DBSCAN-Based Minimum Enclosing Ellipse Using the Control Barrier Function for Safe Navigation of Mobile Robots

This paper aims to reduce the redundant unsafe area in quadratic program approaches based on the Control Barrier Function (CBF) and the Control Lyapunov Function (CLF) for collision avoidance, hereafter referred to as the CBF-CLF approach. Existing CBF-CLF quadratic program approaches typically construct CBF based on Euclidean distance; however, the redundant unsafe area due to obstacles is excessively large, which may prevent finding feasible solutions. To address this issue, this study employs density-based spatial clustering of applications with noise (DBSCAN) and the Minimum Enclosing Ellipse (MEE) to reduce the unsafe area. The proposed approach is referred to as the DBSCAN-MEE-CBF. The effectiveness of the proposed method is demonstrated through both computer simulations and real-world experiments. Specifically, the proposed method reduces the size of the redundant unsafe area by up to 26.52% while maintaining robust collision avoidance.