Publications

A symmetric mathematical model of a wheeled robot with a trailer is considered for various types of coupling between the robot and the trailer. It is shown that for fixed coupling parameters and fixed initial position of the robot with trailer there are two symmetric abnormal extremals. In motion along these trajectories the robot and the trailer traverse normal extremal trajectories for the sub-Riemannian problem on the group of motions of the plane; the coupling point always draws an inflectional elastica or a straight line.

The work investigates the experimental problem of reparking trailer for a wheeled robot with a trailer. The geometric model with kinematic constraints leads to the sub-Riemannian problem. We solve this problem via nilpotent approximation. The corresponding solution is close to optimal and locally minimizes the total kinetic energy of the driving wheels. A full-scale model is designed in a way to avoid phase constraints usually appearing in trailer systems. We perform 64 different experiments with reparking trailer and obtain the satisfactory accuracy: for one maneuver we repark the trailer with maximum angle error equal to 4 degrees.

This article is concerned with developing an intelligent system for the control of a wheeled robot. An algorithm for training an artificial neural network for path planning is proposed. The trajectory ensures steering optimal motion from the current position of the mobile robot to a prescribed position taking its orientation into account. The proposed control system consists of two artificial neural networks. One of them serves to specify the position and the size of the obstacle, and the other forms a continuous trajectory to reach it, taking into account the information received, the coordinates, and the orientation at the point of destination. The neural network is trained on the basis of samples obtained by modeling the equations of motion of the wheeled robot which ensure its motion along trajectories in the form of Euler’s elastica.

This paper is concerned with the problem of optimal path planning for a mobile wheeled robot. Euler elasticas, which ensure minimization of control actions, are considered as optimal trajectories. An algorithm for constructing controls that realizes the motion along the trajectory in the form of an Euler elastica is presented. Problems and special features of the application of this algorithm in practice are discussed. In particular, analysis is made of speedup and deceleration along the elastica, and of the influence of the errors made in manufacturing the mobile robot on the precision with which the prescribed trajectory is followed. Special attention is also given to the problem of forming optimal trajectories of motion along Euler elasticas to a preset point at different angles of orientation. Results of experimental investigations are presented.