Gyroscopic Precession In Motion Modelling Of Ball-Shaped Robots

This study discusses kinematic and dynamic precession models for a rolling ball with a finite contact area and a point contact respectively. In literature, both conventions have been applied. In this paper, we discuss in detail the kinematic and dynamic models to describe the ball precession and the radius of a circular rolling path. The kinematic model can be used if the contact area and friction coefficient are sufficient to prevent slippage. The dynamic precession model has significance in multi-body simulation environments handling rolling balls with ideal point contacts. We have applied both the kinematic and dynamic precession model to evaluate the no-slip condition of the existing GimBall-robot. According to the result, the necessity of an external precession torque may cause slipping at lower velocities than expected if ignoring this torque.Peer reviewe

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

О построении управления движением маятника вращением инерциального маховика

Рассмотрен пример малоприводной механической системы, которая предоставляет собой маятник, управление движением которого происходит благодаря вращению маховика. Получен в явном виде закон управления вращением маховика, обеспечивающего стабилизацию верхнего положения равновесия маятника.Розглянуто приклад малоприводної механічної системи, що являє собою маятник, керування рухом якого відбувається завдяки обертанню маховика. Отримано у явному вигляді закон керування обертанням маховика, який забезпечує стабілізацію верхнього положення рівноваги маятника.An example of the under actuated mechanical system, which is a pendulum, whose motion is controlled by the rotation of a flywheel, is investigated. The explicit form of the control law of the flywheel rotation, which ensures the stabilization of the upper equilibrium position of the pendulum, is obtained

Unified Representation Of Decoupled Dynamic Models For Pendulum-Driven Ball-Shaped Robots

Dynamic models describing the ball-robot motion form the basis for developments in ball-robot mechanics and motion control systems. For this paper, we have conducted a literature review of decoupled forward-motion models for pendulum-driven ball-shaped robots. The existing models in the literature apply several different conventions in system definition and parameter notation. Even if describing the same mechanical system, the diversity in conventions leads into dynamic models with different forms. As a result, it is difficult to compare, reproduce and apply the models available in the literature. Based on the literature review, we reformulate all common variations of decoupled dynamic forward-motion models using a unified notation and formulation. We have verified all reformulated models through simulations, and present the simulation results for a selected model. In addition, we demonstrate the different system behavior resulting from different ways to apply the pendulum reaction torque, a variation that can be found in the literature. For anyone working with the ball-robots, the unified compilation of the reformulated dynamic models provides an easy access to the models, as well as to the related work.Peer reviewe

Control Systems Approach to Balance Stabilization during Human Standing and Walking.

Humans rely on cooperation from multiple sensorimotor processes to navigate a complex world. Poor function of one or more components can lead to reduced mobility or increased risk of falls, particularly with age. At present, quantification and characterization of poor postural control typically focus on single sensors rather than the ensemble and lack methods to consider the overall function of sensors, body dynamics, and actuators. To address this gap, I propose a controls framework based on simple mechanistic models to characterize and understand normative postural behavior. The models employ a minimal set of components that typify human behavior and make quantitative predictions to be tested against human data. This framework is applied to four topics relevant to daily living: sensory integration for standing balance, limb coordination for one-legged balance, momentum usage in sit-to-stand maneuvers, and the energetic trade-offs of foot-to-ground clearance while walking. First, I demonstrate that integration of information from multiple physiological sensors can be modeled by an optimal state estimator. I show how such a model can predict human responses to conflict between visual, vestibular, and other sensors and use visual perturbation experiments to test this model. Second, I demonstrate that feedback control can model multi-limb coordination strategies during one-legged balance. I empirically identify a control law from human subjects and investigate how reducing stance ankle function necessitates greater gains from other limbs. Third, I show the advantages of momentum usage in sit-to-stand maneuvers. Counter to many human movements, this strategy is not performed with energetic economy, requiring excess mechanical work. However, with optimization models, I demonstrate that momentum serves to balance effort between knee and hip. Fourth, I propose a cost model for preferred ground clearance during swing phase of walking. Walking with greater foot lift is costly, but inadvertent ground contact is also costly. Therefore the tradeoff between these costly measures, modulated by movement variability, can explain expected cost of ground clearance. These controls-based models demonstrate the mechanisms behind normative behavior and enables predictions under novel situations. Thus these models may serve as diagnostic tools to identify poor postural control or aid design of intervention procedures.PhDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/116654/1/amyrwu_1.pd

