Basic Robotics Fundamentals presentation.pptx
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Special Square Matrices
1) A symmetric matrix is a matrix whose transpose is equal to itself. A skew-symmetric matrix is a matrix whose transpose is equal to its negative.
2) An orthogonal matrix is a matrix whose transpose is equal to its inverse. The rows of an orthogonal matrix are orthogonal unit vectors.
3) A normal matrix is a matrix that commutes with its transpose, meaning the matrix multiplied by its transpose is equal to the transpose multiplied by the matrix. Symmetric, skew-symmetric, and orthogonal matrices are all examples of normal matrices.
Cinemática en coordenadas normales y tangenciales
This document discusses kinematics in normal and tangential coordinates for curvilinear motion. It describes how to calculate the tangential and normal components of velocity and acceleration for a particle moving along a curved trajectory. The tangential component represents changes in speed, while the normal component represents changes in direction. Equations are provided to calculate acceleration along the tangent (at) and normal (an) directions in terms of velocity, radius of curvature, and derivatives. Examples are given for constant acceleration and trajectories defined as functions of position.
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2. Reflection is defined as a flip across a line or point. Reflections across the x-axis, y-axis, and lines like y=x and y=-x are described.
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Lecture Ch 08
This document discusses rotational motion and provides definitions and equations for key angular quantities such as angular displacement (θ), angular velocity (ω), angular acceleration (α), torque (τ), moment of inertia (I), angular momentum (L), and rotational kinetic energy. It defines these quantities, gives their relationships to linear motion quantities, and provides examples of how to set up and solve problems involving rotational dynamics.
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1) A symmetric matrix is a matrix whose transpose is equal to itself. A skew-symmetric matrix is a matrix whose transpose is equal to its negative.
2) An orthogonal matrix is a matrix whose transpose is equal to its inverse. The rows of an orthogonal matrix are orthogonal unit vectors.
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This document discusses kinematics in normal and tangential coordinates for curvilinear motion. It describes how to calculate the tangential and normal components of velocity and acceleration for a particle moving along a curved trajectory. The tangential component represents changes in speed, while the normal component represents changes in direction. Equations are provided to calculate acceleration along the tangent (at) and normal (an) directions in terms of velocity, radius of curvature, and derivatives. Examples are given for constant acceleration and trajectories defined as functions of position.
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1. The document defines rotation and reflection transformations in 2D and 3D spaces. It discusses rotation matrices for rotating vectors by certain angles like 90°, 180°, and 270° degrees.
2. Reflection is defined as a flip across a line or point. Reflections across the x-axis, y-axis, and lines like y=x and y=-x are described.
3. The adjugate of a matrix is defined as the transpose of its cofactor matrix. Some theorems about the adjugate and inverse of matrices are stated.
Lecture Ch 08
This document discusses rotational motion and provides definitions and equations for key angular quantities such as angular displacement (θ), angular velocity (ω), angular acceleration (α), torque (τ), moment of inertia (I), angular momentum (L), and rotational kinetic energy. It defines these quantities, gives their relationships to linear motion quantities, and provides examples of how to set up and solve problems involving rotational dynamics.
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The document discusses different types of matrices including identity matrices, inverse matrices, transpose matrices, symmetric matrices, orthogonal matrices, upper triangular matrices, lower triangular matrices, and diagonal matrices. It provides examples and properties of each matrix type. Key points covered include that identity matrices satisfy AI = IA = A, inverse matrices satisfy AB = BA = I, the transpose of a matrix is formed by interchanging rows and columns, and orthogonal matrices satisfy AAT = ATA = I.
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Appendex a
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➢The study is very important for the design of gears, cams and
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THE PLANE MOVEMENT. It is when all the particles of a
rigid bodies move along trajectories that are
equidistant from a fixed plane, the body is said to experience
fixed plane motion
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This document discusses forward and inverse kinematics, including:
1. Forward kinematics determines the position of the robot hand given joint variables, while inverse kinematics calculates joint variables for a desired hand position.
2. Homogeneous transformation matrices are used to represent frames, points, vectors and transformations in space.
3. Standard robot coordinate systems include Cartesian, cylindrical, and spherical coordinates. Forward and inverse kinematics equations are provided for position analysis in each system.
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2) It describes how to analyze relative motion problems by attaching a translating reference frame to a moving object and determining the motion relative to that frame, as well as how to determine absolute motion from relative motion.
