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Vol. 7, No. 4

Vol. 7, No. 4, 2011
Mobile robots

Abstract
Citation: Russian Journal of Nonlinear Dynamics: Mobile Robots (From editors), Rus. J. Nonlin. Dyn., 2011, Vol. 7, No. 4, pp. 729-732
DOI:10.20537/nd1104001
Campion G.,  Bastin G.,  D’Andréa-Novel B.
Abstract
The structure of the kinematic and dynamic models of wheeled mobile robots is analyzed. It is shown that, for a large class of possible configurations, they can be classified into five types, characterized by generic structures of the model equations. For each type of model the following questions are addressed: (ir)reducibility and (non)holonomity, mobility and controllability, configuration of the motorization, and feedback equivalence.
Keywords: wheeled mobile robots, kinematic and dynamic models, nonholonomity, control
Citation: Campion G.,  Bastin G.,  D’Andréa-Novel B., Structural properties and classification on kinematic and dynamic models of wheeled mobile robots, Rus. J. Nonlin. Dyn., 2011, Vol. 7, No. 4, pp. 733-769
DOI:10.20537/nd1104002
Zobova A. A.
Abstract
The paper considers a new laconic method for deriving the dynamical equations of nonholonomic systems proposed by Ya.V. Tatarinov in 2003 for description of the dynamics of wheel systems of three different types (piano wheel, carriages with roller-bearing wheels, with differential drive).
Keywords: systems with differential constraints, laconic form of Ya.V. Tatarinov’s equations of motion, mobile vehicles
Citation: Zobova A. A., Application of laconic forms of the equations of motion in the dynamics of nonholonomic mobile robots, Rus. J. Nonlin. Dyn., 2011, Vol. 7, No. 4, pp. 771-783
DOI:10.20537/nd1104003
Borisov A. V.,  Kilin A. A.,  Mamaev I. S.
Abstract
We consider a nonholonomic model of the dynamics of an omni-wheel vehicle on a plane and a sphere. An elementary derivation of equations is presented, the dynamics of a free system is investigated, a relation to control problems is shown.
Keywords: omni-wheel, roller-bearing wheel, nonholonomic constraint, dynamical system, invariant measure, integrability, controllability
Citation: Borisov A. V.,  Kilin A. A.,  Mamaev I. S., An omni-wheel vehicle on a plane and a sphere, Rus. J. Nonlin. Dyn., 2011, Vol. 7, No. 4, pp. 785-801
DOI:10.20537/nd1104004
Krasinskiy A. Y.,  Kayumova D. R.
Abstract
The problem of determining the minimum number of wheel deformation parameters to adequately describe the vehicle dynamics is considered. The necessity to include some system parameter into consideration is proposed to determine via check of stabilization problem solvability (of a given unperturbed motion to nonasymptotic stability in all variables). In this paper, as a test case the problem of stabilization of rectilinear steady motion of the simplest and most studied model of differential drive robot is selected. Computational experiments made via PyStab software show that the formal realization of the controllability criterion for complete system does not always provide the practical solvability of stabilization problem. In this case the stabilizing control is determined by solution of linear-quadratic problem via N.N. Krasovskiy method for controllable linear subsystem. To learn about the stability of the full nonlinear system closed with found control, methods of analytical mechanics and nonlinear stability theory are involved. The study of the robot dynamics is performed by PyStab. This software is intended for automation of research of mechanical systems stability and stabilization problems. In the transition to the numerical consideration along with PyStab NSA software is used since calculation time and the structure of the nonlinear terms of equations of perturbed motion will depend on what stage of the calculations the substitution of numerical parameters of the system is performed.
Keywords: analytical mechanics, stability, stabilization, differential drive robot, wheels deformability
