Calibration of a rotating multibeam Lidar


 Walter May
 2 years ago
 Views:
Transcription
1 Calibration of a rotating multibeam Lidar Naveed Muhammad and Simon Lacroix Abstract This paper presents a technique for the calibration of multibeam laser scanners. The technique is based on an optimization process, which gives precise estimation of calibration parameters starting from a course calibration. Optimization process is based on the comparison of scan data with the ground truth environment. Detailed account of the optimization process and suitability analysis of optimization objective function is described, and results are provided to show the efficacy of calibration technique. I. INTRODUCTION Sensors are an essential part of any mobile robotic system and play an important role in its motion and actions it performs. A very basic requirement for a robot to autonomously move in an environment is to accurately observe its surroundings. Different types of sensors are used for this purpose including cameras and laser scanners. Classically laser scanners consisted of a single laser which (or another part of the sensor) moved in different ways in order to observe the environment in 3D. But recently multiplelaser scanning systems are becoming common. Multilaser scanning systems are very interesting for applications in autonomous mobile robotic systems because they can provide 3D information about their environments in realtime and therefore can efficiently be used for tasks such as environment modeling, obstacle detection, and SLAM. One of these systems is the Velodyne HDLE S. It consists of lasers located on a spinning head which spins at a rate of 5 to 15 Hz and provides 3D data about its surroundings at a rate of 1 million points per second. Another such system is Ibeo LUX which scans its surroundings in four parallel layers. The performance of these scanners depends on their calibration. If the sensor is precisely calibrated it can observe its surroundings more precisely and thus can provide more exploitable data. For instance precise 3D data from an environment can easily be processed to extract line or planar features, whereas extraction of these features can be difficult, unreliable or impossible if the sensor is badly calibrated. A lot of work has been done on the calibration of cameras, multicamera system and omnidirectional vision sensors but calibration techniques for multilaser sensors have not been investigated to that extent. Considering laser scanning systems [1] provide an excellent technique for calibration of a laser scanner fitted on a mobile robot. In [] a procedure for calibrating additive and proportional distance correction factors for a multibeam laser scanner is described. [3] state CNRS; LAAS; 7 Av. du Colonel Roche, F3177 Toulouse, France and University of Toulouse; UPS, INSA, INP, ISAE; LAAS; F3177 Toulouse, France. the calibration of distance correction parameters for a multilaser scanner by comparing distance readings from a Sick lidar. This paper provides a technique for the calibration of a rotating multibeam lidar. Optimization technique is employed to estimate the calibration parameters more precisely. Starting from a coarse calibration, data acquired by the scanner is compared to the ground truth environment to estimate precise calibration parameters. The paper is organized as follows: section II describes the sensor geometry, calibration problem, and the optimization based calibration process. Section III presents the implementation of calibration procedure and results. Section IV concludes and mentions related future works. A. Geometric model II. PROBLEM ANALYSIS This section presents the geometric model of lidar sensor that we used. The lidar is a Velodyne HDLE S [] with lasers in a spinning head. The lasers are grouped in two blocks, with 3 lasers located in the upper block and remaining 3 in the lower block on lidar s spinning head. Lasers in each block are further divided into two groups of 1 lasers each, with one group located towards right and one towards left on the lidar head. Each of the lasers is characterized by five parameters that are required to convert the distance value returned by the laser to 3D point coordinates. These parameters are: Rotational Correction Angle α: angle made by laser beam with yz plane. Vertical Correction Angle θ: angle made by laser beam with xy plane, as shown in fig. 1. Distance Correction Factor D corr : value to be added in the distance returned by corresponding laser. Vertical Offset V offset : distance measured orthogonal to the laser beam, representing the distance of laser beam from origin in a vertical sense. Segment OA in figure 1 represents V offset. Horizontal Offset H offset : horizontal counterpart of V offset. Segment OB in figure represents H offset. As the lidar head spins, its current rotational angle is represented as φ. Each laser has a different value of α so we can define another angle β such that β = φ  α. In this way β represents the orientation of laser beam relative to the current rotational angle of spinning lidar head. Distance value returned by a single laser (D ret ) can be converted to a 3D point P with Cartesian coordinates (P x, P y, P z ) T expressed in lidar frame, using above five
2 7 .//,) $1$.,35 *$'!+, : 9 .//,)$ 1$+(35!"#$%&'() 7$1$+(35 * ' ())&*+ ","(&./ 7"$"#$%& 5 / $! ","1%./ $!"#$%& 71$.,35 ' ())&*+","1%./ 7!# $! ","(&./ "*$'!+, Fig. 1. Lidar unit s side view $"#$%& parameters and the current rotational angle of lidar head, using following equations: D = D ret + D corr (1) D xy = D cos(θ) V offset sin(θ) () P x = D xy sin(β) H offset cos(β) (3) P y = D xy cos(β)+h offset sin(β) () Fig.. Lidar unit s top view P z = D sin(θ)+v offset cos(θ) (5) Among the five calibration parameters D corr, α and θ are the most important. This is because of the fact that errors induced by bad calibration of these parameters in the precision of 3D coordinates of acquired data changes with the distance of scanned object/surface, whereas the errors induced by imprecise calibration of V offset and H offset do not vary with variation in the distance of scanned object. Therefore in this paper we concentrate on the calibration of D corr, α and θ for 1 out of lasers but the same principle can be applied to the calibration of other two parameters and remaining lasers. B. Problems with inaccurate calibration Like any other sensor if a lidar is not calibrated well, the data acquired by the sensor is also inaccurate. Inaccuracies in the acquired data can complicate further processing of data, extraction of landmarks to be used for SLAM for instance. Furthermore this can also result in inaccurate digital terrain maps etc. Fig. 3 shows one example of inaccurate calibration of our multiplebeam lidar. The figure shows segmented view of a planar surface placed at 3m distance from the lidar. Fig. 3. A planar surface, seen from front Each horizontal line in the scan shows the data from a single laser. One can see that the data from all the lasers are not aligned to form a rectangular planar surface, instead the data from different lasers are horizontally misaligned. This misalignment seems to be repeated between every two consecutive lasers which come from right and left sided blocks on the lidar head. Fig. shows another effect of inaccurate calibration. Figure shows the top view of a corner in a room. Ideally, if the calibration parameters for all lasers were accurate and the sensor had lower noise, as seen from top the walls should have looked much thinner and corners much sharper. C. Principle of calibration 1) Principle: The principle lying behind the calibration process is the optimization performed to adjust lidar s calibration parameters so that the 3D data acquired by lidar matches the ground truth (environment).
