1. Manipulator Kinematics
Dr. T. Asokan

2. Introduction to Robotics
Course Contents
Introduction to Robotics
Definition
Classifications
Applications
Kinematics
Object Location and Motion
Transformation Matrices
Homogeneous Transformations
Forward Kinematics
Inverse Kinematics
Differential Relationships
Introduction to Robotics

3. Introduction Robots everywhere, for every one
How do you define a robot
Laws of Robotics
History and Evolution of Robotics
Classifications
Major topic in Robotics

4. Robots every where, for every one?
Dr. T. Asokan

5. NASA's Mars rover Curiosity lands
NASA's Mars rover Curiosity Lander finally landed on after cruising across 350 million miles of interplanetary space for 8-1/2 months and this event is all over the news. Mars is practically on the far side of the Sun from Earth, 154 million miles (1.7 astronomical units) away.
Global Luna Rover Challenge: Indian Participation by “Team Indus”

7. Elderly Assistant

8. Tour..\Videos\CMU_Tour_Guide.avi Guide

9. How do you define a Robot ?
Robotics can be a hobby, a science fiction genre, a scientific/engineering discipline, or an industrial technology. As a sometimes controversial subject, it is often misrepresented in the popular media, by advocates and opponents. No single definition is going to satisfy such a variety of perspectives and interests.

10. Definition
A robot is a software controlled mechanical device that uses sensors to guide one or more of end effectors through programmed motions in a workspace in order to manipulate physical objects.
Robotics is the intelligent connection of perception to action
History
Dr. T. Asokan

11. Robotics- Timeline
#1495 Leonardo DaVinci designs a mechanical device that looks like an armored knight. The mechanisms inside "Leonardo's robot" are designed to make the knight move as if there was a real person inside.
≠ 1920Czechoslovakian playwright Karel Capek introduces the word robot in the play R.U.R. - Rossum's Universal Robots.  The word comes from the Czech robota, which means tedious labor. 
≠ 1942 Isaac Asimov publishes Runaround, in which he defines the Three Laws of Robotics.
≠ 1951 In France, Raymond Goertz designs the first teleoperated articulated arm for the Atomic Energy Commission.  This is generally regarded as the major milestone in force feedback technology. 
≠ 1954George Devol designs the first programmable robot and coins the term Universal Automation, planting the seed for the name of his future company - Unimation.
Dr. T. Asokan

12. 1962 General Motors purchases the first industrial robot from Unimation and installs it on a production line. This manipulator is the first of many Unimates to be deployed.
≠1965 Homogeneous transformations applied to robot kinematics - this remains the foundation of robotics theory today
1970 Professor Victor Scheinman of Stanford University designs the Standard Arm.  Today, its kinematic configuration remains known as the Standard Arm.
1978 Using technology from Vicarm, Unimation develops the PUMA (Programmable Universal Machine for Assembly).  The PUMA can still be found in many research labs today.
1978 Brooks Automation founded 1979 Sankyo and IBM market the SCARA (selective compliant articulated robot arm) developed at Yamanashi University in Japan
1982 Fanuc of Japan and General Motors form joint venture in GM Fanuc to market robots in North America. 
1994 CMU Robotics Institute's Dante II, a six-legged walking robot, explores the Mt. Spurr volcano in Alaska to sample volcanic gases.
1995 Intuitive Surgical formed by Fred Moll, Rob Younge and John Freud to design and market surgical robotic systems.  Founding technology based on the work at SRI, IBM and MIT.
≠ NASA's Mars PathFinder mission captures the eyes and imagination of the world as PathFinder lands on Mars and the Sojourner rover robot sends back images of its travels on the distant planet.
2000 Honda showcases Asimo, the next generation of its series of humanoid robots.
2000 Sony unveils humanoid robots, dubbed Sony Dream Robots (SDR), at Robodex.
2001 Built by MD Robotics of Canada, the Space Station Remote Manipulator System (SSRMS) is successfully launched into orbit and begins operations to complete assembly of International Space Station
Dr. T. Asokan

