2. Dynamics, Control and Trajectory Following


 Wilfrid Holland
 1 years ago
 Views:
Transcription
1 2. Dynamics, Control and Trajectory Following
2 This module Flying vehicles: how do they work? Quick refresher on aircraft dynamics with reference to the magical flying space potato How I learned to stop worrying and love control Attitude control from a robotics perspective Zen and the art of trajectory following Position control and hierarchical architecture
3 Early morning stimulus question 4 What do all aircraft have in common? What differentiates them from nonaircraft? Form groups of 23 people and yell at them until you all agree
4 It s ok, don t be afraid.
5 A quick refresher An aircraft can be thought of as a magical flying space potato* magic *or a flying brick, if you prefer
6 Basic potato dynamics To maneuver, the potato applies magic (which we ll call forces and torques ) It s not important how this magic is produced magic
7 Basic potato dynamics Like all magic potatoes, when not accelerating, forces on the aircraft must be in equilibrium magic mg
8 Basic potato dynamics Unbalanced forces result in an acceleration proportional to the mass/inertia of the potato: magic Resultant acceleration Net force mg
9 Basic potato dynamics We represent the location of the potato in space by a coordinate vector, defined in an fixed inertial reference frame
10 Basic potato dynamics There are lots of ways of representing rotation. eg. rotation matrices, Euler angles, quaternions
11 Basic potato dynamics Given a rigid space potato (a firm assumption), internal forces and torques are generated due to bodyintrinsic rotations*: *You may know of these as gyroscopic and Coriolis forces
12 Basic potato dynamics Now we know enough to write the dynamics of magical and nonmagical forces:
13 Basic potato dynamics But we also care about the angle and trajectory of potato flight the integral of spud velocities:
14 Basic potato dynamics We have the complete equations of motion but where does the magic come from? Aerodynamics!
15 Basic potato dynamics There are lots of different ways of making magic
16 Basic potato dynamics Different magic systems create different couplings between forces in each direction Few aircraft are truly decoupled in all axes It is this crosscoupling that makes control interesting
17 Early morning stimulus question 5 What is this control thing, anyway? How is a controlled system different from a robotic system? Form groups of 23 people and yell at them until you all agree
18 position The control thing: what is it? Control is the process of making current system states converge to desired final states This can be orientation, position, as well as velocities and accelerations This is done by using state measurements to compute commands leading to convergence goal time
19 Example: a simple rotorcraft Consider a supersimple dynamic model of a rotarywing vehicle (a quadrotor in particular) Fixed direction of thrust in the body frame No flapping torques, forces, etc Rotor pairs generate pure torques Assume for now that rotor thrust is constant and exactly equals gravity
20 Underactuation This system is underactuated we have fewer control inputs than states to control* Motion in a desired direction must arise as a result of movement in another direction So what do we do? * This is where smart people start talking about stuff like group theory
21 Attitude control Fortunately, we don t care about every state all at once* instead, let s focus on attitude Helicopters are inherently unstable, so attitude control is important Rotation is approximately decoupled in hover, so we can treat pitch and roll separately *If we did, we would have a deep conversation about controllability
22 Example: PD control Let s consider only pitch things are vastly simplified when crosscoupling is ignored!, This is a secondorder system we can stabilise it with ProportionalDerivative control* *Proofs usually follow statements of this kind
23 Example: PD control We can also use to drive the system to a particular reference angle, We can think of this feedback process as a series of interconnected dynamic systems: PD system dynamics 1
24 Position control But wait a minute pitch angle feeds into the longitudinal position dynamics! We can use a simple linearised model to build a controller for position around hover:, This is also a second order system PD ahoy!
25 Example: PD control We can use as a virtual control term:* The closedloop system will converge to and *Assuming timescale separation of rotational and translational dynamics
26 Cascaded system This builds a nested control structure PD PD attitude dynamics longitudinal dynamics 1 We can use a sequence of desired positions to make the craft follow a desired trajectory, guiding the aircraft through space 1
27 Early morning stimulus question 6 Where does state knowledge come from? Where do reference trajectories come from? Form groups of 23 people and yell at them until you all agree
28 Tip of the iceberg There are more methods of controlling dynamic systems than you can shake a stick at: PD, PID, PD 2 LQR, LQG, backstepping, sliding mode Robust control, adaptive control, etc just to name a few! Each and every one has been applied to UAVs somehow and they ve been done for a variety of coordinate systems: Euler angles, TaitBryan angles Quaternions Rotation matrices Axisangle
