Control program for translational and rotational motion of Uniaxial Wheeled Module

Theoretical mechanics


Аuthors

Chernomorskii A. I.1*, Kuris E. D.2**, Mel'nikov V. E.1***

1. ,
2. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: chernomorsсky@yandex.ru
**e-mail: ekuris@mail.ru
***e-mail: ve_melnik@mail.ru

Abstract

Uniaxial wheeled module (UWM) is one of the most perspective types of unmanned ground vehicle for environmental monitoring tasks, particularly aerodrome. This vehicle is capable of both carrying equipment, and managing angular orientation of the platform, on which it is mounted. Simple algorithms for forming control moments, developed by the UWM wheels’ drive motors, were obtained. These moments provide a quasi-optimal in time UWM movement from the starting position on the horizontal underlying surface to the final position at the given UWM orientation in these points of its stationary positions. Non-holonomic vehicle model was obtained on the assumption of the absence of wheels slippage relative to the underlying surface, and insignificance of the effect of the platform angular movement around wheel axis on the linear movement of the center of UWM wheel axis. Adequacy of this model was confirmed by the results of experimental studies of UWM developed in MAI. Two types of its trajectories of simple configuration, predetermining the minor time of the UWM’s movement realization. It was demonstrated analytically, that it was impossible to transfer the UWM from the starting stationary position to the final one with the given in this position course angle within a single switching of the moments signs. Thus, the first trajectory was split into two stages, and the second into three ones. In each stage, the moments are formed based on maximum principle of Pontryagin in the form of constant in modulus (at each stage) maximum possible values, using at the stages only one simultaneous switching of these moments’ signs.

Travelling times’ comparative evaluation for UWM moving along the two selected trajectories was performed, based on the developed algorithms for forming control moments of wheels’ drive motors. It revealed the dependency of these times from both azimuth angle and course angle of the UWM final position

.

Keywords:

uniaxial wheeled module, stationary positions, analytical solution, control program, torque

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