13. The Laws of Robotics (according to the Handbook of Robotics, or more precisely, Isaac Asimov):
A robot may not injure humanity or, through inaction, allow humanity to come to harm.  (This was added after the initial three laws.)
1 A robot may not injure a human being, or, through inaction, allow a human being to come to harm.
2 A robot must obey the orders given to it by human beings except where such orders would conflict with the First Law.
3 A robot must protect its own existence as long as such protection does not conflict with the First or Second Law.
Dr. T. Asokan

14. Evolution of Robotics Research

15. Enabling Technologies: Automation Pentagon
Challenge: How do we motivate the youngsters to learn all these ?

16. Field and Service Robots Entertainment/Educational Robots
Classifications
Industrial Robots
Field and Service Robots
Entertainment/Educational Robots
Field and Service Robots
Wheeled mobile robots/intelligent vehicles
Walking robots (robot dogs, biped robots, etc.)
Humanoids
Climbing, Crawling robots (robot spiders, Robot Snakes)
Aerial Robots
Medical Robots
Agricultural robots
Dr. T. Asokan

17. Industrial Robots (Manipulators)
Introduction to Robotics

18. Introduction to Robotics
Industrial robots
Pick and Place
Assembly
Welding
Painting
Machining
Introduction to Robotics

19. Mostly, six-axis articulated configuration (serial arm)
Electric/Hydraulic actuation
Robot workcells consist of manipulators, end effector tools, conveyors, sensors (vision, force, proximity etc.)
Programmed through special robot programming languages
Once setup, runs without major deviations
Needs calibration
Online/offline programming
Kinematics, Dynamics and Control

20. Introduction to Robotics
Kinematics
Introduction to Robotics

21. Object Location and Motion
Contents:
Object location
- Position of a point in space
- Location of a rigid body in space
- Homogeneous transformation matrix
Object Motion
Translation (Transformation Matrix) and Inverse
Basic Rotation (Transformation Matrices) and Inverse.
General Rotation
Examples.
Properties of homogeneous transformation matrix.

22. Introduction to Robotics
Given an object in a physical world,
how to describe its position and orientation, and
how to describe its change of position and orientation due to motion
are two basic issues we need to address before talking about having a robot moving physical objects around.
The term location refers to the position and orientation of an object.
Introduction to Robotics

23. Introduction to Robotics
Direct Kinematics
In order to manipulate objects in space, it is required to control both the position and orientation of the tool/end effector in three- dimensional space.
A relationship between the joint variables and the position and orientation of the tool is to be formulated.
Direct Kinematics Problem:
Given the vector of joint variables of a robotic manipulator, determine the position and orientation of the tool with respect to a co-ordinate frame attached to the robot base.
It is necessary to have a concise formulation of a general solution to the direct kinematics problem.
Introduction to Robotics

24. Introduction to Robotics
Co-ordinate frames
If ‘p’ is a vector in Rn, and X={x1, x2, x3 .…xn} be a complete orthonormal set of Rn, then the co-ordinates of p with respect to X are denoted as [p]x and are defined as
The complete orthonormal set X is sometimes called an orthonormal co-ordinate frame.
The ‘k’th co-ordinate of p wrt X is p
[p]2x X2 X1
[p]1x
Introduction to Robotics

25. Co-ordinate TransformationP m2 m1 m3 f1 f2 f3
Fixed link P m2 m1 m3 P m1 m3 m2
Represent position of p wrt fixed frame f={f1,f2,f3} P m1 m3 m2
The two sets of co-ordinates of P are given by
[p]M=[p.m1, p.m2, p.m3]
[p]F=[p.f1, p.f2, p.f3]
The co-ordinate transformation problem is to find the co-ordinates of p wrt F, given the co-ordinates of p wrt M.
Introduction to Robotics