Citation: Krasinskiy A. Y.,  Kayumova D. R., On the Influence of the Wheels Deformability on the Differential Drive Robot Dynamics, Rus. J. Nonlin. Dyn., 2011, Vol. 7, No. 4, pp. 803-822
DOI:10.20537/nd1104005
Kuleshov A. S.,  Hubbard M.,  Peterson D. L.,  Gede G.
Abstract
We present a kinematic analysis and numerical simulation of the toy known as the oloid. The oloid is defined by the convex hull of two equal radius disks whose symmetry planes are at right angles with the distance between their centers equal to their radius. The no-slip constraints of the oloid are integrable, hence the system is essentially holonomic. In this paper we present analytic expressions for the trajectories of the ground contact points, basic dynamic analysis, and observations on the unique behavior of this system.
Keywords: oloid, rolling motion, holonomic system, kinematics
Citation: Kuleshov A. S.,  Hubbard M.,  Peterson D. L.,  Gede G., Motion of the oloid on the horizontal plane, Rus. J. Nonlin. Dyn., 2011, Vol. 7, No. 4, pp. 825-835
DOI:10.20537/nd1104006
Belotelov V. N.
Abstract
The problem of determining the phase coordinates of a pendulum on a cylinder by measurements of the inclination angle of the cylinder relative to the pendulum is formulated and solved. A necessary and sufficient condition for observability is found. A linear Luenberger observer is constructed whose output variables are used to close a linear feedback control system. Numerical experiments are performed showing the possibility of using this type of control (by means of variables of the observer) in a nonlinear model of controlled motion of a pendulum on a cylinder.
Keywords: linear observer, Luenberger observer, inverted pendulum, pendulum on a cylinder, two-wheeled pendulum
Citation: Belotelov V. N., The problem of determining the inclination angle of a pendulum on a cylinder, Rus. J. Nonlin. Dyn., 2011, Vol. 7, No. 4, pp. 837-844
DOI:10.20537/nd1104007
Vorochaeva (Volkova) L. Y.,  Jatsun S. F.
Abstract
The mathematical model of the floating robot moving on the curvilinear trajectory on a liquid environment at the expense of movement of two internal masses and external force of the viscous friction is presented. Results of modeling of movement of the object are received.
Keywords: three-mass robot, force of viscous friction, liquid environment, control system, curvilinear trajectory, program-controlled movement
Citation: Vorochaeva (Volkova) L. Y.,  Jatsun S. F., Control of the three-mass robot moving in the liquid environment, Rus. J. Nonlin. Dyn., 2011, Vol. 7, No. 4, pp. 845-857
DOI:10.20537/nd1104008
Sinyavskiy O. Y.,  Kobrin A. I.
Abstract
Method of reinforcement learning of spiking neural network that controls robot or virtual agent is described. Using spiking neurons as key elements of a network allows us to exploit spatial and temporal structure of input sensory information. Teaching of the network is implemented with a use of reinforcement signals that come from the external environment and reflect the success of agent’s recent actions. A maximization of the received reinforcement is done via modulated minimization of neurons’ informational entropy that depends on neurons’ weights. The laws of weights changes were close to modulated synaptic plasticity that was observed in real neurons. Reinforcement learning algorithm was tested on a task of a resource search in a virtual discrete environment.
Keywords: spiking neuron, adaptive control, reinforcement learning, informational entropy
Citation: Sinyavskiy O. Y.,  Kobrin A. I., Reinforcement learning of a spiking neural network in the task of control of an agent in a virtual discrete environment, Rus. J. Nonlin. Dyn., 2011, Vol. 7, No. 4, pp. 859-875
DOI:10.20537/nd1104009
Abstract
Citation: Books selected for publication in the series «Dynamical Systems and Robotics», Rus. J. Nonlin. Dyn., 2011, Vol. 7, No. 4, pp. 877-888
Abstract
Citation: New books. New issues of «Regular and Chaotic Dynamics», Rus. J. Nonlin. Dyn., 2011, Vol. 7, No. 4, pp. 879-883

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