1. ROBOT VISION LABORATORY 김 형 석 Robot Applications-B http://world.honda.com/run/mov-run-60.html

2. Direct Kinematics Where is my hand? Direct Kinematics: HERE!

3. Serial and Parallel Manipulators

4. PUMA560 Hexapod

5. Links and Joints Joints: Links End Effector Robot Basis 2 DOF ’ s

6. Link Length and Twist Axis i Axis i- 1 a i-1  i-1

7. Denavit-Hartenberg Parameters Axis i- 1 a i-1  i-1 Axis i Link i didi ii

8. Example: PUMA560

9. Inverse Kinematics How do I put my hand here? IK: Choose these angles!

10. What is the reachable space? Take l 1, l 2 fixed and vary  3 Example: Planar 3-link robot l2l2 l3l3 l1l1 Now vary  1 Finally, vary  2

11. Existence of Solutions u A solution to the IKP exists if the target belongs to the workspace u Workspace computation may be hard. In practice is made easy by special design of the robot u The IKP may have more than one solution. How to choose the appropriate one? 2 solutions!

12. An Example: L1L1 L2L2 V3V3

13. Joint Velocity and the Jacobian Look! I ’ m moving!

14. Introduction to Robot Motion Planning Robotics meet Computer Science

15. Example A robot arm is to build an assembly from a set of parts. Tasks for the robot: u Grasping: position gripper on object design a path to this position u Trasferring: determine geometry path for arm avoide obstacles + clearance u Positioning

16. Information required u Knowledge of spatial arrangement of wkspace. E.g., location of obstacles u Full knowledge full motion planning u Partial knowledge combine planning and execution motion planning = collection of problems

17. Basic Problem A simplified version of the problem assumes u Robot is the only moving object in the wkspace u No dynamics, no temporal issues u Only non-contact motions MP = pure “geometrical” problem

18. Components of BMPP (cont.) u The Problem: u Given an initial position and orientation PO init u Given a goal position and orientation PO goal u Generate: continuous path t from PO init to PO goal u t is a continuous sequence of Pos’

19. Mathematic Notion of Path u Need a notion of continuity u Define a distance function d : C x C -> R + u Example : d(q,q’) = max a in A ||a(q) - a(q’)|| d

20. Connect Start and Goal to Roadmap StartGoal

21. Find the Path from Start to Goal Start Goal