical examples are provided to validate the effectiveness of the theoretical resultsThe authors were supported in part by Australian Research Council (DP130103610 and DP160104500) and National Natural Science Foundation of China (61375072 and 61503109) and Nature Science Foundation of Zhejiang Province (LQF030005)

Evolution of Social Power in Social Networks with Dynamic Topology

The recently proposed DeGroot-Friedkin model describes the dynamical evolution of individual social power in a social network that holds opinion discussions on a sequence of different issues. This paper revisits that model, and uses nonlinear contraction analysis, among other tools, to establish several novel results. First, we show that for a social network with constant topology, each individual's social power converges to its equilibrium value exponentially fast, whereas previous results only concluded asymptotic convergence. Second, when the network topology is dynamic (i.e., the relative interaction matrix may change between any two successive issues), we show that each individual exponentially forgets its initial social power. Specifically, individual social power is dependent only on the dynamic network topology, and initial (or perceived) social power is forgotten as a result of sequential opinion discussion. Last, we provide an explicit upper bound on an individual's social power as the number of issues discussed tends to infinity; this bound depends only on the network topology. Simulations are provided to illustrate our results.The work of Mengbin Ye, Brian D. O. Anderson, and Changbin Yu was supported by the Australian Research Council under Grant DP-130103610 and Grant DP-160104500, by 111-Project D17019, by NSFC Projects 61385702 and 61761136005, and by Data61-CSIRO. The work of Mengbin Ye was supported by an Australian Government Research Training Program Scholarship. The work of Ji Liu and Tamer Bas¸ar was supported by the Office of Naval Research MURI Grant N00014-16-1-2710, and by NSF under Grant CCF 11-11342. Recommended by Associate Editor C. M. Kellett

Distributed model-independent consensus of Euler-Lagrange agents on directed networks

This paper proposes a distributed model-independent algorithm to achieve leaderless consensus on a directed network where each fully-actuated agent has self-dynamics described by Euler–Lagrange equations of motion. Specifically, we aim to achieve consensus of the generalised coordinates with zero generalised velocity. We show that on a strongly connected graph, a model-independent algorithm can achieve the consensus objective at an exponential rate if an upper bound on the initial conditions is known a priori. By model-independent, we mean that each agent can execute the algorithm with no knowledge of the equations describing the self-dynamics of any agent. For design of the control laws which achieve consensus, a control gain scalar and a control gain matrix are required to satisfy several inequalities involving bounds on the matrices of the agent dynamic model, bounds on the Laplacian matrix describing the network topology and the set of initial conditions; design of the algorithm therefore requires some knowledge on the bounds of the agent dynamical parameters. Because only bounds are required, the proposed algorithm offers robustness to uncertainty in the parameters of the multiagent system. We systematically show that additional relative velocity information improves the performance of the controller. Numerical simulations are provided to show the effectiveness of the algorithm.This work was supported by the National Natural Science Foundation of China (grant 61375072), and by Data61-CSIRO (formerly NICTA)

Bearing-Only Measurement Self-Localization,Velocity Consensus and Formation Control

Self-localization and formation control tasks are considered when each agent in a multiagent formation observes its neighbors but does not communicate. Each agent is restricted to a predefined motion type on a 2-D plane and collects bearing-only measurements over a time interval to localize neighboring agents. The localization process is used by a three agent formation to achieve velocity consensus combined with formation shape control. Simulations are provided and noisy bearing measurements are investigated.This work was supported in part by the Australian Research Council (ARC) under Grant DP-130103610 and Grant DP-160104500, in part by the National Natural Science Foundation of China under Grant 61375072, and in part by Data61-CSIRO (formerly NICTA)

Non-iterative, fast SE(3) path smoothing

In this paper, we present a fast, non-iterative approach to smooth a noisy input on the Special Euclidean Group, SE(3) manifold. The translational part can be smoothed by a simple Gaussian convolution.We then proposed a novel approach to rotation smoothing. Unlike existing rotation smoothing methods using either iterative optimization methods or stochastic filtering methods, our method allows direct computation of the smoothing result and allows parallelization of the computation. Furthermore, we have done a comparative study on Jia and Evans’s method published in 2014 [1], and shown that our method can better smooth an input rotation sequence, with shorter computational time. The smoothed camera path is then used for video stabilisation, which shows fluid and smooth camera motion.Australian ARC Centre of Excellence for Robotic Vision (CE140100016