# Construction of a mathematical model of the dynamics of an autonomous mobile robot of variable configuration

## Authors

• Natalja Ashhepkova Oles Honchar Dnipro National University, Ukraine

## Keywords:

autonomous mobile robot, manipulator, mathematical model, dynamics, dynamic parameters relationship

## Abstract

This paper considers the construction of a mathematical model of the movement of an autonomous mobile robot (AMR) in variable configuration, taking into account the relationship of the dynamic parameters of a mechanical system.

As an example, the design of AMR with a manipulator is considered.

The object of this study is the dynamics of AMR with a manipulator. The peculiarities of the dynamics of AMR with the manipulator are due to the change in the position of the center of mass of the system with the relative movement of the manipulator and the commensurate non-diagonal and diagonal elements of the inertia tensor calculated relative to the axes of the base coordinate system. The construction of the mathematical model was carried out according to the Nyton-Euler method. The resulting mathematical model contains:

– an equation of motion of the center of mass of the AMR system of variable configuration along the trajectory in the inertial coordinate system;

– an equation of angular motion of AMR in variable configuration in the inertial coordinate system;

– an equation of motion of the manipulator with respect to AMR. In a general case, the center of mass of the AMR platform moves in a horizontal plane. Establishing the relationship of dynamic parameters of the mechanical system will make it possible to maintain functionality and ensure the orientation of AMR in vertical planes despite the movement of the manipulator. As an object of control, AMR with a manipulator is a multi-connected system with a cross-internal connection of control channels, which is formed by the dynamic parameters of a mechanical system. Based on the results of mathematical modeling using the proposed model, it is possible to develop algorithms for adaptive control using cross-connection of channels. This will make it possible to identify reserves to reduce energy consumption, increase stability, improve the efficiency and survivability of AMR in variable configuration during autonomous work under extreme conditions.

## Author Biography

### Natalja Ashhepkova, Oles Honchar Dnipro National University

PhD, Associate Professor

Department of Mechanotronics

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2022-12-30

## How to Cite

Ashhepkova, N. (2022). Construction of a mathematical model of the dynamics of an autonomous mobile robot of variable configuration . Eastern-European Journal of Enterprise Technologies, 6(7 (120), 30–44. https://doi.org/10.15587/1729-4061.2022.269840

## Section

Applied mechanics