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Semelhante a Basic Robotics Fundamentals presentation.pptx
Appendex a
This document provides an overview of trigonometric functions and identities. It defines angles and their measurement in degrees and radians. It discusses trigonometric functions for right triangles, extending the definitions to angles in rectangular coordinate systems. Examples are provided to illustrate evaluating trigonometric functions of various angles. Key relationships between arc length, angle, radius, and area are also summarized.
SinogramReconstruction
This document provides notation and details on a sinogram interpolation technique. It begins by defining notation for continuous and discrete indices used to represent images and sinograms. It then describes how sinograms are formed from images through the forward Radon transform, representing projections of an image at different angles. Warps are introduced as weighted cosine waves that pass through sinogram elements, with conditions defined for valid warps. The algorithm steps are outlined as calculating warp properties from the original image, setting up an equation system to solve for warp weights, and reconstructing sinogram columns from the warps. The technique aims to improve blurry sinograms by exploiting known image properties represented by the warps.
Positive matrix by sarmad baloch
This document contains information about positive definite matrices and eigenvectors/eigenvalues. It provides an example of a positive definite matrix with all positive eigenvalues. It also gives an example of showing that the transpose of a matrix A multiplied by itself (ATA) is positive definite if A is invertible. Finally, it provides an example of finding the eigenvectors and eigenvalues of a 2x2 matrix. The eigenvectors are solutions to Av=λv, where λ is the eigenvalue.
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Atoms in materials are arranged into crystal structures and microstructures.
Periodic arrangement of atoms depends strongly on external factors such as temperature, pressure, and cooling rate during solidification. Solid elements and their compounds are classified into amorphous, polycrystalline, and single crystalline materials. The amorphous solid materials are isotropic in nature because their atomic arrangements are not regular and possess the same properties in all directions. In contrast, the crystalline materials are anisotropic because their atoms are arranged in regular and repeated pattern, and their properties vary with direction. The polycrystalline materials are combinations of several crystals of varying shapes and sizes. The properties of polycrystalline materials are strongly dependent on distribution of crystals sizes, shapes, and orientations within the individual crystal. Diffraction pattern or intensities of X-ray diffraction techniques are used for characterizing and probing arrangement of atoms in each unit cell, position of atoms, and atomic spacing angles because of comparative wavelength of X-ray to atomic size.The X-ray diffraction, which is a non-destructive technique, has wide range of material analysis including minerals, metals, polymers, ceramics, plastics, semiconductors, and solar cells. The technique also has wide industry application including aerospace, power generation, microelectronics, and several others. The X-ray crystallography remained a complex field of study despite wide industrial applications.
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This document discusses properties of symmetric, skew-symmetric, and orthogonal matrices. It defines each type of matrix and provides examples. Key points include:
- Symmetric matrices have Aij = Aji for all i and j. Skew-symmetric matrices have Aij = -Aji. Orthogonal matrices satisfy AT = A-1.
- The eigenvalues of symmetric matrices are always real. The eigenvalues of skew-symmetric matrices are either zero or purely imaginary.
- Any real square matrix can be written as the sum of a symmetric matrix and skew-symmetric matrix.
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1. Lissajous figures describe the patterns that result from combining two harmonic oscillations with different frequencies or phases.
2. The shapes of the Lissajous figures depend on the frequency ratio and phase difference between the two oscillations. Common shapes include straight lines, ellipses, circles, and figure-8 patterns.
3. Lissajous figures can be used to determine the frequency ratio between two oscillations by counting the number of times the pattern crosses the x- and y- axes in a given time period. This provides a way to measure unknown frequencies.
FinalReport
1) The document presents the implementation of a Generalized Multiplicative Extended Kalman Filter (GMEKF) for state estimation of a quadcopter using real sensor data. The GMEKF uses quaternion representations and accounts for nonlinearities and sensor noise.
2) Testing the GMEKF on recorded quadcopter flight data showed the filter did not converge, likely due to inconsistencies in the initial sensor and system noise matrices used. Further work is needed to properly implement the GMEKF equations and account for quaternion geometry.
3) Proper implementation of invariant extended Kalman filters like the GMEKF has been shown to provide good state estimation for various quadcopter trajectories by exploiting symmetries in the system dynamics.
1 diagrams
This document discusses velocity and acceleration diagrams for mechanisms. It introduces concepts like absolute and relative velocity, tangential and radial velocity, and tangential and radial acceleration. It then provides a worked example of determining the maximum acceleration of a piston in a crank mechanism moving at 30 revolutions per minute. Plots of displacement, velocity, and acceleration versus angle are presented, showing that the maximum acceleration occurs when the angle is 0 degrees.
