arXiv subjects

Ming Cao

Publications and source records attributed to Ming Cao.

144 records · Page 8Linked to original sources

arXiv2017

Controlling a triangular flexible formation of autonomous agents

In formation control, triangular formations consisting of three autonomous agents serve as a class of benchmarks that can be used to test and compare the performances of different controllers. We present an algorithm that combines the advantages of both position- and distance-based gradient descent control laws. For example, only two pairs of neighboring agents need to be controlled, agents can work in their own local frame of coordinates and the orientation of the formation with respect to a global frame of coordinates is not prescribed. We first present a novel technique based on adding artificial biases to neighboring agents' range sensors such that their eventual positions correspond to a collinear configuration. Right after, a small modification in the bias terms by introducing a prescribed rotation matrix will allow the control of the bearing of the neighboring agents.

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arXiv2017

Distributed algorithm for controlling scale-free polygonal formations

This paper presents a distributed algorithm for controlling the deployment of a team of mobile agents in formations whose shapes can be characterized by a broad class of polygons, including regular ones, where each agent occupies a corner of the polygon. The algorithm shares the appealing properties of the popular distance-based rigid formation control, but with the additional advantage of requiring the control of fewer pairs of neighboring agents. Furthermore, the scale of the polygon can be controlled by only one pair of neighboring agents. We also exploit the exponential stability of the controlled formation in order to steer the formation as a whole with translations and rotations in a prescribed way. We provide both theoretical analysis and illustrative simulations.

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arXiv2017

Modulus consensus in discrete-time signed networks and properties of special recurrent inequalities

Recently the dynamics of signed networks, where the ties among the agents can be both positive (attractive) or negative (repulsive) have attracted substantial attention of the research community. Examples of such networks are models of opinion dynamics over signed graphs, recently introduced by Altafini (2012,2013) and extended to discrete-time case by Meng et al. (2014). It has been shown that under mild connectivity assumptions these protocols provide the convergence of opinions in absolute value, whereas their signs may differ. This "modulus consensus" may correspond to the polarization of the opinions (or bipartite consensus, including the usual consensus as a special case), or their convergence to zero. In this paper, we demonstrate that the phenomenon of modulus consensus in the discrete-time Altafini model is a manifestation of a more general and profound fact, regarding the solutions of a special recurrent inequality. Although such a recurrent inequality does not provide the uniqueness of a solution, it can be shown that, under some natural assumptions, each of its bounded solutions has a limit and, moreover, converges to consensus. A similar property has previously been established for special continuous-time differential inequalities (Proskurnikov, Cao, 2016). Besides analysis of signed networks, we link the consensus properties of recurrent inequalities to the convergence analysis of distributed optimization algorithms and the problems of Schur stability of substochastic matrices.

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arXiv2017

Taming mismatches in inter-agent distances for the formation-motion control of second-order agents

This paper presents the analysis on the influence of distance mismatches on the standard gradient-based rigid formation control for second-order agents. It is shown that, similar to the first-order case as recently discussed in the literature, these mismatches introduce two undesired group behaviors: a distorted final shape and a steady-state motion of the group formation. We show that such undesired behaviors can be eliminated by combining the standard formation control law with distributed estimators. Finally, we show how the mismatches can be effectively employed as design parameters in order to control a combined translational and rotational motion of the formation.

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arXiv2017

Guidance algorithm for smooth trajectory tracking of a fixed wing UAV flying in wind flows

This paper presents an algorithm for solving the problem of tracking smooth curves by a fixed wing unmanned aerial vehicle travelling with a constant airspeed and under a constant wind disturbance. The algorithm is based on the idea of following a guiding vector field which is constructed from the implicit function that describes the desired (possibly time-varying) trajectory. The output of the algorithm can be directly expressed in terms of the bank angle of the UAV in order to achieve coordinated turns. Furthermore, the algorithm can be tuned offline such that physical constraints of the UAV, e.g. the maximum bank angle, will not be violated in a neighborhood of the desired trajectory. We provide the corresponding theoretical convergence analysis and performance results from actual flights.

