Dr. Lyuba Alboul2026-06-092026-06-09https://dspace.academy.edu.ly/handle/123456789/2240Therefore, we have developed algorithms based on VG called the Central algorithm (CA) and its associate, the Optimisation Central algorithm (OCA). Contrary to VG, CA selects a relatively smaller number of vertices using the so-called Central Baseline (CB), in which the obstacles that intersect with the baseline only are considered, and it generates waypoints, travelling, through which the robots can avoid obstacles to reach their targets. Both algorithms employ a smaller number of obstacles, and this reduces the computational complexity of finding the optimal paths. Thus, it can create paths relatively fast and is convenient for path planning applications in obstacle-rich environments, whilst retaining the advantages of the VG. CA and OCA have made finding the shortest paths simpler because the process of path planning is equipped with pre-calculated step-by-step instructions. All these features make it more efficient than the VG.In this thesis, we propose a new method to design a roadmap-based path planning algorithm in a 2D static environment, which assumes a-priori knowledge of robots’ positions, their goals’ positions, and surrounding obstacles. The new algorithm, called Multi-Robot Path Planning Algorithm (MRPPA), combines Visibility graph VG method with the algebraic connectivity ( 𝜆􀬶) of the graph Laplacian and Dijkstra's algorithm. The MRPPA implies sequential path planning for each robot based on the measured value of algebraic connectivity of the graph Laplacian, and the predefined weight functions to controlling the motion of robots while avoiding inter-robot collision, when planning the path of each robot, considers all the paths already planned for path correction and collisions’ avoidance. The algorithm provides optimality of all planned paths because the paths depend on the order of planning, thus the choice of the right sequence for path planning of robots have significant impact on the performance of the team. VG has been selected because it produces solutions with optimal path lengths, i.e., short distances travelled from start positions to target, especially if combined with Dijkstra’s algorithm. However, VG forces the robots to move near obstacles, and is computationally expensive, because it uses all vertices in the environment.Applications to Robotics