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This document discusses nonlinear control systems using phase plane and phase trajectory methods. It defines nonlinear systems and common physical nonlinearities like saturation, dead zone, relay, and backlash. Phase plane analysis is introduced as a graphical method to study nonlinear systems using a plane with state variables x and dx/dt as coordinates. Key concepts are defined like phase plane, phase trajectory, and phase portrait. Methods for sketching phase trajectories include analytical solutions and graphical methods like isoclines. Examples are given to illustrate phase portraits for different linear systems.
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This document discusses nonlinear control systems using phase plane and phase trajectory methods. It defines nonlinear systems and common physical nonlinearities like saturation, dead zone, relay, and backlash. Phase plane analysis is introduced as a graphical method to study nonlinear systems using a plane with state variables x and dx/dt. Key concepts are defined like phase plane, phase trajectory, and phase portrait. Methods for sketching phase trajectories include analytical solutions and graphical methods using isoclines. Examples are given to illustrate phase portraits for different linear systems.
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The document discusses spatial transformations of twists and wrenches between coordinate frames. It defines transformations for velocities, forces, moments and inertias using skew-symmetric cross product matrices. Euler angles using fixed axes and moving axes are described to represent orientations as rotations about X, Y, Z axes. Joint coordinate systems and anatomical landmarks are defined for the shank. Momentum is defined as linear and angular components and momentum wrenches transform in the same way as force wrenches between frames.
Module 1 Theory of Matrices.pdf
The document provides an overview of matrix theory, including:
1. The definition and notation of matrices, including that a matrix A is represented as Am×n, where m is the number of rows and n is the number of columns.
2. The different types of matrices and operations that can be performed on matrices, such as scalar multiplication, matrix multiplication, and properties like the distributive law.
3. Methods for solving systems of linear equations using matrices, including writing the system in matrix form, reducing the augmented matrix to echelon form, and determining the solution based on the rank.
Gear .pdf
You're right, in the figure shown the addendum circles of the gears are interfering with each other, which is not desirable. Here are a few ways to avoid this interference:
1. Increase the center distance between the gears. This will move the gears further apart and create clearance between the addendum circles.
2. Use gears with a smaller addendum. Reducing the size of the addendum will reduce how far it extends out from the base circle.
3. Apply an offset to one or both gears. By offsetting the gears axially, you can shift one gear up/down relative to the other to create clearance.
4. Use bevel gears or hypoid gears instead of straight spur gears
Linear Algebra Gauss Jordan elimination.pptx
Information related to Gauss-Jordan elimination.
Visit mathsassignmenthelp.com or email info@mathsassignmenthelp.com.
You can also call on +1 678 648 4277 for any assistance with linear algebra assignment.
Mat 223_Ch5-Eigenvalues.ppt
The document provides information about eigenvalues and eigenvectors. It begins by defining eigenvalues and eigenvectors, and how they relate to a matrix A. It then describes how to compute the eigenvalues and eigenvectors of a matrix by finding the characteristic polynomial and solving the characteristic equation. Two examples are provided to illustrate this process. The document also discusses eigenspaces and proves that the set of eigenvectors for a given eigenvalue forms a subspace. It introduces the concept of diagonalization of matrices using similarity transformations.
Tema 1 cinemática de un cuerpo rígido
In this unit we will analyze the plane kinematics of a rigid body
➢The study is very important for the design of gears, cams and
mechanisms, often in mechanical operations,
THE PLANE MOVEMENT. It is when all the particles of a
rigid bodies move along trajectories that are
equidistant from a fixed plane, the body is said to experience
fixed plane motion
Robot kinematics
This document discusses forward and inverse kinematics, including:
1. Forward kinematics determines the position of the robot hand given joint variables, while inverse kinematics calculates joint variables for a desired hand position.
2. Homogeneous transformation matrices are used to represent frames, points, vectors and transformations in space.
3. Standard robot coordinate systems include Cartesian, cylindrical, and spherical coordinates. Forward and inverse kinematics equations are provided for position analysis in each system.
Null space, Rank and nullity theorem
This document provides an overview of row space, column space, and null space of matrices. It defines these concepts and gives examples of finding bases for the row space, column space, and null space. It also introduces the rank-nullity theorem and defines the rank and nullity of a matrix. Examples are provided to demonstrate calculating the rank and nullity. The document appears to be teaching notes for a linear algebra course.