29 Questions?
30 Zwischenspiel.
Quadcopters. Presented by: Andrew Depriest
Quadcopters Presented by: Andrew Depriest What is a quadcopter? Helicopter  uses rotors for lift and propulsion Quadcopter (aka quadrotor)  uses 4 rotors Parrot AR.Drone 2.0 History 1907  BreguetRichet
More informationCHAPTER 1 INTRODUCTION
CHAPTER 1 INTRODUCTION 1.1 Background of the Research Agile and precise maneuverability of helicopters makes them useful for many critical tasks ranging from rescue and law enforcement task to inspection
More informationCONTRIBUTIONS TO THE AUTOMATIC CONTROL OF AERIAL VEHICLES
1 / 23 CONTRIBUTIONS TO THE AUTOMATIC CONTROL OF AERIAL VEHICLES MINH DUC HUA 1 1 INRIA Sophia Antipolis, AROBAS team I3SCNRS Sophia Antipolis, CONDOR team Project ANR SCUAV Supervisors: Pascal MORIN,
More informationOnboard electronics of UAVs
AARMS Vol. 5, No. 2 (2006) 237 243 TECHNOLOGY Onboard electronics of UAVs ANTAL TURÓCZI, IMRE MAKKAY Department of Electronic Warfare, Miklós Zrínyi National Defence University, Budapest, Hungary Recent
More information3D Tranformations. CS 4620 Lecture 6. Cornell CS4620 Fall 2013 Lecture 6. 2013 Steve Marschner (with previous instructors James/Bala)
3D Tranformations CS 4620 Lecture 6 1 Translation 2 Translation 2 Translation 2 Translation 2 Scaling 3 Scaling 3 Scaling 3 Scaling 3 Rotation about z axis 4 Rotation about z axis 4 Rotation about x axis
More informationQuadcopter Dynamics, Simulation, and Control Introduction
Quadcopter Dynamics, Simulation, and Control Introduction A helicopter is a flying vehicle which uses rapidly spinning rotors to push air downwards, thus creating a thrust force keeping the helicopter
More informationGeneral aviation & Business System Level Applications and Requirements Electrical Technologies for the Aviation of the Future EuropeJapan Symposium
General aviation & Business System Level Applications and Requirements Electrical Technologies for the Aviation of the Future EuropeJapan Symposium 26 March 2015 2015 MITSUBISHI HEAVY INDUSTRIES, LTD.
More informationSpacecraft Dynamics and Control. An Introduction
Brochure More information from http://www.researchandmarkets.com/reports/2328050/ Spacecraft Dynamics and Control. An Introduction Description: Provides the basics of spacecraft orbital dynamics plus attitude
More informationMechanics lecture 7 Moment of a force, torque, equilibrium of a body
G.1 EE1.el3 (EEE1023): Electronics III Mechanics lecture 7 Moment of a force, torque, equilibrium of a body Dr Philip Jackson http://www.ee.surrey.ac.uk/teaching/courses/ee1.el3/ G.2 Moments, torque and
More informationAn inertial haptic interface for robotic applications
An inertial haptic interface for robotic applications Students: Andrea Cirillo Pasquale Cirillo Advisor: Ing. Salvatore Pirozzi Altera Innovate Italy Design Contest 2012 Objective Build a Low Cost Interface
More informationDesignSimulationOptimization Package for a Generic 6DOF Manipulator with a Spherical Wrist
DesignSimulationOptimization Package for a Generic 6DOF Manipulator with a Spherical Wrist MHER GRIGORIAN, TAREK SOBH Department of Computer Science and Engineering, U. of Bridgeport, USA ABSTRACT Robot
More informationAerospace Engineering 3521: Flight Dynamics. Prof. Eric Feron Homework 6 due October 20, 2014
Aerospace Engineering 3521: Flight Dynamics Prof. Eric Feron Homework 6 due October 20, 2014 1 Problem 1: Lateraldirectional stability of Navion With the help of Chapter 2 of Nelson s textbook, we established
More informationPID, LQR and LQRPID on a Quadcopter Platform
PID, LQR and LQRPID on a Quadcopter Platform Lucas M. Argentim unielargentim@fei.edu.br Willian C. Rezende uniewrezende@fei.edu.br Paulo E. Santos psantos@fei.edu.br Renato A. Aguiar preaguiar@fei.edu.br
More informationControl and Navigation Framework for Quadrotor Helicopters
Control and Navigation Framework for Quadrotor Helicopters Amr Nagaty, Sajad Saeedi, Carl Thibault, Mae Seto and Howard Li Abstract This paper presents the development of a nonlinear quadrotor simulation
