motion planning: a journey of robots, digital actors, surgical instruments, molecules and other...

Motion Planning:Motion Planning:A Journey of Robots, Digital Actors, A Journey of Robots, Digital Actors,

Surgical Instruments, Molecules Surgical Instruments, Molecules and Other Artifactsand Other Artifacts

Jean-Claude LatombeJean-Claude Latombe

Computer Science DepartmentComputer Science DepartmentStanford UniversityStanford University

Goal of Motion PlanningGoal of Motion Planning

Compute Compute motion strategiesmotion strategies, e.g.:, e.g.:

– geometric paths geometric paths

– time-parameterized trajectoriestime-parameterized trajectories

– sequence of sensor-based motion commandssequence of sensor-based motion commands

To achieve To achieve high-level goals, high-level goals, e.g.:e.g.:

– go from A to B without colliding with obstaclesgo from A to B without colliding with obstacles

– assemble product Passemble product P

– build map of environment Ebuild map of environment E

– find object Ofind object O

Basic ProblemBasic Problem

Extensions to the Basic ProblemExtensions to the Basic Problem Moving obstaclesMoving obstacles

Multiple robotsMultiple robots

Movable objectsMovable objects

Assembly planningAssembly planning

Goal is to acquire Goal is to acquire information by sensinginformation by sensing

– Model buildingModel building

– Object finding/trackingObject finding/tracking Nonholonomic constraintsNonholonomic constraints

Dynamic constraintsDynamic constraints

Optimal planningOptimal planning

Uncertainty in control and Uncertainty in control and sensingsensing

Exploiting task mechanics Exploiting task mechanics (sensorless motions)(sensorless motions)

Physical models and Physical models and deformable objectsdeformable objects

Integration of planning Integration of planning and controland control

OutlineOutline Some historical steps and achievementsSome historical steps and achievements

ApplicationsApplications

Computational approaches:Computational approaches:

– Criticality-based motion planningCriticality-based motion planning

– Random-sampling motion planningRandom-sampling motion planning Some challenging problems aheadSome challenging problems ahead

Early WorkEarly Work

Shakey (Nilsson, 1969): Visibility graphShakey (Nilsson, 1969): Visibility graph

Mathematical FoundationsMathematical Foundations

C = S1 x S1

Lozano-Perez, 1980: Configuration SpaceLozano-Perez, 1980: Configuration Space

Computational AnalysisComputational Analysis

Reif, 1979: Hardness (lower-bound results) Reif, 1979: Hardness (lower-bound results)

Exact General-Purpose Path PlannersExact General-Purpose Path Planners

- Schwarz and Sharir, 1983: - Schwarz and Sharir, 1983: Exact cell Exact cell decomposition based on Collins techniquedecomposition based on Collins technique

- Canny, 1987: - Canny, 1987: Silhouette methodSilhouette method

Heuristic PlannersHeuristic Planners

Goal

Robot

)( GoalpGoal xxkF

0

020

0

,111

if

ifxFObstacle

Khatib, 1986:Khatib, 1986:

Potential FieldsPotential Fields

Nonholonomic RobotsNonholonomic Robots

Laumond, 1986Laumond, 1986

Underactuated RobotsUnderactuated Robots

Lynch, Shiroma, Arai, Lynch, Shiroma, Arai, and Tanie, 1998and Tanie, 1998

Part OrientationPart Orientation

Godlberg, 1993Godlberg, 1993

Assembly Sequence PlanningAssembly Sequence Planning

Wilson, 1994: Wilson, 1994: Non-Directional Blocking GraphsNon-Directional Blocking Graphs

Manipulation PlanningManipulation Planning

Tsai-Yen Li, 1994Tsai-Yen Li, 1994

Deformable ObjectsDeformable Objects

Kavraki, Lamiraux, and Holleman 1998Kavraki, Lamiraux, and Holleman 1998

Target FindingTarget Finding

Guibas, Latombe, LaValle, Guibas, Latombe, LaValle, Lin, and Motwani, 1997Lin, and Motwani, 1997

Integration of Planning and ControlIntegration of Planning and Control

Brock and Khatib, 1999Brock and Khatib, 1999

Robot Programming and PlacementRobot Programming and Placement

David Hsu, 1999David Hsu, 1999

Design for Manufacturing and ServicingDesign for Manufacturing and Servicing

General ElectricGeneral Electric General MotorsGeneral Motors

General MotorsGeneral Motors

Design of Large FacilitiesDesign of Large Facilities

EDF and LAAS-CNRS (MOLOG project), 1999

Verification of Building CodeVerification of Building Code

Charles Han, 1998Charles Han, 1998

Graphic Animation of Digital ActorsGraphic Animation of Digital Actors

Koga, Kondo, Kuffner, and Latombe, 1994Koga, Kondo, Kuffner, and Latombe, 1994

The MotionThe MotionFactoryFactory

PlanSense

Act

Digital Actor = Virtual Robot!


