Global Stabilization of Triangular Systems with Time-Delayed Dynamic Input Perturbations

A control design approach is developed for a general class of uncertain strict-feedback-like nonlinear systems with dynamic uncertain input nonlinearities with time delays. The system structure considered in this paper includes a nominal uncertain strict-feedback-like subsystem, the input signal to which is generated by an uncertain nonlinear input unmodeled dynamics that is driven by the entire system state (including unmeasured state variables) and is also allowed to depend on time delayed versions of the system state variable and control input signals. The system also includes additive uncertain nonlinear functions, coupled nonlinear appended dynamics, and uncertain dynamic input nonlinearities with time-varying uncertain time delays. The proposed control design approach provides a globally stabilizing delay-independent robust adaptive output-feedback dynamic controller based on a dual dynamic high-gain scaling based structure.Comment: 2017 IEEE International Carpathian Control Conference (ICCC

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

Dynamic balancing of underactuated robots

This thesis presents the control of planar underactuated systems that have one less control input than the number of degrees of freedom. The underactuated robots are studied to achieve dynamically stable motions commonly encountered during robot locomotion. This work emphasizes the relation between the underactuated systems and biped locomotion and builds on the previous works in the literature on underactuated robot locomotion. Two planar system models are treated: an acrobatic robot and a compass biped with torso. The dynamic stability of fast periodic trajectories of these systems are regulated by designing asymptotically stable feedback controllers. The resulting internal dynamics of the systems are analyzed and shaped to achieve energy efficiency and robustness of the closed-loop system trajectories. In particular, Bézier polynomial approximations and parameter optimization methods are used to systematically construct the internal dynamics of the systems. Simulation results are presented for dynamically stable orbits of the acrobatic robot and the compass biped with torso

Nonlinear control and synchronization of multiple Lagrangian systems with application to tethered formation flight spacecraft

Thesis (Sc. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2007.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 217-228).This dissertation focuses on the synchronization of multiple dynamical systems using contraction theory, with applications to cooperative control of multi-agent systems and synchronization of interconnected dynamics such as tethered formation flight. Inspired by stable combinations of biological systems, contraction nonlinear stability theory provides a systematic method to reduce arbitrarily complex systems into simpler elements. One application of oscillation synchronization is a fully decentralized nonlinear control law, which eliminates the need for any inter-satellite communications. We use contraction theory to prove that a nonlinear control law stabilizing a single-tethered spacecraft can also stabilize arbitrarily large circular arrays of tethered spacecraft, as well as a three-spacecraft inline configuration. The convergence result is global and exponential due to the nature of contraction analysis. The proposed decentralized control strategy is further extended to robust adaptive control in order to account for model uncertainties. Numerical simulations and experimental results validate the exponential stability of the tethered formation arrays by implementing a tracking control law derived from the reduced dynamics.(cont.) This thesis also presents a new synchronization framework that can be directly applied to cooperative control of autonomous aerospace vehicles and oscillation synchronization in robotic manipulation and locomotion. We construct a dynamical network of multiple Lagrangian systems by adding diffusive couplings to otherwise freely moving or flying vehicles. The proposed tracking control law synchronizes an arbitrary number of robots into a common trajectory with global exponential convergence. The proposed control law is much simpler than earlier work in terms of both the computational load and the required signals. Furthermore, in contrast with earlier work which used simple double integrator models, the proposed method permits highly nonlinear systems and is further extended to adaptive synchronization, partial-joint coupling, and concurrent synchronization. Another contribution of the dissertation is a novel nonlinear control approach for underactuated tethered formation flight spacecraft. This is motivated by a controllability analysis that indicates that both array resizing and spin-up are fully controllable by the reaction wheels and the tether motor. This work reports the first propellant-free underactuated control results for tethered formation flight.(cont.) We also fulfill the potential of the proposed strategy by providing a new momentum dumping method. This dissertation work has evolved based on the research philosophy of balancing theoretical work with practicality, aiming at physically intuitive algorithms that can be directly implemented in real systems. In order to validate the effectiveness of the decentralized control and estimation framework, a new suite of hardware has been designed and added to the SPHERES (Synchronize Position Hold Engage and Reorient Experimental Satellite) testbed. Such recent improvements described in this dissertation include a new tether reel mechanism, a force-torque sensor and an air-bearing carriage with a reaction wheel. This thesis also introduces a novel relative attitude estimator, in which a series of Kalman filters incorporate the gyro, force-torque sensor and ultrasound ranging measurements. The closed-loop control experiments can be viewed at ...by Soon-Jo Chung.Sc.D