More informationSIMULATION AND CONTROL OF A QUADROTOR UNMANNED AERIAL VEHICLE
University of Kentucky UKnowledge University of Kentucky Master's Theses Graduate School 2011 SIMULATION AND CONTROL OF A QUADROTOR UNMANNED AERIAL VEHICLE Michael David Schmidt University of Kentucky,
More informationModeling and Simulation of a Three Degree of Freedom Longitudinal Aero plane System. Figure 1: Boeing 777 and example of a two engine business jet
Modeling and Simulation of a Three Degree of Freedom Longitudinal Aero plane System Figure 1: Boeing 777 and example of a two engine business jet Nonlinear dynamic equations of motion for the longitudinal
More informationBasic Principles of Inertial Navigation. Seminar on inertial navigation systems Tampere University of Technology
Basic Principles of Inertial Navigation Seminar on inertial navigation systems Tampere University of Technology 1 The five basic forms of navigation Pilotage, which essentially relies on recognizing landmarks
More informationMACCCS Center Review Presentation. Xinyan Deng BioRobotics Laboratory School of Mechanical Engineering Purdue University
MACCCS Center Review Presentation Xinyan Deng BioRobotics Laboratory School of Mechanical Engineering Purdue University Lab Experimental Facilities Tow tank PIV systems Wind tunnel Lab Related Work Aerodynamics
More informationLecture 8 : Dynamic Stability
Lecture 8 : Dynamic Stability Or what happens to small disturbances about a trim condition 1.0 : Dynamic Stability Static stability refers to the tendency of the aircraft to counter a disturbance. Dynamic
More informationFigure 1. The Ball and Beam System.
BALL AND BEAM : Basics Peter Wellstead: control systems principles.co.uk ABSTRACT: This is one of a series of white papers on systems modelling, analysis and control, prepared by Control Systems Principles.co.uk
More information1 KINEMATICS OF MOVING FRAMES
1 1 KINEMATICS OF MOVING FRAMES 1.1 Rotation of Reference Frames We denote through a subscript the specific reference system of a vector. Let a vector expressed in the inertial frame be denoted as γx,
More informationQuadrotor Helicopter Flight Dynamics and Control: Theory and Experiment
AIAA Guidance, Navigation and Control Conference and Exhibit 223 August 27, Hilton Head, South Carolina AIAA 27646 Quadrotor Helicopter Flight Dynamics and Control: Theory and Experiment Gabriel M. Hoffmann
More informationThe Design and Implementation of a Quadrotor Flight Controller Using the QUEST Algorithm
The Design and Implementation of a Quadrotor Flight Controller Using the QUEST Algorithm Jacob Oursland Department of Mathematics and Computer Science South Dakota School of Mines and Technology Rapid
More informationOverview of Missile Flight Control Systems
Overview of Missile Flight Control Systems Paul B. Jackson he flight control system is a key element that allows the missile to meet its system performance requirements. The objective of the flight control
More informationCIS 536/636 Introduction to Computer Graphics. Kansas State University. CIS 536/636 Introduction to Computer Graphics
2 Lecture Outline Animation 2 of 3: Rotations, Quaternions Dynamics & Kinematics William H. Hsu Department of Computing and Information Sciences, KSU KSOL course pages: http://bit.ly/hgvxlh / http://bit.ly/evizre
More informationVéronique PERDEREAU ISIR UPMC 6 mars 2013
Véronique PERDEREAU ISIR UPMC mars 2013 Conventional methods applied to rehabilitation robotics Véronique Perdereau 2 Reference Robot force control by Bruno Siciliano & Luigi Villani Kluwer Academic Publishers
More informationErgonomic Remote Control Technique for Horizontal Rotors Equipped UAVs
Ergonomic Remote Control Technique for Horizontal Rotors Equipped UAVs Alpár A. Sándor and Gergely B. Soós Faculty of Information Technology, Pázmány Péter Catholic University H1083 Práter u. 50/a Budapest,
More informationActive Vibration Isolation of an Unbalanced Machine Spindle
UCRLCONF206108 Active Vibration Isolation of an Unbalanced Machine Spindle D. J. Hopkins, P. Geraghty August 18, 2004 American Society of Precision Engineering Annual Conference Orlando, FL, United States
