Anton S. Shiriaev

Norwegian University of Science and Technology, Nidaros, Sør-Trøndelag, Norway

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Publications (135)90.21 Total impact

  • Sergei V. Gusev · Anton S. Shiriaev · Leonid B. Freidovich
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    ABSTRACT: Numerically finding stabilising feedback control laws for linear systems of periodic differential equations is a nontrivial task with no known reliable solutions. The most successful method requires solving matrix differential Riccati equations with periodic coefficients. All previously proposed techniques for solving such equations involve numerical integration of unstable differential equations and consequently fail whenever the period is too large or the coefficients vary too much. Here, a new method for numerical computation of stabilising solutions for matrix differential Riccati equations with periodic coefficients is proposed. Our approach does not involve numerical solution of any differential equations. The approximation for a stabilising solution is found in the form of a trigonometric polynomial, matrix coefficients of which are found solving a specially constructed finite-dimensional semidefinite programming (SDP) problem. This problem is obtained using maximality property of the stabilising solution of the Riccati equation for the associated Riccati inequality and sampling technique. Our previously published numerical comparisons with other methods shows that for a class of problems only this technique provides a working solution. Asymptotic convergence of the computed approximations to the stabilising solution is proved below under the assumption that certain combinations of the key parameters are sufficiently large. Although the rate of convergence is not analysed, it appeared to be exponential in our numerical studies.
    No preview · Article · Jan 2016 · International Journal of Control
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    ABSTRACT: The Integral Quadratic Constraint (IQC) framework developed by Professor Yakubovich and his co-workers, see Yakubovich et.al. (2004), is one of few available constructive tools for establishing robust stability of nonlinear systems. An explicit format of stability conditions, procedures for computing a Lyapunov function and developed libraries of IQCs for common nonlinearities in dynamics, all together have made the approach unique and at the same time so to say automatic for recovering stability conditions for many applications: in the process of analyzing a dynamical system, an engineer is just required to search for a suficiently rich set of IQCs describing nonlinearities in the dynamics so that such nonlinearities can be substituted in analysis by quadratic constraints, which they satisfy. The power of the methodology becomes also its weak part in an analysis of concrete systems. Searching IQCs is the dificult task in new examples, where a lack of a rich set of IQCs for concrete nonlinearities makes the method inconclusive or too rough to detect (in)-stability. The paper is aimed at a discussion of such an example of a nonlinear dynamical system (the classical 3-state Moore-Greitzer compressor model) augmented with the dynamical feedback controller, whose parameters should be adjusted to meet a stability condition. The closed-loop system has several nonlinearities and searching the corresponding IQCs to meet the stability conditions for this example is rather involved. To overcome the problem, we have previously described by different methods a set of parameters for which any solution of the closed loop system, if bounded, will converge to the origin and that the origin is locally asymptotically stable. However, the proof is incomplete without showing a boundedness of all solutions. To solve the task we have re-used some of the IQC framework ideas, where the method has been utilized and the corresponding IQCs have been found only for unbounded trajectories, if they would be present in closed loop system. The arguments have allowed completing the proof of stability and illustrating deliberate use of the IQC framework aimed at analysis of behavior of specific trajectories.
    Preview · Article · Dec 2015
  • Sergey Kolyubin · Leonid Paramonov · Anton Shiriaev
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    ABSTRACT: This work is aimed at a comprehensive discussion of algorithms for the kinematic parameters identification of robotic manipulators. We deal with an open-loop geometric calibration task, when a full 6D robot's end-effector pose is measured. Effective solutions of such a task is of high interest in many practical applications, because it can dramatically improve key robot characteristics. On the first step, we select optimal calibration configurations. A comparative analysis of three different algorithms and two observability indexes used for numerical optimization is provided. Afterwards, using the acquired and pre-processed experimental data we identify modified Denavit-Hartenberg parameters of the manipulator. Estimates are obtained resolving original nonlinear forward kinematics relations. Finally, we compare nominal and calibrated geometric parameters and show how much deviations in these parameters affect robot positioning accuracy. To the best of our knowledge, such integrated efforts are new for the KUKA LWR4+ robot and Nikon K610 optical coordinate measuring machine (CMM), which were used in the study. Discussion of practical issues on how to organise the experiment is an additional contribution of this work. The proposed procedure is highly automated and can be implemented to improve manipulator's performance on a periodic basis.