3 Fig.. Top view of a corner in a room From the sensor geometry described in section IIA we already have the knowledge to convert raw lidar data into 3D point cloud. An environment can be designed and created to acquire lidar data, which will then be converted to 3D point cloud data. The choice of environment depends on the sensor to be calibrated. The environment must also allow the selection/definition of a cost function which can be used to quantitatively compare the acquired 3D point cloud data and the real environment. This cost function should provide lower costs for better matches between computed point cloud and the real environment and vice versa. Another important requirement for the cost function is that for successful optimization of calibration parameters, the cost function should be sensitive to each one of them. In other words, varying the value of each calibration parameter should result in variation in the cost value provided by our cost function. With these conditions satisfied, starting with the initial estimates of calibration parameters, an optimization process can be performed to get precise estimates of the calibration parameters for each laser. ) Calibration Environment: Keeping in view the above mentioned criteria for the selection of a suitable environment, a.m wide planar wall on a flat surface was used as the calibration environment. The wall was scanned by placing the lidar at multiple distances and orientations from the wall. First the wall was scanned by aligning x axis of lidar s fixed frame to the wall, and moving the lidar at various distances ranging from 1 to 1m, and then by aligning lidar s y axis to the wall and moving it at various distances ranging from to m. More details are provided in section III. D. Cost/Objective function for optimization 1) Criteria for choosing the cost function: A cost function is required to perform the desired optimization process for the estimation of calibration parameters. This cost function must allow the comparison of 3D data acquired by the sensor and the ground truth environment. As described in section IIC.1 this cost function should provide higher costs if there is more difference between the acquired 3D data and ground truth environment, and similarly should provide lower costs as the match between acquired 3D data and real environment improves. Another and very important requirement for this cost function is that it should be sensitive to each one of the parameters to be estimated/optimized. It means that the cost provided by this function must vary when the values of the parameters to be optimized are varied, and of course this increase or decrease in the cost should be in accordance with the first criteria for cost function i.e. the cost should be lower for better matches between the acquired 3D data and ground truth and vice versa. Our choice of the cost function is described below followed by suitability analysis of the function for desired optimization to be successful. ) Chosen cost function: As the basic structure in our experiment environment was a plane (a wall), the cost function chosen for optimization was the variance of 3D data in the sense of plane s thickness. Ideally a plane scanned from the front must have zero thickness so this seems to be an intuitive choice for the cost function. When the wall was scanned with the lidar s fixed frame s y axis aligned to the wall, the cost for the current scan is the average squared perpendicular distance of x coordinate(p x ) of each point P to mean x coordinate of all the points in current scan. Mathematically this can be represented by: C y = Σ(P x,i P x,mean ) /n () where C y represents the cost of a scan when the wall was aligned to y axis of lidar s fixed frame, and n is the total number of points in the current scan. Similarly C x i.e. cost of a given scan when the wall was aligned to x axis of lidar s fixed frame is given by: C x = Σ(P y,i P y,mean ) /n (7) 3) Suitability analysis: The suitability of the defined cost function depends on the criterion that cost function is sensitive to the variation in each of the parameters to be optimized. As the cost function depends on the variance of x and y coordinates of 3D data, the suitability of chosen cost function can be ensured by finding the partial derivatives of P x and P y with respect to each of the three calibration parameters to be optimized i.e. D corr, α and θ. Nonzero partial derivatives ensure that cost function is sensitive to the corresponding calibration parameter. Using equations 3 and, required partial derivatives with respect to D corr are given as: P x / D corr = cos θ sin β () P y / D corr = cos θ cos β (9) From P x / D corr it is clear that the conditions that make the partial derivative equal to zero are θ = 9 and β =. This makes intuitive sense as θ = 9 means that laser is physically pointing upwards and in such a situation it is
4 impossible to scan a plane (wall) which is parallel to the laser. Similarly π½ = means that the laser is parallel to the plane being scanned and therefore the laser would not hit the plane as long as π½ remains 9. In our case the values for π for all lasers in the lidar are much smaller than 9. And as the lidar rotates the value of π½ is constantly changing and therefore we are never necessarily taking the scan while fixing the value of π½ =. Similarly, the conditions that make ππ₯ / π·ππππ equal to zero are π = 9 and π½ = 9. As with the previous case, the condition π½ = 9 does not pose any problem because the lidar is constantly rotating as we acquire the data. Therefore our chosen cost function is suitable to be used for the estimation of π·ππππ using optimization. Required partial derivatives with respect to π are given by: ππ₯ / π = π· sin π½ sin π πππ π π ππ‘ sin π½ cos π (1) ππ¦ / π = π· cos π½ sin π πππ π π ππ‘ cos π½ cos π (11) The conditions which make ππ₯ / π and ππ¦ / π equal to zero are π½ = and π½ = 9 respectively. As with the case for π·π πππ, for the constantly rotating lidar, these partial derivatives remain nonzero for the type of 3D datasets that we are using. Therefore our chosen cost function is suitable