Feedback Control of Multiple Nonholonomic Mechanical Systems: Geometry, Passivity, and Communication

本课题的主要目标是为多个非完整机械系统提供一种系统反馈控制综合方法。该项目将通过提供利用非完整机械系统的拉格朗日结构进行反馈控制的方法，而不是像通常所做的（或假设的）那样不必要地取消它们，从而大大提高当前技术的水平。特别是，这个项目将依赖于两个基本的，但非常直观的，非完整机械系统的概念/性质：几何和被动。由此得到的反馈控制律将具有更强的鲁棒性，并且开环拉格朗日动力学的抵消更少；直观上引人注目，因为它是基于能源相关的被动属性和可视化的几何概念；并且能够通过使用强大的被动性论证来确保与广泛的人类/环境的交互稳定性。该项目还将解决代理间通信拓扑（即谁与谁通信）的约束问题，并提供根据底层通信拓扑（即信息图）为每个代理合成分布式（或分散）反馈控制的方法。我们还将建立一个由三个移动机械手组成的实验试验台来验证/演示/刺激理论结果。这个项目还将几个强大的概念结合在一起，这些概念经常被分开使用：几何力学、被动、开关控制和通信。通过这样做，它也会在它们的界面上产生新的研究方向。非完整机械系统包括许多实际重要的系统：轮式移动机器人（例如汽车），移动机械手（即轮式移动平台顶部的灵巧机械手）和（欠驱动）卫星，仅举几例。一组多个机器人将产生更引人注目的应用，例如使用多个移动机械手从灾难现场远程救援人类受害者，多个护士机器人在医院协作运送病人；制造/建筑中的协作机器人柔性材料处理，以及使用多个自主卫星的重型物体的协作机载运输。该项目将为这些强大的应用奠定理论基础，尽管这些应用有可能极大地造福于我们的日常生活，但尚未实现，主要原因是缺乏充分考虑机器人开环拉格朗日动力学、通信约束以及与人类/环境的安全交互的精确和安全反馈控制方法。本项目还将以一些有趣的示范形式向公众展示所获得的成果，并积极吸引科技领域代表性不足群体的学生参与其研究活动。

The main goal of this project is to provide a systematic feedback control synthesis methodology for multiple nonholonomic mechanical systems. This project will substantially advance the state of current technology by providing ways to exploit the Lagrangian structure of the nonholonomic mechanical systems for their feedback control, rather than unnecessarily cancel them out as usually done (or assumed) so far. In particular, this project will rely on the two fundamental, yet, very intuitive, concepts/properties of the nonholonomic mechanical systems: geometry and passivity. The resultant feedback control law will then be more robust with less cancellation of the open-loop Lagrangian dynamics; intuitively compelling, since it is based on energy-related passivity property and visualizable geometric concepts; and able to provably ensure interaction stability with a wide class of humans/environments by using the powerful passivity-argument. This project will also address constraints on the inter-agent communication topology (i.e. who communicates with whom) and provide ways to synthesize distributed (or decentralized) feedback control for each agent according to the underlying communication topology (i.e. information graph). We will also build an experimental test-bed consisting of three mobile manipulators to validate/demonstrate/stimulate theoretical results. This project will also combine several powerful concepts together, which have been often used disjointly: geometric mechanics, passivity, switching control, and communication. By doing so, it would also generate new research directions situated at their interface.Nonholonomic mechanical systems encompass many practically important systems: wheeled mobile robots (e.g. automobile), mobile manipulators (i.e. dexterous manipulator on the top of wheeled mobile platform), and (under-actuated) satellites, to name just a few. A group of multiple of them would make even more compelling applications such as teleoperated rescue of a human victim from disastrous sites using multiple mobile manipulators, collaborative patient transport in hospitals by multiple nurse robots; cooperative robotic flexible material handling in manufacturing/construction, and cooperative air-borne transport of a heavy object using multiple autonomous satellites. This project will lay theoretical foundations for such powerful applications, which, although having potentials to greatly benefit our daily life, have not been materialized yet, mainly due to the lack of ways to precisely and safely feedback control them with full considerations on the robots' open-loop Lagrangian dynamics, communication constraints, and safe-interaction with humans/environments. This project will also exhibit the obtained results to the public in the form of some interesting demonstrations and actively pursue students from under-represented groups in the science and technology fields to involve them into its research activities.