26. Co-ordinate Transformation Matrix
Let F={f1, f2,f3,.. fn} and M={m1, m2,m3,.. mn } be co-ordinate frames of Rn with F being an orthonormal frame. Then for each point p in Rn,
The matrix A is known as Co-ordinate transformation matrix. f1 f2 f3
Fixed link P m1 m3 m2
Example:
Introduction to Robotics

27. Inverse Co-ordinate Transformation
Let F and M be two orthonormal co-ordinate frames in Rn, having the same origin, and let A be the co-ordinate Transformation matrix that maps M co-ordinates to F co-ordinates, then the transformation matrix which maps F coordinates into M coordinates is given by A-1 , where
A-1=AT
Introduction to Robotics

28. Introduction to Robotics
Rotations f3 m2 m1 m3
In order to specify the position and orientation of the mobile tool in terms of a co-ordinate frame attached to the fixed base, co-ordinate transformations involving both rotations and translations are required. m3 f2 m2
Rotation and Translation of co-ordinate frame m1 f1
Introduction to Robotics

29. Fundamental rotations
If the mobile coordinate frame is obtained from the fixed coordinate frame F by rotating M about one of the unit vectors of F, then the resulting coordinate transformation matrix is called a fundamental rotation matrix. f2
In the space R3, there are 3 possibilities.
Introduction to Robotics

30. Fundamental rotations
The kth row and the kth column of Rk(f) are identical to the k th row and the k th column of identity matrix. In the remaining 2x2 matrix, the diagonal terms are while the off diagonal terms are The sign of the off diagonal term above the diagonal is (-1)k.
Pattern
Example
Introduction to Robotics

31. Introduction to Robotics
Composite Rotations
A Sequence of fundamental rotations about the unit vectors cause composite rotations.
Algorithm for composite rotation
Initialise rotation matrix to R=I, which corresponds to F and M being coincident
If the mobile frame M is rotated by an amount f about the kth unit vector of F, then pre-multiply R by Rk(f). -> [Rk(f).R]
If the mobile frame M is rotated by an amount , f about it’s own kth vector, then post-multiply R by Rk(f). -> [R . Rk(f)]
If there are more rotations go back to 2. The resulting matrix maps M to F
Introduction to Robotics

32. Yaw-Pitch-Roll Transformation matrix
Introduction to Robotics

33. Introduction to Robotics
Class Work
Suppose we rotate tool about the fixed axes, starting with yaw of p/2, followed by pitch of –p/2 and finally, a roll of p/2, what is the resulting composite rotation matrix?
Assignment 1
Suppose a point P at the tool tip has mobile co-ordinates [p]M= [0,0,.6]T, Find [p]F following YPR transformation of 45, 60 and 90 degrees respectively.
Introduction to Robotics

34. Homogeneous co-ordinates
We need pure rotations and translations to characterize the position and orientation of a point relative to the co-ordinate frame attached to the base.
While a rotation can be represented by a 3x3 matrix, it is not possible to represent translation by the same.
We need to move to a higher dimensional space, the four dimensional space of homogeneous co-ordinates.
Definition: Let q be a point in R3, and let F be an orthonormal coordinate frame of R3 . If s is any non zero scale factor, then the homogeneous coordinates of q with respect to F are denoted as [q]F and defined:
In robotics we use s=1 for convenience
Introduction to Robotics

35. Homogeneous Transformation matrix
If a physical point in three-dimensional space is expressed in terms of its homogeneous co-ordinates and we want to change from one coordinate frame to another, we use a 4x4 homogeneous transformation matrix.
In general T is
The 3x3 matrix R is a rotation matrix
P is a 3x1 translation vector
h is a perspective vector, set to zero
In terms of a robotic arm, P represents the position of the tool tip, R its orientation.
Introduction to Robotics