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arXiv2017

Target assignment for robots constrained by limited communication range

This paper investigates the task assignment problem for multiple dispersed robots constrained by limited communication range. The robots are initially randomly distributed and need to visit several target locations while minimizing the total travel time. A centralized rendezvous-based algorithm is proposed, under which all the robots first move towards a rendezvous position until communication paths are established between every pair of robots either directly or through intermediate peers, and then one robot is chosen as the leader to make a centralized task assignment for the other robots. Furthermore, we propose a decentralized algorithm based on a single-traveling-salesman tour, which does not require all the robots to be connected through communication. We investigate the variation of the quality of the assignment solutions as the level of information sharing increases and as the communication range grows, respectively. The proposed algorithms are compared with a centralized algorithm with shared global information and a decentralized greedy algorithm respectively. Monte Carlo simulation results show the satisfying performance of the proposed algorithms.

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arXiv2017

A guiding vector field algorithm for path following control of nonholonomic mobile robots

In this paper we propose an algorithm for path following control of the nonholonomic mobile robot based on the idea of the guiding vector field (GVF). The desired path may be an arbitrary smooth curve in its implicit form, that is, a level set of a predefined smooth function. Using this function and the robot's kinematic model, we design a GVF, whose integral curves converge to the trajectory. A nonlinear motion controller is then proposed which steers the robot along such an integral curve, bringing it to the desired path. We establish global convergence conditions for our algorithm and demonstrate its applicability and performance by experiments with real wheeled robots.

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arXiv2016

Synchronization of Pulse-Coupled Oscillators and Clocks under Minimal Connectivity Assumptions

Populations of flashing fireflies, claps of applauding audience, cells of cardiac and circadian pacemakers reach synchrony via event-triggered interactions, referred to as pulse couplings. Synchronization via pulse coupling is widely used in wireless sensor networks, providing clock synchronization with parsimonious packet exchanges. In spite of serious attention paid to networks of pulse coupled oscillators, there is a lack of mathematical results, addressing networks with general communication topologies and general phase-response curves of the oscillators. The most general results of this type (Wang et al., 2012, 2015) establish synchronization of oscillators with a delay-advance phase-response curve over strongly connected networks. In this paper we extend this result by relaxing the connectivity condition to the existence of a root node (or a directed spanning tree) in the graph. This condition is also necessary for synchronization.

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arXiv2016

Distributed scaling control of rigid formations

Recently it has been reported that biased range-measurements among neighboring agents in the gradient distance-based formation control can lead to predictable collective motion. In this paper we take advantage of this effect and by introducing distributed parameters to the prescribed inter-distances we are able to manipulate the steady-state motion of the formation. This manipulation is in the form of inducing simultaneously the combination of constant translational and angular velocities and a controlled scaling of the rigid formation. While the computation of the distributed parameters for the translational and angular velocities is based on the well-known graph rigidity theory, the parameters responsible for the scaling are based on some recent findings in bearing rigidity theory. We carry out the stability analysis of the modified gradient system and simulations in order to validate the main result.

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arXiv2016

Controlling rigid formations of mobile agents under inconsistent measurements

Despite the great success of using gradient-based controllers to stabilize rigid formations of autonomous agents in the past years, surprising yet intriguing undesirable collective motions have been reported recently when inconsistent measurements are used in the agents' local controllers. To make the existing gradient control robust against such measurement inconsistency, we exploit local estimators following the well known internal model principle for robust output regulation control. The new estimator-based gradient control is still distributed in nature and can be constructed systematically even when the number of agents in a rigid formation grows. We prove rigorously that the proposed control is able to guarantee exponential convergence and then demonstrate through robotic experiments and computer simulations that the reported inconsistency-induced orbits of collective movements are effectively eliminated.