    No preview · Article · Nov 2015 · Journal of Physics Conference Series
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    ABSTRACT: We consider a model of a 24-degree-of-freedom monkey robot that is supposed to perform a brachiation locomotion, i.e. to swing from one row of a horizontal ladder to the next one using the arms. The robot hand is constructed as a planar hook so that the contact point, about which the robot swings, is a passive hinge. We identify the 10 most relevant degrees of freedom for this underactuated mechanical system and formulate a tractable search procedure consisting on the following steps: (a) to introduce a parametrized family of coordination patterns to be enforced on the dynamics with respect to a path coordinate; (b) to formulate geometric equality constraints that are necessary to achieve a periodic locomotion; (c) to generate trajectories from integrable reduced dynamics associated with the passive hinge; (d) to evaluate the energetic cost of transport. Moreover, we observe that a linear approximation of the reduced dynamics can be used for trajectory generation, which allows us to incorporate computation of an approximate gradient of the cost function into the search algorithm significantly improving the computational efficiency.
    No preview · Article · Sep 2015 · Autonomous Robots
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    ABSTRACT: Abstract— We approach a problem of motion planning and stabilization for a benchmark example, known as the “Butterfly” robot. It was proposed as a benchmark challenge for developing systematic techniques for nonprehensile rolling manipulation. A dynamical model of the underactuated system with a non-unilateral contact is derived. The recently proposed methodologies, known as virtual-holonomic-constraints-based motion planning and transverse-linearization-based orbital stabilization, are appropriately extended to suit the task. Finally, the feasibility is demonstrated through a hardware implementation and an experimental validation of the concept.
    Full-text · Conference Paper · May 2015
  • L. Freidovich · A. Shiriaev · U. Mettin · P. La Hera · A. Sandberg
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    ABSTRACT: We consider the motion-planning problem for a three-link planar pendulum equipped with two actuators. The goal is to create a synchronized periodic motion of all three degrees of freedom, which represents a human-like behavior. It can be orbitally stabilized with some known technique. The approach is motivated by analysis of recorded motion data of human actors and is based on the idea of imposing a set of virtual holonomic constraints to ensure invariance of linear geometric relations among the three generalized coordinates. The main contribution of the paper is a description of the set of achievable periodic motions in terms of amplitudes and periods.
    No preview · Article · Mar 2015
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    ABSTRACT: We present a new control strategy for an underactuated two-link robot, called inertia wheel pendulum. The system consists of a free planar rotational pendulum and a symmetric disk, attached to its end and directly controlled by a DC-motor. The goal is to create stable oscillations of the pendulum, which is not directly actuated. We exploit a recently proposed feedback control design strategy, based on motion planning via virtual holonomic constraints. This strategy is shown to be useful for design of regulators for achieving orbitally exponentially stable oscillatory motions. The main contribution is a step-by-step recipe on how to achieve oscillations with pre-specified amplitude from a given range and an arbitrary independently chosen period.
    No preview · Article · Mar 2015
  • I.R. Manchester · K.S. Andersson · A. Eklund · A.S. Shiriaev
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    ABSTRACT: Accurate estimates of the compliance and outflow resistance of the human cerebrospinal fluid system are important for diagnosis of a medical condition known as hydrocephalus. In this paper we design an observer which provides simultaneous on-line estimates of the outflow resistance and compliance, to our knowledge the first method to do so. It's performance is experimentally verified using the same apparatus used to perform actual patient diagnoses and a specially designed physical model of the human cerebrospinal fluid system.
    No preview · Article · Mar 2015
  • A.S. Shiriaev · H. Ludvigsen · O. Egeland · A.L. Fradkov
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    ABSTRACT: The paper contains a detailed analysis of the application of the passification approach to the problem of rendering the hyperbolic upright equilibrium of the simplified model of the Furuta pendulum globally attractive. It is shown that any smooth feedback control passifying the system with the naturally defined storage functions does not provide the desired property. Based on the idea of the VSS-like modification of the speed-gradient method, stabilizing regulator is suggested and studied both theoretically and by simulations.
    No preview · Article · Mar 2015
  • Sergey A. Kolyubin · Leonid Paramonov · Anton S. Shiriaev