Design of an Adaptive Super-Twisting Control for the Cart-Pole Inverted Pendulum System

A cart-pole inverted pendulum system is one of the underactuated systems that has been used in many applications. This research aims to study the design and the effectiveness of the Adaptive Super-Twisting controller to stabilize the system by comparing it with other previous control methods. A stabilization control of the pendulum upright using the Adaptive Super-Twisting algorithm (ASTA), was investigated. The proposed controller was designed based on the decoupling algorithm method to solve the coupled control input in the system model. We then compared the proposed stabilizing controller with first-order sliding mode control (FOSMC) and Super-Twisting algorithm (STA) in Matlab/Simulink simulation and realistic computer simulation. We developed the computer simulation using anyKode Marilou software, which adopted Open-Dynamic Engine (ODE) as a physics engine. In Matlab/Simulink simulation, we considered three different scenarios: a nominal system, a system with uncertainty, and a disturbed system. Meanwhile, in a computer simulation, we only presented the comparison of different controllers' performances for the realized system. Both results showed that the three controllers could stabilize the pendulum upright with a 0.1 rad initial angular position around the vertical axis. Under the same conditions, the ASTA and STA controllers had similar performances; they both have less chattering and faster convergence than the FOSMC approach. However, the FOSMC approach had the least energy delivered and smallest errors than the other two approaches

Vibration, Control and Stability of Dynamical Systems

From Preface: This is the fourteenth time when the conference “Dynamical Systems: Theory and Applications” gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and Ministry of Science and Higher Education of Poland. It is a great pleasure that our invitation has been accepted by recording in the history of our conference number of people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to participate in the conference for the first time. With proud and satisfaction we welcomed over 180 persons from 31 countries all over the world. They decided to share the results of their research and many years experiences in a discipline of dynamical systems by submitting many very interesting papers. This year, the DSTA Conference Proceedings were split into three volumes entitled “Dynamical Systems” with respective subtitles: Vibration, Control and Stability of Dynamical Systems; Mathematical and Numerical Aspects of Dynamical System Analysis and Engineering Dynamics and Life Sciences. Additionally, there will be also published two volumes of Springer Proceedings in Mathematics and Statistics entitled “Dynamical Systems in Theoretical Perspective” and “Dynamical Systems in Applications”

Ballbot-Inspired orbital refueling depot and fluid-slosh effects on Spacecraft attitude dynamics

Orbital refueling has become a subject of increasing interest as longer, deep space missions and manned missions to the Moon and Mars are being contemplated once again. For fueling depots to become part of the infrastructure in space capable of enhancing deployment and service operations, there remains a slew of technical, operational, and engineering challenges which must be overcome. In this thesis, focus is placed mainly on the issue of fluid slosh and its effects on the spacecraft dynamics and the design of an attitude control system. In pursuit of overcoming the attitude tracking errors and instability from the fluid slosh, a novel satellite design is presented based on an omnidirectional ball-balanced robot (ball-bot) which aims at minimizing the control effort required to stabilize the satellite while also maximizing the amount of fuel it can carry. The satellite is comprised of two primary elements: a spherical tank, containing the fuel payload and a cuboid bus, containing the attitude control system (ACS) and other subsystems. The satellite bus is mobile and can displace itself over the surface of the sphere and has a sunshield which is deployed in orbit which shields the spherical tank from solar radiation. The cube is mobile and can displace itself on the surface of the sphere to point to the sun ensuring the protection of the fuel payload. A presentation of the state-of-the-art of orbital fuel depots is first presented, and subsequently, a contextualization of orbital dynamics, along with the mathematical modeling of the satellite, is carried out, complemented by a discussion about the limitations of the work and the assumptions of the model. A simulation of the satellite¿s dynamics with the fluid slosh is conducted using Simulink and the sun-tracking of the cuboid-bus with Mathematica. Finally, a set of conclusions are presented and recommendations for future research and improvements, based on the conclusions, are made.Objectius de Desenvolupament Sostenible::9 - Indústria, Innovació i Infraestructur