More informationDynamics. Basilio Bona. DAUINPolitecnico di Torino. Basilio Bona (DAUINPolitecnico di Torino) Dynamics 2009 1 / 30
Dynamics Basilio Bona DAUINPolitecnico di Torino 2009 Basilio Bona (DAUINPolitecnico di Torino) Dynamics 2009 1 / 30 Dynamics  Introduction In order to determine the dynamics of a manipulator, it is
More informationModelling and control of quadcopter
Teppo Luukkonen Modelling and control of quadcopter School of Science Mat2.418 Independent research project in applied mathematics Espoo, August 22, 211 A? Aalto University School of Science This document
More informationKINEMATICS OF PARTICLES RELATIVE MOTION WITH RESPECT TO TRANSLATING AXES
KINEMTICS OF PRTICLES RELTIVE MOTION WITH RESPECT TO TRNSLTING XES In the previous articles, we have described particle motion using coordinates with respect to fixed reference axes. The displacements,
More information8.012 Physics I: Classical Mechanics Fall 2008
MIT OpenCourseWare http://ocw.mit.edu 8.012 Physics I: Classical Mechanics Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. MASSACHUSETTS INSTITUTE
More informationOrigins of the Unusual Space Shuttle Quaternion Definition
47th AIAA Aerospace Sciences Meeting Including The New Horizons Forum and Aerospace Exposition 58 January 2009, Orlando, Florida AIAA 200943 Origins of the Unusual Space Shuttle Quaternion Definition
More informationLecture L222D Rigid Body Dynamics: Work and Energy
J. Peraire, S. Widnall 6.07 Dynamics Fall 008 Version.0 Lecture L  D Rigid Body Dynamics: Work and Energy In this lecture, we will revisit the principle of work and energy introduced in lecture L3 for
More informationMechanical Design of a 6DOF Aerial Manipulator for assembling bar structures using UAVs
Mechanical Design of a 6DOF Aerial Manipulator for assembling bar structures using UAVs R. Cano*. C. Pérez* F. Pruaño* A. Ollero** G. Heredia** *Centre for Advanced Aerospace Technologies, Seville, Spain
More informationSIX DEGREEOFFREEDOM MODELING OF AN UNINHABITED AERIAL VEHICLE. A thesis presented to. the faculty of
SIX DEGREEOFFREEDOM MODELING OF AN UNINHABITED AERIAL VEHICLE A thesis presented to the faculty of the Russ College of Engineering and Technology of Ohio University In partial fulfillment of the requirement
More informationCE801: Intelligent Systems and Robotics Lecture 3: Actuators and Localisation. Prof. Dr. Hani Hagras
1 CE801: Intelligent Systems and Robotics Lecture 3: Actuators and Localisation Prof. Dr. Hani Hagras Robot Locomotion Robots might want to move in water, in the air, on land, in space.. 2 Most of the
More informationControl of a Quadrotor Helicopter Using Visual Feedback
Control of a Quadrotor Helicopter Using Visual Feedback Erdinc Altu~*, James P. Ostrowski*, Robert Mahony** *GRASP Lab. University of Pennsylvania, Philadelphia, PA 1914, USA **Dep. of Eng., Australian
More informationZMART Technical Report The International Aerial Robotics Competition 2014
ZMART Technical Report The International Aerial Robotics Competition 2014 ZJU s MicroAerial Robotics Team (ZMART) 1 Zhejiang University, Hangzhou, Zhejiang Province, 310027, P.R.China Abstract The Zhejiang
More informationControl of a quadrotor UAV (slides prepared by M. Cognetti)
Sapienza Università di Roma Corso di Laurea in Ingegneria Elettronica Corso di Fondamenti di Automatica Control of a quadrotor UAV (slides prepared by M. Cognetti) Unmanned Aerial Vehicles (UAVs) autonomous/semiautonomous
More informationMathematical Model and Simulation for a Helicopter with Tail Rotor
Mathematical Model and Simulation for a Helicopter with Tail Rotor TULIO SALAZAR School of Mechanical Engineering and Automation Beijing University of Aeronautics and Astronautics XueYuan Road No.37, HaiDian
More informationBehavioral Animation Simulation of Flocking Birds
Behavioral Animation Simulation of Flocking Birds Autonomous characters determine their actions Simulating the paths of individuals in: flocks of birds, schools of fish, herds of animals crowd scenes 1.