    No preview · Chapter · Jan 2015
  • A.S. Shiriaev · L.B. Freidovich · M.W. Spong
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    ABSTRACT: We study the problem of motion planning for underactuated mechanical systems. The idea is to reduce complexity by imposing via feedback a sufficient number of invariants and then to compute a projection of the dynamics onto an induced invariant sub-manifold of the closed-loop system. The inspiration comes from two quite distant methods, namely the method of virtual holonomic constraints, originally invented for planning and orbital stabilization of gaits of walking machines, and the method of controlled Lagrangians, primarily invented as a nonlinear technique for stabilization of (relative) equilibria of controlled mechanical systems. Both of these techniques enforce the presence of particular invariants that can be described as level sets of conserved quantities induced in the closed-loop system. We link this structural feature of both methods to a procedure to transform a Lagrangian system with control inputs via a feedback action into a control-free Lagrangian system with a sufficient number of first integrals for the full state space or an invariant sub-manifold. In both cases, this transformation allows efficient (analytical) description of a new class of trajectories of forced mechanical systems appropriate for further orbital stabilization. For illustration purposes, we approach the challenging problem for a controlled mechanical system with two passive degrees of freedom: planning periodic (or bounded) forced upper-hemisphere trajectories of the spherical pendulum on a puck. Another example of the technique is separately reported in [21].
    No preview · Article · Sep 2014 · IEEE Transactions on Automatic Control
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    ABSTRACT: This article is concerned with the generic structure of the motion coordination system resulting from the application of the method of virtual holonomic constraints (VHCs) to the problem of the generation and robust execution of a dynamic humanlike motion by a humanoid robot. The motion coordination developed using VHCs is based on a motion generator equation, which is a scalar nonlinear differential equation of second order. It can be considered equivalent in function to a central pattern generator in living organisms. The relative time evolution of the degrees of freedom of a humanoid robot during a typical motion are specified by a set of coordination functions that uniquely define the overall pattern of the motion. This is comparable to a hypothesis on the existence of motion patterns in biomechanics. A robust control is derived based on a transverse linearization along the configuration manifold defined by the coordination functions. It is shown that the derived coordination and control architecture possesses excellent robustness properties. The analysis is performed on an example of a real human motion recorded in test experiments.
    Full-text · Article · Aug 2014 · Biological Cybernetics
  • Sergey A. Kolyubin · Anton S. Shiriaev
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    ABSTRACT: Increasing safety and efficiency of autonomous vessels also requires advanced navigation strategies. For the marine systems the task is even more complex than, e.g. for field robots, since hydrodynamic effects should be taken into account also. It is becoming even more challenging for underactuated vessels. Indeed, utilizing the virtual holonomic constraints approach we illustrate that regardless the control law implemented and for any desired geometrical path to follow, velocity profile of the underactuated ship has to satisfy additional constraints imposed as a second order differential equation of the system reduced dynamics. We consider a 4 DOF (surge, sway, roll, yaw) model for a single propeller-twin rudder surface vessel and derive conditions for planning a motion consistent with the system dynamics properties. Straight line and circular path are considered as special cases followed by the practical remarks. This analysis can used as a basis for further orbitally tracking controller design.
    No preview · Conference Paper · Aug 2014
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    ABSTRACT: Working with forestry machines requires a great deal of training to be sufficiently skilled to operate forestry cranes. In view of this, it would be desirable within the forestry industry to introduce automated motions, such as those seen in robotic arms, to shorten the training time and make the work of the operator easier. Motivated by this fact, we have developed two experimental platforms for testing control systems and motion-planning algorithms in real time. They correspond to a laboratory setup and a commercial version of a hydraulic manipulator used in forwarder machines. The aim of this article is to present the results of this development by providing an overview of our trajectory-planning algorithm and motion-control method, with a subsequent view of the experimental results. For motion control, we design feedback controllers that are able to track reference trajectories based on sensor measurements. Likewise, we provide arguments to design controllers in an open-loop for machines that lack sensing devices. Relying on the tracking efficiency of these controllers, we design time-efficient reference trajectories of motions that correspond to logging tasks. To demonstrate performance, we provide an overview of extensive testing done on these machines.
    No preview · Article · May 2014 · Journal of Field Robotics