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arXiv2016

Distributed rotational and translational maneuvering of rigid formations and their applications

Recently it has been reported that range-measurement inconsistency, or equivalently mismatches in prescribed inter-agent distances, may prevent the popular gradient controllers from guiding rigid formations of mobile agents to converge to their desired shape, and even worse from standing still at any location. In this paper, instead of treating mismatches as the source of ill performance, we take them as design parameters and show that by introducing such a pair of parameters per distance constraint, distributed controller achieving simultaneously both formation and motion control can be designed that not only encompasses the popular gradient control, but more importantly allows us to achieve constant collective translation, rotation or their combination while guaranteeing asymptotically no distortion in the formation shape occurs. Such motion control results are then applied to (a) the alignment of formations orientations and (b) enclosing and tracking a moving target. Besides rigorous mathematical proof, experiments using mobile robots are demonstrated to show the satisfying performances of the proposed formation-motion distributed controller.

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arXiv2016

Structural balance and opinion separation in trust-mistrust social networks

Structural balance theory has been developed in sociology and psychology to explain how interacting agents, e.g., countries, political parties, opinionated individuals, with mixed trust and mistrust relationships evolve into polarized camps. Recent results have shown that structural balance is necessary for polarization in networks with fixed, strongly connected neighbor relationships when the opinion dynamics are described by DeGroot-type averaging rules. We develop this line of research in this paper in two steps. First, we consider fixed, not necessarily strongly connected, neighbor relationships. It is shown that if the network includes a strongly connected subnetwork containing mistrust, which influences the rest of the network, then no opinion clustering is possible when that subnetwork is not structurally balanced; all the opinions become neutralized in the end. In contrast, it is shown that when that subnetwork is indeed structurally balanced, the agents of the subnetwork evolve into two polarized camps and the opinions of all other agents in the network spread between these two polarized opinions. Second, we consider time-varying neighbor relationships. We show that the opinion separation criteria carry over if the conditions for fixed graphs are extended to joint graphs. The results are developed for both discrete-time and continuous-time models.

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arXiv2016

Modulus Consensus over Networks with Antagonistic Interactions and Switching Topologies

In this paper, we study the discrete-time consensus problem over networks with antagonistic and cooperative interactions. Following the work by Altafini [IEEE Trans. Automatic Control, 58 (2013), pp. 935--946], by an antagonistic interaction between a pair of nodes updating their scalar states we mean one node receives the opposite of the state of the other and naturally by an cooperative interaction we mean the former receives the true state of the latter. Here the pairwise communication can be either unidirectional or bidirectional and the overall network topology graph may change with time. The concept of modulus consensus is introduced to characterize the scenario that the moduli of the node states reach a consensus. It is proved that modulus consensus is achieved if the switching interaction graph is uniformly jointly strongly connected for unidirectional communications, or infinitely jointly connected for bidirectional communications. We construct a counterexample to underscore the rather surprising fact that quasi-strong connectivity of the interaction graph, i.e., the graph contains a directed spanning tree, is not sufficient to guarantee modulus consensus even under fixed topologies. Finally, simulation results using a discrete-time Kuramoto model are given to illustrate the convergence results showing that the proposed framework is applicable to a class of networks with general nonlinear node dynamics.

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arXiv2016

Synchronization of Goodwin's oscillators under boundedness and nonnegativeness constraints for solutions

In the recent paper by Hamadeh et al. (2012) an elegant analytic criterion for incremental output feedback passivity (iOFP) of cyclic feedback systems (CFS) has been reported, assuming that the constituent subsystems are incrementally output strictly passive (iOSP). This criterion was used to prove that a network of identical CFS can be synchronized under sufficiently strong linear diffusive coupling. A very important class of CFS consists of biological oscillators, named after Brian Goodwin and describing self-regulated chains of enzymatic reactions, where the product of each reaction catalyzes the next reaction, while the last product inhibits the first reaction in the chain. Goodwin's oscillators are used, in particular, to model the dynamics of genetic circadian pacemakers, hormonal cycles and some metabolic pathways. In this paper we point out that for Goodwin's oscillators, where the individual reactions have nonlinear (e.g. Mikhaelis-Menten) kinetics, the synchronization criterion, obtained by Hamadeh et al., cannot be directly applied. This criterion relies on the implicit assumption of the solution boundedness, dictated also by the chemical feasibility (the state variables stand for the concentrations of chemicals). Furthermore, to test the synchronization condition one needs to know an explicit bound for a solution, which generally cannot be guaranteed under linear coupling. At the same time, we show that these restrictions can be avoided for a nonlinear synchronization protocol, where the control inputs are "saturated" by a special nonlinear function (belonging to a wide class), which guarantees nonnegativity of the solutions and allows to get explicit ultimate bounds for them. We prove that oscillators synchronize under such a protocol, provided that the couplings are sufficiently strong.

