CAREER: Topological Abstraction for Robot Path Planning

高自由度机器人系统，如那些涉及一个或多个柔性电缆，多机器人系统，机器人操纵器和软机械臂，在自动化工业，家用机器人，医疗机器人，现场机器人和社会机器人中无处不在。电缆可以被多机器人系统用来拖曳或运输大的负载，机器人可以使用固定的绳索来供电或通信，在没有gps的环境中执行长期任务。在隐私问题日益严重的社会政治环境中，多智能体系统需要新的创新来实现无需协调的规划。铰接式机器人机械手用于各种工业应用，如自动化制造，以及在微创辅助腹腔镜手术。这个学院早期职业发展（Career）项目通过使用拓扑抽象技术来解决具有高维配置空间的系统的复杂性降低的基本问题，目的是实现快速有效的规划。与该项目的研究目标相结合的是教育计划，旨在培养当前和未来一代复杂自主系统科学和技术的工程师和研究人员，这些系统日益成为我们现代社会的一部分。作为该项目的组成部分，STEM教育将通过建立一个包括研究生、本科生和K-12学生的指导生态系统来推进。来自弱势群体的学生将参与研究活动，目的是开发一个全面的和可扩展的教育计划。在这个项目中，将开发新的理论和算法工具来实现高维构型空间的拓扑抽象，目的是允许使用拓扑路径规划方法对高自由度系统进行有效的最优路径规划。将为多个机器人在有障碍物的平面域上导航的联合构型空间开发同伦不变量，从而降低涉及系留多机器人系统、约束人机团队和大型多智能体系统规划等问题的复杂性。将开发用于空间域中有效计算同伦不变量的新算法，从而与基于搜索的规划算法直接融合，并应用于涉及电缆的空间系统。该项目超越了同伦，发展了对同伦概念的深度推广的理论基础，这将为发现和计算称为Reeb结构的新型拓扑结构铺平道路，该结构适用于关节和软机器人机械手的构型空间降维。所有这些基本的进步将允许开发高效的路径规划算法，并保证高自由度系统的完整性和最优性，例如空间、多机器人系统和涉及一条或多条柔性电缆的人机系统；无协调多智能体系统；铰接机械臂和可变形的操纵器。所开发的算法将在真实的机器人平台上实现和评估。该项目由跨部门机器人基础研究项目支持，由工程（ENG）和计算机与信息科学与工程（CISE）联合管理和资助。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

High degree-of-freedom robotic systems such as those involving one or more flexible cables, multi-robot systems, robotics manipulators and soft robotic arms, are ubiquitous in automation industries, household robotics, medical robotics, field robotics and social robots. Cables can be used by multi-robot systems to tug or transport large loads, and robots can use fixed tethers for power supply or communication for long-term missions in GPS-denied environments. Multi-agent systems need new innovations for coordination-free planning in a sociopolitical environment in which privacy concerns are on the rise. Articulated robotic manipulators are used in a variety of industrial applications such as automated manufacturing, as well as in minimally invasive assisted laparoscopic surgery. This Faculty Early Career Development (CAREER) project addresses the fundamental question of complexity reduction for such systems with high-dimensional configuration spaces using techniques of topological abstraction with an aim of achieving fast & efficient planning. Integrated with the research objectives of this project are educational plans aimed at training current and future generation of engineers & researchers in the science and technologies of complex autonomous systems that are increasingly becoming part of our modern society. As an integral part of the project, STEM education will be advanced through establishment of a mentoring ecosystem involving graduate, undergraduate & K-12 students. Students from underrepresented groups will be involved in the research activities with an aim of developing a comprehensive & scalable education program.In this project novel theoretical and algorithmic tools will be developed for achieving topological abstraction of high-dimensional configuration spaces with an aim of allowing efficient optimal path planning for high degree-of-freedom systems using Topological Path Planning methods. Homotopy invariants will be developed for joint configuration spaces of multiple robots navigating on planar domains with obstacles, resulting in complexity reduction in problems involving tethered multi-robot systems, constrained human-robot teams, and planning for large multi-agent systems without coordination. Novel algorithms for efficient computation of homotopy invariants in spatial domains will be developed, leading to direct amalgamation with search-based planning algorithms with application to spatial systems involving cables. The project goes beyond homotopy to develop the theoretical foundations of a deep generalization to the notion of homotopy, which will pave the way for the discovery and computation of novel topological constructions called Reeb structures that are suitable for dimensionality reduction of configuration spaces of articulated and soft robotic manipulators. All these fundamental advances will allow development of efficient path planning algorithms with completeness and optimality guarantees for high degree-of-freedom systems such as spatial, multi-robot systems & human-robot systems involving one or more flexible cables; coordination-free multi-agent systems; and articulated robotic arms & deformable manipulators. The developed algorithms will be implemented and evaluated on real robotic platforms.This project is supported by the cross-directorate Foundational Research in Robotics program, jointly managed and funded by the Directorates for Engineering (ENG) and Computer and Information Science and Engineering (CISE).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.