О стабилизации поступательных движений вращением эксцентрикового маховика

Построено управление вращением эксцентрикового маховика, которое обеспечивает глобальную асимптотическую устойчивость положения равновесия трансляционного осциллятора с вращающимся актуатором. Показана робастность такого управления и предложен способ оценки области робастности в пространстве параметров механической системы. Полученные результаты проиллюстрированы на примере конкретной модели.Побудовано керування обертанням ексцентрикового маховика, яке забезпечує глобальну асимптотичну стійкість положення рівноваги трансляційного осцилятора з обертовим актуатором. Показано робастність такого керування і запропоновано спосіб оцінки області робастності у просторі параметрів механічної системи. Отримані результати проілюстровані на прикладі конкретної моделі.A control by eccentric balance wheel rotation is built which provides the globally asymptotically stability of equilibrium of the translational oscillator with rotating actuator. It is shown that such control is robust. A way of estimating the region of robustness in the space of the system parameters of mechanical system is suggested. The obtained results are illustrated on an example of the concrete model

О построении управления поступательным движением вращением эксцентрикового маховика

Рассмотрен пример малоприводной механической системы TORA. Получен в явном виде закон управления вращением эксцентрикового маховика, который обеспечивает стабилизацию положения равновесия TORA.Розглянуто приклад малоприводної механічної системи TORA. Отримано у явному вигляді закон керування обертанням ексцентрикового маховика, який забезпечує стабілізацію положення рівноваги TORA.The underactuated mechanical system TORA is investigated. The explicit form of a control law for the eccentric flywheel rotation, which ensures the stabilization of the equilibrium position of TORA, is obtained

A Constructive Methodology for the IDA-PBC of Underactuated 2-DoF Mechanical Systems with Explicit Solution of PDEs

This paper presents a passivity-based control strategy dealing with underactuated two-degree-of-freedom (2-DoF) mechanical systems. Such a methodology, which is based on the interconnection and damping assignment passivity-based control (IDA-PBC), rooted within the port-controlled Hamiltonian framework, can be applied to a very large class of underactuated 2-DoF mechanical systems. The main contribution, compared to the previous literature, is that the new methodology does not involve the resolution of any partial differential equation, since explicit solutions are given, while no singularities depending on generalised momenta are introduced by the controller. The proposed strategy is applied to two case studies: a) the stabilisation of a translational oscillator with a rotational actuator (TORA) system; b) the gait generation for an underactuated compass-like biped robot. The performances of the presented solution are evaluated through numerical simulations

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

The Frequency-Amplitude Response of a Class of Nonholonomic Systems

Nonholonomic systems have been investigated as models for locomotion due to the similarity between nonholonomic constraints and the no-slip condition of wheels or the Kutta condition of swimmers\u27 tails. The focus of most past research has been on kinematic nonholonomic systems. However, an increasing body of research points to benefits that dynamic components of these systems, such as underactuated degrees of freedom, can provide. This work investigates the effect of adding stiff degrees of freedom to the Chaplygin sleigh, a classical nonholonomic system that has been used in the past as a swimming model. Observed resonance behavior is shown to greatly increase net velocity of the sleigh at certain ranges of forcing frequency and amplitude. A change to the formulation of the nonholonomic constraint is also considered where the constraint point is defined as fixed with respect to the flow field around the body, which is defined by potential flow theory. The reduced effective inertia resulting from this change improves performance at high forcing frequency, but reduces performance for slower forcing

Energy Shaping of Underactuated Systems via Interconnection and Damping Assignment Passivity-Based Control with Applications to Planar Biped Robots

The sought goal of this thesis is to show that total energy shaping is an effective and versatile tool to control underactuated mechanical systems. The performance of several approaches, rooted in the port-Hamiltonian formalism, are analyzed while tackling distinct control problems: i) equilibrium stabilization; ii) gait generation; iii) gait robustication. Firstly, a constructive solution to deal with interconnection and damping assignment passivity-based control (IDA-PBC) for underactuated two-degree-of-freedom mechanical systems is proposed. This strategy does not involve the resolution of any partial differential equation, since explicit solutions are given, while no singularities depending on generalized momenta are introduced by the controller. The methodology is applied to the stabilization of a translational oscillator with a rotational actuator system, as well as, to the gait generation for an underactuated compass-like biped robot (CBR). Then, the problem of gait generation is addressed using dissipative forces in the controller. In this sense, three distinct controllers are presented, namely simultaneous interconnection and damping assignment passivity-based control with dissipative forces, energy pumping-and-damping passivity-based control (EPD-PBC), and energy pumping-or-damping control. Finally, EPD-PBC is used to increase the robustness of the gait exhibited by the CBR over uncertainties on the initial conditions. The passivity of the system is exploited, as well as, its hybrid nature (using the hybrid zero dynamics method) to carry out the stability analysis. Besides, such an approach is applied to new gaits that are generated using IDA-PBC. Numerical case studies, comparisons, and critical discussions evaluate the performance of the proposed approaches

