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- 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

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