Due to the accumulation error caused by the odometer's reading, there is a significant error in the robot's pose estimation and mapping using the traditional Rao-Blackwellised particle filter-simultaneous localization and mapping (RBPF-SLAM) in indoor navigation; meanwhile, the conventional path planning method has low real-time performance and dynamic obstacle avoidance under sudden environmental changes. To solve this problem, we propose an indoor real-time laser SLAM control method with biological inspired neural network (BINN), which combines high computational efficiency and precision of RBPF-SLAM and BINN's real-time dynamic obstacle avoidance. First, we use the robot's pose difference between the current and the previous time to replace the odometer's reading as the input of the suggested distribution function in RBPF-SLAM to extract new particles. Then, the BINN is used to avoid the dynamic obstacles in real-time path planning. Finally, the BINN is used to relocate the robot in real-time path planning and correct the robot's pose. Comparison between simulation and real experimental results show that the robot positioning error of our proposed model is less than 10%, and the mapping error is less than 9%. Moreover, compared with A*
and Dijkstra in terms of path qualities, the length, the number of turns, and the planning time of the path planned by BINN, reductions of 7.09%, 14.29%, and 6.97% are obtained, respectively, which effectively improve the positioning and mapping accuracy of indoor navigation and the real-time performance of dynamic path planning. Our proposed model is also applicable in other fields, such as unmanned driving and logistics transportation.