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Hands-on Sessions on
Learning Robot Kinematics using RoboAnalyzer*
Mr. Rajeevlochana G. ChittawadigiPhD Scholar at IIT Delhi/ Asst. Professor, Dept of Mech Engg.
Amrita Vishwa Vidyapeetham, Bengaluru
*Developed at IIT DelhiFeb 25, 2020: FDP (IITK)
Contents
• Robotics• Robotics Education• Homogenous Transformation• Denavit-Hartenberg Parameters• Forward Kinematics• Inverse Kinematics• Motion Planning (Virtual Robot Module)
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Robotics
• Design, development, control and application
– Industries– Academics – Research– Entertainment– Medical applications etc.
•Included in curriculum of universities
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Source: Mechatronics Lab and PAR Lab, IIT Delhi
Robotics Education
Courses* usually include:
1. Theory:– Design and working of robot in
the form of drawing and pictures– Mathematically intensive
2. Practical:– CAD modeling and simulation– Real robots in action– Not many institutes have facilities
*Mechanical Engineering Source: http://images.google.com4
Robotics Concepts
• Homogenous Transformations• DH Parameters• Kinematics• Dynamics• Motion Planning• … • Difficult to Visualize
RoboAnalyzer Software: Priceless!!
Free to use: http://www.roboanalyzer.com
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RoboAnalyzer
• 3D Model Based Robotics Learning and Teaching Software• Developed by Prof. S. K. Saha and Team (IIT Delhi)• Main Developer: Mr. Rajeevlochana G. Chittawadigi• Other Developers
– Dr. Suril V Shah– Mr. Ratan Sadanand– Mr. Ravi Joshi– Mr. Amit Jain– Ms. Jyoti Bahuguna– Mr. Sasanka Sekhar Sinha– Mr. Sai Vikas Maram– Mr. Yashaswi Kuruganti– … 6
RoboAnalyzer Website:
• http://www.RoboAnalyzer.com• Download latest versoin (V7.5) from
http://www.roboanalyzer.com/downloads.html• After download, unzip it• RoboAnalyzer.exe
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Homogenous Transformation Matrix (HTM) Module
• Top Panel Button of RoboAnalyzer Window• Translation
– Local Frame– Global Frame
• Rotation– Local Frame– Global Frame
• Homogenous Transformation Matrix (HTM)
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Task 1: Translation in HTM
• Translate along X (2 units), Y (3 units) and Z (4 units) axes• Observe the last column (fourth) of the HTM
• Translation alone is commutative
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• Rotate about local X (90 deg), Y (90 deg) and Z (90 deg) axes.• Reverse the order now• Observe the first 3x3 matrix of the HTM
– Direction Cosine– Projection of smaller axis vector on bigger frame– 3 columns => 3 vector projections
• Rotation is not commutative
Task 2: Rotation in HTM
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Task 3: Local v/s Global in HTM
• Rotate about local Z (90 deg), R1• Rotate about local Y (90 deg), R2• Rotate about local X (90 deg), R3• Translate about global Z (10 units), T4• Rotate about global X (90 deg), R5• Rotate about local X (90 deg), R6
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Task 3: Local v/s Global in HTM
• Current transformation => Multiplication of individual HTMs
• Local transformation => Post-Multiplication of HTMs
• Global transformation => Pre-Multiplication of HTMs
Geometric Model of a Serial Robot
• Robot • moves in Cartesian frame• controlled at joints
• Mapping• Geometric model
• Robot Architecture
• Denavit-Hartenberg (DH) Parameters
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Joint Axes
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Joint Axes
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Joint Axes
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Joint Axes
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DH Parameters
• Geometrical description
• 4 parameters• Joint offset (b)• Joint angle (θ)• Link length (a)• Twist angle (α)
• Relates frames attached on consecutive links
X1
θ1
θ2
α2
b1
a1
b2
a2
X2
Z2
Z1
X3
Z3
α1
Demo
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Visualize DH Parameters
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A. 3 DOF and 3R Robot
B. Modify DH Parameters
C. Visualize with Animation
Kinematics
Study of motion of links without considering the forces
Forward Kinematics
Joint Angles
θ1 and θ2
Inverse Kinematics
Demo
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Forward Kinematics
• Joint to Cartesian space• End-effector configuration
in base frame
T2
T3
T1
Tee = T1 T2 T3 =[ ]Q Px
Py
Pz
0 0 0 1
Demo
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Task 4: Transformations
• RoboAnalyzer Main Application• 2R Robot (Spatial)• DH Parameters
• Verify Transformation
• Try for Different Joint Angles
=
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Task 5: Forward Kinematics
• KUKA KR5 Arc• FKin• Animation• Plots • Verify Position of
EE Config• Try Different Motion
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Task 6: Inverse Kinematics
• Ikin Button• MTAB Aristo Robot• IKin: 8 Solutions• Verify in RA• Visualize in RA• Try Different Robots
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Virtual Robot Module
• Joint Jogging• Cartesian Jogging• 17 Robots• Integration with
MATLAB• Interface with
Physical Teach Pendant
Demo
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Task 7: Virtual Robot Module
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Task 7: Virtual Robot Module
Start drawing from the first position to draw the Home below in YZ plane. Input the coordinates in the Excel file and saveit as .CSV file (In CSV File as: 800,0,800,90,0,90). One Excel file is included in the directory for help.
Dynamics
Forward Dynamics Inverse Dynamics
Study of forces and moments causing the motion of links
Due to complexity, these are usually not taught in most of the UG courses
Inverse Dynamics
Join
t Acc
l.
Forward Dynamics
Join
t For
ce
Demo
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Task 8: Inverse Dynamics
• Idyn on 2R serial robot• First Perform Fkin to generate a trajectory• Next click on Idyn to get the joint torques.
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Task 9: Forward Dynamics
• Fdyn on 1R robot demo.• Some anomalies discussed.
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Demo
RoboAnalyzer Team• Subir K. Saha (1996- present)• S. Goel and S. Ramakrishnan (1996-97)• A. Patle (2000-01)• Rajat Jain (2009-10)• Suril V. Shah (2007-11)• Rajeevlochana G. Chittawadigi (2009 – 2013, 2015-present)• Amit Jain (2010-11)• Jyoti Bahuguna (2011-12)• Ratan Sadanand (2012-15)• Ravi Joshi (2014-15)• Keshav Bimbraw and Ishaan Mehta (2016 Summer)• Sasanka Sekhar Sinha (2017-present)• Sai Vikas Maram and Yashaswi Kuruganti (2018-19)
The feedback/suggestion of the below are sincerely acknowledged:• Mr. Arun Dayal Udai (2010): Suggested importing of CAD files in STL format• Dr. Sandipan Bandyopadhyay (2012): Suggested to make RA/VRM as an API/COM server to be integrated
with other software• Prof. Sudipto Mukherjee (2012-13): Suggested an interfacing with MATLAB• Dr. Nayan Kakoty (2013): Suggested to have custom trajectory file input for joints
Prof. Peter Corke (2015): Discussion on integration of RoboAnalyzer (VRM) with Robotics Toolbox• Mr. Vinay Gupta (2016): Suggestion on having a link in the software for online feedback and contact form• Mr. Dharmender Jaitly, Dr. Majid Koul, Mr. Aamir Hayat, Mr. Riby Boby, many more
www.roboanalyzer.com
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Complementary
• Illustrations• Examples• Effective!!!
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Feedbackhttp://www.roboanalyzer.com/feedback.html
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