On Observer-Based Control of Nonlinear Systems

Filtering and reconstruction of signals play a fundamental role in modern signal processing, telecommunications, and control theory and are used in numerous applications. The feedback principle is an important concept in control theory. Many different control strategies are based on the assumption that all internal states of the control object are available for feedback. In most cases, however, only a few of the states or some functions of the states can be measured. This circumstance raises the need for techniques, which makes it possible not only to estimate states, but also to derive control laws that guarantee stability when using the estimated states instead of the true ones. For linear systems, the separation principle assures stability for the use of converging state estimates in a stabilizing state feedback control law. In general, however, the combination of separately designed state observers and state feedback controllers does not preserve performance, robustness, or even stability of each of the separate designs. In this thesis, the problems of observer design and observer-based control for nonlinear systems are addressed. The deterministic continuous-time systems have been in focus. Stability analysis related to the Positive Real Lemma with relevance for output feedback control is presented. Separation results for a class of nonholonomic nonlinear systems, where the combination of independently designed observers and state-feedback controllers assures stability in the output tracking problem are shown. In addition, a generalization to the observer-backstepping method where the controller is designed with respect to estimated states, taking into account the effects of the estimation errors, is presented. Velocity observers with application to ship dynamics and mechanical manipulators are also presented

Robust Model Predictive Control for Linear Parameter Varying Systems along with Exploration of its Application in Medical Mobile Robots

This thesis seeks to develop a robust model predictive controller (MPC) for Linear Parameter Varying (LPV) systems. LPV models based on input-output display are employed. We aim to improve robust MPC methods for LPV systems with an input-output display. This improvement will be examined from two perspectives. First, the system must be stable in conditions of uncertainty (in signal scheduling or due to disturbance) and perform well in both tracking and regulation problems. Secondly, the proposed method should be practical, i.e., it should have a reasonable computational load and not be conservative. Firstly, an interpolation approach is utilized to minimize the conservativeness of the MPC. The controller is calculated as a linear combination of a set of offline predefined control laws. The coefficients of these offline controllers are derived from a real-time optimization problem. The control gains are determined to ensure stability and increase the terminal set. Secondly, in order to test the system's robustness to external disturbances, a free control move was added to the control law. Also, a Recurrent Neural Network (RNN) algorithm is applied for online optimization, showing that this optimization method has better speed and accuracy than traditional algorithms. The proposed controller was compared with two methods (robust MPC and MPC with LPV model based on input-output) in reference tracking and disturbance rejection scenarios. It was shown that the proposed method works well in both parts. However, two other methods could not deal with the disturbance. Thirdly, a support vector machine was introduced to identify the input-output LPV model to estimate the output. The estimated model was compared with the actual nonlinear system outputs, and the identification was shown to be effective. As a consequence, the controller can accurately follow the reference. Finally, an interpolation-based MPC with free control moves is implemented for a wheeled mobile robot in a hospital setting, where an RNN solves the online optimization problem. The controller was compared with a robust MPC and MPC-LPV in reference tracking, disturbance rejection, online computational load, and region of attraction. The results indicate that our proposed method surpasses and can navigate quickly and reliably while avoiding obstacles

Advanced Feedback Linearization Control for Tiltrotor UAVs: Gait Plan, Controller Design, and Stability Analysis

Three challenges, however, can hinder the application of Feedback Linearization: over-intensive control signals, singular decoupling matrix, and saturation. Activating any of these three issues can challenge the stability proof. To solve these three challenges, first, this research proposed the drone gait plan. The gait plan was initially used to figure out the control problems in quadruped (four-legged) robots; applying this approach, accompanied by Feedback Linearization, the quality of the control signals was enhanced. Then, we proposed the concept of unacceptable attitude curves, which are not allowed for the tiltrotor to travel to. The Two Color Map Theorem was subsequently established to enlarge the supported attitude for the tiltrotor. These theories were employed in the tiltrotor tracking problem with different references. Notable improvements in the control signals were witnessed in the tiltrotor simulator. Finally, we explored the control theory, the stability proof of the novel mobile robot (tilt vehicle) stabilized by Feedback Linearization with saturation. Instead of adopting the tiltrotor model, which is over-complicated, we designed a conceptual mobile robot (tilt-car) to analyze the stability proof. The stability proof (stable in the sense of Lyapunov) was found for a mobile robot (tilt vehicle) controlled by Feedback Linearization with saturation for the first time. The success tracking result with the promising control signals in the tiltrotor simulator demonstrates the advances of our control method. Also, the Lyapunov candidate and the tracking result in the mobile robot (tilt-car) simulator confirm our deductions of the stability proof. These results reveal that these three challenges in Feedback Linearization are solved, to some extents.Comment: Doctoral Thesis at The University of Toky

Trajectory Optimization and Machine Learning to Design Feedback Controllers for Bipedal Robots with Provable Stability

