Alexey S. Matveev

Saint Petersburg State University, Sankt-Peterburg, St.-Petersburg, Russia

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Publications (132)93.64 Total impact

  • Source
    Anton V. Proskurnikov · Alexey Matveev · Ming Cao
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    ABSTRACT: 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.
    Full-text · Article · Jun 2016 · IEEE Transactions on Automatic Control
  • Alexey S. Matveev · Anna A. Semakova · Andrey V. Savkin
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    ABSTRACT: We consider a single planar non-holonomic Dubins-car like robot traveling with a constant and given longitudinal speed and controlled by the angular velocity, which is upper limited in absolute value. There also is a group of moving targets in the plane. The robot measures only the relative distances to the targets and cannot distinguish among them. A sliding mode control law is proposed that drives the root mean square distance to the targets to a pre-specified value. This law is justified by a non-local convergence result, along with description of the domain of convergence. Specifically, we first disclose requirements to the averaged characteristics of the group’s motion, which should be necessarily met in order for the constant-speed robot with a limited turning capacity be able to maintain the desired root mean square distance to the group. Then we show that under slight and partly unavoidable enhancements of these necessary conditions, the proposed controller does drive this distance to the desired value and ensures its stable maintenance afterwards provided that the controller is properly tuned. Recommendations on its tuning are also provided. The convergence and performance of the control law are confirmed by computer simulations.
    No preview · Article · Mar 2016
  • Source
    Anna A. Semakova · Kirill S. Ovchinnikov · Alexey S. Matveev
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    ABSTRACT: Several nonholonomic Dubins-car like robots travel over paths with bounded curvatures in a plane that contains an a priori unknown region. The robots are anonymous to one another and do not use communication facilities. Any of them has access to the current distance to the region and can determine the relative positions and orientations of the companion robots within a finite and given visibility range. We present a distributed navigation and guidance strategy under which every robot autonomously converges to the desired distance to the region with always respecting a given safety margin, the robots do not collide with one another, and the entire team ultimately sweeps over the respective equidistant curve at a speed exceeding a given threshold, thus forming a kind of a sweeping barrier at the perimeter of the region. Mathematically rigorous justification of the proposed strategy is offered; its effectiveness is confirmed by extensive computer simulations.
    Preview · Article · Dec 2015
  • Source
    Alexey S. Matveev
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    ABSTRACT: The paper provides an overview of some key contributions to the theory of optimal control performed by V.A. Yakubovich, with the focus on the fundamental findings in linearquadratic optimal regulation and entailed developments in global nonconvex optimization. Along with the works of V.A. Yakubovich, the paper broadly reports on relevant findings of his collaborators, especially in the area of nonconvex global optimization.
    Preview · Article · Dec 2015
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    ABSTRACT: A non-holonomic Dubins-car like robot should detect, locate, and track the boundary of an a priori unknown dynamic environmental scalar field. The field is measured by an on-board sensor in a point-wise fashion at the robot's location. The focus is on unsteady boundaries that arbitrarily evolve over time, and, e.g., may change shapes and sizes. We present a sliding mode control method for localizing and tracking such boundaries: the robot is steered to the boundary and circulates in its close proximity afterwards. The proposed control algorithm does not require estimation of the spatial gradient of the field and is non-demanding with respect to both computation and motion. Its mathematically rigorous justification is provided. The effectiveness of the proposed guidance law is confirmed by computer simulations and experiments with a real wheeled robot.
    No preview · Article · Dec 2015
  • Alexey S. Matveev · Michael C. Hoy · Andrey V. Savkin
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    ABSTRACT: We consider a single kinematically controlled robot with bounded control inputs. It travels in a 2-D region supporting an unknown unsteady scalar field. A single sensor provides the field value at the current location of the robot. We present a reactive navigation strategy that drives the robot to the time-varying spatial maximum of the field, and subsequently maintains proximity to this location. This strategy is based on a novel paradigm of kinematic control, and is distinct from the conventional imperative of aligning the velocity vector with the field gradient. It does not employ estimation of any field gradient- or derivative-dependent quantities, like the rate at which the field measurement evolves over time, and is nondemanding with respect to both computation and motion. Its convergence is rigorously justified for smooth dynamic fields under some technical and partly unavoidable assumptions. Simulation results and experiments with a real wheeled robot confirm the applicability and performance of the proposed navigation approach.
