Coordinated set stabilization : application to robotic manipulators

考虑一下设计算法的问题，该算法使一组机器人操作器协同工作，为飞机机身涂漆。附着在每个机器人末端执行器上的画笔负责停留在描述机身形状的表面上。通过反馈控制，每个机器人的末端执行器都受到限制，只能沿着描述机身的表面移动。在地面上，机器人团队必须相互沟通和合作，协调他们的动作，这样他们就不会经常在同一区域进行不必要的油漆，并有效地完成任务。**受上述例子的部分激励，本研究项目研究了非线性控制系统在其输出空间中预先指定的集合上的协调问题。给定一个非线性控制系统的异构集合，目标是设计一个反馈控制律，每个系统一个，驱动每个系统的闭环输出到其预先定义的目标集。目标集必须是不变的，换句话说，如果每个系统都在其目标集上初始化，那么它将保持在目标集上。一旦进入目标集，系统应该以最优方式协作完成特定于应用程序的任务。本文主要研究(a)非线性系统的集镇定，同时保证目标集上所需的动力学；(b)非线性控制系统的协调集镇定，重点是欧拉-拉格朗日系统；(c)协调集镇定算法的实验验证。该方案的预期结果是分布式非线性控制算法，其有效性在数学上得到了证明，并在实验室设备上进行了实验验证。**这项研究的部分动机是工业化国家出现的自组织工厂，作为提高生产率和与发展中国家低成本制造业竞争的一种方式。北美和欧洲正在大力增加工业价值创造。工业制造的下一个阶段是向“智能工厂”的转变，被描述为工业革命的第四阶段。“工业4.0”或“物联网”的概念正在使北美的制造流程现代化，并提高工业制造的生产率。“物联网”被认为是一项颠覆性技术，将改变生活、商业和全球经济。例如，波音公司正在使用一个机器人团队，共同工作，为波音777的机翼涂漆。这些机器人提高了产量，并大大减少了涂装机翼所需的时间，从4.5小时减少到24分钟。**本研究旨在为非线性动力学系统的协调集镇定控制算法的设计提供系统的方法。我们试图在数学上证明算法的正确性，同时也通过实验证明它们在移动机器人操纵器上的有效性。能够协同工作的移动机器人非常适合于可重构的柔性制造系统。解决本提案中考虑的与非线性控制算法设计相关的基本问题有望帮助实现制造业中的“物联网”。

Consider the problem of designing algorithms that make a collection of robotic manipulators work together to paint the fuselage of an aircraft. The paintbrush attached to the end-effector of each robot is charged with staying on the surface that describes the shape of the fuselage. Each robot's end-effector is restricted, through feedback control, to move along the surface describing the fuselage. On the surface, the team of robots must communicate and co-operate to coordinate their motions so that they do not unnecessarily paint over the same region too often and efficiently complete the task.**Partially motivated by the above example, the proposed research project studies the coordination of nonlinear control systems on pre-specified sets in their output spaces. Given a heterogeneous collection of nonlinear control systems, the objective is to design a feedback control laws, one for each system, that drive the closed-loop output of each system to its pre-defined target set. The target sets must be invariant, in other words, if each system is initialized on its target set, it remains on the target set. Once on the target set, the systems should cooperatively complete application specific tasks in an optimal manner. This proposal focuses on (a) set stabilization of nonlinear systems while ensuring desired dynamics on the target set (b) coordinated set stabilization for nonlinear control systems with emphasis on Euler-Lagrange systems (c) experimental verification of coordinated set stabilization algorithms. The expected outcomes of this proposal are distributed nonlinear control algorithms whose effectiveness are mathematically proven and demonstrated experimentally on laboratory equipment.**This research is partly motivated by the emergence of self-organizing factories in industrialized nations as a way to increase productivity and compete with low-cost manufacturing in developing nations. North America and Europe are moving to significantly increase industrial value creation. The next stage of industrial manufacturing, a move towards `smart factories', has been described as a fourth stage of the industrial revolution. This notion of `industry 4.0', or `the internet of things', is modernizing manufacturing processes and increasing productivity in industrial manufacturing in North America. The 'internet of things' has been identified as a disruptive technology that will transform life, business, and the global economy. For example, Boeing is using a team of robots, working together, to paint the wings of the Boeing 777. These robots have boosted output and dramatically reduced the time required to paint the wings from 4.5 hours to 24 minutes.**This research aims to generate systematic methods to design control algorithms for coordinated set stabilization of systems with nonlinear dynamics. We seek to mathematically prove the correctness of the algorithms while also experimentally demonstrating their effectiveness on mobile robotic manipulators. Mobile robotic manipulators that can work co-operatively are well suited to re-configurable, flexible manufacturing systems. Solving the fundamental problems considered in this proposal related to the design of nonlinear control algorithms promises to help enable the 'internet of things' in manufacturing.