More informationAbstract. Introduction
SPACECRAFT APPLICATIONS USING THE MICROSOFT KINECT Matthew Undergraduate Student Advisor: Dr. Troy Henderson Aerospace and Ocean Engineering Department Virginia Tech Abstract This experimental study involves
More informationCHAPTER 6 DESIGN OF SIX DEGREES OF FREEDOM AIRCRAFT MODEL AND LONGITUDINAL AUTOPILOT FOR AUTONOMOUS LANDING
148 CHAPTER 6 DESIGN OF SIX DEGREES OF FREEDOM AIRCRAFT MODEL AND LONGITUDINAL AUTOPILOT FOR AUTONOMOUS LANDING 6.1 INTRODUCTION This chapter deals with the development of six degrees of freedom (6DOF)
More informationPhysics Notes Class 11 CHAPTER 5 LAWS OF MOTION
1 P a g e Inertia Physics Notes Class 11 CHAPTER 5 LAWS OF MOTION The property of an object by virtue of which it cannot change its state of rest or of uniform motion along a straight line its own, is
More informationPath Tracking for a Miniature Robot
Path Tracking for a Miniature Robot By Martin Lundgren Excerpt from Master s thesis 003 Supervisor: Thomas Hellström Department of Computing Science Umeå University Sweden 1 Path Tracking Path tracking
More informationThis week. CENG 732 Computer Animation. The Display Pipeline. Ray Casting Display Pipeline. Animation. Applying Transformations to Points
This week CENG 732 Computer Animation Spring 20062007 Week 2 Technical Preliminaries and Introduction to Keframing Recap from CEng 477 The Displa Pipeline Basic Transformations / Composite Transformations
More informationLecture L5  Other Coordinate Systems
S. Widnall, J. Peraire 16.07 Dynamics Fall 008 Version.0 Lecture L5  Other Coordinate Systems In this lecture, we will look at some other common systems of coordinates. We will present polar coordinates
More informationLecture PowerPoints. Chapter 7 Physics: Principles with Applications, 6 th edition Giancoli
Lecture PowerPoints Chapter 7 Physics: Principles with Applications, 6 th edition Giancoli 2005 Pearson Prentice Hall This work is protected by United States copyright laws and is provided solely for the
More informationWind Turbines. Wind Turbines 2. Wind Turbines 4. Wind Turbines 3. Wind Turbines 5. Wind Turbines 6
Wind Turbines 1 Wind Turbines 2 Introductory Question Wind Turbines You and a child half your height lean out over the edge of a pool at the same angle. If you both let go simultaneously, who will tip
More informationCAMRAD II COMPREHENSIVE ANALYTICAL MODEL OF ROTORCRAFT AERODYNAMICS AND DYNAMICS
CAMRAD II COMPREHENSIVE ANALYTICAL MODEL OF ROTORCRAFT AERODYNAMICS AND DYNAMICS 1 CAMRAD II IS AN AEROMECHANICAL ANALYSIS OF HELICOPTERS AND ROTORCRAFT INCORPORATING ADVANCED TECHNOLOGY multibody dynamics
More informationThe TwoBody Problem
The TwoBody Problem Abstract In my short essay on Kepler s laws of planetary motion and Newton s law of universal gravitation, the trajectory of one massive object near another was shown to be a conic
More informationIntroduction to Computer Graphics MariePaule Cani & Estelle Duveau
Introduction to Computer Graphics MariePaule Cani & Estelle Duveau 04/02 Introduction & projective rendering 11/02 Prodedural modeling, Interactive modeling with parametric surfaces 25/02 Introduction
More informationEssential Mathematics for Computer Graphics fast
John Vince Essential Mathematics for Computer Graphics fast Springer Contents 1. MATHEMATICS 1 Is mathematics difficult? 3 Who should read this book? 4 Aims and objectives of this book 4 Assumptions made
More informationE X P E R I M E N T 8
E X P E R I M E N T 8 Torque, Equilibrium & Center of Gravity Produced by the Physics Staff at Collin College Copyright Collin College Physics Department. All Rights Reserved. University Physics, Exp 8:
More information2.1 Force and Motion Kinematics looks at velocity and acceleration without reference to the cause of the acceleration.
