Motion Algorithms: Motion Algorithms: Planning, Simulating, Analyzing Planning, Simulating, Analyzing Motion of Physical Objects Motion of Physical Objects Jean-Claude Latombe Computer Science Department Stanford University
Mar 21, 2016
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 tankair 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 CompletenessIn 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 ProjectsRobot 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