Output feedback controllers for set stabilization

在许多应用中，适当的控制设计规范是稳定系统状态空间的适当定义的子集。这与涉及稳定均衡的传统控制设计形成了鲜明对比。设置稳定化是合适的规范的应用包括轮式机器人的队形控制；控制两足机器人的行走运动；汽车、轮船或飞机的路径跟踪(使车辆的位置接近并跟随一条路径)；创建虚拟约束生物医学机器人以及耦合振荡器的同步。这一研究计划研究了非线性控制系统状态下不变集的镇定问题，在这种状态下，只有测量的输出而不是系统的整个状态向量可用于反馈。由此产生的控制设计方法将被用于设计机器人应用的路径跟踪控制器。以前，我们使用集合稳定化来解决移动机器人、磁悬浮系统和机械手等机器人应用中的路径跟踪和同步路径跟踪问题。在这些应用中，反馈控制器可以获得机器人的完整状态信息。这是不现实的，因为通常由于传感器的成本和技术限制，反馈控制器只能访问不包含完整状态信息的测量输出。例如，我们假设移动机器人可以使用GPS信号，这在采矿和水下应用中是不现实的。在本研究中，我们研究了集合输出镇定的三个方面：(1)将我们首创的部分信息横向反馈线性化技术推广到多输入系统；(2)结合非线性状态估计的最新进展，结合(1)设计镇定控制器；(3)设计输出反馈路径跟踪控制器，并在物理机器人上实现。简而言之，本研究的目的是提供系统的方法来设计和实现输出反馈控制算法以实现机组的镇定。我们从数学上证明了算法的正确性，并在滑铁卢大学我们最先进的机器人研究设施RoboHub中展示了它们的实用性。这项研究将具有应用和理论影响；理论影响在于将可测横向反馈线性化的充要条件推广到多输入系统。其实际影响在于利用这一理论开发出只使用机器人车载传感器的路径跟踪控制器。这个项目开发的HQP将学习设计先进的非线性控制算法，同时也在最先进的机器人平台上实施他们的设计。这些技能是实现机器人技术和自主系统的基础，这些领域是加拿大拥有竞争优势和新兴产业的领域。

In many applications the appropriate control design specification is to stabilize a suitably defined subset of a system's state-space. This stands in contrast to conventional control design which concerns stabilizing equilibria. Applications where set stabilization is the appropriate specification include formation control of wheeled robots; control the walking motion of a bipedal robot; path following for a car, ship or airplane (make the position of the vehicle approach and follow a path); the creation of virtual constraints biomedical robots and the synchronization of coupled oscillators. This proposed research program studies stabilization of invariant sets in the state of nonlinear control systems in which only a measured output, not the entire state vector of the system, is available for feedback. The resulting control design methodology will be used to design path following controllers for robotic applications. Previously, we used set stabilization to solve path following and synchronized path following problems for robotic applications including mobile robots, magnetic levitation systems and manipulators. In these applications the feedback controller had access to the full-state information of the robot. This is not realistic because often, owing to the cost of sensors and technological limitations, the feedback controller only has access to a measured output which does not contain the full state information. For instance, we have assumed that a GPS signal is available to mobile robots which is unrealistic in mining and underwater applications. In this research we study three aspects of output stabilization of sets: (1) extend the technique we pioneered called transverse feedback linearization with partial information to multiple-input systems (2) employ recent advances in nonlinear state estimation in conjunction with the results from (1) to design stabilizing controllers and (3) design output feedback path following controllers and implement them on physical robots. In short, this research aims to produce systematic methods to design and implement output feedback control algorithms for set stabilization. We mathematically prove the correctness of the algorithms and demonstrate their utility in our state-of-the-art robotics research facility, the RoboHub, at the University of Waterloo. This research will have applied and theoretical impact; theoretical impact lies in extending the necessary and sufficient conditions for measurable transverse feedback linearization to multiple-input systems. The practical impact lies in using this theory to develop path following controllers that only use a robot's onboard sensors. The HQP developed by this project will learn to design advanced nonlinear control algorithms while also implementing their designs on state-of-the-art robotic platforms. These skills are fundamental to enabling robotics technology and autonomous systems, areas where Canada has a competitive advantage and a burgeoning industry.