In this paper, a cooperative sweeping strategy with deadlock avoidance of complete coverage path planning for multiple cleaning robots in a changing and unstructured environment is proposed, using biologically inspired neural networks. Cleaning tasks require a special kind of trajectory being able to cover every unoccupied area in specified cleaning environments, which is an essential issue for cleaning robots and many other robotic applications. Multiple robots can improve the work capacity, share the cleaning tasks, and reduce the time to complete sweeping tasks. In the proposed model, the dynamics of each neuron in the topologically organized neural network is characterized by a shunting neural equation. Each cleaning robot treats the other robots as moving obstacles. The robot path is autonomously generated from the dynamic activity landscape of the neural network, the previous robot location and the other robot locations. The proposed model algorithm is computationally efficient. The feasibility is validated by simulation studies on three cases of two cooperating cleaning robots. The multiple cleaning robots sweeping will not be trapped in deadlock situations.