    No preview · Article · Sep 2015 · IEEE Transactions on Control Systems Technology
  • Source
    Anton Proskurnikov · Alexey Matveev
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    ABSTRACT: This paper addresses consensus problems in nonlinearly coupled networks of dynamic agents described by a common and arbitrary linear model. Interagent interaction rules are uncertain but satisfy the standard sector condition with known sector bounds; both the agent's model and interaction topology are time-invariant. A novel frequency-domain criterion for consensus is offered that is similar to and extends the classical Popov's absolute stability criterion.
    Full-text · Article · Aug 2015 · Cybernetics, IEEE Transactions on
  • K. Ovchinnikov · A. Semakova · A. Matveev
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    ABSTRACT: Several anonymous Dubins-car like mobile robots travel in a planar environment that hosts a scalar field, like the level of radiation or concentration of a contaminant. The objective is to co-operatively detect and localize the boundary of the set where the field value exceeds a certain threshold. The robots suffer from deficits of competence, communication, perception, and maneuverability: they do not know the field profile a priory, are not aware of the team size, cannot communicate with and recognize one another, can measure only the value of the field at the current location, are subjected to nonholonomic constraints, and are able to move along paths of only limited curvatures. We propose a new decentralized navigation strategy that drives all robots to the desired environmental boundary, with subsequent stable circulation along it. This strategy is based on an autonomous control of every robot, prevents collisions between them and ultimately ensures their pseudo-uniform distribution over the boundary to better utilize the resources of the team for representatively portraying the boundary. Furthermore, the proposed control scheme does not employ gradient estimation, which typically needs ineffective concentration of robots into tight clusters, and is non-demanding with respect to both computation and motion. Its mathematically rigorous justification is provided. The effectiveness of the proposed guidance law is confirmed by computer simulations and real-world experiments.
    No preview · Article · May 2015 · Robotics and Autonomous Systems
  • Alexey S. Matveev · Michael C. Hoy · Andrey V. Savkin
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    ABSTRACT: We present a reactive strategy for the navigation of a mobile robot in dynamic a priori unknown environments densely cluttered with moving and deforming obstacles. Mathematically rigorous analysis of this law with the proof of its global convergence is provided; its performance is confirmed by computer simulations.
    No preview · Article · Apr 2015 · Automatica
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We consider a single non-holonomic Dubins-like robot traveling with a constant longitudinal speed in an a priori unknown and unsteady planar environment. The robot should detect, locate, and track the boundary of a dynamic environmental scalar field. The field is measured by an on-board sensor in a point-wise fashion at the robot's location. The focus is on unsteady boundaries that evolve over time in an arbitrary fashion, including deformations, i.e., changes of shapes and sizes. We present a sliding mode control method for localizing and tracking such boundaries: the robot is steered to the boundary and circulates in its close proximity afterwards. The proposed control algorithm does not require estimation of the spatial gradient of the field and is non-demanding with respect to both computation and motion. The paper offers the proofs of technical facts required for rigorous justification of non-local convergence of the proposed control law, as well as theoretical illustrations of its performance in specific scenarios.
    Full-text · Article · Apr 2015
  • Source
    A. Proskurnikov · A. Matveev · M. Cao
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    ABSTRACT: The mechanism of reaching consensus in multi-agent systems has been exhaustively studied in recent years, motivated by numerous applications in engineering and science. Most consensus algorithms examined in the literature are based on the assumption about mutual trust and cooperation between the agents, implemented in the form of attractive couplings between the agents that render the values of the agents' states closer. However, in opinion dynamics of social groups, competition or antagonism between some pairs of agents is ubiquitous, which is usually characterized by the repulsive coupling, and may lead to clustering and polarization of opinions. A simple yet insightful model of opinion dynamics with antagonistic interactions was proposed recently by C. Altafini, which examined conventional first-order consensus algorithms with static signed interaction graphs, where the positive weight of an arc implies cooperation between the two agents and the negative one corresponds to antagonism. This protocol establishes modulus consensus, where the opinions become the same in modulus but may differ in sign. In the present paper, we extend the modulus consensus model to the case where the network topology is time-varying and undirected. We give necessary and sufficient conditions under which the consensus protocol with the time-varying signed Laplacian establishes agreement of opinions in moduli, whose signs may be opposite, so that the agents' opinions either reach consensus or polarize.