2.1 Force and Motion Kinematics looks at velocity and acceleration without reference to the cause of the acceleration. Dynamics looks at the cause of acceleration: an unbalanced force. Isaac Newton was
More informationChapter 10 Rotational Motion. Copyright 2009 Pearson Education, Inc.
Chapter 10 Rotational Motion Angular Quantities Units of Chapter 10 Vector Nature of Angular Quantities Constant Angular Acceleration Torque Rotational Dynamics; Torque and Rotational Inertia Solving Problems
More informationG U I D E T O A P P L I E D O R B I T A L M E C H A N I C S F O R K E R B A L S P A C E P R O G R A M
G U I D E T O A P P L I E D O R B I T A L M E C H A N I C S F O R K E R B A L S P A C E P R O G R A M CONTENTS Foreword... 2 Forces... 3 Circular Orbits... 8 Energy... 10 Angular Momentum... 13 FOREWORD
More informationNewton s Laws of Motion
Physics Newton s Laws of Motion Newton s Laws of Motion 4.1 Objectives Explain Newton s first law of motion. Explain Newton s second law of motion. Explain Newton s third law of motion. Solve problems
More informationResearch Methodology Part III: Thesis Proposal. Dr. Tarek A. Tutunji Mechatronics Engineering Department Philadelphia University  Jordan
Research Methodology Part III: Thesis Proposal Dr. Tarek A. Tutunji Mechatronics Engineering Department Philadelphia University  Jordan Outline Thesis Phases Thesis Proposal Sections Thesis Flow Chart
More informationDynamics of Rotational Motion
Chapter 10 Dynamics of Rotational Motion PowerPoint Lectures for University Physics, Twelfth Edition Hugh D. Young and Roger A. Freedman Lectures by James Pazun Modified by P. Lam 5_31_2012 Goals for Chapter
More informationMotion Control of 3 DegreeofFreedom DirectDrive Robot. Rutchanee Gullayanon
Motion Control of 3 DegreeofFreedom DirectDrive Robot A Thesis Presented to The Academic Faculty by Rutchanee Gullayanon In Partial Fulfillment of the Requirements for the Degree Master of Engineering
More informationA Simple Model for Ski Jump Flight Mechanics Used as a Tool for Teaching Aircraft Gliding Flight
eπεριοδικό Επιστήμης & Τεχνολογίας 33 A Simple Model for Ski Jump Flight Mechanics Used as a Tool for Teaching Aircraft Gliding Flight Vassilios McInnes Spathopoulos Department of Aircraft Technology
More informationFull design of a lowcost quadrotor UAV by student team
Full design of a lowcost quadrotor UAV by student team JeanBaptiste Devaud, Stéphane Najko, Pierre Le Nahédic, Cédric Maussire, Etienne Zante, Julien Marzat To cite this version: JeanBaptiste Devaud,
More informationComparison of Fixed and Variable Pitch Actuators for Agile Quadrotors
Comparison of Fixed and Variable Pitch Actuators for Agile Quadrotors Mark Cutler N. Kemal Ure Bernard Michini Jonathan P. How This paper presents the design, analysis and experimental testing of a variablepitch
More informationRotation: Moment of Inertia and Torque
Rotation: Moment of Inertia and Torque Every time we push a door open or tighten a bolt using a wrench, we apply a force that results in a rotational motion about a fixed axis. Through experience we learn
More informationAVIONICS SYSTEM FOR A SMALL UNMANNED HELICOPTER PERFORMING AGRESSIVE MANEUVERS
AVIONICS SYSTEM FOR A SMALL UNMANNED HELICOPTER PERFORMING AGRESSIVE MANEUVERS V. Gavrilets 1, A. Shterenberg 2, M. A. Dahleh 3, E. Feron 4, M.I.T., Cambridge, MA Abstract: An Xcell60 5 ft rotor diameter
More informationAOE 3134 Complete Aircraft Equations
AOE 3134 Complete Aircraft Equations The requirements for balance and stability that we found for the flying wing carry over directly to a complete aircraft. In particular we require the zerolift pitch
More informationRobotics. Lecture 3: Sensors. See course website http://www.doc.ic.ac.uk/~ajd/robotics/ for up to date information.
