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									Intelligent Robotics Lecture

Tomáš Pajdla 2008
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Advanced Robotics

Lecture 1

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ROBOT R.U.R. (Rossum's Universal Robots) by Karel Čapek. Rossum's robots are biological creations that have skin mixed in a vat, and their nerves and digestive tracts spun on spindles, and are then assembled like automobiles. They resemble more modern conceptions of manmade life forms such as the Replicants in Blade Runner.

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ROBOT

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GENERAL

MANIPULATOR

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We shall learn how to solve dvanced kinematic problems for manipulators with 6-degrees-of-freedom.

The general solution to this problem exists. 1. Kinematic calibration 2. Motion planning 3. Eye-hand systems

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Industrial Robotic Applications

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Precision for industry Low (e.g. manipulation) ± 5 mm in the whole working space ± 0.5 mm locally … often available

High (e.g. laser welding) ± 0.5 mm in the whole working space ± 0.05 mm locally … often not available

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Modeling kinematics – calibration – absolute acuracy ± 0.05 mm

Robot-Vision calibration (courtesy Neovision s.r.o.)
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Precision for robotic surgery

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http://www.cts.usc.edu/rsi-article-robotputsuscatforefront.html

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Two kinds of manipulators

1. Serial manipulators 2. Parallel manipulators

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Serial manipulators

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KUKA manipulator

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Serial manipulators

Stäubli (courtesy Neovision s.r.o.)

Mitsubishi (courtesy Neovision s.r.o.)

1. Direct kinematic task – easy 2. Inverse kinematic task – difficult
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Parallel manipulators

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Stewart-Gough Platform

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Parallel manipulators

Sliding Star (courtesy of Prof. Valášek, CTU Prague)

1. Direct kinematic task – difficult 2. Inverse kinematic task – easy
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Kinematics in robotics

Three main problems

1. Direct kinematic task (přímá kinematická úloha) 2. Inverse kinematic task (inverzní kinematická úloha) 3. Kinematic calibration (kalibrace kinematiky)

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Direct kinematic task

flange frame

z

x

world frame

y

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Inverse kinematic task

flange frame

z

x

world frame

y

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Kinematic calibration

z

x

world frame

y

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Kinematic Calibration

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Robot Calibration

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Kinematic Calibration

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Solving kinematic tasks

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Solving kinematic tasks 1968 Donald L. Pieper (Ph.D. thesis) The inverse kinematics of any serial manipulator with six revolute joints, and with three consecutive joints intersecting, can be solved in closedform, i.e., analytically.

1989 M. Raghavan, B. Roth. Kinematic Analysis of the 6R Manipulator of General Geometry. Int. Symp. Robotics. Research. Pp. 314-320, Tokyo 1989/1990. A general technique for computing inverse kinematics for any serial manipulator with six revolute joints. … leads to solving an algebraic equation of degree 16.
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Solving kinematic tasks Algebraic equation of degree 16 … up to 16 solutions

4 typical solutions

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Solving kinematic tasks

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Stäubli TX-90 – Geometry

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Kinematic model

flange frame z x z y

x

world frame

y

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The Standard Kinematic model in Denavit-Hartenberg Convention Stäubli TX 90

TX-90 (6 axis, RRRRRR) [Staubli] α -1.5708 0.0 -1.5708 1.5708 -1.5708 0.0 a 50.0 425.0 0.0 0.0 0.0 0.0 θ 0.0 0.0 0.0 0.0 0.0 0.0 d 350.0 50.0 0.0 425.0 0.0 100.0

6 non-trivial parameteres

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The Standard Kinematic model in Denavit-Hartenberg Convention ABB IBR 140

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The Standard Kinematic model in Denavit-Hartenberg Convention ABB IBR 140

IBR-140 (6 axis) [ABB] α -1.5708 0.0 -1.5708 1.5708 -1.5708 0.0 a 70.0 360.0 0.0 0.0 0.0 0.0 θ 0.0 0.0 0.0 0.0 0.0 0.0 d 352.0 0.0 0.0 380.0 0.0 65.0

5 non-trivial parameteres

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The Standard Kinematic model in Denavit-Hartenberg Convention Stäubli TX 90

RV-6S (6 axis, RRRRRR) [Mitsubishi] α -1.5708 0.0 -1.5708 1.5708 -1.5708 0.0 a 85.0 280.0 100.0 0.0 0.0 0.0 θ 0.0 0.0 0.0 0.0 0.0 0.0 d 350.0 0.0 0.0 315.0 0.0 85.0

6 non-trivial parameteres

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Special versus General Mechanisms Special simple & tractable
α -1.5708 0.0 -1.5708 1.5708 -1.5708 0.0 a 70.0 360.0 0.0 0.0 0.0 0.0 θ d 352.0 0.0 0.0 380.0 0.0 65.0 α -1.42 0.10 -1.57 1.58 -1.59 0.07

×

General complicated & hard
a 70.1 360.0 0.2 0.1 0.4 0.2 θ - (+0.2) - (+0.1) - (- 0.3) - (+0.1) - (- 0.1) - (- 0.2) d 352.0 0.2 0.3 380.2 0.1 65.1

6 non-trivial parameters

×

18 (+6) non-trivial parameters

High precision → Small misalignments important → General mechanisms
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SOLVING 1 ALGEBRAIC EQUATION 1 equation, 1 variable → companion matrix → eigenvalues

... a simple rule

It works when eig works, i.e. order 100 in Matlab is often OK.
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