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    ABSTRACT: We propose a novel method to analyze how human operators use hydraulic manipulators of heavy-duty equipment. The approach is novel in the sense that it applies knowledge of motion planning and optimization techniques used in robotics. As an example, we consider the case of operating a forestry crane. To that end, we use motion data that has been recorded during standard operation with the help of sensors and a data acquisition unit. The data backs up the notion that operators work by performing repeatable patterns observed in the trajectories of the manipulator's joints. We show how this nominal behavior is computed, and consequently, this allows us to present the following: $hbox{1)}$ an analytical procedure to analyze motions, $hbox{2)}$ how to represent the “performance” of the operator in a 2-D plot, $hbox{3)}$ an example of how to use this information to suggest customized control settings, and $hbox{4)}$ some complementary ideas needed for improving efficiency through automation.
    No preview · Article · Jan 2014 · IEEE Transactions on Human-Machine Systems
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    ABSTRACT: This work presents an extension of a design procedure for dynamic output feedback design for systems with nonlinearities satisfying quadratic constraints. In this work we used an axial gas compressor model described by the 3-state Moore-Greitzer compressor model (MG) that has some challenges for output feedback control design (Planovsky and Nikolaev 1990), (Rubanova 2013). The more general constraints for the investigation of the robustness with respect to parametric uncertainties and measurement noise are shown.
    No preview · Article · Jan 2014
  • Anton S. Shiriaev · Leonid B. Freidovich · Mark W. Spong
    [Show abstract] [Hide abstract]
    ABSTRACT: We study the problem of motion planning for underactuated mechanical systems. The idea is to reduce complexity by imposing via feedback a sufficient number of invariants and then compute a projection of the dynamics onto an induced invariant sub-manifold of the closed-loop system. The inspiration comes from two quite distant methods, namely the method of virtual holonomic constraints, originally invented for planning and orbital stabilization of gaits of walking machines, and the method of controlled Lagrangians, primarily invented as a nonlinear technique for stabilization of (relative) equilibria of controlled mechanical systems. Both of these techniques enforce the presence of particular invariants that can be described as level sets of conserved quantities induced in the closed-loop system. We link this structural feature of both methods to a procedure to transform a Lagrangian system via a feedback action into a new dynamical system with a sufficient number of first integrals for the full state space or an invariant sub-manifold. In both cases, this transformation allows efficient (analytical) description of a new class of trajectories of forced mechanical systems appropriate for further orbital stabilization. The contribution is illustrated with a spherical pendulum example that is discussed in detail.
    No preview · Conference Paper · Dec 2013
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    Anton S. Shiriaev · Leonid B. Freidovich · Mark W. Spong
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    ABSTRACT: A new approach to trajectory planning for underactuated mechanical systems is presented and discussed based on analysis of feasible behaviors of a standard 2-DOF benchmark example — the cart–pendulum system. Following the Controlled Lagrangians approach of Bloch et al. (2000) [7], we present and re-establish known conditions and forms of feedback control laws for this example, which are leading to an equivalent completely integrable closed-loop Euler–Lagrange system; and then extend them. As shown, full integrability and, in particular, the presence of a linear in velocities first integral of dynamics plays the key role in an elegant new procedure for trajectory planning.
    Full-text · Article · Dec 2013 · European Journal of Control
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    ABSTRACT: We consider planning and implementation of fast motions for industrial manipulators constrained to a given geometric path. With such a problem formulation, which is quite reasonable for many standard operation scenarios, it is intuitively clear that a feedback controller should be designed to achieve orbital stabilization of a time-optimal trajectory instead asymptotic. We propose an algorithm to convert an asymptotically stabilizing controller into an orbitally stabilizing one and check achievable performance in simulations and, more importantly, in experiments performed on a standard industrial robot ABB IRB 140 with the IRC5-system extended with an open control interface. It is verified that the proposed re-design allows significantly reduced deviations of the actual trajectories from the desired one at high speeds not only for a chosen base feedback design but also outperforming the state-of-the-art commercial implementation offered by ABB Robotics.
    No preview · Conference Paper · Nov 2013
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    Denis Efimov · Wilfrid Perruquetti · Anton Shiriaev
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    ABSTRACT: The paper extends the notion of oscillations in the sense of Yakubovich to hybrid dynamics. Several sufficient stability and instability conditions for a forward invariant set are presented. The consideration is illustrated by the analysis of a model of two-link compass-gait biped robot.
    Full-text · Article · Sep 2013 · Nonlinear Analysis Hybrid Systems

Publication Stats

1k Citations
90.21 Total Impact Points

Institutions

  • 1998-2014
    • Norwegian University of Science and Technology
      • Department of Engineering Cybernetics
      Nidaros, Sør-Trøndelag, Norway
  • 2005-2013
    • Umeå University
      • Department of Applied Physics and Electronics
      Umeå, Västerbotten, Sweden
  • 2012
    • NTNU Samfunnsforskning
      Nidaros, Sør-Trøndelag, Norway
  • 2001-2004
    • University of Southern Denmark
      Odense, South Denmark, Denmark
  • 2000-2004
    • Odense University Hospital
      Odense, South Denmark, Denmark
    • Russian Academy of Sciences
      • Institute of the Problems of Mechanical Engineering
      Moskva, Moscow, Russia