    Full-text · Article · Feb 2015 · Proceedings of the IEEE Conference on Decision and Control
  • Source
    Alexey S. Matveev · Michael C. Hoy · Andrey V. Savkin
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    ABSTRACT: We consider a single kinematically controlled robot with a bounded control range. The robot travels in a two-dimensional region supporting an unknown unsteady scalar field. A single sensor provides the field value at the current location of the robot. The paper is concerned with a reactive navigation strategy to drive the robot to the time-varying location where the field attains its spatial maximum, with subsequent keeping the robot close to this location. This strategy is based on a novel paradigm of kinematic control different from conventionally trying to align the velocity vector with the field gradient, does not employ estimation of the entire field gradient or derivative-dependent quantities, like the rate at which the available field reading evolves over time, and is non-demanding with respect to both computation and motion. The paper presents the proofs of the technical facts required to justify convergence of the proposed algorithm.
    Full-text · Article · Feb 2015
  • K. Ovchinnikov · A. Semakova · A. Matveev
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    ABSTRACT: We consider a team of nonholonomic Dubins-car like robots traveling forward over paths with bounded curvatures in a planar region supporting an unknown scalar field. Every robot measures the field value at its location and has no communication facilities; the robots are anonymous to one another. The objective is to detect and localize the level set where the unknown field assumes a given value. We present a new distributed navigation and guidance strategy that ensures convergence of all robots to the desired level set and its subsequent display via stable circulation of the robots along this set. Moreover, this strategy prevents collisions between the robots and ultimately provides their sub-uniform distribution over the level set, so that the entire team effectively and representatively portrays this set. The proposed control strategy does not employ gradient estimation, which typically needs ineffective concentration of robots into tight clusters, and is non-demanding with respect to both computation and motion. Its mathematically rigorous justification is provided. The effectiveness of the proposed guidance law is confirmed by computer simulations and real-world experiments.
    No preview · Article · Jan 2015
  • A. Yu. Pogromsky · A.S. Matveev
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    ABSTRACT: By the data rate theorem, the smallest capacity of the communication channel for which the observation problem is solvable is equal to the topological entropy of the open-loop system. A similar result holds true for control problems under communication constraints. Therefore, in real applications, it is important to estimate the topological entropy to find limitations caused by limited data rate of the communication channels. We show that such an estimate can be found by the direct Lyapunov method.
    No preview · Article · Jan 2015 · Lecture Notes in Control and Information Sciences
  • Chao Wang · Alexey S. Matveev · Andrey V. Savkin · Ray Clout · Hung T. Nguyen
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    ABSTRACT: We present a novel motorized semi-autonomous mobile hospital bed guided by a human operator and a reactive navigation algorithm. The proposed reactive navigation algorithm is launched when the sensory device detects that the hospital bed is in the potential danger of collision. The semi-autonomous hospital bed is able to safely and quickly deliver critical neurosurgery (head trauma) patients to target locations in dynamic uncertain hospital environments such as crowded hospital corridors while avoiding en-route steady and moving obstacles. We do not restrict the nature or the motion of the obstacles, meaning that the shapes of the obstacles may be time-varying or deforming and they may undergo arbitrary motions. The only information available to the navigation system is the current distance to the nearest obstacle. Performance of the proposed navigation algorithm is verified via theoretical studies. Simulation and experimental results also confirm the performance of the reactive navigation algorithm in real world scenarios.
    No preview · Article · Dec 2014 · Robotica
  • Alexey S. Matveev · Michael C. Hoy · Andrey V. Savkin
