Robot Study/Introduction to Robotics

Information

Purpose: Learning basic knowledge of robotics Lecture: CS223A, Stanford University Date: Jan 21, 2019 ~

• Prerequite
• Linear Algebra
• Numerical Analysis

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)

1. 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

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