# On the Intersection of Computational Geometry Algorithms with Mobile Robot Path Planning
## 1 Introduction  
Computing geometric (CG) attributes of groups of geometric objects in space, such as the straightforward above/below connection of a given point concerning a particular line, is the focus of CG. CG is more broadly concerned with creating and evaluating geometric problem-solving algorithms. In the mathematical discipline of CG [1], practical algorithms for resolving geometric input and output issues are designed, analyzed, and put into practice. It can also refer to the solid modeling methods used to control surfaces, curves, and pattern recognition. The late 1970s saw the creation of this field, which quickly advanced through the 1990s to reach its current state. The study of sorting and searching algorithms employed in one-dimensional spaces to address problems involving multi-dimensional inputs led to the development of computation-based geometry. Its story also influenced insights from computational graph theories used in natural geometric settings. Problems in two-dimensional and, rarely, three-dimensional space were the primary emphasis of this field in the beginning [2]. Most researchers assume that the space's dimension is a tiny constant when considering mathematical issues within multi-dimensional environments. However, scholars who concentrated on discrete algorithms rather than numerical analysis were the ones who founded this field. They also focused on the characteristics of geometric problems rather than conventional continuous questions. As a result, most of the objects in this field are flat and straight, including lines, polygons, planes, and line segments. It occasionally employs curved things like circles, but avoids solid modeling issues with intricate curves and surfaces [3]. Robotics is the study of the creation and application of robots. Robots are geometric items that function in a three-dimensional space or the actual world; therefore, it stands to reason that geometry issues emerge frequently. The design of robots and the work cells in which they must function present additional geometric challenges. The majority ofindustrial robots are fixed-base robot arms. The parts that the robot arm manipulates must be provided in a way that makes it simple for the robot to grip them. It might be necessary to paralyze some components for the robot to work on them. Before the robot can work on them, they might need to be turned toward a known orientation. All of these issues are geometric, occasionally with a kinematic element. The path planning issue, in which a robot must discover a path across an environment with obstacles, is discussed in detail in a later section of this review. We examine simple, complex path-planning problems in this article. The broader issue of task planning has several sub-problems, one of which is motion planning. Giving a robot high-level tasks, such as \"vacuuming the room\", and then letting the robot decide how to carry them out is desirable. Planning motions, the sequence in which to complete sub-tasks, and other things fall within this category. **Methodology:** This is a brief review of the intersection of CG and mobile robot path planning. To provide a structured overview, this paper adopts a systematic review methodology as discussed below:  
1. First, the scope of path planning is clearly demarcated into two primary areas: single-robot and multi-robot systems;
2. The review predominantly focuses on the literature published between 2016 and 2023, considering papers using CG in mobile robots, ensuring relevance and incorporation of the latest advancements in the field; however, to discuss the foundational work on computational geometry, we have considered pioneering works from the years 1969 to 2008;
3. We also have taken articles from the winners of CG-SHOP 2021, as they are the most relevant and recent works on the discussed topic;
4. During the literature search, keywords such as \"computational geometry in robot path planning\", \"single-robot path planning\", \"multi-robot coordination\", and \"kinodynamic path planning\" were employed.