Me101 lecture25-sd
The document discusses kinematics concepts related to curvilinear motion and relative motion analysis. It contains the following key points in 3 sentences:
1) It provides an example problem involving determining the velocity and acceleration of a ball moving in a helical path due to the rotational motion of a power screw.
2) It describes how to analyze relative motion problems by attaching a translating reference frame to a moving object and determining the motion relative to that frame, as well as how to determine absolute motion from relative motion.
3) It discusses concepts like inertial reference frames, constrained motion problems involving connected particles with one or two degrees of freedom, and how to set up and solve examples involving these kinematics topics.
MC0082 –Theory of Computer Science
The document defines equivalence relation and provides two examples. It then proves some properties about equivalence relations on real numbers. It proves mathematical induction for a formula relating sums and cubes. It proves properties about spanning trees and connectivity in graphs. It also proves that congruence modulo m is an equivalence relation by showing it satisfies the properties of reflexivity, symmetry, and transitivity. Finally, it explains the concepts of transition graphs and transition tables for representing finite state automata.
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NONLINEAR CONTROL SYSTEM(Phase plane & Phase Trajectory Method).pdf
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Mobile Security Framework - MobSF is a free and open source automated mobile application security testing environment designed to help security engineers, researchers, developers, and penetration testers to identify security vulnerabilities, malicious behaviours and privacy concerns in mobile applications using static and dynamic analysis. It supports all the popular mobile application binaries and source code formats built for Android and iOS devices. In addition to automated security assessment, it also offers an interactive testing environment to build and execute scenario based test/fuzz cases against the application.
This talk covers:
Using MobSF for static analysis of mobile applications.
Interactive dynamic security assessment of Android and iOS applications.
Solving Mobile app CTF challenges.
Reverse engineering and runtime analysis of Mobile malware.
How to shift left and integrate MobSF/mobsfscan SAST and DAST in your build pipeline.
The Microsoft 365 Migration Tutorial For Beginner.pptx
This presentation will help you understand the power of Microsoft 365. However, we have mentioned every productivity app included in Office 365. Additionally, we have suggested the migration situation related to Office 365 and how we can help you.
You can also read: https://www.systoolsgroup.com/updates/office-365-tenant-to-tenant-migration-step-by-step-complete-guide/
Monitoring and Managing Anomaly Detection on OpenShift.pdf
Monitoring and Managing Anomaly Detection on OpenShift
Overview
Dive into the world of anomaly detection on edge devices with our comprehensive hands-on tutorial. This SlideShare presentation will guide you through the entire process, from data collection and model training to edge deployment and real-time monitoring. Perfect for those looking to implement robust anomaly detection systems on resource-constrained IoT/edge devices.
Key Topics Covered
1. Introduction to Anomaly Detection
- Understand the fundamentals of anomaly detection and its importance in identifying unusual behavior or failures in systems.
2. Understanding Edge (IoT)
- Learn about edge computing and IoT, and how they enable real-time data processing and decision-making at the source.
3. What is ArgoCD?
- Discover ArgoCD, a declarative, GitOps continuous delivery tool for Kubernetes, and its role in deploying applications on edge devices.
4. Deployment Using ArgoCD for Edge Devices
- Step-by-step guide on deploying anomaly detection models on edge devices using ArgoCD.
5. Introduction to Apache Kafka and S3
- Explore Apache Kafka for real-time data streaming and Amazon S3 for scalable storage solutions.
6. Viewing Kafka Messages in the Data Lake
- Learn how to view and analyze Kafka messages stored in a data lake for better insights.
7. What is Prometheus?
- Get to know Prometheus, an open-source monitoring and alerting toolkit, and its application in monitoring edge devices.
8. Monitoring Application Metrics with Prometheus
- Detailed instructions on setting up Prometheus to monitor the performance and health of your anomaly detection system.
9. What is Camel K?
- Introduction to Camel K, a lightweight integration framework built on Apache Camel, designed for Kubernetes.
10. Configuring Camel K Integrations for Data Pipelines
- Learn how to configure Camel K for seamless data pipeline integrations in your anomaly detection workflow.
11. What is a Jupyter Notebook?
- Overview of Jupyter Notebooks, an open-source web application for creating and sharing documents with live code, equations, visualizations, and narrative text.
12. Jupyter Notebooks with Code Examples
- Hands-on examples and code snippets in Jupyter Notebooks to help you implement and test anomaly detection models.
