Motion Algorithms:Motion Algorithms:Planning, Simulating, Analyzing Planning, Simulating, Analyzing

Motion of Physical ObjectsMotion of Physical Objects

Jean-Claude Latombe

Computer Science DepartmentStanford University

About Myself

Born a long time ago in South-East of France

Pernes-les-Fontaines

About MyselfAbout 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-…)

Research InterestsResearch Interests

1980-84: Artificial Intelligence, Computer Vision, Robotics

1987-92: Robot Motion Planning 1993-98: Motion Planning 1998-…: Motion Algorithms

Fundamental QuestionFundamental QuestionAre two given points connected by a path?

How Do You Get There?How Do You Get There?

?

How Do You Get There?How Do You Get There?

Problems:• Geometric complexity• Space dimensionality

Increasing ComplexityIncreasing Complexity

New ProblemsNew ProblemsAssembly planning

Target finding

From Simulation to Real RobotsFrom Simulation to Real Robots

Space RobotsSpace Robots

air bearing

gas tank

air thrusters

obstacles

robot

Modular Reconfigurable Modular Reconfigurable RobotsRobots

Xerox, ParcXerox, Parc

Casal and Yim, 1999

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

Stability constraints

RadiosurgeryRadiosurgery

From Robots to Other Agents: From Robots to Other Agents: Digital ActorsDigital Actors

Simulation of Deformable Simulation of Deformable ObjectsObjects

Study of Molecular MotionStudy of Molecular Motion

Ligand bindingProtein folding

Basic Tool: Configuration SpaceBasic Tool: Configuration Space

Approximate the free space by random sampling

Probabilistic Roadmaps

[Lozano-Perez, 80]

Probabilistic Roadmap (PRM)Probabilistic Roadmap (PRM)

free space

Probabilistic Roadmap (PRM)Probabilistic Roadmap (PRM)

free space

mmbb

mmgg

milestone

local path

First Assumption of PRM First Assumption of PRM PlanningPlanning

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

ProblemProblem

Exact Collision Checking Exact Collision Checking of Path Segmentsof Path Segments

• Idea: Use distance computation in workspace rather than pure collision checking

D = 2Lx|dq1|+L|dq2| 3Lxmax{|dq1|,|dq2|}

d

q1

q2

If D d then no collision

Exact Collision Checker in Exact Collision Checker in ActionAction

Second Assumption of PRM Second Assumption of PRM PlanningPlanning

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

Probabilistic CompletenessProbabilistic 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 IssueNarrow-Passage Issue

Application to BiologyApplication to Biology

vi

vj

Pij

otherwise. ,

1

;0 if ,)/exp(

i

iji

Bij

ij

N

EN

TkE

P

Markov chain + first-step analysis ensemble properties

Current ProjectsCurrent Projects

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

Pakistan Afghanistan Tadjikistan

Cho-Oyu, 8200m, ~27,000ft (Tibet)

Muztagh Ata, 7,600m, 25,000ft (Xinjiang, China)

Third Pillar of Dana(California)

Thailand

Rock-Climbing RobotRock-Climbing Robot

With Tim Bretl and Prof. Steve Rock

Half-Dome, NW Face, Summer of 2010 …

Tim Bretl