Citation: S , omîtc˘ a, I.-A.; Brad, S.; Florian, V.; Deaconu, S , .-E. Improving Path Accuracy of Mobile Robots in Uncertain Environments by Adapted Bézier Curves. Electronics 2022, 11, 3568. https://doi.org/10.3390/ electronics11213568 Academic Editor: Felipe Jiménez Received: 19 September 2022 Accepted: 27 October 2022 Published: 1 November 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2022 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/). electronics Article Improving Path Accuracy of Mobile Robots in Uncertain Environments by Adapted Bézier Curves Ioana-Alexandra S , omîtc˘ a 1 , Stelian Brad 2, * , Vlad Florian 2 and S , tefan-Eduard Deaconu 3 1 Department of Mathematics, Faculty of Automation and Computer Sciences, Technical University of Cluj-Napoca, Baritiu Street, No. 26-28, 400027 Cluj-Napoca, Romania 2 Department of Engineering Design and Robotics, Faculty of Industrial Engineering, Robotics and Management of Production, Technical University of Cluj-Napoca, B-dul Muncii, No. 103-105, 400144 Cluj-Napoca, Romania 3 Department of Computer Science, Faculty of Mathematics and Computer Science, University of Bucharest, Academiei Street, No. 14, 010014 Bucharest, Romania * Correspondence: stelian.brad@staff.utcluj.ro Abstract: An algorithm that presents the best possible approximation for the theoretical Bézier curve and the real path on which a mobile robot moves in a dynamic environment with mobile obstacles and boundaries is introduced in this paper. The algorithm is tested on a set of scenarios that comprehensively cover critical situations of obstacle avoidance. The selection of scenarios is made by deploying robot navigation performances into constraints and further into descriptive characteristics of the scenarios. Computer-simulated environments are created with dedicated tools (i.e., Gazebo) and modeling and programming technologies (i.e., Robot Operating System (ROS) and Python). It is shown that the proposed algorithm improves the performance of the path for robot navigation in a highly dynamic environment, with dense mobile obstacles. Keywords: mobile robots; path planning; local planner; Bézier curves; dynamic environments 1. Introduction A Bézier curve is a parametric curve, very well-known nowadays due to its multiple applications in science and engineering. It can approximate with high fidelity various forms found in nature and in society (medical image reconstruction [1], human organs [2], facial recognition [3], shape description [4], computer graphics and animation [5], traffic control [6], bus parking [7], automatic parking [8], path planning for robots [9–19], etc). Bézier curves were discovered by a French engineer named Piere Bézier [20]. He used them for the first time in designing Renault and Citroen cars to improve the aesthetics of the car’s shape [21]. Due to the increased interest in autonomous vehicle applications, in this paper, the authors introduce a Bézier curve-driven algorithm for improving mobile robot navigation. This research might be expanded to autonomous cars, too. However, initially testing such algorithms on less costly vehicles, such as mobile robots, is desirable. The major challenge is to prove that autonomous navigation driven by such algorithms among fixed and mobile obstacles is carried out safely, without collisions, and smoothly. Up to this moment, the scientific literature reports a variety of developments in the field of robot path planning [22–25], etc. To focus the research from this paper, investigations for documenting the state of the art were conducted using Clarivate Analytics and Scopus. Past research was collected using the keyword “path planning”, which returned 5945 independent titles. The investigation was refined by looking inside this set with the keyword “Bézier curves”. The range of articles narrowed to 260. This resulting subset was analyzed, and it was concluded that the articles introduced in the next section are relevant to the purpose of this work. Electronics 2022, 11, 3568. https://doi.org/10.3390/electronics11213568 https://www.mdpi.com/journal/electronics