Abstract
A companion robot is capable of performing a variety of activities and thus supporting the elderly and people withdisabilities. It should be able to overcome obstacles on its own, respond to what is happening around it in real-time, andcommunicate with its surroundings. It is particularly important to pay attention to these issues, as a companion robot is likely tobecome a participant in traffic. The aim of the research is to develop a mathematical model that takes into account the use of twonavigation solutions in the companion robot. Thanks to this, it will be possible to use the obtained mathematical relationships tocompare various types of navigation and make a rational choice, enabling the implementation of the assumed activities in aspecific external environment. What is new in this article is the analysis of several navigation methods and the presentation ofresearch carried out in real time using an actual robot.
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