to be used for the estimation of π using optimization. Similarly it can be shown that our cost function is also suitable for the optimization of the third calibration parameter πΌ, but its analysis is not being presented here for brevity s sake Fig. 5. view Three scans with wall aligned to xaxis of lidar s fixed frame, top III. I MPLEMENTATION AND R ESULTS A. Implementation The optimization was implemented using Matlab function π ππππππ [5]. The dataset used for optimization consisted of six scans of the wall. For three scans, the lidar s fixed frame s π¦ ππ₯ππ was aligned to the wall and scans were taken at, and m from the wall. For the other three scans, lidar s π₯ ππ₯ππ was aligned to the wall and scans were taken at 1, 1 and 1m from the wall. This distribution of data over a range of distances is very important. Sufficiently distributed data is necessary to ensure the estimation of calibration parameters to be independent of any bias on a specific distance. Fig. 5 shows the top view of three scans (at 1, 1 and 1m) of the wall superimposed in a single plot. Fig. shows other three scans (at, and m) of the wall superimposed in a single plot. B. Results Optimization was performed starting from the default calibration data provided by the manufacturer. One way to quantitatively judge improvement in the optimized calibration parameters is to compare the standard deviations in the depth of planar data (i.e. the standard deviations of π₯ πππππππππ‘ππ of data points for datasets when the wall was aligned to π¦ ππ₯ππ of lidar s fixed frame and vice versa) for default and optimized calibration parameters. Table I shows improvements in standard deviations for depth of planar data used for optimization Fig.. Three scans with wall aligned to yaxis of lidar s fixed frame It is important to validate the optimized calibration parameters for data which was not used in the optimization process. Table II shows the improvement in standard deviations for depth of planar data when the wall was scanned from the distances of 1 and 1m and these sets were not used in the optimization process. It is worth mentioning that average standard deviation for depth of planar data for a single laser was found to be.5m. This indicates the noise in the sensor and is the lower bound for any optimization process that is performed to improve the calibration parameters for the sensor. C. Effect of using insufficiently distributed data for optimization If the data used for optimization is not sufficiently distributed in terms of distance, the resulting estimation of calibration parameters can be highly biased on the distance at which the data used for optimization was taken. Table III
5 TABLE I STANDARD DEVIATIONS (IN METERS) IN DEPTH OF PLANAR DATA m.73.9 m.31.3 m m m m.9.15 TABLE II STANDARD DEVIATIONS (IN METERS) FOR DATA NOT USED IN OPTIMIZATION 1m m fitting step in the calibration process which will remove the obligation of scanning the planar surface by keeping it aligned to x or y axis of lidar s fixed frame. We also aim to work on the calibration of sensor in robot s frame and possibly simultaneous calibration of multiple sensors together. REFERENCES [1] J. Underwood, A. Hill, and S. Scheding, Calibration of range sensor pose on mobile platforms, in IEEE/RSJInternational Conference on Intelligent Robots and Systems, SanDiego (CA), USA, Oct. 7. [] P. Stone et al., DARPA Urban Challenge Technical Report, Austin Robot Technology, 7. [3] J. Bohren et al., Little Ben, The Ben Franklin Racing Team s Entry in the 7 DARPA Urban Challenge, Journal of Field Robotics, vol 5,, pp [] Velodyne Lidar Inc., HDLE S User s Manual, Velodyne Lidar, Inc. 35 Digital Drive, Morgan Hill, CA 9537,. [5] The Mathworks, Matlab Optimization function: fmincon, 9, Website as at 15/9/9. shows the change in standard deviations in depths of planar data when only the dataset taken by placing the lidar at 1m from the wall was used for the optimization process. It is worth noticing that here for data at 1m, we have reached the maximum possible improvement in the estimation of calibration parameters (standard deviation with recalibrated parameters approaching.5m). But the important point here is that standard deviations for data at and m actually become worse as a result of biased optimization process. A. Conclusion IV. CONCLUSION AND FUTURE WORKS Laser scanners are becoming more and more useful in the field of robotics. With recent innovations like the multibeam lidars providing rich and fast 3D scans of the environment, these sensors have a great potential for being employed on mobile robots and changing the ways these robots sense and act in their environments. As for any other sensor, precise calibration is very important for these sensors to be useful. We have presented a technique for precise calibration of a rotating multibeam lidar, and the principle can be extended to similar sensors. The paper has presented how optimization can be employed to perform precise calibration starting from a course set of calibration parameters. B. Future works In near future we aim to make this calibration process more generic. Currently we are working on adding a plane TABLE III BIASED ESTIMATION OF CALIBRATION PARAMETERS m m m m m m.9.93
Automatic Labeling of Lane Markings for Autonomous Vehicles
Automatic Labeling of Lane Markings for Autonomous Vehicles Jeffrey Kiske Stanford University 450 Serra Mall, Stanford, CA 94305 jkiske@stanford.edu 1. Introduction As autonomous vehicles become more popular,
More information3D Scanner using Line Laser. 1. Introduction. 2. Theory
. Introduction 3D Scanner using Line Laser Di Lu Electrical, Computer, and Systems Engineering Rensselaer Polytechnic Institute The goal of 3D reconstruction is to recover the 3D properties of a geometric
More informationREAL TIME 3D FUSION OF IMAGERY AND MOBILE LIDAR INTRODUCTION
REAL TIME 3D FUSION OF IMAGERY AND MOBILE LIDAR Paul Mrstik, Vice President Technology Kresimir Kusevic, R&D Engineer Terrapoint Inc. 1401 Antares Dr. Ottawa, Ontario K2E 8C4 Canada paul.mrstik@terrapoint.com
More informationTHREE DIMENSIONAL GEOMETRY
