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Complete coverage path planning requires the robot path to cover every part of the workspace, which is an essential issue in cleaning robots and many other robotic applications such as vacuum robots, painter robots, land mine detectors, lawn mowers, automated harvesters, and window cleaners. In this paper, a novel neural network approach is proposed for complete coverage path planning with obstacle avoidance of cleaning robots in nonstationary environments. The dynamics of each neuron in the topologically organized neural network is characterized by a shunting equation derived from Hodgkin and Huxley's (1952) membrane equation. There are only local lateral connections among neurons. The robot path is autonomously generated from the dynamic activity landscape of the neural network and the previous robot location. The proposed model algorithm is computationally simple. Simulation results show that the proposed model is capable of planning collision-free complete coverage robot paths.