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    ABSTRACT: A nonholonomic under-actuated robot with bounded control travels in a 3D region. A single sensor provides the value of an unknown scalar field at the current location of the robot. We present a new kinematic control paradigm to drive the robot to the maximizer of the field, which is different from conventionally trying to align the velocity vector with the field gradient. The proposed strategy does not employ gradient estimation and is non-demanding with respect to both computation and motion. Its mathematically rigorous analysis and justification are provided. Simulation results confirm the applicability and performance of the proposed guidance approach.
    No preview · Article · Jul 2014 · Automatica
  • Source
    Alexey S. Matveev · Michael C. Hoy · Andrey V. Savkin
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    ABSTRACT: We present a method for guidance of a Dubins-like vehicle with saturated control towards a target in a steady simply connected maze-like environment. The vehicle always has access to to the target relative bearing angle (even if the target is behind the obstacle or is far from the vehicle) and the distance to the nearest point of the maze if it is within the given sensor range. The proposed control law is composed by biologically inspired reflex-level rules. Mathematically rigorous analysis of this law is provided; its convergence and performance are confirmed by computer simulations and experiments with real robots.
    Full-text · Article · Mar 2014
  • Michael Hoy · Alexey S. Matveev · Andrey V. Savkin
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    ABSTRACT: We review a range of techniques related to navigation of unmanned vehicles through unknown environments with obstacles, especially those that rigorously ensure collision avoidance (given certain assumptions about the system). This topic continues to be an active area of research, and we highlight some directions in which available approaches may be improved. The paper discusses models of the sensors and vehicle kinematics, assumptions about the environment, and performance criteria. Methods applicable to stationary obstacles, moving obstacles and multiple vehicles scenarios are all reviewed. In preference to global approaches based on full knowledge of the environment, particular attention is given to reactive methods based on local sensory data, with a special focus on recently proposed navigation laws based on model predictive and sliding mode control.
    No preview · Article · Mar 2014 · Robotica
  • A. Zakhar'eva · A. S. Matveev · M. C. Hoy · A. V. Savkin
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    ABSTRACT: We consider a team of autonomous kinematically controlled non-holonomic planar Dubins car-like vehicles. The team objective is to encircle a given target so that all vehicles achieve a common and pre-specified distance from it and are uniformly distributed over the respective circle, and the entire formation rotates around the target with a prescribed angular velocity. The robots do not communicate with each other and any central decision-maker. The sensing capacity of any vehicle is heavily restricted: It has access only to the distance to the target and to the distances to the companion vehicles that are in a given disc sector centered at the vehicle at hand; no robot can distinguish between its companions, and does not know their parameters. A distributed control law is proposed, and mathematically rigorous proofs of its non-local convergence as well as collision avoidance property are presented. The performance of the control law is illustrated by computer simulations and experiments with real robots.
    No preview · Article · Feb 2014 · Robotica
  • Source
    A. Yu Pogromsky · A. S. Matveev · Antoine Chaillet · B. Ruffer
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    ABSTRACT: The paper deals with global stability analysis of linear control systems with saturation in feedback driven by an external input. Various new criteria based on non-quadratic Lyapunov functions are proposed, that unlike many previous results, offer better account for the role of the external excitation by providing input-dependent conditions for stability of solutions. For example, it is shown that even if the system fails to satisfy the incremental version of the circle criterion, the stability is guaranteed whenever the uniform root mean square value of the input signal is less than a computable threshold. The general theoretical results are illustrated in the case of the double integrator closed by a saturated linear feedback with an external excitation.
    Full-text · Conference Paper · Dec 2013

Publication Stats

1k Citations
93.64 Total Impact Points

Institutions

  • 2002-2016
    • Saint Petersburg State University
      • • Faculty of Mathematics and Mechanics
      • • Department of Mathematical Physics
      Sankt-Peterburg, St.-Petersburg, Russia
  • 2001-2014
    • University of New South Wales
      • School of Electrical Engineering and Telecommunications
      Kensington, New South Wales, Australia
  • 1999-2001
    • University of Western Australia
      • School of Electrical, Electronic and Computer Engineering
      Perth City, Western Australia, Australia