1. Robotics Reprise on levels of language Movement in a crowded workspace Review for midterm Lab: Complete pick up, travel, deposit exercise. Homework: study for midterm. Post proposal for library research project.

3. Movement Move to position P. Note: position P may involve –2D (planar) position, –2D+orientation, –2D+orientation+positioning/setting of gripper or other tooling –3D (space) position, –3D position + orientation (3 dimensions) –3D position + orientation + positioning of tooling + (maybe) state of tooling (on or off)

4. How do we get there? Called: movement in crowded workspace Two approaches: –Assuming the workspace is known, calculate path (trajectory) ahead of time advantages: more efficient during operations Disadvantages: difficult calculation. Objects may have moved—that is, workspace may not be known. –Move incrementally, using sensors, may involve backtracking

5. AI terms Brute force –Try everything Heuristics –Use some special method, may not get the best answer Closed form, algorithmic solution –Guaranteed best approach

6. Backtracking Brute force (but efficient brute force) Enumerate (all at once or incrementally) solutions to problem and try them out –Implicit or explicit tree representing solutions If there is a failure, mark solution as bad and go back to last known branching point. Applications other than robotic movement: –Sudoku (see Flash examples on my site) –Position 8 queens on chess board so no 2 are on same horizontal, vertical or diagonal line –Stage in compilation that examines if sentence satisfies a rule in a grammar

7. Geometry Polygon is closed planar figure with straight lines as sides Polygon is set of vertices and edges, each vertex connected to exactly 2 edges and the line segment defining each edge intersects with exactly two other edges Convex polygon is such that for any two points inside the polygon, the edge/line segment connecting those points also is in the polygon A concave polygon is one that is not convex

8. Class exercise Draw a polygon Draw a figure with straight edges that is not a polygon Draw a convex polygon Draw a concave polygon.

9. Polyhedron Vertices, edges, faces, indication of presence of material (typically done using normals: outward pointing vectors) Flat sides Nominally curved surfaces (spheres, conic sections) approximated using facets

10. Back to robots Moving through a crowded workspace also called: the piano mover’s problem, wayfinding, moving in a crowded workspace, motion planning. Many approaches involve ‘growing’ the obstacles and shrinking the piano/robot and doing this in multiple dimensions. –Growing may be in high[er] dimension space. Many approaches involve general AI techniques, including backtracking and A* Possible research paper topic! Possible posting topic

11. Sources A* article http://www.policyalmanac.org/games/aStarTutori al.htm http://www.policyalmanac.org/games/aStarTutori al.htm Obstacle avoidance article http://www.aboutjens.com/dump/Reading/AI/Nav igation/Automated_Static_and_Dynamic_Obstac le_Avoidance_in_Arbitrary_3D_Polygonal_Worl ds1.pdf http://www.aboutjens.com/dump/Reading/AI/Nav igation/Automated_Static_and_Dynamic_Obstac le_Avoidance_in_Arbitrary_3D_Polygonal_Worl ds1.pdf Program http://code.google.com/p/straightedge/http://code.google.com/p/straightedge/ Animations http://gamma.cs.unc.edu/videos/robotics/ http://gamma.cs.unc.edu/videos/robotics/

12. Midterm review ?

13. Library research project Proposal due March 22 REQUIRED –Please make constructive comments on each other’s proposals. Paper and presentation due April 9 –1 page: summary (abstract), 1 illustration, standard bibliography, proof-read! –Formal presentation: PowerPoint and/or other visuals Try prezi.com

14. [Way to get to] Topics Postings (and/or my suggestions for postings) Something you want to explore and work on in the future

15. Lab Complete pickup, travel, deposit, move away exercise. –use sensor or absolute value for pickup location –deposit in known absolute or relative location understand which! Start planning for parallel parking –tribot plus side mounted ultrasonic, optionally bumper –travel along parking lane determining where there is a spot. –back up / swivel. May use recorded path moves.

16. Homework Study for midterm: see on-line guide, review lecture charts, postings, suggested questions by students. Prepare proposal for library research project