Data-Driven Methods for Geometric Systems

The tools of geometric mechanics provide a compact representation of locomotion dynamics as ``the reconstruction equation''. We have found this equation yields a convenient form for estimating models directly from observation data. This convenience draws from the method's relatively rare feature of providing high accuracy models with little effort. By little effort, we point to the modeling process's low data requirements and the property that nothing about the implementation changes when substituting robot kinematics, material properties, or environmental conditions, as long as some intuitive baseline features of the dynamics are shared. We have applied data-driven geometric mechanics models toward optimizing robot behaviors both physical and simulated, exploring robots' ability to recover from injury, and efficiently creating libraries of maneuvers to be used as building blocks for higher-level robot tasks. Our methods employed the tools of data-driven Floquet analysis, providing a phase that we used as a means of grouping related measurements, allowing us to estimate a reconstruction equation model as a function of phase in the neighborhood of an observed behavior. This tool allowed us to build models at unanticipated scales of complexity and speed. Our use of a perturbation expansion for the geometric terms led to an improved estimation procedure for highly damped systems containing nontrivial but non-dominating amounts of momentum. Analysis of the role of passivity in dissipative systems led to another extension of the estimation procedure to robots with high degrees of underactuation in their internal shape, such as soft robots. This thesis will cover these findings and results, simulated and physical, and the surprising practicality of data-driven geometric mechanics.PHDRoboticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/168033/1/babitt_1.pd

DESIGN, MODELING, AND FABRICATION OF MICROROBOT LEGS

This dissertation presents work done in the design, modeling, and fabrication of magnetically actuated microrobot legs. Novel fabrication processes for manufacturing multi-material compliant mechanisms have been used to fabricate effective legged robots at both the meso and micro scales, where the meso scale refers to the transition between macro and micro scales. This work discusses the development of a novel mesoscale manufacturing process, Laser Cut Elastomer Refill (LaCER), for prototyping millimeter-scale multi-material compliant mechanisms with elastomer hinges. Additionally discussed is an extension of previous work on the development of a microscale manufacturing process for fabricating micrometer-sale multi-material compliant mechanisms with elastomer hinges, with the added contribution of a method for incorporating magnetic materials for mechanism actuation using externally applied fields. As both of the fabrication processes outlined make significant use of highly compliant elastomer hinges, a fast, accurate modeling method for these hinges was desired for mechanism characterization and design. An analytical model was developed for this purpose, making use of the pseudo rigid-body (PRB) model and extending its utility to hinges with significant stretch component, such as those fabricated from elastomer materials. This model includes 3 springs with stiffnesses relating to material stiffness and hinge geometry, with additional correction factors for aspects particular to common multi-material hinge geometry. This model has been verified against a finite element analysis model (FEA), which in turn was matched to experimental data on mesoscale hinges manufactured using LaCER. These modeling methods have additionally been verified against experimental data from microscale hinges manufactured using the Si/elastomer/magnetics MEMS process. The development of several mechanisms is also discussed: including a mesoscale LaCER-fabricated hexapedal millirobot capable of walking at 2.4 body lengths per second; prototyped mesoscale LaCER-fabricated underactuated legs with asymmetrical features for improved performance; 1 centimeter cubed LaCER-fabricated magnetically-actuated hexapods which use the best-performing underactuated leg design to locomote at up to 10.6 body lengths per second; five microfabricated magnetically actuated single-hinge mechanisms; a 14-hinge, 11-link microfabricated gripper mechanism; a microfabricated robot leg mechansim demonstrated clearing a step height of 100 micrometers; and a 4 mm x 4 mm x 5 mm, 25 mg microfabricated magnetically-actuated hexapod, demonstrated walking at up to 2.25 body lengths per second

Adaptive Backstepping Integral Sliding Mode Control for 5DOF Barge-Type OFWT under Output Constraint

This article presents a new control solution for a dynamical model of a translational oscillator with a rotational actuator (TORA) based on multi-body dynamics for a barge-type offshore floating wind turbine (OFWT). TORA has been employed as an active structural control strategy. The solution of bounding the output movements of platform pitch and tower bending angle to a certain limit, along with mitigating the OFWT vibrations due to environmental disturbances and uncertainties, is presented in this novel control framework. This new control algorithm consists of a high-gain observer (HGO)-based adaptive backstepping integral sliding mode control (ISMC) and a barrier Lyapunov function (BLF). This guarantees satisfying the constraints on the states and effectively resolves the problem of the unavailability of the system states. The proposed control law based on the BLF has been compared with an adaptive backstepping ISMC to show the efficiency of the output-constraint control scheme. Through MATLAB/SIMULINK numerical simulations and their numeric error table, the effectiveness of the proposed control scheme has been examined. The results confirm the validity and efficiency of the proposed control approaches

Feedback Control of a Hovercraft over a Wireless Link

Nonlinear underactuated systems (i.e. systems with fewer control inputs than configuration variables) present significant challenges for automatic control. This thesis explores feedback control of an underactuated hovercraft over a wireless communication channel using techniques from nonlinear control theory. A family of control laws stabilizing the hovercraft <em>reduced dynamics</em> - including zero velocity, constant forward/reverse velocity, and constant angular velocity stabilization - are derived. Lyapunov arguments are used to prove convergence of the reduced dynamics under the control laws. It is shown that heading cannot be stabilized by a continuously differentiable state feedback law. In response, two hybrid control algorithms for heading stabilization are proposed. The control laws are demonstrated on a real R/C hovercraft using a distributed autopilot and a Bluetooth network. A two-dimensional aided INS is developed using a MEMs IMU and the "Cricket" RF/ultrasonic ranging system. Experimental and simulated results from a high-fidelity model are shown to agree nicely