This thesis combines recent advances in trajectory optimization of hybrid dynamical systems with machine learning and geometric control theory to achieve unprecedented performance in bipedal robot locomotion. The work greatly expands the class of robot models for which feedback controllers can be designed with provable stability. The methods are widely applicable beyond bipedal robots, including exoskeletons, and prostheses, and eventually, drones, ADAS, and other highly automated machines. One main idea of this thesis is to greatly expand the use of multiple trajectories in the design of a stabilizing controller. The computation of many trajectories is now feasible due to new optimization tools. The computations are not fast enough to apply in the real-time, however, so they are not feasible for model predictive control (MPC). The offline “library” approach will encounter the curse of dimensionality for the high-dimensional models common in bipedal robots. To overcome these obstructions, we embed a stable walking motion in an attractive low-dimensional surface of the system's state space. The periodic orbit is now an attractor of the low-dimensional state-variable model but is not attractive in the full-order system. We then use the special structure of mechanical models associated with bipedal robots to embed the low-dimensional model in the original model in such a manner that the desired walking motions are locally exponentially stable. The ultimate solution in this thesis will generate model-based feedback controllers for bipedal robots, in such a way that the closed-loop system has a large stability basin, exhibits highly agile, dynamic behavior, and can deal with significant perturbations coming from the environment. In the case of bipeds: “model-based” means that the controller will be designed on the basis of the full floating-base dynamic model of the robot, and not a simplified model, such as the LIP (Linear Inverted Pendulum). By “agile and dynamic” is meant that the robot moves at the speed of a normal human or faster while walking off a curb. By “significant perturbation” is meant a human tripping, and while falling, throwing his/her full weight into the back of the robot.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145992/1/xda_1.pd

Recent Advances in Robust Control

Robust control has been a topic of active research in the last three decades culminating in H_2/H_\infty and \mu design methods followed by research on parametric robustness, initially motivated by Kharitonov's theorem, the extension to non-linear time delay systems, and other more recent methods. The two volumes of Recent Advances in Robust Control give a selective overview of recent theoretical developments and present selected application examples. The volumes comprise 39 contributions covering various theoretical aspects as well as different application areas. The first volume covers selected problems in the theory of robust control and its application to robotic and electromechanical systems. The second volume is dedicated to special topics in robust control and problem specific solutions. Recent Advances in Robust Control will be a valuable reference for those interested in the recent theoretical advances and for researchers working in the broad field of robotics and mechatronics

Dynamic Bipedal Locomotion: From Hybrid Zero Dynamics to Control Lyapunov Functions via Experimentally Realizable Methods

Robotic bipedal locomotion has become a rapidly growing field of research as humans increasingly look to augment their natural environments with intelligent machines. In order for these robotic systems to navigate the often unstructured environments of the world and perform tasks, they must first have the capability to dynamically, reliably, and efficiently locomote. Due to the inherently hybrid and underactuated nature of dynamic bipedal walking, the greatest experimental successes in the field have often been achieved by considering all aspects of the problem; with explicit consideration of the interplay between modeling, trajectory planning, and feedback control. The methodology and developments presented in this thesis begin with the modeling and design of dynamic walking gaits on bipedal robots through hybrid zero dynamics (HZD), a mathematical framework that utilizes hybrid system models coupled with nonlinear controllers that results in stable locomotion. This will form the first half of the thesis, and will be used to develop a solid foundation of HZD trajectory optimization tools and algorithms for efficient synthesis of accurate hybrid motion plans for locomotion on two underactuated and compliant 3D bipeds. While HZD and the associated trajectory optimization are an existing framework, the resulting behaviors shown in these preliminary experiments will extend the limits of what HZD has demonstrated is possible thus far in the literature. Specifically, the core results of this thesis demonstrate the first experimental multi-contact humanoid walking with HZD on the DURUS robot and then through the first compliant HZD motion library for walking over a continuum of walking speeds on the Cassie robot. On the theoretical front, a novel formulation of an optimization-based control framework is introduced that couples convergence constraints from control Lyapunov functions (CLF)s with desirable formulations existing in other areas of the bipedal locomotion field that have proven successful in practice, such as inverse dynamics control and quadratic programming approaches. The theoretical analysis and experimental validation of this controller thus forms the second half of this thesis. First, a theoretical analysis is developed which demonstrates several useful properties of the approach for tuning and implementation, and the stability of the controller for HZD locomotion is proven. This is then extended to a relaxed version of the CLF controller, which removes a convergence inequality constraint in lieu of a conservative CLF cost within a quadratic program to achieve tracking. It is then explored how this new CLF formulation can fully leverage the planned HZD walking gaits to achieve the target performance on physical hardware. Towards this goal, an experimental implementation of the CLF controller is derived for the Cassie robot, with the resulting experiments demonstrating the first successful realization of a CLF controller for a 3D biped on hardware in the literature. The accuracy of the robot model and synthesized HZD motion library allow the real-time control implementation to regularize the CLF optimization cost about the nominal walking gait. This drives the controller to choose smooth input torques and anticipated spring torques, as well as regulate an optimal distribution of feasible ground reaction forces on hardware while reliably tracking the planned virtual constraints. These final results demonstrate how each component of this thesis were brought together to form an effective end-to-end implementation of a nonlinear control framework for underactuated locomotion on a bipedal robot through modeling, trajectory optimization, and then ultimately real-time control.</p

