[[TableOfContents]] == Information == Purpose: Learning basic knowledge of robotics Lecture: CS223A, Stanford University Date: Jan 21, 2019 ~ * Prerequite - Linear Algebra - Numerical Analysis (or graphics programming experience) == Reference == Material: Copy from Stanford Video clips: https://www.youtube.com/watch?v=0yD3uBshJB0&list=PL65CC0384A1798ADF == Study List == === Lecture 1: Spatial Description === General Manipulator: Robot Arm, using Revolute joint, Prismatic joint - Robot Arm: base, link, joint, end-effector - Revolute joint: Rotation movement, 1 Degree of Fredom(DoF) - Prismatic joint: Linear movement, 1 DoF - Denote joint type using ε(0 for revolute, 1for prismatic) Discription of body1 (9 parameters) - Link location: 3 points (Each point has 3 parameters) Discription of body2 (6 parameters) - Body orientation: 3 parameter - Point on the body: 3 parameter => Robot arm(n:links, 1: base) has n DoF Transformation - Pure Rotation - Pure Translation - General Tasformation - Inverse Transformation Configuration Representation There is no universial agreement in the field of robotics as to what is the best orientation representation. Because each representation hase advantages and shortcomings - Direction Cosines: - Euler angle representation: ZYX, angle(α, β, γ) - Fixed angle representation: XYZ, angle(γ, β, α) - Inverse of an orientation representation === Lecture 2: Direct Kinematics === Previous - Independent of the structure of the manipulator Introduction - A set of parameters specific to each manipulator - ex) rotation, translation, link of manipulator - Forware Kinematics - Inverse Kinematics Link Description - Manipulator: Consist of a chain of links from base - Consecutive links are connected by joints which exert the degree of freedom. D-H Parameter - link length(a): length along the common normal from axis (i-1) to axis i - link twist(α): angle between this parallel line and axis (i-1) - link offset(θ): distance alont the line on axis i between the common normal for link (i-1) and common normal for link i - joint angle(d): angle between the two common normal for link (i-1) and common normal for link i - Revolute joint: joint angle(variable), link offset(constant) - Prismatic joint: joint angle(constant), link offset(variable) - a, α: describe link - d, θ: describe the link's connection Conventions for First and Last Link - Once robot structure is set link length & link twist is determined. - a(i) and α(i) depend on joint axes i and i+1 Axes 1 to n: determined => a(1), a(2), ,,,, a(n-1) and α(1), α(2), ,,,,a(n-1) - d(i) and θ(i) depend on Attaching Frames to links - ex1) RRR (Revolute-Revolute-Revolute) Manipulator - ex2) RPRR (Revolute-Prismatic-Revolute-Revolute) Manipulator Propagation of Frames - Show how to calculate matrix about D-H parameter - Reference http://www.adrian.zentner.name/content/projects/xml/x3d/robot/res/Denavit-Hartenberg.gif Kinematics of Manipulators - Example of robot arm (Stanford Scheinman Arm) - Reference http://infolab.stanford.edu/pub/voy/museum/pictures/display/robots/StanfordArm.jpg Direct(forward) Kinematics - Mapping between the joint space of dimension n and the task space of manipulator of dimension m - Called the "Geometric Model of the manipulator" (It is determinded solely by knowing the geometry of manipulator) - q(i) = ε'(i)θ(i) + ε(i)d(i) - X = f(q) === Lecture 3: Inverse Kinematics === Introduction - Difficult task: Multiplicity or non-existence of potential soultions - Problem: find q given T(B,W) or x / find q = f^(-1)(x) Closed Form Solutions Algebraic: solution is found using the fact that θ1+θ2+θ3 = a0 Geometric: there are two possible solutions Piper's Solution ??? Existence of Solution - If these two equations are correct, solution of the inverse kinematics exists - However, sometimes there is no solution because of limitation of robot model Workplace of the Manipulator - Workspace: the set of points that can be reached with the mainpulator - Joint limitation is always defined by the mechanical design of the manipulator * Related question: # of possible solutions - Reachable Workspace: the set of points that can be reached in at least one conficuration of the manipulator - Dextrous workspace: the set of points that can be reached by any possible orientation of the end-effector, important in the motion planning with obstacles (Reachable Workspace > Dextrous workspace) # of Solutions 6R manipulator: 16 solutions 5RP manipulator: 16 solutions 4R2P manipulator: 8 solutions 3R3P manipulator: 2 solutions in-parallel structures: 40 solutions - Puma Robot Reference https://d2t1xqejof9utc.cloudfront.net/screenshots/pics/45f6b6d1d881d687d15e29d47f181a6f/large.PNG - Stanford Scheinman Arm Reference http://infolab.stanford.edu/pub/voy/museum/pictures/display/robots/IMG_2404ArmFrontPeekingOut.JPG === Lecture 4: The Jacobian === Previous - Establish the mathematical models which describe the relationships between the static configurations of a mechanism and its end-effector Introduction - Establish the relationship between δx and δq - The relationship between δx and δq is described by the Jacobian matirx - This matrix is key to the relationship between joint torques and end-effector forces Differential Motion - X = f(q) Reference https://ipfs.io/ipfs/QmXoypizjW3WknFiJnKLwHCnL72vedxjQkDDP1mXWo6uco/I/m/74e93aa903c2695e45770030453eb77224104ee4.svg == Comments == 선배님 너무 멋있어여 - [조예진] * 새싹 준비입니다 - [우준혁] == Closed == == Back page == * [우준혁]