1. Algorithmic Robotics and Motion Planning Dan Halperin Tel Aviv University Fall 2006/7 Introduction abridged version

2. Robots, take I

3. An extremely brief history of robotics The RUR robot which appeared in an adaption of Czech author Karel Capek's Rossum's Universal Robots. Circa 1930's. For more, see, e.g., pages.cpsc.ucalgary.ca/~jaeger/visual Media/robotHistory.html UNIMATE becomes the first industrial robot in use. It was used at the General Motors factory in New Jersey. NASA's PathFinder lands on Mars,1997 Honda ’ s ASIMO 2002

4. Motion planning: the basic problem Let B be a system (the robot) with k degrees of freedom moving in a known environment cluttered with obstacles. Given free start and goal placements for B decide whether there is a collision free motion for B from start to goal and if so plan such a motion.

5. A disc moving among discs ?

6. Terminology  Workspace  Configuration  Degree of freedom (dof)

7. Configuration space of a robot system with k degrees of freedom  the space of parametric representation of all possible robot configurations  C-obstacles: the expanded obstacles  the robot -> a point  k dimensional space  point in configuration space: free, forbidden, semi-free  path -> curve

10. C-obstacles Q - a polygonal object that moves by translation P - a set of polygonal obstacles reference point

11. Minkow s ki sums and translational C-obstacles  A  B= {a+b | a  A, b  B}  Let -A denote A with the ref point at the origin and rotated by 180 deg around the origin  The robot A(q) intersects the obstacle B iff q  B  -A  Minkowski sums of convex polygons: complexity and construction

12. More complex systems  Already in the plane, if we allow rotation as well, the problem has 3 dofs  Bodies translating and rotating in 3-space  Industrial manipulators (typically have 4,5, or 6 dofs)  New designs, multi-robot systems, and other moving artifacts have many more dofs

13. Types of solutions  Exact  Heuristic  Hybrid  A major component in practical solutions: collision detection

14. Cluterred environments

15. Oskar http://www.cs.tau.ac.il/~efif/applications/puzzles/oskar/oskar.php

16. Algorithmic robotics, automation assembly planning  Movable separability  Assembly planning with two hands  Motion space [Snoeyink-Stolfi 93]

17. Robots, take II

18. Beyond the basic mop problem  Moving obstacles  Multiple robots  Movable objects  Uncertainty  Nonholonomic constraints  Dynamic constraints  …

19. Optimality, path quality  Length  Clearance  Group motion: tradeoff Kamphuis-Overmas, http://www.cs.uu.nl/centers/give/movie/screenshots_videos.php

20. Kinematics  Link  Joint  Base  Tcp  Kinematic chain  Direct kinematics  Inverse kinematics

21. Robots with many dofs http://www.youtube.com/watch?v=k-VgI4wNyTo

22. Sensorless manipulaion Example: the parallel jaw gripper [Goldberg]

23. Course outline see www.cs.tau.ac.il/~danha/courses/robotics07.html

24. THE END