RI: Small: Exploiting Global Structure in Robot Decision Problems

有些决策问题，比如装洗碗机或组装家具，需要对一系列步骤进行明确的规划，而另一些决策问题，比如抓住一个物体或突然转向以避开一辆停下来的汽车，则可以在很大程度上通过学习反射来完成。在机器人领域，人们仍然不太清楚为什么有些问题需要规划，而另一些问题可以通过反射来解决。本计画探讨如何将数学之分支拓扑学的技术应用于机器人决策问题的基本性质研究。通过开发应用拓扑学来优化、分析和可视化机器人运动的大型数据集的算法，研究人员希望更好地理解规划和学习之间的灰色地带。最终，这种更好的理解可以帮助其他工程师开发出更灵敏、更有能力和更强大的机器人行为。本研究的技术目标是分析机器人决策问题与其解决方案之间的数学关系，以揭示运动规划和控制学习之间联系的基本问题。打破了传统的规划模式，开发一个算法，解决个别的问题查询，该项目研究的全球拓扑特性的连续变化的相关问题的实例。具体来说，它研究了拓扑复杂性的某些特征如何与学习和规划算法的性能相关。基于这种理解，开发了新的算法、拓扑度量和可视化技术，以帮助利用拓扑结构进行更快的规划和更准确的学习。该奖项反映了NSF的法定使命，并已被认为值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

Some decision problems, like loading a dishwasher or assembling furniture, require explicit planning about a sequence of steps, while others, like grasping an object or swerving to avoid a stopped car, can be performed largely through learned reflexes. In robotics, it is still poorly understood why some problems require planning and why others can be solved via reflex. This project explores how techniques from topology, a branch of mathematics, can be applied to study the fundamental nature of robot decision problems. By developing algorithms that apply topology to optimize, analyze, and visualize large datasets of robot motions, the researchers hope to better understand the gray area between planning and learning. Ultimately, this better understanding could help other engineers develop more responsive, capable, and robust robot behaviors. The technical goal of this research is to analyze the mathematical relation connecting robot decision problems to their solutions in order to shed light on fundamental questions surrounding the connection between motion planning and control learning. Breaking from the classical planning paradigm of developing an algorithm that solves individual problem queries, the project studies the global topological characteristics of continuous variations of related problem instances. Specifically, it investigates how certain features of topological complexity relate to the performance of learning and planning algorithms. Based on this understanding, new algorithms, topological metrics, and visualization techniques are developed to help exploit topological structure for faster planning and more accurate learning. The proposed methods are evaluated on benchmark problems in redundant inverse kinematics, legged robots, and agile autonomous vehicles.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.