Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our User Agreement and Privacy Policy.

Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our Privacy Policy and User Agreement for details.

Successfully reported this slideshow.

Like this presentation? Why not share!

5,119 views

Published on

My dissertation defense due on Nov 20th :D

No Downloads

Total views

5,119

On SlideShare

0

From Embeds

0

Number of Embeds

72

Shares

0

Downloads

0

Comments

0

Likes

4

No embeds

No notes for slide

- 1. OPTIMIZATION OF TOOL PATH IN A ROBOTIC ENVIRONMENT BY MUKUND V. NARASIMHAN DISSERTATION MECHANICAL ENGINEERING DEPARTMENT THE UNIVERSITY OF TEXAS AT ARLINGTON November 20 th 2006
- 2. Electronic Assembly
- 3. <ul><li>Robots are a tailor made fit for the electronics industry. </li></ul><ul><li>Important for military and consumer electronics </li></ul><ul><li>Reason: Quality, Quantity, Ergonomics and Economics </li></ul><ul><li>Robots can perform a variety of tasks </li></ul><ul><ul><ul><li>Assembling circuit boards. </li></ul></ul></ul><ul><ul><ul><li>Inspection </li></ul></ul></ul><ul><ul><ul><li>Testing </li></ul></ul></ul><ul><ul><ul><li>Pick and Place </li></ul></ul></ul><ul><ul><ul><li>Welding and soldering </li></ul></ul></ul><ul><ul><ul><li>Spray painting etc. </li></ul></ul></ul>
- 4. <ul><ul><ul><li>In the future, hiring managers will prefer robots over humans. </li></ul></ul></ul><ul><ul><ul><li>Low Labor Costs </li></ul></ul></ul><ul><ul><ul><li>Can work for 24 X 7 X 365 </li></ul></ul></ul><ul><ul><ul><li>Maximum productivity </li></ul></ul></ul><ul><ul><ul><li>Efficiency </li></ul></ul></ul>
- 5. <ul><li>Challenges </li></ul><ul><li>Rising Costs </li></ul><ul><li>Rising Demands </li></ul><ul><li>Shrinking Energy Generating Resources </li></ul><ul><li>Need of Optimization </li></ul><ul><li>Optimum Use of Energy Resources </li></ul><ul><li>Minimizing Overhead Costs </li></ul><ul><li>Maximizing Profits. </li></ul>
- 6. <ul><li>Objective: </li></ul><ul><li>For increased efficiency, low overhead & energy costs and maximum profits, optimization of tool path is the primary need. </li></ul><ul><li>Use of robots to match the supply demand equation triggers a need to minimize setting up times. </li></ul><ul><li>Efficient Inverse Kinematics Solver to ensure low production times. </li></ul><ul><li>Integration of optimized tool path and inverse kinematics solver a must for increased productivity. </li></ul>
- 7. <ul><li>A new algorithm to optimize the tool path of the robotic manipulator. </li></ul><ul><li>Developing a better joint transformation technique. </li></ul><ul><li>Use of Workspace to ensure intended target points are within the reach of the manipulator. </li></ul><ul><li>Developing a New Inverse Kinematics solver. </li></ul>
- 8. <ul><li>Robotic tool has to traverse to various locations for machining, assembly and for pick or place operations. </li></ul><ul><li>These locations or co-ordinate points are similar to the nodes/cities in Traveling Salesman Problem. </li></ul><ul><li>Therefore the optimization of the tool path is similar to obtaining a solution to a symmetric TSP. </li></ul><ul><li>For Robot’s manipulator to reach these locations, there is a need to know joint parameters and link orientations. </li></ul>
- 9. <ul><li>Insertion and Reordering Algorithm. </li></ul><ul><li>Piecewise Insertion and Reordering Algorithm. </li></ul><ul><li>New Notation using 6 parameters. </li></ul><ul><li>Workspace Generating Algorithm. </li></ul><ul><li>Inverse Kinematics (IK) Solver. </li></ul><ul><li>Extension of IK Solver to analyze Planar Mechanisms. </li></ul>Contributions
