A Two Level Fuzzy PRM for Manipulation Planning

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A Two Level Fuzzy PRM for Manipulation Planning

• Lydia E. Kavraki

Presentation Frederic Mazzella
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The problem to solve
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Introduction

• Two level approach to solve the manipulation
  problem
• 1. Build a manipulation graph
• 2. Do the actual motion planning using PRM
  planners
• Uses a new kind of roadmap fuzzy roadmap,
  (extension of Probabilistic RoadMap (PRM))

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Overview

• I. Problem definition
• II. PRM vs. Fuzzy PRM
• III. Algorithm of Fuzzy PRM
• IV. Fuzzy PRM for manipulation
• V. Experimental results

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I. Problem definition
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• Robots manipulating movable objects among static
  obstacles
• Objects only move when grasped (no fly)
• Solution sequence of transfer and transit paths
• Transfer path the object is grasped
• and moved by the robot
• Transit path the object is left
• in a stable position while the robot
• changes its grasp.

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Assumptions

• Finite set of possible grasps
• We do not need to know the inverse kinematics

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II. PRM vs. Fuzzy PRM
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Basis of PRM

• Build a roadmap of nodes in the C-space
• Test close nodes for connection with a local
  planner
• If the local planner succeeds, the edge is
  inserted in the roadmap
• Expansion step add extra nodes in difficult
  regions
• For individual queries
• Insert start and goal configurations in the
  roadmap
• Search and build a path in the roadmap

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Whats new with fuzzy PRM?

• The edges are annotated by a probability
• This probability is an estimate of the chance
  that the edge is feasible
• Initially, the probability of an edge is low
• After it is guaranteed to be collision free,
  probability 1
• Search for a path of high probability
• Edge probability using
• general PRM 0,1
• fuzzy PRM 0,1

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Features of fuzzy PRM

• Drastically reduces the number of collision
  checks
• Solves basic point-to-point path planning
• Can handle robots with many dof
• Not complete, just as PRM

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III. Algorithm of fuzzy PRM
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• Two phases
• learning phase
• Construction and expansion steps
• Query phase
• Update, search and upgrade steps

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LEARNING PHASE Construction step

• Inserts some randomly chosen collision free robot
  configurations as nodes into the fuzzy roadmap
• Connects each of the nodes to its closest
  neighbors with edges (no collision check)
• Assign a probability p(e) to each edge
• check_dist final resolution
• d(e) euclidean distance

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LEARNING PHASE Expansion step

• Explores the neighborhood of the nodes with a
  small degree ( difficult regions)

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QUERY PHASE Update step

• Add start and goal nodes
• Connect them to the roadmap

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QUERY PHASE Search step

• Find the most probable path, i.e. the path that
  maximizes p(t)
• p(ei) probability of edge ei
• Method minimize log(p(t)) with Dijkstras
  algorithm.

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QUERY PHASE Upgrade step

• Handles the actual verification of the path
• Check for collision on the straight line (in the
  C-space) between two nodes

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IV. Fuzzy PRM for Manipulation
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• Two level approach
• 1. Build a fuzzy roadmap (analog of manipulation
  graph)
• 2. Solve the multiple point-to-point path
  planning problems incurred by the fuzzy roadmap,
  using fuzzy PRM

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The fuzzy roadmap
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• Each node of the manipulation graph represents a
  landmark containing
• The object orientation
• The grasp relations
• The robot configurations
• Edges are transit or transfer actions

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Fuzzy roadmap vs manipulation graph

• Fuzzy roadmap (0,1)
• Fully connected
• Assign actual P(e) during the query phase (never
  assign 0)
• For this application
• Manipulation graph (0,1)
• When queried, will contain only edges that we
  know are feasible
• But difficult edges may be wrongfully deleted
  (P(e) 0) because we use a probabilistic planner
  at the 2nd level, thus we have to decide on some
  maximal search time

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Completeness issues

• With a normal manipulation graph, using a
  probabilistic planner, we could assign a
• probability 0 when the query is difficult,
• and thus never find a solution
• Using a fuzzy roadmap, no edge will be assigned a
  probability 0, and if there were sufficient nodes
  in the learning phase and if one path is actually
  feasible, this method will find it

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V. Experimental results
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• 7 stable placements of the object, 14 landmarks
  in the fuzzy roadmap
• On a 400MHz Pentium II running Windows NT
• 163 seconds,12MB of RAM

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Conclusions

• An algorithm for manipulation planning was
  successfully implemented
• for a single robot arm
• manipulating a single movable object
• with a finite set of stable placements
• This was done by extending the PRM framework
  using a fuzzy roadmap (edge probability annotated
  roadmap)