Chapter 11 THREE DIMENSIONAL GEOMETRY 111 Overview 1111 Direction cosines of a line are the cosines of the angles made by the line with positive directions of the coordinate axes 111 If l, m, n are the
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 informationRobot Perception Continued
Robot Perception Continued 1 Visual Perception Visual Odometry Reconstruction Recognition CS 685 11 Range Sensing strategies Active range sensors Ultrasound Laser range sensor Slides adopted from Siegwart
More informationChapter 5 Polar Coordinates; Vectors 5.1 Polar coordinates 1. Pole and polar axis
Chapter 5 Polar Coordinates; Vectors 5.1 Polar coordinates 1. Pole and polar axis 2. Polar coordinates A point P in a polar coordinate system is represented by an ordered pair of numbers (r, ΞΈ). If r >
More informationChapter 11. Assembly Modeling. Evaluation chapter. Logon to for more details. Learning Objectives
Chapter 11 Assembly Modeling Learning Objectives After completing this chapter you will be able to: Insert components into an assembly file. Create bottomup assemblies. Insert components into a product
More informationPNI White Paper Written in collaboration with Miami University. Accurate Position Tracking Using Inertial Measurement Units
PNI White Paper Written in collaboration with Miami University Accurate Position Tracking Using Inertial Measurement Units David Vincent February This white paper presents an overview of inertial position
More informationFigure 1.1 Vector A and Vector F
CHAPTER I VECTOR QUANTITIES Quantities are anything which can be measured, and stated with number. Quantities in physics are divided into two types; scalar and vector quantities. Scalar quantities have
More informationCopyright 2011 Casa Software Ltd. www.casaxps.com. Centre of Mass
Centre of Mass A central theme in mathematical modelling is that of reducing complex problems to simpler, and hopefully, equivalent problems for which mathematical analysis is possible. The concept of
More informationStatic Environment Recognition Using Omnicamera from a Moving Vehicle
Static Environment Recognition Using Omnicamera from a Moving Vehicle Teruko Yata, Chuck Thorpe Frank Dellaert The Robotics Institute Carnegie Mellon University Pittsburgh, PA 15213 USA College of Computing
More informationPhysics Spring Experiment #8 1 Experiment #8, Magnetic Forces Using the Current Balance
Physics 182  Spring 2012  Experiment #8 1 Experiment #8, Magnetic Forces Using the Current Balance 1 Purpose 1. To demonstrate and measure the magnetic forces between current carrying wires. 2. To verify
More informationThe SternGerlach Experiment
Chapter The SternGerlach Experiment Let us now talk about a particular property of an atom, called its magnetic dipole moment. It is simplest to first recall what an electric dipole moment is. Consider
More information3D Scanners. Javad Malaquti. Intelligent Robotics Seminar. Winter Semester 2013/
3D Scanners Intelligent Robotics Seminar Javad Malaquti Winter Semester 2013/14 16.12.2013 Agenda Introduction Point Cloud TimeofFlight 3D Laser Scanner Triangulation Based 3D Laser Scanner Structured
More informationStress and Deformation Analysis. Representing Stresses on a Stress Element. Representing Stresses on a Stress Element con t
Stress and Deformation Analysis Material in this lecture was taken from chapter 3 of Representing Stresses on a Stress Element One main goals of stress analysis is to determine the point within a loadcarrying
More informationThe process components and related data characteristics addressed in this document are:
TM Tech Notes Certainty 3D November 1, 2012 To: General Release From: Ted Knaak Certainty 3D, LLC Re: Structural Wall Monitoring (#1017) rev: A Introduction TopoDOT offers several tools designed specifically
More informationSection 1.1. Introduction to R n
The Calculus of Functions of Several Variables Section. Introduction to R n Calculus is the study of functional relationships and how related quantities change with each other. In your first exposure to
More informationBending of Beams with Unsymmetrical Sections
Bending of Beams with Unsmmetrical Sections Assume that CZ is a neutral ais. C = centroid of section Hence, if > 0, da has negative stress. From the diagram below, we have: Ξ΄ = Ξ± and s = Ξ±Ο and Ξ΄ Ξ΅ = =
More informationLecture 8 : Coordinate Geometry. The coordinate plane The points on a line can be referenced if we choose an origin and a unit of 20
Lecture 8 : Coordinate Geometry The coordinate plane The points on a line can be referenced if we choose an origin and a unit of 0 distance on the axis and give each point an identity on the corresponding
More informationClass XI Chapter 5 Complex Numbers and Quadratic Equations Maths. Exercise 5.1. Page 1 of 34
Question 1: Exercise 5.1 Express the given complex number in the form a + ib: Question 2: Express the given complex number in the form a + ib: i 9 + i 19 Question 3: Express the given complex number in
More informationVector Algebra II: Scalar and Vector Products
Chapter 2 Vector Algebra II: Scalar and Vector Products We saw in the previous chapter how vector quantities may be added and subtracted. In this chapter we consider the products of vectors and define
More informationMeasuring the Earth s Diameter from a Sunset Photo
Measuring the Earth s Diameter from a Sunset Photo Robert J. Vanderbei Operations Research and Financial Engineering, Princeton University rvdb@princeton.edu ABSTRACT The Earth is not flat. We all know
More informationMobile Robot Localization using Range Sensors : Consecutive Scanning and Cooperative Scanning
International Mobile Journal Robot of Control, Localization Automation, using and Range Systems, Sensors vol. : Consecutive 3, no. 1, pp. Scanning 114, March and 2005 Cooperative Scanning 1 Mobile Robot
More information1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number
1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number A. 3(x  x) B. x 3 x C. 3x  x D. x  3x 2) Write the following as an algebraic expression
More informationThis document describes methods of assessing the potential for wedge sliding instability, using stereonet kinematic analysis.