36. Introduction to Robotics
The fundamental operations of rotations and translations can each be regarded as special cases of the general 4x4 homogeneous transformation matrix.
Using homogeneous coordinates, translations also can be represented by 4x4 matrices.
In terms of homogeneous coordinate frames, the translation of M can be represented by a 4x4 matrix, denoted Tran (p), where m2 f2 m2 f3 f1 m1 m3 p1 p3 p2
Tran (p) is known as the fundamental homogeneous Translation matrix
Introduction to Robotics

37. Inverse Homogeneous Transformation
If T be a homogeneous transformation matrix with rotation R and translation p between two orthonormal coordinate frames and if h=0,s=1, then the inverse transformation is:
Composite Homogeneous Transformations
Example:
Self Study: Screw Transformation, screw pitch
Introduction to Robotics

38. Forward Kinematics -Arm Equation
Contents:
Kinematic Parameters
- Joint Parameters
Link Parameters
Assignment of coordinate frames
Normal, Sliding and Approach Vectors
Denavit-Hartenberg (DH) representation
The arm matrix
Arm equation
Examples.

39. Links and Joints- Numbering
By convention, the joints and links of a robotic arm are numbered outward starting with the fixed base, which is 0. The last link is the tool or end- effector.
For an n-axis robot, there are n+1 links interconnected by n joints
Joint k connects link k-1 to link k
Link 0 1 2 3
Joint 1 j2 j3
Link 0 1 2 3
Joint 1 j2 j3
Introduction to Robotics

40. Introduction to Robotics
Joint Parameters
Link k
Link k-1
Joint k dk Xk
The relative position and orientation of two successive links can be specified by two joint parameters, joint angle and joint distance
Yk-1
Zk-1
Xk-1
Yk-1
Zk-1
Xk-1
Yk-1
Zk-1
Xk-1
Joint k connects link k-1 to link k. The parameters associated with joint k are defined w.r.t zk-1, which is aligned with the axis of joint k.
The joint angle, qk , is the rotation about zk-1 needed to make axis xk-1 parallel with axis xk.
Joint distance dk, is the translation along zk-1 needed to make axis xk-1 intersect with axis xk.
Thus joint angle is a rotation about axis of joint k, while joint distance is a translation along joint axis
For each joint, it will always be the case that one of these parameters is fixed.
Introduction to Robotics

41. Introduction to Robotics
Link Parameters
Zk-1 Zk ak
Link k
The relative position and orientation of the axes of two successive joints can be specified by two link parameters, link length and link twist angle
Link k connects joint k to joint k+1. The parameters associated with link k are defined w.r.t xk, which is a common normal between the axes of joint k and k+1.
Link length, ak, is the translation along xk needed to make axis zk-1 intersect zk
Twist angle, ak, is the rotation about xk needed to make axis zk-1 parallel with axis zk
The two link parameters are always constant and are specified as part of the mechanical design.
Introduction to Robotics

42. Kinematic Parameters……
Arm Parameter
Symbol
Revolute Joint (R)
Prismatic Joint (P)
Joint Angle q
Variable
Fixed
Joint Distance d
Link Length a
Link Twist angle
For an n-axis robot manipulator, the 4n kinematic parameters constitute the minimal set needed to specify the kinematic configuration of the robot.
Introduction to Robotics

43. Normal, Sliding and Approach Vectors
The orientation of a tool can be represented in Joint coordinates by YPR convention.
In rectangular or Cartesian coordinates the same can be represented by a rotation matrix R= [r1, r2, r3 ] where the three columns of R correspond to the normal, sliding and approach vectors resply.
Approach vector is aligned with the roll axis and points away from wrist. Consequently, it represents the direction in which the tool is pointing
r3 Approach vector
r1, Normal vector
r2 ,Sliding vector
Sliding vector is orthogonal to the approach vector and aligned with the open-close axis of the tool.
Yaw, Pitch and Roll motions are rotations about normal, sliding and approach vectors
Introduction to Robotics