Correct-By-Construction Control Synthesis for Systems with Disturbance and Uncertainty

This dissertation focuses on correct-by-construction control synthesis for Cyber-Physical Systems (CPS) under model uncertainty and disturbance. CPSs are systems that interact with the physical world and perform complicated dynamic tasks where safety is often the overriding factor. Correct-by-construction control synthesis is a concept that provides formal performance guarantees to closed-loop systems by rigorous mathematic reasoning. Since CPSs interact with the environment, disturbance and modeling uncertainty are critical to the success of the control synthesis. Disturbance and uncertainty may come from a variety of sources, such as exogenous disturbance, the disturbance caused by co-existing controllers and modeling uncertainty. To better accommodate the different types of disturbance and uncertainty, the verification and control synthesis methods must be chosen accordingly. Four approaches are included in this dissertation. First, to deal with exogenous disturbance, a polar algorithm is developed to compute an avoidable set for obstacle avoidance. Second, a supervised learning based method is proposed to design a good student controller that has safety built-in and rarely triggers the intervention of the supervisory controller, thus targeting the design of the student controller. Third, to deal with the disturbance caused by co-existing controllers, a Lyapunov verification method is proposed to formally verify the safety of coexisting controllers while respecting the confidentiality requirement. Finally, a data-driven approach is proposed to deal with model uncertainty. A minimal robust control invariant set is computed for an uncertain dynamic system without a given model by first identifying the set of admissible models and then simultaneously computing the invariant set while selecting the optimal model. The proposed methods are applicable to many real-world applications and reflect the notion of using the structure of the system to achieve performance guarantees without being overly conservative.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145933/1/chenyx_1.pd

Robust hybrid control for autonomous vehicle motion planning

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2001.Includes bibliographical references (p. 141-150).This dissertation focuses on the problem of motion planning for agile autonomous vehicles. In realistic situations, the motion planning problem must be solved in real-time, in a dynamic and uncertain environment. The fulfillment of the mission objectives might also require the exploitation of the full maneuvering capabilities of the vehicle. The main contribution of the dissertation is the development of a new computational and modelling framework (the Maneuver Automaton), and related algorithms, for steering underactuated, nonholonomic mechanical systems. The proposed approach is based on a quantization of the system's dynamics, by which the feasible nominal system trajectories are restricted to the family of curves that can be obtained by the interconnection of suitably defined primitives. This can be seen as a formalization of the concept of "maneuver", allowing for the construction of a framework amenable to mathematical programming. This motion planning framework is applicable to all time-invariant dynamical systems which admit dynamic symmetries and relative equilibria. No other assumptions are made on the dynamics, thus resulting in exact motion planning techniques of general applicability. Building on a relatively expensive off-line computation phase, we provide algorithms viable for real-time applications. A fundamental advantage of this approach is the ability to provide a mathematical foundation for generating a provably stable and consistent hierarchical system, and for developing the tools to analyze the robustness of the system in the presence of uncertainty and/or disturbances.(cont.) In the second part of the dissertation, a randomized algorithm is proposed for real-time motion planning in a dynamic environment. By employing the optimal control solution in a free space developed for the maneuver automaton (or for any other general system), we present a motion planning algorithm with probabilistic convergence and performance guarantees, and hard safety guarantees, even in the face of finite computation times. The proposed methodologies are applicable to a very large class of autonomous vehicles: throughout the dissertation, examples, simulation and experimental results are presented and discussed, involving a variety of mechanical systems, ranging from simple academic examples and laboratory setups, to detailed models of small autonomous helicopters.by Emilio Frazzoli.Ph.D

New Approaches in Automation and Robotics

The book New Approaches in Automation and Robotics offers in 22 chapters a collection of recent developments in automation, robotics as well as control theory. It is dedicated to researchers in science and industry, students, and practicing engineers, who wish to update and enhance their knowledge on modern methods and innovative applications. The authors and editor of this book wish to motivate people, especially under-graduate students, to get involved with the interesting field of robotics and mechatronics. We hope that the ideas and concepts presented in this book are useful for your own work and could contribute to problem solving in similar applications as well. It is clear, however, that the wide area of automation and robotics can only be highlighted at several spots but not completely covered by a single book