Robotics Lecture 3: Sensors See course website http://www.doc.ic.ac.uk/~ajd/robotics/ for up to date information. Andrew Davison Department of Computing Imperial College London Review: Locomotion Practical
More informationAttitude Control and Dynamics of Solar Sails
Attitude Control and Dynamics of Solar Sails Benjamin L. Diedrich A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Aeronautics & Astronautics University
More informationDATA COLLECTION FOR DEVELOPING A DYNAMIC MODEL OF A LIGHT HELICOPTER
DATA COLLECTION FOR DEVELOPING A DYNAMIC MODEL OF A LIGHT HELICOPTER Stefano Geluardi 1,2, Frank Nieuwenhuizen 1, Lorenzo Pollini 2, and Heinrich H. Bülthoff 1 1 Max Planck Institute for Biological Cybernetics,
More informationThe aerodynamic center
The aerodynamic center In this chapter, we re going to focus on the aerodynamic center, and its effect on the moment coefficient C m. 1 Force and moment coefficients 1.1 Aerodynamic forces Let s investigate
More informationAerodynamics of Flight
Chapter 2 Aerodynamics of Flight Introduction This chapter presents aerodynamic fundamentals and principles as they apply to helicopters. The content relates to flight operations and performance of normal
More informationMODELLING A SATELLITE CONTROL SYSTEM SIMULATOR
National nstitute for Space Research NPE Space Mechanics and Control Division DMC São José dos Campos, SP, Brasil MODELLNG A SATELLTE CONTROL SYSTEM SMULATOR Luiz C Gadelha Souza gadelha@dem.inpe.br rd
More informationIf you want to use an inertial measurement system...
If you want to use an inertial measurement system...... which technical data you should analyse and compare before making your decision by Dr.Ing. Edgar v. Hinueber, CEO imar Navigation GmbH Keywords:
More informationDevelopment Of Robust Flight Control Design For Unmanned Aerial Helicopter
Development Of Robust Flight Control Design For Unmanned Aerial Helicopter May Zin Tun, Zaw Min Naing, Hla Myo Tun Abstract: A complete flight control scheme with detailed design methodology is proposed
More informationPHYSICS 149: Lecture 4
PHYSICS 149: Lecture 4 Chapter 2 2.3 Inertia and Equilibrium: Newton s First Law of Motion 2.4 Vector Addition Using Components 2.5 Newton s Third Law 1 Net Force The net force is the vector sum of all
More informationThe dynamic equation for the angular motion of the wheel is R w F t R w F w ]/ J w
Chapter 4 Vehicle Dynamics 4.. Introduction In order to design a controller, a good representative model of the system is needed. A vehicle mathematical model, which is appropriate for both acceleration
More informationWorksheet #1 Free Body or Force diagrams
Worksheet #1 Free Body or Force diagrams Drawing FreeBody Diagrams Freebody diagrams are diagrams used to show the relative magnitude and direction of all forces acting upon an object in a given situation.
More informationChapter 5 Newton s Laws of Motion
Chapter 5 Newton s Laws of Motion Force and Mass Units of Chapter 5 Newton s First Law of Motion Newton s Second Law of Motion Newton s Third Law of Motion The Vector Nature of Forces: Forces in Two Dimensions
More informationDynamics and Control of an Elastic Dumbbell Spacecraft in a Central Gravitational Field
Dynamics Control of an Elastic Dumbbell Spacecraft in a Central Gravitational Field Amit K. Sanyal, Jinglai Shen, N. Harris McClamroch 1 Department of Aerospace Engineering University of Michigan Ann Arbor,
More informationWorld Leader in Flight Control Systems and Critical Control Applications
World Leader in Flight Control Systems and Critical Control Applications Exceeding Expectations Since 1951 Over the last 60 years, Moog has developed a reputation throughout the world as a company whose
More informationACTUATOR DESIGN FOR ARC WELDING ROBOT
ACTUATOR DESIGN FOR ARC WELDING ROBOT 1 Anurag Verma, 2 M. M. Gor* 1 G.H Patel College of Engineering & Technology, V.V.Nagar388120, Gujarat, India 2 Parul Institute of Engineering & Technology, Limda391760,
More informationLecture L6  Intrinsic Coordinates
S. Widnall, J. Peraire 16.07 Dynamics Fall 2009 Version 2.0 Lecture L6  Intrinsic Coordinates In lecture L4, we introduced the position, velocity and acceleration vectors and referred them to a fixed
More informationObjective: Equilibrium Applications of Newton s Laws of Motion I
Type: Single Date: Objective: Equilibrium Applications of Newton s Laws of Motion I Homework: Assignment (111) Read (4.14.5, 4.8, 4.11); Do PROB # s (46, 47, 52, 58) Ch. 4 AP Physics B Mr. Mirro Equilibrium,
More information2008 FXA DERIVING THE EQUATIONS OF MOTION 1. Candidates should be able to :
Candidates should be able to : Derive the equations of motion for constant acceleration in a straight line from a velocitytime graph. Select and use the equations of motion for constant acceleration in
More informationHow to Turn an AC Induction Motor Into a DC Motor (A Matter of Perspective) Steve Bowling Application Segments Engineer Microchip Technology, Inc.
