IRO

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IRO

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Shared by: Junaid Khan
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5/25/2009
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Intelligent Robotics Lecture Tomáš Pajdla 2008 1 Advanced Robotics Lecture 1 2 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. 3 4 ROBOT = A GENERAL MANIPULATOR 5 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 6 Industrial Robotic Applications 7 8 9 10 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 11 Modeling kinematics – calibration – absolute acuracy ± 0.05 mm Robot-Vision calibration (courtesy Neovision s.r.o.) 13 14 Precision for robotic surgery 15 http://www.cts.usc.edu/rsi-article-robotputsuscatforefront.html 16 17 Two kinds of manipulators 1. Serial manipulators 2. Parallel manipulators 18 Serial manipulators J KUKA manipulator 19 Serial manipulators Stäubli (courtesy Neovision s.r.o.) Mitsubishi (courtesy Neovision s.r.o.) 1. Direct kinematic task – easy 2. Inverse kinematic task – difficult 20 Parallel manipulators J Stewart-Gough Platform 21 Parallel manipulators Sliding Star (courtesy of Prof. Valášek, CTU Prague) 1. Direct kinematic task – difficult 2. Inverse kinematic task – easy 22 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) 23 Direct kinematic task flange frame z x world frame y 24 Inverse kinematic task flange frame z x world frame y 25 Kinematic calibration z x world frame y 26 Kinematic Calibration 27 Robot Calibration 28 Kinematic Calibration 29 30 32 Solving kinematic tasks 33 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. 34 Solving kinematic tasks Algebraic equation of degree 16 … up to 16 solutions 4 typical solutions 35 Solving kinematic tasks 36 Stäubli TX-90 – Geometry 37 Kinematic model flange frame z x z y x world frame y 38 39 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 40 The Standard Kinematic model in Denavit-Hartenberg Convention ABB IBR 140 41 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 42 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 43 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 44 45 46 47 48 49 50 51 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. 52

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