Randomized motion planning
Sponsored Links
This presentation is the property of its rightful owner.
1 / 55

Randomized Motion Planning PowerPoint PPT Presentation


  • 64 Views
  • Uploaded on
  • Presentation posted in: General

Randomized Motion Planning. Jean-Claude Latombe Computer Science Department Stanford University. Goal of Motion Planning. Answer queries about connectivity of a space Classical example: find a collision-free path in robot configuration space among static obstacles

Download Presentation

Randomized Motion Planning

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Randomized Motion Planning

Jean-Claude Latombe

Computer Science DepartmentStanford University


Goal of Motion Planning

  • Answer queries about connectivity of a space

  • Classical example: find a collision-free path in robot configuration space among static obstacles

  • Examples of additional constraints:

    • Kinodynamic constraints

    • Visibility constraints


Outline

  • Bits of history

  • Approaches

  • Probabilistic Roadmaps

  • Applications

  • Conclusion


Early Work

Shakey (Nilsson, 1969): Visibility graph


C = S1 x S1

Mathematical Foundations

Lozano-Perez, 1980: Configuration Space


Computational Analysis

Reif, 1979: Hardness (lower-bound results)


Exact General-Purpose Path Planners

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

- Canny, 1987: Silhouette method


Heuristic Planners

Khatib, 1986:

Potential Fields


Other Types of Constraints

E.g., Visibility-Based Motion Planning

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


Outline

  • Bits of history

  • Approaches

  • Probabilistic Roadmaps

  • Applications

  • Conclusion


Criticality-Based Motion Planning

  • Principle:

    • Select a property P over the space of interest

    • Compute an arrangement of cells such that P stays constant over each cell

    • Build a search graph based on this arrangement

  • Example: Wilson’s Non-Directional Blocking Graphs for assembly planning

  • Other examples:

    • Schwartz-Sharir’s cell decomposition

    • Canny’s roadmap


Criticality-Based Motion Planning

  • Advantages:

    • Completeness

    • Insight

  • Drawbacks:

    • Computational complexity

    • Difficult to implement


Sampling-Based Motion Planning

  • Principle:

    • Sample the space of interest

    • Connect sampled points by simple paths

    • Search the resulting graph

  • Example:Probabilistic Roadmaps (PRM’s)

  • Other example:Grid-based methods (deterministic sampling)


Sampling-Based Motion Planning

  • Advantages:

    • Easy to implement

    • Fast, scalable to many degrees of freedom and complex constraints

  • Drawbacks:

    • Probabilistic completeness

    • Limited insight


Outline

  • Bits of history

  • Approaches

  • Probabilistic Roadmaps

  • Applications

  • Conclusion


Motivation

Computing an explicit representation of the admissible

space is hard, but checking that a point lies in the

admissible space is fast


milestone

mg

mb

Probabilistic Roadmap (PRM)

admissible space

[Kavraki, Svetska, Latombe,Overmars, 95]


Sampling Strategies

  • Multi vs. single query strategies

  • Multi-stage strategies

  • Obstacle-sensitive strategies

  • Lazy collision checking

  • Probabilistic biases (e.g., potential fields)


endgame region

m’ = f(m,u)

mg

mb

PRM With Dynamic Constraints in State x Time Space

[Hsu, Kindel, Latombe, and Rock, 2000]


Relation to Art-Gallery Problems

[Kavraki, Latombe, Motwani, Raghavan, 95]


Narrow Passage Issue


Desirable Properties of a PRM

  • Coverage:The milestones should see most of the admissible space to guarantee that the initial and goal configurations can be easily connected to the roadmap

  • Connectivity:There should be a 1-to-1 map between the components of the admissible space and those of the roadmap


Complexity Measures

  • e-goodness[Kavraki, Latombe, Motwani, and Raghavan, 1995]

  • Path clearance[Kavraki, Koulountzakis, and Latombe, 1996]

  • e-complexity[Overmars and Svetska, 1998]

  • Expansiveness[Hsu, Latombe, and Motwani, 1997]


