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.

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).

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.

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.

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.

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.

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.

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.