Output feedback controllers for set stabilization

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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.