mathematics Article Predicate-Based Model of Problem-Solving for Robotic Actions Planning Oleksandr Tsymbal 1,† , Paolo Mercorelli 2, * ,† and Oleg Sergiyenko 3,†   Citation: Tsymbal, O.; Mercorelli, P.; Sergiyenko, O. Predicate-Based Model of Problem-Solving for Robotic Actions Planning. Mathematics 2021, 9, 3044. https://doi.org/10.3390/ math9233044 Academic Editor: António M. Lopes Received: 2 October 2021 Accepted: 19 November 2021 Published: 26 November 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1 Faculty of Automatics and Computerized Technologies, Kharkiv National University of Radio Electronics, Nauki Avenue 14, 61166 Kharkiv, Ukraine; oleksandr.tsymbal@nure.ua 2 Institute of Product and Process Innovation, Leuphana University of Lüneburg, Universitätsallee 1, D-21335 Lüneburg, Germany 3 Faculty of Engineering, Autonomous University of Baja California, Blvd. Benito Juárez, Mexicali 21280, Mexico; srgnk@uabc.edu.mx * Correspondence: paolo.mercorelli@leuphana.de; Tel.: +49-4131-677-1896 † The authors contributed equally to this work. Abstract: The aim of the article is to describe a predicate-based logical model for the problem- solving of robots. The proposed article deals with analyses of trends of problem-solving robotic applications for manufacturing, especially for transportations and manipulations. Intelligent agent- based manufacturing systems with robotic agents are observed. The intelligent cores of them are considered from point of view of ability to propose the plans of problem-solving in the form of strategies. The logical model of adaptive strategies planning for the intelligent robotic system is composed in the form of predicates with a presentation of data processing on a base of set theory. The dynamic structures of workspaces, and a possible change of goals are considered as reasons for functional strategies adaptation. Keywords: adaptation; problem-solving; robotics; predicates; manufacturing system 1. Introduction Mobile robots are remarkable cases of highly developed technology and systems. The robot community has developed a complex analysis to meet the increased demands of the control challenges pertaining to the movement of robots. The research on mobile robots has attracted many researchers in recent years. In practical application, very often, the robot operating system (ROS) is used for the communication between the robot and its control system. Different control systems are applied in Robotino. For instance, in [1,2], a linear model predictive control is used for optimal motion control, with a great advantage obtained in terms of global optimality and in computational load. This paper is an extension of work originally presented in SPEEDAM 2020 [3], which proposed an analysis of a computer-integrated system of mobile robots application for transportation and the manipulation of goods inside manufacturing workspaces, and connected to works of P. Mercorelli and O. Sergiyenko: the consideration of a set theory- based dynamic model to describe problem-solving processes in the execution of mobile robots’ paths or manipulation tasks. The description of a logical model as a key element of the decision-making system for robotic applications was connected to works of O. Tsymbal. Modern manufacturing systems are described by an intensive application of infor- mation technologies on the base of computer networks, artificial intelligence, and digital technologies, and must correspond to requirements of mobility, of fast responses to the changing quality of products, of small sizes, specific, individual, customer, and environ- mental demands. In the last two decades, industrial engineers and scientists have spent a substantial amount of time and effort in researching the advanced production systems and their influence in the global market [4,5]. Mathematics 2021, 9, 3044. https://doi.org/10.3390/math9233044 https://www.mdpi.com/journal/mathematics