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Yang and Meng (2000) proposed a biologically inspired neural network model for robot trajectory generation. The generated robot path in a static environment is optimal in the sense of the shortest robot path, which is demonstrated by descriptive analysis and simulations studies, without any rigorous theoretical analysis on the optimality. In this paper, theoretical analysis of the global stability of the neural network system is presented. In addition, the shortest path in a static environment is rigorously proved, and the condition resulting in an optimal solution is formulated. Two case studies of path planning in static and dynamic environments are conducted to demonstrate the effectiveness of the algorithm.