Control Of Nonh=holonomic Systems

Many real-world electrical and mechanical systems have velocity-dependent constraints in their dynamic models. For example, car-like robots, unmanned aerial vehicles, autonomous underwater vehicles and hopping robots, etc. Most of these systems can be transformed into a chained form, which is considered as a canonical form of these nonholonomic systems. Hence, study of chained systems ensure their wide applicability. This thesis studied the problem of continuous feed-back control of the chained systems while pursuing inverse optimality and exponential convergence rates, as well as the feed-back stabilization problem under input saturation constraints. These studies are based on global singularity-free state transformations and controls are synthesized from resulting linear systems. Then, the application of optimal motion planning and dynamic tracking control of nonholonomic autonomous underwater vehicles is considered. The obtained trajectories satisfy the boundary conditions and the vehicles\u27 kinematic model, hence it is smooth and feasible. A collision avoidance criteria is set up to handle the dynamic environments. The resulting controls are in closed forms and suitable for real-time implementations. Further, dynamic tracking controls are developed through the Lyapunov second method and back-stepping technique based on a NPS AUV II model. In what follows, the application of cooperative surveillance and formation control of a group of nonholonomic robots is investigated. A designing scheme is proposed to achieves a rigid formation along a circular trajectory or any arbitrary trajectories. The controllers are decentralized and are able to avoid internal and external collisions. Computer simulations are provided to verify the effectiveness of these designs

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

Sliding mode control applied in trajectory-tracking of WMRs and autonomous vehicles

Tese de doutoramento apresentada à Fac. de Ciências e Tecnologia da Universidade de CoimbraThe thesis is structured as follows: • Chapter 2: Trajectory tracking problems are summarized. • Chapter 3: Kinematic and dynamic modeling of theWMRs and car-like robots are presented. • Chapter 4: The concept of sliding mode are first introduced. Then the fundamentals of SMC are summarized, including basic definitions, methods of sliding surface and control law design, robustness properties and the methods on handling chattering problems. New sliding-mode trajectory-tracking and slidingmode path-following controllers for WMRs and car-like vehicles, are also proposed in this chapter. • Chapter 5: The trajectory/path planning are developed, including the velocity profile. • Chapter 6: A model with two freedom degrees is considered for the HNC model. The user comfort is examined not only in the time domain, but also in the frequency domain. • Chapter 7: Experimental results obtained with the implementation of the proposed controllers in RobChair are summarized and discussed. • Chapter 8: Finally, conclusions are drawn and some suggestions for future work are provided

Non-Linear Robust Observers For Systems With Non-Collocated Sensors And Actuators

Challenges in controlling highly nonlinear systems are not limited to the development of sophisticated control algorithms that are tolerant to significant modeling imprecision and external disturbances. Additional challenges stem from the implementation of the control algorithm such as the availability of the state variables needed for the computation of the control signals, and the adverse effects induced by non-collocated sensors and actuators. The present work investigates the adverse effects of non-collocated sensors and actuators on the phase characteristics of flexible structures and the ensuing implications on the performance of structural controllers. Two closed-loop systems are considered and their phase angle contours have been generated as functions of the normalized sensor location and the excitation frequency. These contours were instrumental in the development of remedial actions for rendering structural controllers immune to the detrimental effects of non-collocated sensors and actuators. Moreover, the current work has focused on providing experimental validation for the robust performances of a self-tuning observer and a sliding mode observer. The observers are designed based on the variable structure systems theory and the self-tuning fuzzy logic scheme. Their robustness and self-tuning characteristics allow one to use an imprecise model of the system and eliminate the need for the extensive tuning associated with a fixed rule-based expert fuzzy inference system. The first phase of the experimental work was conducted in a controlled environment on a flexible spherical robotic manipulator whose natural frequencies are configuration-dependent. Both controllers have yielded accurate estimates of the required state variables in spite of significant modeling imprecision. The observers were also tested under a completely uncontrolled environment, which involves a 16-ft boat operating in open-water under different sea states. Such an experimental work necessitates the development of a supervisory control algorithm to perform PTP tasks, prescribed throttle arm and steering tasks, surge speed and heading tracking tasks, or recovery maneuvers. This system has been implemented herein to perform prescribed throttle arm and steering control tasks based on estimated rather than measured state variables. These experiments served to validate the observers in a completely uncontrolled environment and proved their viability as reliable techniques for providing accurate estimates for the required state variables

Nonlinear control of underactuated mechanical systems with application to robotics and aerospace vehicles

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2001.Includes bibliographical references (leaves 308-316).This thesis is devoted to nonlinear control, reduction, and classification of underactuated mechanical systems. Underactuated systems are mechanical control systems with fewer controls than the number of configuration variables. Control of underactuated systems is currently an active field of research due to their broad applications in Robotics, Aerospace Vehicles, and Marine Vehicles. The examples of underactuated systems include flexible-link robots, nobile robots, walking robots, robots on mobile platforms, cars, locomotive systems, snake-type and swimming robots, acrobatic robots, aircraft, spacecraft, helicopters, satellites, surface vessels, and underwater vehicles. Based on recent surveys, control of general underactuated systems is a major open problem. Almost all real-life mechanical systems possess kinetic symmetry properties, i.e. their kinetic energy does not depend on a subset of configuration variables called external variables. In this work, I exploit such symmetry properties as a means of reducing the complexity of control design for underactuated systems. As a result, reduction and nonlinear control of high-order underactuated systems with kinetic symmetry is the main focus of this thesis. By "reduction", we mean a procedure to reduce control design for the original underactuated system to control of a lowerorder nonlinear or mechanical system. One way to achieve such a reduction is by transforming an underactuated system to a cascade nonlinear system with structural properties. If all underactuated systems in a class can be transformed into a specific class of nonlinear systems, we refer to the transformed systems as the "normal form" of the corresponding class of underactuated systems. Our main contribution is to find explicit change of coordinates and control that transform several classes of underactuated systems, which appear in robotics and aerospace applications, into cascade nonlinear systems with structural properties that are convenient for control design purposes. The obtained cascade normal forms are three classes of nonlinear systems, namely, systems in strict feedback form, feedforward form, and nontriangular linear-quadratic form. The names of these three classes are due to the particular lower-triangular, upper-triangular, and nontriangular structure in which the state variables appear in the dynamics of the corresponding nonlinear systems. The triangular normal forms of underactuated systems can be controlled using existing backstepping and feedforwarding procedures. However, control of the nontriangular normal forms is a major open problem. We address this problem for important classes of nontriangular systems of interest by introducing a new stabilization method based on the solutions of fixed-point equations as stabilizing nonlinear state feedback laws. This controller is obtained via a simple recursive method that is convenient for implementation. For special classes of nontriangular nonlinear systems, such fixed-point equations can be solved explicitly ...by Reza Olfati-Saber.Ph.D

Sliding Mode Control

The main objective of this monograph is to present a broad range of well worked out, recent application studies as well as theoretical contributions in the field of sliding mode control system analysis and design. The contributions presented here include new theoretical developments as well as successful applications of variable structure controllers primarily in the field of power electronics, electric drives and motion steering systems. They enrich the current state of the art, and motivate and encourage new ideas and solutions in the sliding mode control area