Anton S. Shiriaev

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We present a constructive tool for generation and orbital stabilization of periodic solutions for underactuated nonlinear systems. Our method can be applied to any mechanical system with a number of independent actuators smaller than the number of degrees of freedom by one. The synthesized feedback control law is nonlinear and time-dependent. It is derived(More)
This paper provides an introduction to several problems and techniques related to controlling periodic motions of dynamical systems. In particular, we define and discuss problems of motion planning and orbit planning, analysis methods such as the classical Poincaré first-return map and the transverse linearization, and exponentially orbitally stabilizing(More)
The paper suggests an explicit form of a general integral of motion for some classes of dynamical systems including n-degrees of freedom Euler–Lagrange systems subject to (n− 1) virtual holonomic constraints. The knowledge of this integral allows to extend the classical results due to Lyapunov for detecting a presence of periodic solutions for a family of(More)
The Furuta pendulum consists of an arm rotating in the horizontal plane and a pendulum attached to its end. Rotation of the arm is controlled by a DC motor, while the pendulum is moving freely in the plane, orthogonal to the arm. Motivated, in particular, by possible applications for walking/running/balancing robots, we consider the Furuta pendulum as a(More)
Abstract: The problem is to create a hybrid periodic motion, reminiscent of walking, for a model of an underactuated biped robot. We show how to construct a transverse linearization analytically and how to use it for stability analysis and for design of an exponentially orbitally stabilizing controller. In doing so, we extend a technique recently developed(More)
• Non-linear dynamics modelling description for simulating the behaviour of forestry cranes 2014 • Modeling an industrial flotation process: A case study at the mining company Boliden AB 2012 • Modeling dynamics of an electro-hydraulic servo actuated manipulator: A case study of a forestry forwarder crane 2012 • Underactuated mechanical systems:(More)
This paper is devoted to the problem of global (local) stabilization of a prescribed subset of the state space for a passive a$ne nonlinear system. It is assumed that the desired attractive set can be described as an inverse image of zero value of some smooth nonnegative function, and that this function does not increase along the solutions of the unforced(More)