作为具有可证保证的在线随机最短路径导航的神谕的Dijkstra算法

中文摘要 AI 辅助

与人类和关键设施协同运行的移动机器人必须以低成本到达目标，尽管事先通常未知地图的真实遍历成本且执行存在不完美性。求解基础随机最短路径问题的精确规划器，如值迭代，其计算量随地图直径增长，而Dijkstra算法速度快，但一旦存在随机转移通常被认为不精确。本研究表明，Dijkstra算法可在比文献中常引用的因果性条件弱得多的条件下保持为精确规划引擎，该条件是在确定化地图上定义的约简成本的非负性。基于此特性，提出了在线学习器DORA（Dijkstra Oracle Reduced-cost Algorithm）用于机器人导航，该算法每回合仅调用固定次数的最短路径神谕，不估计转移核，且当与动态障碍物接触的概率必须保持在预算内时，添加对数存活权重。在涉及网格世界导航、定向钻井和无人机监控的三个其他基准的数值实验中，该学习器与给定真实转移核的乐观值迭代性能相当，同时规划器工作量减少4.5至19.3倍，与确定化重规划相比，学习期间的接触次数减少17倍，且接触率保持在跨度两个数量级的预算内。这些结果表明，最短路径搜索支持安全高效的在线导航和路径规划任务。

英文摘要

Mobile robots that operate in side by side with humans and critical facilities must reach their goals at low cost, despite often unknown true traversal costs of the map apriori and imperfect actuation. Planners that solve the underlying stochastic shortest path problem exactly, such as value iteration, require computation that grows with the diameter of the map, whereas Dijkstra's algorithm is fast but is usually considered inexact once transitions are stochastic. This study shows that Dijkstra's algorithm can remain an exact planning engine under a condition that is much weaker than the causality condition often invoked in the literature, namely nonnegativity of a reduced cost defined on the determinized map. Building on this characterization, an online learner DORA (Dijkstra Oracle Reduced-cost Algorithm) is proposed for robot navigation that calls a shortest path oracle a fixed number of times per episode, never estimates a transition kernel, and adds a logarithmic survival weight when the probability of contact with a dynamic obstacle must stay within a budget. In the numerical experiments involving three other benchmarks that cover grid world navigation, directional drilling, and drone surveillance, the learner matches optimistic value iteration that is given the true transition kernel while performing 4.5 to 19.3 times less planner work, reduces contacts during learning by a factor of seventeen relative to determinize and replan, and keeps the contact rate within budgets that span two orders of magnitude. These results indicate that shortest path search supports safe and efficient online navigation and path planning tasks.

发表机构

• King Fahd University of Petroleum and Minerals (KFUPM)（法赫德国王石油与矿产大学）
• Islamic University of Madinah（麦地那伊斯兰大学）
• Universitas Muhammadiyah Yogyakarta（日惹穆罕默迪亚大学）

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