To address the shortcomings of traditional bionic algorithms in path planning, such as inefficient search processes, extended planning distances and times, and suboptimal dynamic obstacle avoidance, this paper introduces a fusion algorithm called NRBO-DWA. This algorithm is specifically applied to plan the path for a tube-changing robot in a knitting workshop. The process begins with spatial modeling based on the actual parameters of the workshop, followed by the development of a comprehensive, objective function for the robot in line with the relevant constraints. The NRBO algorithm is then integrated with the DWA algorithm to boost its dynamic obstacle avoidance capabilities, while a path correction mechanism is introduced to minimize unnecessary detours. Finally, a comparative experiment is designed to evaluate the algorithm against the GA, PSO, and SSA algorithms. Simulation results demonstrate that in a dynamically complex 3D environment, the NRBO-DWA algorithm outperforms in terms of higher 3D search efficiency, shorter total path length, and faster planning times.