Wedge Failure Kinematic analysis on a stereonet This document describes methods of assessing the potential for wedge sliding instability, using stereonet kinematic analysis. 1. The traditional approach
More informationPolarization of Light
Polarization of Light References Halliday/Resnick/Walker Fundamentals of Physics, Chapter 33, 7 th ed. Wiley 005 PASCO EX997A and EX999 guide sheets (written by Ann Hanks) weight Exercises and weights
More informationUsing Optech LMS to Calibrate Survey Data Without Ground Control Points
Challenge An Optech client conducted an airborne lidar survey over a sparsely developed river valley. The data processors were finding that the data acquired in this survey was particularly difficult to
More informationComputer Graphics: Visualisation Lecture 3. Taku Komura Institute for Perception, Action & Behaviour
Computer Graphics: Visualisation Lecture 3 Taku Komura tkomura@inf.ed.ac.uk Institute for Perception, Action & Behaviour Taku Komura Computer Graphics & VTK 1 Last lecture... Visualisation can be greatly
More informationA PHOTOGRAMMETRIC APPRAOCH FOR AUTOMATIC TRAFFIC ASSESSMENT USING CONVENTIONAL CCTV CAMERA
A PHOTOGRAMMETRIC APPRAOCH FOR AUTOMATIC TRAFFIC ASSESSMENT USING CONVENTIONAL CCTV CAMERA N. Zarrinpanjeh a, F. Dadrassjavan b, H. Fattahi c * a Islamic Azad University of Qazvin  nzarrin@qiau.ac.ir
More informationStage Metrology Concepts: Application Specific Testing. Hans Hansen Sr. Systems Design Engineer BSME, MSE 2/28/2008
Stage Metrology Concepts: Application Specific Testing Hans Hansen Sr. Systems Design Engineer BSME, MSE 2/28/2008 Topics Review of Stage Error Definitions Setting Stage Specifications for Applications
More informationCinema Projection Distortion
This paper was presented at: The 141st SMPTE Technical Conference and Exhibition Displays for the Theater and Home Session November 20, 1999 Cinema Projection Distortion Ronald A. Petrozzo Stuart W. Singer
More informationThe Vector or Cross Product
The Vector or ross Product 1 ppendix The Vector or ross Product We saw in ppendix that the dot product of two vectors is a scalar quantity that is a maximum when the two vectors are parallel and is zero
More informationAccurate Air Flow Measurement in Electronics Cooling
Accurate Air Flow Measurement in Electronics Cooling Joachim Preiss, Raouf Ismail Cambridge AccuSense, Inc. Email: info@degreec.com Air is the most commonly used medium to remove heat from electronics
More informationTeam Information.
Picture of vehicle: Name of vehicle: Kurt3D Picture of team leader: Name of team leader: Andreas NΓΌchter Team Name: Kurt3D Team Email: andreas.nuechter@informatik.uniosnabrueck.de Website: http://www.informatik.uniosnabrueck.de/nuechter
More informationBasic Electrical Theory
Basic Electrical Theory Mathematics Review PJM State & Member Training Dept. Objectives By the end of this presentation the Learner should be able to: Use the basics of trigonometry to calculate the different
More informationTWODIMENSIONAL TRANSFORMATION
CHAPTER 2 TWODIMENSIONAL TRANSFORMATION 2.1 Introduction As stated earlier, Computer Aided Design consists of three components, namely, Design (Geometric Modeling), Analysis (FEA, etc), and Visualization
More informationAnalysis of Stresses and Strains
Chapter 7 Analysis of Stresses and Strains 7.1 Introduction axial load = P / A torsional load in circular shaft = T / I p bending moment and shear force in beam = M y / I = V Q / I b in this chapter, we
More informationSOURCE LOCALIZATION WITH VECTOR SENSOR ARRAY DURING THE MAKAI EXPERIMENT
OURCE LOCALIZATION WITH VECTOR ENOR ARRAY DURING THE MAKAI EXPERIMENT Paulo antos a, Paulo Felisberto a, Paul Hursky b a Institute for ystems and Robotics, University of Algarve, Campus de Gambelas 8005139,
More informationRenishaw 2008. apply innovation TM. Calibrating 5axis machines to improve part accuracy. 5Align
Calibrating 5axis machines to improve part accuracy 5Align Productive Process Pyramid TM Understanding and tracking machine behaviour Process verification Thermal compensation Incycle process control
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 informationLINEAR EQUATIONS IN TWO VARIABLES
66 MATHEMATICS CHAPTER 4 LINEAR EQUATIONS IN TWO VARIABLES The principal use of the Analytic Art is to bring Mathematical Problems to Equations and to exhibit those Equations in the most simple terms that
More informationRange sensors. Sonar. Laser range finder. Time of Flight Camera. Structured light. 4a  Perception  Sensors. 4a 45
R. Siegwart & D. Scaramuzza, ETH Zurich  ASL 4a 45 Range sensors Sonar Laser range finder Time of Flight Camera Structured light Infrared sensors Noncontact bump sensor (1) sensing is based on light intensity.
