Quadruped robots have the distinct ability to adapt their body and step height to navigate through cluttered environments. Nonetheless, for these robots to utilize their full potential in real-world scenarios, they require awareness of their environment and obstacle geometry. We propose a novel multi-agent robotic system that incorporates cutting-edge technologies. The proposed solution features a 3D neural reconstruction algorithm that enables navigation of a quadruped robot in both static and semi-static environments. The prior areas of the environment are also segmented according to the quadruped robots' abilities to pass them. Moreover, we have developed an adaptive neural field optimal motion planner (AN-FOMP) that considers both collision probability and obstacle height in 2D space. Our new navigation and mapping approach enables quadruped robots to adjust their height and behavior to navigate under arches and push through obstacles with smaller dimensions. The multi-agent mapping operation has proven to be highly accurate, with an obstacle reconstruction precision of 82%. Moreover, the quadruped robot can navigate with 3D obstacle information and the ANFOMP system, resulting in a 33.3% reduction in path length and a 70% reduction in navigation time. The developed project with code is available on GitHub ^{1 1} https://github.com/Iana-Zhura/NeuroSwarm.