- 10. <ul><li>The Traveling Salesman Problem (TSP) </li></ul><ul><li>A deceptively simple combinatorial optimization problem. </li></ul><ul><li>A Salesman who wants to visit a number of cities cyclically. </li></ul><ul><li>Conditions – </li></ul><ul><li> Visit each city once </li></ul><ul><li> Need to get back to the start city at the end of the tour. </li></ul><ul><li>The hard part </li></ul><ul><li>if one considers n cities. </li></ul><ul><li>Requires atleast (n-1)! steps. </li></ul><ul><li>if one considers a problem with 10 cities then its equal to figuring out the minimum of 9! equal to 362,880 different paths. </li></ul><ul><li>This will increase rather exponentially as n increases and it will take ages to verify each route and figure out the minimum length. </li></ul>
- 11. INSERTION & REORDERING ALGORITHM
- 12. <ul><li>Insertion & Reordering Algorithm </li></ul><ul><li>Insertion part Mainly to find the best non-intersecting path </li></ul><ul><li>Reordering part Stacking the points in the same order as the best path obtained from the insertion step. </li></ul>Step 1: Two points out of the n available points is considered. The shortest path between two points will be the straight line connecting them. Step 2: The third point is considered and could be inserted in any of the available three positions, 3-1-2, 1-3-2, 1-2-3. Step 3: The line crossing algorithm is applied to the paths in the set to check if any segment of the path intersect. All such paths whose segments intersect are rejected. Step 4: Among the available paths in the result set, the one with the least length is selected. Step 5: The steps 2 to 4 is repeated till all the n points are exhausted. This completes one cycle. Then the entire process is repeated for number of iterations till the value of the path length is stabilized.
- 13. <ul><li>This algorithm may take a longer time if the number of nodes increase. </li></ul><ul><li>Using the algorithm for number of iterations makes it a hopeless candidate as it would eat up the time required to complete the process. </li></ul><ul><li>Piece-wise Insertion & Reordering Algorithm </li></ul><ul><li>Similar to the parent algorithm with a slight difference. </li></ul><ul><li>The start and end points are defined </li></ul><ul><li>Rest of the points is fitted between them. </li></ul><ul><li>The non-intersecting path with the least length is generated at the end of one cycle. </li></ul><ul><li>The points are reordered based on this path and the entire process is iterated till a stable solution is obtained. </li></ul>
- 14. Path Optimization Results
- 16. Djibouti Cities
- 17. Western Sahara Cities.
- 22. ROBOTICS
- 23. <ul><li>Denavit and Hartenberg (1955), modeled and analyzed mechanical systems by developing the first symbolic notation, D-H notation </li></ul><ul><li>Four parameters (a, α, β, s) to describe the shape and joint characteristics of each link. </li></ul><ul><li>This notation is used extensively in the analysis of robotic manipulators and mechanisms. But some complications arise while analyzing certain mechanisms as </li></ul><ul><li>Problem D-H notation only defines relative joint positions, due to its joint definition. </li></ul><ul><li>It also fails when adjacent joint axes are not parallel or normal to each other. </li></ul><ul><li>A modified notation was developed by Sheth and Uicker (1972) whose purpose was to improve and extend the use of D-H notation to determine the exact joint position in space. </li></ul><ul><li>S-U notation introduced six constant joint parameters (a, b, c, α, β, ), plus a variable part that contains the same number of parameters as the degrees of freedom of the joint. </li></ul>ROBOTIC NOTATION AND TRANSFORMATION