More informationIMU Components An IMU is typically composed of the following components:
APN064 IMU Errors and Their Effects Rev A Introduction An Inertial Navigation System (INS) uses the output from an Inertial Measurement Unit (IMU), and combines the information on acceleration and rotation
More information11.1. Objectives. Component Form of a Vector. Component Form of a Vector. Component Form of a Vector. Vectors and the Geometry of Space
11 Vectors and the Geometry of Space 11.1 Vectors in the Plane Copyright Cengage Learning. All rights reserved. Copyright Cengage Learning. All rights reserved. 2 Objectives! Write the component form of
More informationCH205: Fluid Dynamics
CH05: Fluid Dynamics nd Year, B.Tech. & Integrated Dual Degree (Chemical Engineering) Solutions of Mid Semester Examination Data Given: Density of water, Ο = 1000 kg/m 3, gravitational acceleration, g
More informationRobot Sensors. Outline. The Robot Structure. Robots and Sensors. Henrik I Christensen
Robot Sensors Henrik I Christensen Robotics & Intelligent Machines @ GT Georgia Institute of Technology, Atlanta, GA 303320760 hic@cc.gatech.edu Henrik I Christensen (RIM@GT) Sensors 1 / 38 Outline 1
More informationApplication Report. Propeller Blade Inspection Station
34935 SE Douglas Street, Suite, Snoqualmie, WA 9874 Ph: 4253965577 Fax: 425396586 Application Report Propeller Blade Inspection Station Prepared By Kyle Johnston, Ph. D. Metron Systems Inc.5.5 3 2.5
More informationChapter 2 Lead Screws
Chapter 2 Lead Screws 2.1 Screw Threads The screw is the last machine to joint the ranks of the six fundamental simple machines. It has a history that stretches back to the ancient times. A very interesting
More informationIntroduction to Vectors
Introduction to Vectors A vector is a physical quantity that has both magnitude and direction. An example is a plane flying NE at 200 km/hr. This vector is written as 200 Km/hr at 45. Another example is
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 informationdiscuss how to describe points, lines and planes in 3 space.
Chapter 2 3 Space: lines and planes In this chapter we discuss how to describe points, lines and planes in 3 space. introduce the language of vectors. discuss various matters concerning the relative position
More informationSensor Data Consistency Monitoring for the Prevention of Perceptual Failures in Outdoor Robotics
Sensor Data Consistency Monitoring for the Prevention of Perceptual Failures in Outdoor Robotics Thierry Peynot, James Underwood and Abdallah Kassir Abstract This work aims to promote integrity in autonomous
More informationMEMs Inertial Measurement Unit Calibration
MEMs Inertial Measurement Unit Calibration 1. Introduction Inertial Measurement Units (IMUs) are everywhere these days; most particularly in smart phones and other mobile or handheld devices. These IMUs
More informationAutomotive Applications of 3D Laser Scanning Introduction
Automotive Applications of 3D Laser Scanning Kyle Johnston, Ph.D., Metron Systems, Inc. 34935 SE Douglas Street, Suite 110, Snoqualmie, WA 98065 4253965577, www.metronsys.com 2002 Metron Systems, Inc
More informationTHE BENEFITS OF REVERSE ENGINEERING FOR ENSURING PIPELINE INTΓGRITY
THE BENEFITS OF REVERSE ENGINEERING FOR ENSURING PIPELINE INTΓGRITY Author: JΓ©rΓ΄meAlexandre Lavoie, Product Manager ABSTRACT Today, now more than ever before, mounting public concern over pipeline safety
More informationFixplot Instruction Manual. (data plotting program)
Fixplot Instruction Manual (data plotting program) MANUAL VERSION2 2004 1 1. Introduction The Fixplot program is a component program of Eyenal that allows the user to plot eye position data collected with
More informationIMPORTANT NOTE ABOUT WEBASSIGN:
Week 8 homework IMPORTANT NOTE ABOUT WEBASSIGN: In the WebAssign versions of these problems, various details have been changed, so that the answers will come out differently. The method to find the solution
More informationIntroduction to SolidWorks Software
Introduction to SolidWorks Software Marine Advanced Technology Education Design Tools What is SolidWorks? SolidWorks is design automation software. In SolidWorks, you sketch ideas and experiment with different
More informationE190Q Lecture 5 Autonomous Robot Navigation
E190Q Lecture 5 Autonomous Robot Navigation Instructor: Chris Clark Semester: Spring 2014 1 Figures courtesy of Siegwart & Nourbakhsh Control Structures Planning Based Control Prior Knowledge Operator
More information2. Spin Chemistry and the Vector Model
2. Spin Chemistry and the Vector Model The story of magnetic resonance spectroscopy and intersystem crossing is essentially a choreography of the twisting motion which causes reorientation or rephasing
More information2D GEOMETRIC SHAPE AND COLOR RECOGNITION USING DIGITAL IMAGE PROCESSING
2D GEOMETRIC SHAPE AND COLOR RECOGNITION USING DIGITAL IMAGE PROCESSING Sanket Rege 1, Rajendra Memane 2, Mihir Phatak 3, Parag Agarwal 4 UG Student, Dept. of E&TC Engineering, PVG s COET, Pune, Maharashtra,
More informationVECTORAL IMAGING THE NEW DIRECTION IN AUTOMATED OPTICAL INSPECTION