Kuffner, 1999Kuffner, 1999

Vision module imageActor camera image


Segment environmentSegment environment Render false-color scene offscreen Render false-color scene offscreen Scan pixels & record IDsScan pixels & record IDs

Simulated VisionSimulated Vision

Surgical PlanningSurgical Planning

Cyberknife System (Accuray, Inc.) Cyberknife System (Accuray, Inc.) CARABEAMER Planner CARABEAMER Planner

Tombropoulos, 1997 Tombropoulos, 1997

Prediction of Molecular MotionsPrediction of Molecular Motions

Amit Singh, 1999Amit Singh, 1999

Approaches to Motion PlanningApproaches to Motion Planning

Goal: Goal: Answer queries about the connectivity of a Answer queries about the connectivity of a certain space (e.g., the collision-free subset of certain space (e.g., the collision-free subset of configuration space)configuration space)


Old view (Latombe, 1991):Old view (Latombe, 1991):

– RoadmapsRoadmaps

– Cell decompositionCell decomposition

– Potential fieldPotential field


Old view (Latombe, 1991):Old view (Latombe, 1991):

– RoadmapsRoadmaps

– Cell decompositionCell decomposition

– Potential fieldPotential field New View (Latombe, 2000):New View (Latombe, 2000):

– Finding criticalities Finding criticalities

– Random samplingRandom sampling

Criticality-Based Motion PlanningCriticality-Based Motion Planning

Retraction onRetraction onVoronoi DiagramVoronoi Diagram

(O’Dunlaing and Yap, 1982)(O’Dunlaing and Yap, 1982)


Part orientationPart orientation (Goldberg, 1993) (Goldberg, 1993)


Non-Directional Blocking Graphs Non-Directional Blocking Graphs for assembly planning (Wilson, 1994)for assembly planning (Wilson, 1994)

Criticality-Based Motion PlanningCriticality-Based Motion PlanningNon-Directional Preimage for Non-Directional Preimage for landmark-based navigation (Lazanas, 1995)landmark-based navigation (Lazanas, 1995)

Criticality-Based Motion PlanningCriticality-Based Motion PlanningTarget finding (Guibas, Latombe, LaValle, Target finding (Guibas, Latombe, LaValle, Lin, and Motwani, 1997) Lin, and Motwani, 1997)


Example of an information state = (1,1,0)Example of an information state = (1,1,0)

0 : the target does not hide beyond the edge

1 : the target may hide beyond the edge


Recontaminated area


Advantage:Advantage:

– CompletenessCompleteness Drawbacks:Drawbacks:

– Computational complexity Computational complexity

– Difficult to implementDifficult to implement

Random-Sampling PlanningRandom-Sampling Planning

admissible space

qqbb

qqgg

milestone

[Kavraki, Svetska, Latombe,Overmars, 95][Kavraki, Svetska, Latombe,Overmars, 95]

(Probabilistic Roadmap)(Probabilistic Roadmap)

MotivationMotivationComputing an explicit representation of the admissibleComputing an explicit representation of the admissiblespace is hard, but checking that a point lies in the space is hard, but checking that a point lies in the admissible space is fast admissible space is fast

Why Does it Work?Why Does it Work?

