Three-Dimensional Path Planning: Navigating through Rough Mereology

TL;DR

The paper addresses 3D path planning for drones under uncertainty by leveraging rough mereology to form mereological potential fields. It presents a 3D square-fill expansion from the goal, a Weighted Euclidean distance-based path search to favor feasible routes, and subsequent field filtering and path smoothing to produce clear trajectories. Key contributions include adapting the square-fill method to 3D with 24-neighbor exploration, integrating rough inclusion-based proximity metrics, and achieving real-time, camera-driven environment calibration via OpenCV for gate/obstacle detection. The work demonstrates end-to-end viability from real-time sensing to obstacle-aware navigation, highlighting practical potential for drone deployment in cluttered 3D spaces using mereological reasoning.

Abstract

In this paper, we present an innovative technique for the path planning of flying robots in a 3D environment in Rough Mereology terms. The main goal was to construct the algorithm that would generate the mereological potential fields in 3-dimensional space. To avoid falling into the local minimum, we assist with a weighted Euclidean distance. Moreover, a searching path from the start point to the target, with respect to avoiding the obstacles was applied. The environment was created by connecting two cameras working in real-time. To determine the gate and elements of the world inside the map was responsible the Python Library OpenCV [1] which recognized shapes and colors. The main purpose of this paper is to apply the given results to drones.

Figures (9)

• Figure 1: The visualization of an idea of neighbors creating in 3-dimensional space. The N, W, S, E, NE, SE, SW, and NW represent the world direction. Values x, y, z determines 3 dmiensions.
• Figure 2: The middle point inside the cube determines the specific goal point. Values x,y, and z determine the dimension, +1/-1 is a sample value of the declared distance. In that case, we received 24 new neighbors, which are generated in each iteration of an algorithm. What is important is that the central point determines the goal point only in the first iteration of an algorithm, after that the central point turns to each neighbor created in the previous iteration.
• Figure 3: The Rough Mereological Potential Field algorithm constructed in 3-dimensional environment. The below case represents the goal point located at the center of a cube without any obstacles. The bigger cube represents the gate for a robot.
• Figure 4: The Rough Mereological Potential Field algorithm constructed in 3-dimensional environment. The below case represents the goal point located at the center of a cube with only one obstacle. The bigger cube represents the gate for a robot.
• Figure 5: The Rough Mereological Potential Field algorithm constructed in 3-dimensional environment. The below case represents the goal point located at the point (120,120,120) represented as a blue cube with three red obstacles. The bigger cube represents the gate for a robot.