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arXiv2015

Products of Generalized Stochastic Sarymsakov Matrices

In the set of stochastic, indecomposable, aperiodic (SIA) matrices, the class of stochastic Sarymsakov matrices is the largest known subset (i) that is closed under matrix multiplication and (ii) the infinitely long left-product of the elements from a compact subset converges to a rank-one matrix. In this paper, we show that a larger subset with these two properties can be derived by generalizing the standard definition for Sarymsakov matrices. The generalization is achieved either by introducing an "SIA index", whose value is one for Sarymsakov matrices, and then looking at those stochastic matrices with larger SIA indices, or by considering matrices that are not even SIA. Besides constructing a larger set, we give sufficient conditions for generalized Sarymsakov matrices so that their products converge to rank-one matrices. The new insight gained through studying generalized Sarymsakov matrices and their products has led to a new understanding of the existing results on consensus algorithms and will be helpful for the design of network coordination algorithms.

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arXiv2015

Opinion Dynamics in Social Networks with Hostile Camps: Consensus vs. Polarization

Most of the distributed protocols for multi-agent consensus assume that the agents are mutually cooperative and "trustful," and so the couplings among the agents bring the values of their states closer. Opinion dynamics in social groups, however, require beyond these conventional models due to ubiquitous competition and distrust between some pairs of agents, which are usually characterized by repulsive couplings and may lead to clustering of the opinions. A simple yet insightful model of opinion dynamics with both attractive and repulsive couplings was proposed recently by C. Altafini, who examined first-order consensus algorithms over static signed graphs. This protocol establishes modulus consensus, where the opinions become the same in modulus but may differ in signs. In this paper, we extend the modulus consensus model to the case where the network topology is an arbitrary time-varying signed graph and prove reaching modulus consensus under mild sufficient conditions of uniform connectivity of the graph. For cut-balanced graphs, not only sufficient, but also necessary conditions for modulus consensus are given.

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arXiv2013

Asynchronous Decentralized Event-triggered Control

In this paper we propose an approach to the implementation of controllers with decentralized strategies triggering controller updates. We consider set-ups with a central node in charge of the computation of the control commands, and a set of not co-located sensors providing measurements to the controller node. The solution we propose does not require measurements from the sensors to be synchronized in time. The sensors in our proposal provide measurements in an aperiodic way triggered by local conditions. Furthermore, in the proposed implementation (most of) the communication between nodes requires only the exchange of one bit of information (per controller update), which could aid in reducing transmission delays and as a secondary effect result in fewer transmissions being triggered.

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arXiv2010

Control of one-dimensional guided formations using coarse information

Motivated by applications in intelligent highway systems, the paper studies the problem of guiding mobile agents in a one-dimensional formation to their desired relative positions. Only coarse information is used which is communicated from a guidance system that monitors in real time the agents' motions. The desired relative positions are defined by the given distance constraints between the agents under which the overall formation is rigid in shape and thus admits locally a unique realization. It is shown that even when the guidance system can only transmit at most four bits of information to each agent, it is still possible to design control laws to guide the agents to their desired positions. We further delineate the thin set of initial conditions for which the proposed control law may fail using the example of a three-agent formation. Tools from non-smooth analysis are utilized for the convergence analysis.

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