Randomized%20Motion%20Planning:%20New%20Ideas%20and%20Applications

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Randomized Motion Planning New Ideas and
Applications

• Sam Hasinoff
• CPSC 515
• April 7, 2000

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Introduction
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Configuration Space

• One dimension per DOF
• Examples
• Planar robot 3 DOF
• Rigid body 6 DOF
• PUMA 6 DOF
• Human character 80 DOF
• Curse of dimensionality

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Simple Motion Planning

• Complete geometric description of robot and
  obstacles known a priori
• Only easy kinematic constraints
• Essentially static
• Rigid objects
• P-SPACE Hard Reif, 1979

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Previous Work

• Complete (lt4 DOF)
• Visibility graph, A Nilsson, 1969
• Resolution Complete (4-5 DOF)
• Cell decomposition 1980s
• Probabilistic Complete (6 DOF)
• Potential Field Latombe, 1991
• Roadmap Kavraki et al., 1996

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Roadmap Motion Planner
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Basic RoadmapAlgorithm 1

• PREPROCESSING
• generate r milestones
• pick a configuration q at random from C
• if (CLEARANCE(q) gt 0) store q as a milestone
• for each pair of milestones m1 and m2 with
  distance less than d, do CONNECT(m1,m2)
• invoke RESAMPLE to expand the roadmap by s-r
  milestones

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Basic Roadmap Algorithm 2

• QUERY PROCESSING
• for istart,end
• if some milestone m sees qi then mim
• else try g times to pick q in the neighbourhood
  of qi such that q sees both qi and a milestone m
• return if mstart and mend are in the same
  component

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CLEARANCE(q)Quinlan, 1994

• Sphere trees for distance computation
• Tile surface polygons
• Heuristics build the tree and guide search
• Fast for establishing approx bounds

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CONNECT(m1,m2)Local Planner

• Straight-line segments in C
• Uses CLEARANCE to determine adjacency between two
  configurations
• Recursively breaks line segment between m1 and m2
  until
• Endpoints of the segment are adjacent or
• One the endpoints is not in free space

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RESAMPLEA useful heuristic

• Create additional milestones, biased towards
  special areas
• Low milestone density
• Near low-degree milestones
• Near free space boundary
• Works in general
• Narrow passages still a problem

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State of the Art

• Applied to complicated, many-DOF manufacturing
  problems
• Fast enough for planar robots with moving
  obstacles
• Non-holonomic constraints
• Manipulation problems

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Future Research

• Faster distance calculation (90 time)
• hardware, KDS
• Path quality
• smoothness, realism, optimality
• Coordinating multiple robots
• Deformable objects
• Getting a negative answer

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References

• Latombe, J.C. 1999. Motion planning A journey of
  robots, molecules, digital actors, and other
  artifacts. IJRR 18(11)1119-1128.