Biomedical Knowledge Graphs for Data Scientists and Bioinformaticians
Dmitrii Kamaev, PhD
Senior Product Owner - QIAGEN
Generating privacy-protected synthetic data using Secludy and Milvus
During this demo, the founders of Secludy will demonstrate how their system utilizes Milvus to store and manipulate embeddings for generating privacy-protected synthetic data. Their approach not only maintains the confidentiality of the original data but also enhances the utility and scalability of LLMs under privacy constraints. Attendees, including machine learning engineers, data scientists, and data managers, will witness first-hand how Secludy's integration with Milvus empowers organizations to harness the power of LLMs securely and efficiently.
Astute Business Solutions | Oracle Cloud Partner |
Your goto partner for Oracle Cloud, PeopleSoft, E-Business Suite, and Ellucian Banner. We are a firm specialized in managed services and consulting.
Principle of conventional tomography-Bibash Shahi ppt..pptx
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Taking AI to the Next Level in Manufacturing.pdf
Read Taking AI to the Next Level in Manufacturing to gain insights on AI adoption in the manufacturing industry, such as:
1. How quickly AI is being implemented in manufacturing.
2. Which barriers stand in the way of AI adoption.
3. How data quality and governance form the backbone of AI.
4. Organizational processes and structures that may inhibit effective AI adoption.
6. Ideas and approaches to help build your organization's AI strategy.
zkStudyClub - LatticeFold: A Lattice-based Folding Scheme and its Application...
Folding is a recent technique for building efficient recursive SNARKs. Several elegant folding protocols have been proposed, such as Nova, Supernova, Hypernova, Protostar, and others. However, all of them rely on an additively homomorphic commitment scheme based on discrete log, and are therefore not post-quantum secure. In this work we present LatticeFold, the first lattice-based folding protocol based on the Module SIS problem. This folding protocol naturally leads to an efficient recursive lattice-based SNARK and an efficient PCD scheme. LatticeFold supports folding low-degree relations, such as R1CS, as well as high-degree relations, such as CCS. The key challenge is to construct a secure folding protocol that works with the Ajtai commitment scheme. The difficulty, is ensuring that extracted witnesses are low norm through many rounds of folding. We present a novel technique using the sumcheck protocol to ensure that extracted witnesses are always low norm no matter how many rounds of folding are used. Our evaluation of the final proof system suggests that it is as performant as Hypernova, while providing post-quantum security.
Paper Link: https://eprint.iacr.org/2024/257
Digital Banking in the Cloud: How Citizens Bank Unlocked Their Mainframe
Inconsistent user experience and siloed data, high costs, and changing customer expectations – Citizens Bank was experiencing these challenges while it was attempting to deliver a superior digital banking experience for its clients. Its core banking applications run on the mainframe and Citizens was using legacy utilities to get the critical mainframe data to feed customer-facing channels, like call centers, web, and mobile. Ultimately, this led to higher operating costs (MIPS), delayed response times, and longer time to market.
Ever-changing customer expectations demand more modern digital experiences, and the bank needed to find a solution that could provide real-time data to its customer channels with low latency and operating costs. Join this session to learn how Citizens is leveraging Precisely to replicate mainframe data to its customer channels and deliver on their “modern digital bank” experiences.
June Patch Tuesday
Ivanti’s Patch Tuesday breakdown goes beyond patching your applications and brings you the intelligence and guidance needed to prioritize where to focus your attention first. Catch early analysis on our Ivanti blog, then join industry expert Chris Goettl for the Patch Tuesday Webinar Event. There we’ll do a deep dive into each of the bulletins and give guidance on the risks associated with the newly-identified vulnerabilities.
[OReilly Superstream] Occupy the Space: A grassroots guide to engineering (an...
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- 6. Skew Symmetric Matrices Complex Case: When axis of rotation are not fixed Angular velocity is the result of multiple rotations about distinct axis. For general representation of angular velocities Skew symmetric Matrices were
- 8. Definition Skew matrix is a square matrix A whose transpose is also its negative; that is, it satisfies the condition -A = AT. If the entry in the ith row and jth column is aij,i.e. A = (aij) then the skew symmetric condition is aij = −aji. For example, the following matrix is skew- symmetric:
- 10. Properties
- 12. Derivative of rotation matrix Differentiating both sides 1
- 13. Which shows that S is a skew symmetric Now as Multiplying both sides of equation-01 by R we get
- 16. Angular Velocity and Acceleration Kinematics Suppose that rotation Matrix R is time varying i.e.R=R(t) Time derivative of R is(as proved above)
- 18. Thanks