[Kavraki, Latombe, Motwani, Raghavan, 95]

Relation with Art-Gallery problemsRelation with Art-Gallery problems

In Theory, Random-Sampling Planning…In Theory, Random-Sampling Planning…

Is Is probabilistically completeprobabilistically complete, i.e., whenever a , i.e., whenever a solution exists, the probability that it finds one solution exists, the probability that it finds one tends toward 1 as the number tends toward 1 as the number NN of milestones of milestones increasesincreases

Under general hypotheses, the rate of convergence Under general hypotheses, the rate of convergence is exponential in is exponential in NN, i.e.:, i.e.:

Prob[failure] = Prob[failure] = KK exp(- exp(-NN)) Computational gain is obtained against a “small” Computational gain is obtained against a “small”

loss of completeness loss of completeness

Expansiveness of Admissible SpaceExpansiveness of Admissible Space

Expansiveness of Admissible SpaceExpansiveness of Admissible Space

Lookout of Lookout of F1F1

The admissible space is expansive if each of its subsets has a large lookout

Prob[failure] = K exp(-N)

In practice, Random-Sampling Planners…In practice, Random-Sampling Planners…

Are fastAre fast Deal effectively with many-dof robots Deal effectively with many-dof robots Deal well with complex admissibility constraintsDeal well with complex admissibility constraints Are easy to implementAre easy to implement Have solved complex problemsHave solved complex problems

Real-Time Planning with Dynamic ConstraintsReal-Time Planning with Dynamic Constraints

air bearingair bearing

gaz tankgaz tank

air thrustersair thrustersobstacles

robotrobot

(Kindel, Hsu, Latombe, and Rock, 2000)(Kindel, Hsu, Latombe, and Rock, 2000)

Total duration : 40 secTotal duration : 40 sec

Interactive Planning of Manipulation MotionsInteractive Planning of Manipulation Motions

ReachReach

GrabGrab

TransferTransfer

ReleaseRelease

ReturnReturn

Kuffner, 1999Kuffner, 1999

Random-Sampling Radiosurgical PlanningRandom-Sampling Radiosurgical Planning

Cyberknife (Neurosurgery Dept., Stanford, Cyberknife (Neurosurgery Dept., Stanford, Accuray) Accuray)

Tombropoulos, 1997Tombropoulos, 1997

CARABEAMER PlannerCARABEAMER Planner


Dose to the Critical Region

Critical

Tumor

Fall-off of Dose Around the Tumor

Dose to theTumor Region

Fall-off of Dosein the Critical Region


• 2000 < Tumor < 22002000 < B2 + B4 < 22002000 < B4 < 22002000 < B3 + B4 < 22002000 < B3 < 22002000 < B1 + B3 + B4 < 22002000 < B1 + B4 < 22002000 < B1 + B2 + B4 < 22002000 < B1 < 22002000 < B1 + B2 < 2200

• 0 < Critical < 5000 < B2 < 500

T

C

B1

B2

B3B4

T

Sample CaseSample Case

50% Isodose Surface

80% Isodose Surface

Conventional system’s plan CARABEAMER’s plan

Randomized Next-Best View PlanningRandomized Next-Best View Planning

(Gonzalez, 2000)(Gonzalez, 2000)

Reconfiguration Planning for Modular RobotsReconfiguration Planning for Modular Robots

Xerox, ParcXerox, Parc

Mark Yim, 1999Mark Yim, 1999

Planning Minimally Invasive SurgeryPlanning Minimally Invasive SurgeryProcedures Amidst Soft Tissue StructuresProcedures Amidst Soft Tissue Structures

Truly Autonomous Interactive Digital Actors Truly Autonomous Interactive Digital Actors with Nice-Looking Motionswith Nice-Looking Motions

A Bug’s Life (Pixar/Disney) Toy Story (Pixar/Disney)

Tomb Raider 3 (Eidos Interactive) Final Fantasy VIII (SquareOne)The Legend of Zelda (Nintendo)

Antz (Dreamworks)

Generating Energetically Plausible Generating Energetically Plausible Docking and Folding Motions of ProteinsDocking and Folding Motions of Proteins

ConclusionConclusion Over the last decade there has been tremendousOver the last decade there has been tremendous

progress in motion planning and its applicationprogress in motion planning and its application Though motion planning originated in robotics, Though motion planning originated in robotics,

applications are now very diverse: design, applications are now very diverse: design, manufacturing, graphic animation, video games, manufacturing, graphic animation, video games, surgery, biology, etc…surgery, biology, etc…

Most future problems in motion planning are Most future problems in motion planning are likely to be motivated by applications that are likely to be motivated by applications that are regarded today as non-robotics applicationsregarded today as non-robotics applications

motion planning: a journey of robots, digital actors, surgical instruments, molecules and other...

Documents

sensing u

outline u

basic problem u

based motion commands

control slide

object o slide

basic problem slide

criticalitybased motion