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

本计画的主要目的是提供一个系统的多非完整机械系统的回馈控制综合方法。 该项目将通过提供利用非完整力学系统的拉格朗日结构进行反馈控制的方法，而不是像迄今为止通常所做的（或假设的）那样不必要地抵消它们，从而大大推进当前技术的发展。 特别是，该项目将依赖于非完整力学系统的两个基本但非常直观的概念/性质：几何和无源性。 由此产生的反馈控制律将更加鲁棒，开环拉格朗日动力学的抵消更少;直观上令人信服，因为它是基于能量相关的无源性属性和可视化的几何概念;并且能够通过使用强大的无源性参数来可证明地确保与广泛类别的人类/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，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（或分散式）反馈控制的方法。 我们还将建立一个实验测试台，由三个移动的机械手验证/演示/刺激理论结果。 这个项目也将联合收割机几个强大的概念，这是经常使用的分离：几何力学，被动，开关控制和通信。 非完整力学系统包括许多具有实际意义的系统：轮式移动的机器人（如汽车）、移动的机械手（即位于轮式移动的平台上的灵巧机械手）和（欠驱动的）卫星等。 一组多个他们将使更引人注目的应用，如远程救援的人类受害者从灾难现场使用多个移动的机械手，合作病人运输医院的多个护士机器人，合作机器人灵活的材料处理在制造/建设，合作的空中运输的一个沉重的物体使用多个自主卫星。 该项目将为这些强大的应用奠定理论基础，这些应用虽然有可能极大地造福于我们的日常生活，但尚未实现，主要是由于缺乏方法来精确和安全地反馈控制它们，并充分考虑机器人的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。 该项目还将以一些有趣的示范形式向公众展示所取得的成果，并积极争取科学和技术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.