Mobile Robot Path Planning: an Efficient Distance Computation between Obstacles using Discrete Boundary Model (DBM) Md. Nasir Uddin Laskar, TaeChoong Chung Artificial Intelligence Lab, Dept. of Computer Engineering Kyung Hee University, Korea {nasir, tcchung}@khu.ac.kr Abstract. Finding the minimum distance between two obstacles is very crucial for robot path planning and localization, especially for the cleaning and industrial robots. Knowledge of minimum distance is needed for a mobile robot to avoid the obstacles and have the efficient trajectory. This problem has been solved in many different ways. In this paper we present an approach to find the minimum distance between two obstacles that leads to a computationally linear time solution O(pq) in the number of vertices producing minimum number of p and q. The algorithm performs in two phases. Model the obstacle first to build the efficient Bounding Volume Hierarchy (BVH) Tree by generating minimum number of potential points (p and q) to provide the minimum distance and then it finds the required minimum distance using the BVH tree. This method can also handle the case of non-convex objects. Keywords: Path planning, discrete boundary model, obstacle avoidance, distance computation 1 Introduction The distance determination algorithm is mostly popular in the field of robot path planning [1], where the trajectory of a robot through a workspace with objects (obstacles) is planned in order to have a collision free trajectory. Robot path planning is a discipline that deals with the automatic generation of feasible paths for robots in the presence of obstacles. So, finding the minimum distance between two obstacles is essential for a robot to avoid the obstacles and choose the trajectory to its destination [2]. Unlike other distance calculation algorithms, the proposed algorithm finds the pair of the closed points on the boundary surfaces using simple sphere bounding volume hierarchy (BVH) technique with less computational complexity. This DBM method performs better than the combinatorial global optimization method described in [3]. For convex objects, where two objects are checked for interference, such as the one described by Maruyama [4], is the ancestor of some of the distance computation algorithms used nowadays. Some analytical methods like [5], compute the distance 87