Collision-free tracking for a mobile robot based on purely geometric planning

A purely geometric planning method for a mobile robot in unknown environments is proposed to ensure collision avoidance with obstacles within the safety time interval while moving toward 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 distinct point classes. Each point class is then identified as a directed closed-loop rectangle representing the obstacle. A relative orientation kd-tree is designed to store the vertices of the obstacles and determine which obstacles should be considered in the obstacle avoidance algorithm. A velocity divider is introduced to obtain a linear convex area of possible obstacle avoidance velocities. Linear planning is then used to calculate the optimal obstacle avoidance velocity for control. A virtual reference point method is proposed to address the problem of an unreachable goal in a singular configuration. Experimental results show that the directed closed-loop rectangle and relative orientation kd-tree facilitate rapid updates of required obstacle points with low-cost sensor equipment. A deterministic path for a given scenario is demonstrated, confirming the reliability of the geometric planning method for the obstacle avoidance velocity region and the optimal obstacle avoidance velocity. The proposed algorithm is further validated in scenarios with multiple obstacles and dynamic environments involving moving obstacles.