Comparative Analysis of Cartesian, Cylindrical and Spherical Grids in a Graph-Based Obstacle-Avoidance Planner for Industrial Robots

This paper presents a comparative analysis of three workspace discretization strategies, Cartesian, cylindrical and spherical, integrated into a graph-based path planning application developed in Python and connected to RoboDK. The study starts from the observation that the workspace of an articulated industrial robot is not naturally aligned with a uniform Cartesian partitioning, and this aspect can influence the internal structure of the graph and the planning effort. For the initial analysis, the three discretizations were tested for the same start-goal pair and for resolutions ranging from 1500 mm to 600 mm. All three variants led to the same validated route, with a length of 3292.215 mm, which shows that the main differences did not occur at the level of the final geometric solution, but at the level of the internal structure of the graph. On average, the spherical discretization generated the most compact graph, with 101.7 nodes and 256.4 edges, compared to 277.3 nodes and 724.9 edges for the Cartesian discretization. The average planning time was also shorter for the spherical discretization, 0.0069 s, compared to 0.0150 s for the Cartesian discretization and 0.0127 s for the cylindrical discretization. At the 600 mm resolution, the spherical discretization used approximately 63% fewer nodes and 66% fewer edges than the Cartesian discretization, while retaining a larger number of candidate routes. The evaluation was then extended by 180 additional trials, performed on two scenarios and on several start-goal pairs. Of these, 151 led to valid routes, corresponding to an overall success rate of 83.9%. The results show that the spatial representation influences the graph size, connectivity, planning time and length of validated routes. However, additional tests also show that these effects depend on the scenario and the criterion analyzed. The spherical discretization produced the most compact graphs, but did not lead in all cases to the shortest routes or the highest success rate. Therefore, the contribution of the paper consists in a controlled comparative evaluation of the influence of the spatial representation on a graph-based planning pipeline, not in demonstrating the universal superiority of a single discretization.