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# Robot Manipulation Basics

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Robot Manipulation is the basic science in Robotics. Most of the modern theories arise from the classical concepts of robot manipulation.

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### Robot Manipulation Basics

1. 1. Introduction to Robot Manipulation
2. 2. Why Robot Manipulation ?
3. 3. Why Robot Manipulation ?
4. 4. Why Robot Manipulation ? Robot Manipulation is a core robot technology A. Basic fundamentals of robotics lies in robot manipulation - kinematics & dynamics - motion planning & control - higher mathematics and AI B. Direct application to industry - robot manipulators are still a growing market - technology is now being applied beyond conventional areas - new research on interactive robots is centered around it
5. 5. New Application Areas Medical & Surgery Small Industries (e.g. Pharmaceuticals)
6. 6. New Application Areas Rehabilitation & Helpers Military & Homeland Security
7. 7. New Application Areas Future Service Robots (German Service Robotics Initiative DESIRE)
8. 8. Robot Arms in Action ABB Robotics Motion Control Video
9. 9. Structure of A Robot Manipulator Links A Robot Arm is a KINEMATIC CHAIN which is comprised of a. Links b. Joints Joints End Flange Base
10. 10. Kinematic Chains Open Loop Closed Loop
11. 11. Manipulator Kinematics Position Kinematics: The mathematics behind making the robot move to a desired position. Typically used in: a. Pick & Place operations b. Assembly operations c. Stacking and loading Velocity Kinematics: The mathematics behind making the robot move with desired velocities. Typically used in: a. Cutting / Machining b. Painting Operations c. Scanning areas
12. 12. Forward & Inverse Kinematics Forward Kinematics: I know: The position / velocity of each robot joint. I need to find out: The end position / velocity of the robot Inverse Kinematics: I know: The desired position / velocity of the end point where the robot must reach I need to find out: The position / velocity of each robot joint
13. 13. Forward & Inverse Kinematics Forward Kinematics: !! SY I know: The position / velocity of each robot joint. I need to find out: The end position / velocity of the robot EA !! EX Inverse Kinematics: PL I know: The desired position / velocity of the end point where the robot must reach M I need to find out: The position / velocity of each robot joint O C
14. 14. Forward Kinematics Forward Kinematics: Joint 2 Angle What is the end point location (X, Y) if the joint Y angles are: End Point Joint 1 = 30º and Joint 2 = 60º Given the 3 link lengths (a1, a2 and a3) are 10mm each Joint 1 Angle X
15. 15. Forward Kinematics Forward Kinematics: Joint 2 Angle What is the end point location (X, Y) if the joint Y angles are: End Point Joint 1 = 30º and Joint 2 = 60º Given the 3 link lengths (a1, a2 and a3) are 10mm each Joint 1 Angle X a1 = a2 = a3 = 10mm x = a2*sin (j1) + a3*sin (j1 + j2) = 10 * 0.5 + 10 * 1 = 15mm y = a2*cos (j1) + a3*cos (j1 + j2) = 10 * 0.866 + 10 * 0 = 8.66mm
16. 16. Inverse Kinematics Inverse Kinematics: Joint 2 Angle Lets say that the end point is at (15, 8.66) mm Y End Point Given the 3 link lengths (a1, a2 and a3) are 10mm each What are the joint angles? Joint 1 Angle X Is it only 30 & 60 ? Solve: Hint Cos(A+B) = CosA.CosB – SinA.SinB
17. 17. Inverse Kinematics From the FK equations: x = a2*sin (j1) + a3*sin (j1 + j2) Joint 2 Angle y = a2*cos (j1) + a3*cos (j1 + j2) Y End Point Simplifying the notations x = a2.s1 + a3.s12 y = a2.c1 + a3.c12 If we square and add, we get Joint 1 Angle x2 + y2 = a22 + a32 + 2a2a3 [ s1.s12 + c1. c12 ] X which is to say x2 + y2 = a22 + a32 + 2a2a3 c2 Thus c2 = (x2 + y2 – a22 – a32) / 2(a2.a3) Remember: cos(-x) = cos(x)
18. 18. Inverse Kinematics Now that we have solved joint 2 = j2 Joint 2 Angle x = a2.s1 + a3.s12 Y y = a2.c1 + a3.c12 End Point x = a2.s1 + a3s1c2 + a3s2c1 y = a2.c1 + a3c1c2 – a3s1s2 x = s1 [ a2 + a3 c2 ] + a3s2 c1 y = c1 [ a2 + a3 c2 ] – a3s2 s1 Joint 1 Angle let k1 = a2 + a3 c2 and k2 = a3s2 x = k1 s1 + k2 c1 X y = k1 c1 + k2 s1 Substituting: k1 = r cos (t) and k2 = r sin (t) we will get t + j1 = Atan2 ( y, x) where t = Atan2( k2, k1)
19. 19. Inverse Kinematics Final Solution Solution 1 = [ 30, 60 ] ..... obviously Solution 2 = [90, -60 ] In principle: Inverse Kinematics will almost always give you more than one solution!
20. 20. Summarizing Robot Manipulators cover the core concepts of robot design & control Manipulators are necessarily kinematic chains with links and joints (drives) The crux of robot arm control is based on the theory of kinematic Kinematics are used in both Position and Velocity domain Kinematics are of two kinds – Forward and Inverse Kinematics Forward Kinematics is easy and is used mainly for Analysis Inverse Kinematics is complex and is used for robot control and operations Classical Industrial Robots have structures to easy out complex calculations Modern day robots are equipped with powerful computers and hence there is no restriction on the structure
21. 21. Thank You info@robots-alive.com blog.robots-alive.com www.robots-alive.com