- 24. <ul><li>The Cylindrical-Bryant angles notation or C-B notation in short, was developed by Yih (1991) to model and analyze spatial robots. </li></ul><ul><li>This uses Cylindrical and Bryant angles transformation matrices to describe the shape and joint characteristics of each link. </li></ul><ul><li>Unlike D-H notation, C-B notation permits determination of exact joint positions in space. This exact joint position is the actual location of the physical joint center in space. </li></ul><ul><li>This notation uses five parameters ( , h, r, α, β) and in some cases six parameters ( , h, r, α, β, ) to describe the link shape and joint behavior. Even this notation has a problem as there are no variables to represent the transformation in the y-direction. </li></ul>EFFECTIVE SYMBOLIC NOTATION
- 25. x z x y x z x z z x Auxiliary Joints Difficulties using CB Notation
- 26. DIRECT KINEMATICS DISPLACEMENT VELOCITY ACCELERATION
- 27. ROBOT RESULTS
- 28. Cincinnati Milacron T3 Robot 0 0 0 0 0 -135,135 6 (R) 90 0 0 0.369 0 -90,90 5 (R) 0 -90 0 0.205 0 -90,90 4 (R) 0 0 0 1.067 0 -150,0 3 (R) 0 0 0 1.067 0 0,90 2 (R) 0 90 0 0 1.5 -120,120 1 (R) Beta (deg) Alpha(deg) b (m) r (m) h (m) (deg) Joint
- 29. Slice of the Workspace
- 30. WorkSpace
- 31. KR 60 P/2 from KUKA Roboter GmbH 0 0 0 0 0 -350,350 6 (R) 90 0 0 0.21 0 -120,120 5 (R) -90 0 0 0 0.893 -350,350 4 (R) 90 0 0 0.507 0 -60,210 3 (R) 0 0 1.4 0 0 -110,40 2 (R) 0 90 0 0.7 0.99 -185,185 1 (R) (deg) (deg) b (m) r (m) h (m) (deg) Joint
- 32. Slice of the Workspace
- 33. WorkSpace
- 34. Motoman UPJ Robot 0 0 0 0 0 -360,360 6 (R) 90 0 0 0.9 0 -120,120 5 (R) -90 0 0 0 2.2 -170,170 4 (R) 90 0 0.298 0.497 0 -55,175 3 (R) 0 0 2.6 0 0 -90,85 2 (R) 0 90 0 0 2.9 -160,160 1 (R) (deg) (deg) b (m) r (m) h (m) (deg) Joint
- 35. Slice of the Workspace
- 36. WorkSpace
- 37. Bendix AA/CNC Industrial Robot 0 0 0 0 0 -360,360 6 (R) 90 0 0 0.146 0 -20,200 5 (R) -90 0 0 0 0.109 -95,95 4 (R) 0 0 0 0 0,0.61 0 3 (P) 90 0 0 0.659 0 -45,225 2 (R) 0 90 0 0 1.067 -95,95 1 (R) (deg) (deg) b (m) r (m) h (m) (deg) Joint
- 38. Slice of the Workspace
- 39. WorkSpace
- 40. Denso HS-E Series Horizontal Articulated Robot 0 0 0 0 0.36 0,360 5 (R) 0 0 0 0 0,2 0 4 (P) 180 0 0 2.25 0 -145,145 3 (R) 0 0 0 1.25 0 -155,155 2 (R) 0 0 0 0 3.62 0,0 1 (R) (deg) (deg) b (m) r (m) h (m) (deg) Joint
- 41. Cartesian Robot 0 0 0 0 0,2 0 3 (P) 0 90 0 0 0,5 0 2 (P) 90 0 0 0 0,2 0 1 (P) (deg) (deg) b (m) r (m) h (m) (deg) Joint
- 42. Slice of Workspace WorkSpace
- 43. Inverse Kinematics
- 44. <ul><li>A target point is given and the values of the joint parameters have to be determined to reach that specific point. </li></ul><ul><li>Inverse kinematics does the reverse of direct kinematics. </li></ul><ul><li>Inverse kinematic equations of a manipulator are nonlinear and hence difficult to solve. </li></ul><ul><li>The difficulties faced in solving this kind of problem </li></ul><ul><li> Multiple to infinite solutions. </li></ul><ul><li> No solutions because of divergence. </li></ul><ul><li> No closed-form (analytical or approximate) solution. </li></ul>Inverse Kinematics
- 45. Inverse Kinematics of Milacron Robot
- 46. Application of Inverse Kinematics Solver

No public clipboards found for this slide

Be the first to comment