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

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

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 ( )  CEO, ITMI ( )  Stanford (1987-…)

Research Interests  : Artificial Intelligence, Computer Vision, Robotics  : Robot Motion Planning  : Motion Planning  1998-…: Motion Algorithms

Fundamental Question Are two given points connected by a path?

How Do You Get There? ?

Problems: Geometric complexity Space dimensionality

Increasing Complexity

New Problems Assembly planning Target finding

Target Finding

From Simulation to Real Robots

Space Robots air bearing gas tank air thrusters obstacles robot

Modular Reconfigurable Robots Xerox, Parc Casal and Yim, 1999

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

Radiosurgery

From Robots to Other Agents: Digital Actors

Simulation of Deformable Objects

Study of Molecular Motion Ligand binding Protein folding

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

Probabilistic Roadmap (PRM) free space

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

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

Problem

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

Exact Collision Checker in Action

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

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).

Narrow-Passage Issue

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

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)

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

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

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