VECTORAL IMAGING THE NEW DIRECTION IN AUTOMATED OPTICAL INSPECTION Mark J. Norris Vision Inspection Technology, LLC Haverhill, MA mnorris@vitechnology.com ABSTRACT Traditional methods of identifying and
More information0.1 Dielectric Slab Waveguide
0.1 Dielectric Slab Waveguide At high frequencies (especially optical frequencies) the loss associated with the induced current in the metal walls is too high. A transmission line filled with dielectric
More informationAutomated Staircase Detection, Alignment & Traversal
Automated Staircase Detection, Alignment & Traversal Mike Fair & David P. Miller School of Aerospace & Mechanical Engineering University of Oklahoma mwfair@yahoo.com, dpmiller@ou.edu Introduction: Lola
More informationAn introduction to 3D draughting & solid modelling using AutoCAD
An introduction to 3D draughting & solid modelling using AutoCAD Faculty of Technology University of Plymouth Drake Circus Plymouth PL4 8AA These notes are to be used in conjunction with the AutoCAD software
More informationNumber Sense and Operations
Number Sense and Operations representing as they: 6.N.1 6.N.2 6.N.3 6.N.4 6.N.5 6.N.6 6.N.7 6.N.8 6.N.9 6.N.10 6.N.11 6.N.12 6.N.13. 6.N.14 6.N.15 Demonstrate an understanding of positive integer exponents
More informationModule 6: Pinhole camera model Lecture 30: Intrinsic camera parameters, Perspective projection using homogeneous coordinates
The Lecture Contains: Pinhole camera model 6.1 Intrinsic camera parameters A. Perspective projection using homogeneous coordinates B. Principalpoint offset C. Imagesensor characteristics file:///d /...0(Ganesh%20Rana)/MY%20COURSE_Ganesh%20Rana/Prof.%20Sumana%20Gupta/FINAL%20DVSP/lecture%2030/30_1.htm[12/31/2015
More informationThe elements used in commercial codes can be classified in two basic categories:
CHAPTER 3 Truss Element 3.1 Introduction The single most important concept in understanding FEA, is the basic understanding of various finite elements that we employ in an analysis. Elements are used for
More informationELEMENTS OF VECTOR ALGEBRA
ELEMENTS OF VECTOR ALGEBRA A.1. VECTORS AND SCALAR QUANTITIES We have now proposed sets of basic dimensions and secondary dimensions to describe certain aspects of nature, but more than just dimensions
More information7.3 Volumes Calculus
7. VOLUMES Just like in the last section where we found the area of one arbitrary rectangular strip and used an integral to add up the areas of an infinite number of infinitely thin rectangles, we are
More informationPhysics 41, Winter 1998 Lab 1  The Current Balance. Theory
Physics 41, Winter 1998 Lab 1  The Current Balance Theory Consider a point at a perpendicular distance d from a long straight wire carrying a current I as shown in figure 1. If the wire is very long compared
More informationA System for Capturing High Resolution Images
A System for Capturing High Resolution Images G.Voyatzis, G.Angelopoulos, A.Bors and I.Pitas Department of Informatics University of Thessaloniki BOX 451, 54006 Thessaloniki GREECE email: pitas@zeus.csd.auth.gr
More informationAmpere's Law. Introduction. times the current enclosed in that loop: Ampere's Law states that the line integral of B and dl over a closed path is 0
1 Ampere's Law Purpose: To investigate Ampere's Law by measuring how magnetic field varies over a closed path; to examine how magnetic field depends upon current. Apparatus: Solenoid and path integral
More informationExample 1. Example 1 Plot the points whose polar coordinates are given by
Polar Coordinates A polar coordinate system, gives the coordinates of a point with reference to a point O and a half line or ray starting at the point O. We will look at polar coordinates for points
More informationStructured light systems
Structured light systems Tutorial 1: 9:00 to 12:00 Monday May 16 2011 Hiroshi Kawasaki & Ryusuke Sagawa Today Structured light systems Part I (Kawasaki@Kagoshima Univ.) Calibration of Structured light
More informationRelating Vanishing Points to Catadioptric Camera Calibration
Relating Vanishing Points to Catadioptric Camera Calibration Wenting Duan* a, Hui Zhang b, Nigel M. Allinson a a Laboratory of Vision Engineering, University of Lincoln, Brayford Pool, Lincoln, U.K. LN6
More informationSection 1.8 Coordinate Geometry
Section 1.8 Coordinate Geometry The Coordinate Plane Just as points on a line can be identified with real numbers to form the coordinate line, points in a plane can be identified with ordered pairs of
More informationCHAPTER 5 QC Test For Radiographic Equipment. Prepared by: Kamarul Amin bin Abdullah @ Abu Bakar School of Medical Imaging KLMUC
CHAPTER 5 QC Test For Radiographic Equipment Prepared by: Kamarul Amin bin Abdullah @ Abu Bakar School of Medical Imaging KLMUC Lesson Outcomes Describe the objectives of each QC test done.(importance)
More informationASSESSMENT OF VISUALIZATION SOFTWARE FOR SUPPORT OF CONSTRUCTION SITE INSPECTION TASKS USING DATA COLLECTED FROM REALITY CAPTURE TECHNOLOGIES
ASSESSMENT OF VISUALIZATION SOFTWARE FOR SUPPORT OF CONSTRUCTION SITE INSPECTION TASKS USING DATA COLLECTED FROM REALITY CAPTURE TECHNOLOGIES ABSTRACT Chris Gordon 1, Burcu Akinci 2, Frank Boukamp 3, and
More informationMATH 304 Linear Algebra Lecture 24: Scalar product.