1 How to Turn an AC Induction Motor Into a DC Motor (A Matter of Perspective) Steve Bowling Application Segments Engineer Microchip Technology, Inc. The territory of highperformance motor control has
More informationQuadrotor Helicopter Flight Dynamics and Control: Theory and Experiment
Quadrotor Helicopter Flight Dynamics and Control: Theory and Experiment Gabriel M. Hoffmann Haomiao Huang Steven L. Waslander Claire J. Tomlin Quadrotors are rapidly emerging as a popular platform for
More informationProp Rotor Acoustics for Conceptual Design. Final Report NASA Grant NAG 2918. Valana L. Wells Arizona State University
Prop Rotor Acoustics for Conceptual Design Final Report NASA Grant NAG 2918 Valana L. Wells Arizona State University April 1996 Abstract The report describes a methodology for the simple prediction of
More informationRS platforms. Fabio Dell Acqua  Gruppo di Telerilevamento
RS platforms Platform vs. instrument Sensor Platform Instrument The remote sensor can be ideally represented as an instrument carried by a platform Platforms Remote Sensing: Groundbased airborne spaceborne
More informationForces on a Model Rocket
Forces on a Model Rocket This pamphlet was developed using information for the Glenn Learning Technologies Project. For more information, visit their web site at: http://www.grc.nasa.gov/www/k12/aboutltp/educationaltechnologyapplications.html
More informationPrerequisites 20122013
Prerequisites 20122013 Engineering Computation The student should be familiar with basic tools in Mathematics and Physics as learned at the High School level and in the first year of Engineering Schools.
More informationRobot TaskLevel Programming Language and Simulation
Robot TaskLevel Programming Language and Simulation M. Samaka Abstract This paper presents the development of a software application for Offline robot task programming and simulation. Such application
More informationFluid Mechanics Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur
Fluid Mechanics Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture  20 Conservation Equations in Fluid Flow Part VIII Good morning. I welcome you all
More informationVirtual CRASH 3.0 Staging a Car Crash
Virtual CRASH 3.0 Staging a Car Crash Virtual CRASH Virtual CRASH 3.0 Staging a Car Crash Changes are periodically made to the information herein; these changes will be incorporated in new editions of
More informationLecture L293D Rigid Body Dynamics
J. Peraire, S. Widnall 16.07 Dynamics Fall 2009 Version 2.0 Lecture L293D Rigid Body Dynamics 3D Rigid Body Dynamics: Euler Angles The difficulty of describing the positions of the bodyfixed axis of
More informationCatapult Engineering Pilot Workshop. LA Tech STEP 20072008
Catapult Engineering Pilot Workshop LA Tech STEP 20072008 Some Background Info Galileo Galilei (15641642) did experiments regarding Acceleration. He realized that the change in velocity of balls rolling
More informationAvailable online at www.sciencedirect.com Available online at www.sciencedirect.com
Available online at www.sciencedirect.com Available online at www.sciencedirect.com Procedia Procedia Engineering Engineering () 9 () 6 Procedia Engineering www.elsevier.com/locate/procedia International
More informationTracking of Small Unmanned Aerial Vehicles
Tracking of Small Unmanned Aerial Vehicles Steven Krukowski Adrien Perkins Aeronautics and Astronautics Stanford University Stanford, CA 94305 Email: spk170@stanford.edu Aeronautics and Astronautics Stanford
More informationHomework 4. problems: 5.61, 5.67, 6.63, 13.21
Homework 4 problems: 5.6, 5.67, 6.6,. Problem 5.6 An object of mass M is held in place by an applied force F. and a pulley system as shown in the figure. he pulleys are massless and frictionless. Find
More information