CAREER: Hierarchical Abstractions for Planning and Control of Robotic Swarms

机器人群体规划和控制的层次抽象（分层抽象）由于最近在计算、通信、传感器和执行器技术方面的进步，现在有可能建立由数百个小型廉价的地面、空中和水下机器人组成的团队。它们很轻，便于运输和部署，可以放在小地方。这样的自主代理群为单个故障提供了更高的鲁棒性，可以覆盖更广的区域，并通过并行性提高了计算能力。然而，在过去十年中，规划和控制如此庞大的具有有限通信和计算能力的智能体团队是一个备受关注的难题。为了适应在复杂环境中具有非平凡运动学或动力学运动的大量机器人，该项目提出了分层抽象。在较低的层次上，连续抽象通过提取群体的一组基本特征来降低问题的维度，同时正确捕获机器人的约束。在更高的层次上，离散抽象关注环境的复杂性，并将规划和控制问题从连续系统的无限维世界映射到有限状态自动机的可决定世界。提出的算法导致了群集高级规范语言HILLS和机器人自动部署语言LARAD的发展。在这些框架中，机器人的运动计划是用一种高级语言，用离散系统语言的字符串或时间逻辑公式来表述的，这种语言捕捉了环境的复杂性。HILLS和LARAD作为仿真软件包实现，也用于群体机器人的实验平台。虽然该项目旨在为群体问题提供解决方案，但它解决了形状理论和著名的“n体问题”中的基本问题，这些问题传统上是在理论物理学中研究的，并在原子物理学和天体力学等领域找到了应用。另一方面，使用一种独特的离散抽象方法，本工作试图扩大已知的可决定连续系统和混合系统的类别。最后，本项目的分层抽象体系结构通过创建一个框架为移动机器人的规划和控制开辟了一个新的方向，在这个框架中，处理环境复杂性的强大离散算法可以无缝地与非平凡机器人动力学的连续控制律相结合。这项研究是高度跨学科的，涵盖的主题从传统的“连续”领域，如几何非线性控制，到“离散”领域，如形式分析，以及机器人和生物学之间的边界应用领域。教育计划的重点是通过引入混合系统、系统生物学、几何规划与控制和生物信息学等研究生和本科生课程，在上述领域之间建立桥梁。它还涉及丰富的外展活动，包括指导高中教师，为参加机器人竞赛的高中生提供评判和建议，以及指导代表性不足的少数民族本科生。

Hierarchical Abstractions for Planning and Control of Robotic SwarmsCalin BeltaAs a result of recent advances in computation, communication, sensor, and actuator technology, it is now possible to build teams of hundreds of small and inexpensive ground, air, and underwater robots. They are light, easy to transport and deploy, and can fit into small places. Such swarms of autonomous agents provide increased robustness to individual failures, the possibility to cover wide regions, and improve computational power through parallelism. However, planning and controlling such large teams of agents with limited communication and computation capabilities is a difficult problem that received a lot of attention in the past decade.To accommodate large numbers of robots with nontrivial kinematics or dynamics moving in complicated environments, this project proposes hierarchical abstractions. At a lower level, continuous abstractions reduce the dimension of the problem by extracting a set of essential features of the swarm, while correctly capturing the robot constraints. At a higher level, discrete abstractions focus on the complexity of the environment and map the planning and control problem from the infinite dimensional world of continuous systems to the decidable world of finite state automata. The proposed algorithms lead to the development of HILLS, a High Level Specification Language for Swarms, and LARAD, a LAnguage for Robot Automated Deployment. In these frameworks, robotic motion plans are formulated in a high level language in terms of strings or temporal logic formulas in the language of a discrete system capturing the complexity of the environment. HILLS and LARAD are implemented as simulation packages and also used in experimental platforms for swarming robotics.While aimed to providing a solution to the swarming problem, this project addresses fundamental issues in shape theory and the well-known "n-body problem," which are traditionally studied in theoretical physics and find applications in areas such as atomic physics and celestial mechanics. On the other hand, using a unique approach to discrete abstractions, this work attempts to enlarge the class of known decidable continuous and hybrid systems. Finally, the hierarchical abstraction architectures of this project open a new direction in planning and control of mobile robots by creating a framework in which powerful discrete algorithms dealing with the complexity of the environment can be seamlessly combined with continuous control laws for nontrivial robot dynamics.This research is highly interdisciplinary, covering topics ranging from traditionally "continuous" areas, such as geometric nonlinear control, to "discrete" areas such as formal analysis, as well as application areas at the boundary between robotics and biology. The educational plan is focused on building bridges among the above areas by introducing graduate and undergraduate courses on Hybrid Systems, Systems Biology, Geometric Planning and Control, and Bioinformatics. It also involves a rich spectrum of outreach activities, including mentoring of high school teachers, judging and advising high school students participating in robotics competitions, and mentoring under-represented minority undergraduate students.