本文为美国密苏里科技大学（作者：Grant Gilbert Arthur Rivera）的硕士论文，共46页。

路径规划用于但不限于机器人、遥测、航空航天和医疗应用。路径规划的目标是在避开障碍物的同时，确定从起始点到目的地的路径。由于时间、地形、速度限制和许多其他因素都会影响路径的最佳性，因此这条路径可能并不总是最短的。然而，在本文中，路径的长度、计算时间和平滑度是唯一被考虑的约束，路径的长度是最重要的。有多种算法可以用于路径规划，但蚁群优化（ACO）、神经网络和A*将是本文研究的算法。一般迷宫的求解问题已经有了大量的研究，但是本文的贡献是将蚁群优化扩展到迷宫路径规划中，为神经网络的应用创造了一个新的机会，并在A*算法中加入了鸟瞰图。

本文所使用的蚁群优化算法能够找到一条通向目标的路径，但与本文所讨论的神经网络和A*算法相比，需要更长的计算时间。本文使用Hopfield型神经网络传播能量来创建场景，并使用梯度下降来寻找距离最短的路径，但是本文修改了场景的创建方式，以防止神经网络陷入局部极小。最后一个贡献是将鸟瞰图应用到A*算法中，以了解更多有关环境的信息，这有助于创建更短、更平滑的路径。

Path planning is used in, but not limited to robotics, telemetry, aerospace, and medical applications. The goal of the path planning is to identify a route from an origination point to a destination point while avoiding obstacles. This path might not always be the shortest in distance as time, terrain, speed limits, and many other factors can affect the optimality of the path. However, in this thesis, the length, computational time, and the smoothness of the path are the only constraints that will be considered with the length of the path being the most important. There are a variety of algorithms that can be used for path planning but Ant Colony Optimization (ACO), Neural Network, and A* will be the only algorithms explored in this thesis. The problem of solving general mazes has been greatly researched, but the contributions of this thesis extended Ant Colony Optimization to path planning for mazes, created a new landscape for the Neural Network to use, and added a bird’s eye view to the A* Algorithm. The Ant Colony Optimization that was used in this thesis was able to discover a path to the goal, but it was jagged and required a larger computational time compared to the Neural Network and A* algorithm discussed in this thesis. The Hopfield-type neural network used in this thesis propagated energy to create a landscape and used gradient decent to find the shortest path in terms of distance, but this thesis modified how the landscape was created to prevent the neural network from getting trapped in local minimas. The last contribution was applying a bird’s eye view to the A* algorithm to learn more about the environment which helped to create shorter and smoother paths.

1.       引言

2. ACO文献回顾

3. ACO具体实现

4. 神经网络文献回顾

5. 神经网络具体实现

6. A*文献回顾

7. A*具体实现

8. 结论

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