Expansiveness of Admissible Space


Lookout of F1

Prob[failure] = K exp(-r)

Expansiveness of Admissible Space

The admissible space is

expansive if each of its subsets has a large lookout


Expansive

Poorly expansive

Two Very Different Cases


A Few Remarks

  • Big computational saving is achieved at the cost of slightly reduced completeness

  • Computational complexity is a function of the shape of the admissible space, not the size needed to describe it

  • Randomization is not really needed; it is a convenient incremental scheme


Outline

  • Bits of history

  • Approaches

  • Probabilistic Roadmaps

  • Applications

  • Conclusion


Design for Manufacturing and Servicing

General Motors

General Motors

General Electric

[Hsu, 2000]


Robot Programming and Placement

[Hsu, 2000]


Graphic Animation of Digital Actors

The MotionFactory

[Koga, Kondo, Kuffner, and Latombe, 1994]


Digital Actors With Visual Sensing

Simulated Vision

Kuffner, 1999

  • Segment environment

  • Render false-color scene offscreen

  • Scan pixels & record IDs

Actor camera image

Vision module image


Humanoid Robot

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


Space Robotics

robot

obstacles

air thrusters

gaz tank

air bearing

[Kindel, Hsu, Latombe, and Rock, 2000]


Total duration : 40 sec


Autonomous Helicopter

[Feron, 2000] (AA Dept., MIT)


y2

q2

(Grasp Lab - U. Penn)

d

q1

y1

x2

x1

Interacting Nonholonomic Robots


Map Building

[Gonzalez, 2000]


Next-Best View Computation


Map Building

[Gonzalez, 2000]


Map Building

[Gonzalez, 2000]


Radiosurgical Planning

Cyberknife System (Accuray, Inc.) CARABEAMER Planner [Tombropoulos, Adler, and Latombe, 1997]


  • •2000 < Tumor < 2200

    • 2000 < B2 + B4 < 2200

    • 2000 < B4 < 2200

    • 2000 < B3 + B4 < 2200

    • 2000 < B3 < 2200

    • 2000 < B1 + B3 + B4 < 2200

    • 2000 < B1 + B4 < 2200

    • 2000 < B1 + B2 + B4 < 2200

    • 2000 < B1 < 2200

    • 2000 < B1 + B2 < 2200

T

T

B1

C

B2

B4

  • •0 < Critical < 500

    • 0 < B2 < 500

B3

Radiosurgical Planning


Sample Case

50% Isodose Surface

80% Isodose Surface

Conventional system’s plan

CARABEAMER’s plan


Reconfiguration Planning for Modular Robots

Casal and Yim, 1999

Xerox, Parc


Prediction of Molecular Motions

Protein folding

Ligand-protein binding

[Apaydin, 2000]

[Singh, Latombe, and Brutlag, 1999]


Capturing Energy Landscape

[Apaydin, 2000]


Outline

  • Bits of history

  • Approaches

  • Probabilistic Roadmaps

  • Applications

  • Conclusion


Conclusion

  • PRM planners have successfully solved many diverse complex motion problems with different constraints (obstacles, kinematics, dynamics, stability, visibility, energetic)

  • They are easy to implement

  • Fast convergence has been formally proven in expansive spaces. As computers get more powerful, PRM planners should allow us to solve considerably more difficult problems

  • Recent implementations solve difficult problems with many degrees of freedom at quasi-interactive rate


Issues

  • Relatively large standard deviation of planning time

  • No rigorous termination criterion when no solution is found

  • New challenging applications…


Planning Minimally Invasive SurgeryProcedures Amidst Soft-Tissue Structures


Planning Nice-Looking Motions for Digital Actors

Toy Story (Pixar/Disney)

Antz (Dreamworks)

A Bug’s Life (Pixar/Disney)

Tomb Raider 3 (Eidos Interactive)

The Legend of Zelda (Nintendo)

Final Fantasy VIII (SquareOne)


Dealing with 1,000s of Degrees of Freedom

Protein folding


Main Common Difficulty

Formulating motion constraints


  • Login