1. Motion Algorithms: Planning, Simulating, Analyzing Motion of Physical Objects Jean-Claude Latombe Computer Science Department Stanford University

2. About Myself  Born a long time ago in South-East of France Pernes-les-Fontaines

3. About Myself  Born a long time ago in South-East of France  Studied in Grenoble (Eng. EE, MS EE, PhD CS 1977 )  CS Professor, Grenoble (1980-84)  CEO, ITMI (1984-87)  Stanford (1987-…)

4. Research Interests  1980-84: Artificial Intelligence, Computer Vision, Robotics  1987-92: Robot Motion Planning  1993-98: Motion Planning  1998-…: Motion Algorithms

6. Fundamental Question Are two given points connected by a path?

7. How Do You Get There? ?

8. Problems: Geometric complexity Space dimensionality

9. Increasing Complexity

10. New Problems Assembly planning Target finding

11. Target Finding

12. From Simulation to Real Robots

13. Space Robots air bearing gas tank air thrusters obstacles robot

14. Modular Reconfigurable Robots Xerox, Parc Casal and Yim, 1999

16. Humanoid Robot [Kuffner and Inoue, 2000] (U. Tokyo) Stability constraints

17. Radiosurgery

18. From Robots to Other Agents: Digital Actors

19. Simulation of Deformable Objects

20. Study of Molecular Motion Ligand binding Protein folding

21. Basic Tool: Configuration Space Approximate the free space by random sampling  Probabilistic Roadmaps [Lozano-Perez, 80]

22. Probabilistic Roadmap (PRM) free space

23. Probabilistic Roadmap (PRM) free space mbmbmbmb mgmgmgmg milestone local path

24. First Assumption of PRM Planning Collision tests can be done efficiently. [Quinlan, 94; Gottschalk, Lin, Manocha, 96]  Several thousand collision checks per second for 2 objects of 500,000 triangles each on a 1-GHz PC

25. Problem

26. Exact Collision Checking of Path Segments Idea: Use distance computation in workspace rather than pure collision checking D = 2L x |dq 1 |+L|dq 2 |  3L x max{|dq 1 |,|dq 2 |} d q1q1 q2q2 If D  d then no collision

27. Exact Collision Checker in Action

28. Second Assumption of PRM Planning A relatively small number of milestones and local paths are sufficient to capture the connectivity of the free space.

29. Probabilistic Completeness In an expansive space, the probability that a PRM planner fails to find a path when one exists goes to 0 exponentially in the number of milestones (~ running time).

30. Narrow-Passage Issue

31. Application to Biology vivi vjvj P ij Markov chain + first-step analysis  ensemble properties

32. Current Projects Robot motion planning Funding: General Motors, ABB Collaborator: Prinz (ME), Rock (AA) Study of molecular motions (folding, binding) Funding: NSF-ITR (with Duke and UNC), BioX Collaborators: Guibas (CS), Brutlag (Biochemistry), Levitt (Structural Biology), Pande (Chemistry), Lee (Cellular B.) Surgical simulation (deformable tissue, suturing, visual and haptic feedback) Funding: NSF, NIH, BioX Collaborators: Salisbury (CS+Surgery), Girod (Surgery), Krummel (Surgery) Modeling and simulation of deformable objects Funding: NSF-ITR (with UPenn and Rice) Collaborators: Guibas (CS), Fedkiw (CS)

33. PakistanAfghanistan Tadjikistan Cho-Oyu, 8200m, ~27,000ft (Tibet) Muztagh Ata, 7,600m, 25,000ft (Xinjiang, China) Third Pillar of Dana (California) Thailand

34. Rock-Climbing Robot With Tim Bretl and Prof. Steve Rock

35. Half-Dome, NW Face, Summer of 2010 … Tim Bretl