In real world applications there exist arbitrarily shaped obstacles in the workspace during complete coverage path planning of cleaning robots. A cleaning robot should be able to sweep in a variety of corners and in the vicinity of arbitrarily shaped obstacles in an indoor environment. Consequently, the robot is required not only to effectively avoid the obstacles, but also to delicately cover every area in the vicinity of obstacles. In the paper, a solution to vicinity problem of obstacles in complete coverage path planning is proposed using neural-neighborhood analysis. The path planner is a biologically inspired neural network. The proposed model is capable of planning a real-time path to reasonably cover every area in the vicinity of obstacles. The robot path is autonomously generated through the dynamic neural activity landscape of the neural network and the previous robot location. The effectiveness of the proposed approach is verified through computer simulations.