Collision-Free Tracking for a Mobile Robot Based on Purely Geometric Planning

Abstract

A purely geometric planning method for a mobile robot in unknown environments is proposed to ensure robot collision avoidance against obstacles within the safety time interval while moving to the goal. The robot initially detects a point cloud of obstacles using a 2D LiDAR. Euclidean clustering is employed to classify the point cloud into point classes. The obstacle is then identified as a directed closed-loop rectangle for each point class. A relative orientation kd-tree is designed to store the vertices of the obstacles and to determine the obstacles to be considered in the obstacle avoidance algorithm. A velocity divider is introduced to obtain a linear convex area of possible obstacle avoidance velocities. Thus, linear planning is employed to calculate the optimal obstacle avoidance velocity for control. A virtual reference point method is proposed to solve the problem of an unreachable goal in a singular configuration. Experimental results show that the directed closed-loop rectangle and the relative orientation kd-tree facilitate the quick updating of required obstacle points with low-cost sensor equipment. The deterministic path for a given scenario can be obtained, demonstrating the reliability of geometric planning for both the obstacle avoidance velocity region and the optimal obstacle avoidance velocity. The proposed algorithm is finally validated for multiple obstacles and dynamic environments with moving obstacles.