MATH 304 Linear Algebra Lecture 24: Scalar product. Vectors: geometric approach B A B A A vector is represented by a directed segment. Directed segment is drawn as an arrow. Different arrows represent
More informationCASE HISTORY #2. APPLICATION: Piping Movement Survey using Permalign Laser Measurement System
CASE HISTORY #2 APPLICATION: Piping Movement Survey using Permalign Laser Measurement System EQUIPMENT: DresserClark Hot Gas Expander (Turbine), 60inch Inlet Flange HISTORY: Piping support modifications
More information6. Vectors. 1 20092016 Scott Surgent (surgent@asu.edu)
6. Vectors For purposes of applications in calculus and physics, a vector has both a direction and a magnitude (length), and is usually represented as an arrow. The start of the arrow is the vector s foot,
More information3D Vision An enabling Technology for Advanced Driver Assistance and Autonomous Offroad Driving
3D Vision An enabling Technology for Advanced Driver Assistance and Autonomous Offroad Driving AIT Austrian Institute of Technology Safety & Security Department Christian Zinner Safe and Autonomous Systems
More informationIndustrial Robotics. Training Objective
Training Objective After watching the program and reviewing this printed material, the viewer will learn the basics of industrial robot technology and how robots are used in a variety of manufacturing
More informationChapter 24 Physical Pendulum
Chapter 4 Physical Pendulum 4.1 Introduction... 1 4.1.1 Simple Pendulum: Torque Approach... 1 4. Physical Pendulum... 4.3 Worked Examples... 4 Example 4.1 Oscillating Rod... 4 Example 4.3 Torsional Oscillator...
More informationMECE 3400 Summer 2016 Homework #1 Forces and Moments as Vectors
ASSIGNED 1) Knowing that Ξ± = 40, determine the resultant of the three forces shown: 2) Two cables, AC and BC, are tied together at C and pulled by a force P, as shown. Knowing that P = 500 N, Ξ± = 60, and
More informationTwo vectors are equal if they have the same length and direction. They do not
Vectors define vectors Some physical quantities, such as temperature, length, and mass, can be specified by a single number called a scalar. Other physical quantities, such as force and velocity, must
More informationReinforced Concrete Design SHEAR IN BEAMS
CHAPTER Reinforced Concrete Design Fifth Edition SHEAR IN BEAMS A. J. Clark School of Engineering Department of Civil and Environmental Engineering Part I Concrete Design and Analysis 4a FALL 2002 By Dr.
More informationCALIBRATION OF A ROBUST 2 DOF PATH MONITORING TOOL FOR INDUSTRIAL ROBOTS AND MACHINE TOOLS BASED ON PARALLEL KINEMATICS
CALIBRATION OF A ROBUST 2 DOF PATH MONITORING TOOL FOR INDUSTRIAL ROBOTS AND MACHINE TOOLS BASED ON PARALLEL KINEMATICS E. Batzies 1, M. Kreutzer 1, D. Leucht 2, V. Welker 2, O. Zirn 1 1 Mechatronics Research
More informationHumanlike Arm Motion Generation for Humanoid Robots Using Motion Capture Database
Humanlike Arm Motion Generation for Humanoid Robots Using Motion Capture Database Seungsu Kim, ChangHwan Kim and Jong Hyeon Park School of Mechanical Engineering Hanyang University, Seoul, 133791, Korea.
More informationSession 7 Bivariate Data and Analysis
Session 7 Bivariate Data and Analysis Key Terms for This Session Previously Introduced mean standard deviation New in This Session association bivariate analysis contingency table covariation least squares
More informationExam 1 Sample Question SOLUTIONS. y = 2x
Exam Sample Question SOLUTIONS. Eliminate the parameter to find a Cartesian equation for the curve: x e t, y e t. SOLUTION: You might look at the coordinates and notice that If you don t see it, we can
More informationCS100B Fall 1999. Professor David I. Schwartz. Programming Assignment 5. Due: Thursday, November 18 1999
CS100B Fall 1999 Professor David I. Schwartz Programming Assignment 5 Due: Thursday, November 18 1999 1. Goals This assignment will help you develop skills in software development. You will: develop software
More informationThe Electronic Level Device of Many Uses
IQ901 IQ90319 The Electronic Level Device of Many Uses author GEORGE J. SCHUETZ Director of Precision Gages Mahr Federal Inc. Providence, Rhode Island abstract The electronic level is a very precise
More informationThe accurate calibration of all detectors is crucial for the subsequent data
Chapter 4 Calibration The accurate calibration of all detectors is crucial for the subsequent data analysis. The stability of the gain and offset for energy and time calibration of all detectors involved
More information2.1 COLOR AND GRAYSCALE LEVELS
2.1 COLOR AND GRAYSCALE LEVELS Various color and intensitylevel options can be made available to a user, depending on the capabilities and design objectives of a particular system. General purpose rasterscan
More informationDetermining Polar Axis Alignment Accuracy
Determining Polar Axis Alignment Accuracy by Frank Barrett 7/6/008 Abstract: In order to photograph dim celestial objects, long exposures on the order of minutes or hours are required. To perform this
More informationMetropoGIS: A City Modeling System DI Dr. Konrad KARNER, DI Andreas KLAUS, DI Joachim BAUER, DI Christopher ZACH
MetropoGIS: A City Modeling System DI Dr. Konrad KARNER, DI Andreas KLAUS, DI Joachim BAUER, DI Christopher ZACH VRVis Research Center for Virtual Reality and Visualization, Virtual Habitat, Inffeldgasse
More informationPhysics 210 Q ( PHYSICS210BRIDGE ) My Courses Course Settings
1 of 16 9/7/2012 1:10 PM Logged in as Julie Alexander, Instructor Help Log Out Physics 210 Q1 2012 ( PHYSICS210BRIDGE ) My Courses Course Settings Course Home Assignments Roster Gradebook Item Library
More information