compression d'images

Document Sample
compression d'images Powered By Docstoc
					FADPRM : Une Nouvelle approche de
  Planification de Trajectoire pour
       Robots Bras Articulés

                  Khaled Belghith
  Étudiant au Doctorat - Université de Sherbrooke

                    4 Octobre 2006

 Introduction to Path Planning
   Motivation
   Detailed description
                                  CANADARM II
   Experimental results
 FADPRM within Roman Tutor
 Conclusion
                 Path Planning 1/2

Source : J-C Latombe’s Website -
                 Path Planning 2/2

   Goal :
       Compute a collision-free path for a rigid or articulated object
        (typically a robot) among obstacles

   Input :
       Geometry of robot and obstacles
       Kinematics of robot (degrees of freedom)
       Initial and goal configurations

   Output :
       Continuous sequence of collision-free robot configurations
        connecting initial and goal configurations
              Path Planning - Complexity

       Problem Complexity depends on :
           Space dimension (2D/3D, number of degrees of freedom)
           Density and geometry of obstacles (collision detection),
            environment characteristics (dynamic,…)
           Constraints on robot manipulation (singularities,…)


        J-C Latombe’s Website -
     Path Planning - Methodology
 General Methodology :

               Continuous representation
           (Configuration space + constraints, …)

      (Random sampling, grid-based decomposition, …)

                  Search in a Graph
                 (blind, best first, A*,…)
        Path Planning - Applications
 Applications :                                             *


 * J-C Latombe’s Website -

            FADPRM : Motivation
 Hard constraints : obstacle avoidance
 Soft constraints : zones with degrees of
     Danger areas that must be avoided as much as

     Desirable areas the robot
   should stay in as much as possible

 Large configuration spaces,
dynamic environments
Robot manipulations on the ISS
                         Robot arm operated
                          via three monitors
                         No direct view of
                          the station’s
                         Each monitor
                          mapped to a camera
                         14 cameras in all
                         FADPRM computes
                          a path along safe
                             No collision with
                              ISS structure
                             Best camera
                             Other constraints
        FADPRM : A PRM Approach

   FADPRM : Flexible Anytime Dynamic Probabilistic
    Roadmap Method

   PRM approaches suitable for large configuration

   PRM Approach :
       Sampling the configuration space probabilistically
       The graph constructed is a simplified representation of the
        free configuration space
       Using a local planner (very fast) to check that an edge
        between two nodes is collision free
          FADPRM : A PRM Approach

     • Efficiency-driven
     • Robots with many dofs (high-dim C-
     • Static environments

   Selection of a node to expand according to a sampling measure
   Expansion from n : sampling a new node within the neighbourhood of n
   Efficiency of PRM approaches depends on the sampling measure
   A good measure should take into account visibility properties (for ex :
    sampling measure conversely proportional to density of nodes)
          FADPRM : A PRM Approach

     FADPRM : a single query lazy collision PRM approach
          Expansion done starting from
      initial and goal configurations            *
         Collision detection delayed
      until a candidate path is found

     FADPRM : a flexible approach
         Free workspace segmented into zones, each assigned a degree of
          desirability dd (in [0 1])
         Each Configuration q in the graph assigned a
                   q.dd = average of dd of overlapping zones
         Path-dd = average of q.dd configurations in the path (optimal path =
          with highest dd)

    * J-C Latombe’s Website -
        FADPRM - Sampling Measure

   Implements a balance between :
       A random sampling as in a normal PRM
       An anytime dynamic A* (AD*) exploration of the roadmap (the

   AD* a generalization of the familiar A* Algorithm to deal
    with dynamically changing environments

   AD* has also the anytime capability :

       Provides a solution path quickly and incrementally improves it if
        more time is available

The Algorithm
        FADPRM - The Algorithm 1/5

   Search is done backward from the goal towards the initial
    configuration (current configuration)
       Because the robot is moving towards the goal

   OPEN : probabilistic priority queue contains :
       Nodes on the frontier of current roadmap
       Nodes that have to be expanded

   CLOSED : list containing non frontier and already
    expanded nodes

   Search consists on picking nodes from OPEN and
    generating their predecessors
         FADPRM - The Algorithm 2/5
   A node n in OPEN has a key priority proportional to:

        (1 − β) / density (n) + β ∗ f (n),
                    β is the inflation factor with 0 ≤ β ≤ 1
        density (n) proportional to density of nodes around n

        f (n) estimate to the goal : takes into account node’s dd and the
         Euclidean distance

   Nodes in OPEN are selected for expansion in decreasing

   A predecessor of n is randomly generated within a short
    neighbourhood radius from n
    FADPRM - How it works


      FADPRM - The Algorithm 3/5
     (1 − β) / density (n) + β ∗ f (n),
                 β is the inflation factor with 0 ≤ β ≤ 1
   With β = 0, FADPRM behaves like a normal PRM

   With β = 1, selection of a node is a best-first strategy like
    in A*
       Balance between fast-solution search and best-solution

       An initial path is generated with β = 0, β is then
       increased by a small quantity and a new path is
       computed again, and so on…
      FADPRM - The Algorithm 4/5

     (1 − β) / density (n) + β ∗ f (n),
                 β is the inflation factor with 0 ≤ β ≤ 1
   β near 1 gives better solutions but take more time
   We have a higher probability of getting a better path at
    each iteration
       This is the anytime capability of FADPRM
   The robot may start executing the first path found and
    concurrently, the path continues being improved

   Changes in the environment cause update of the roadmap
    and re-planning
    FADPRM - Replanning


        FADPRM - The Algorithm 5/5
   The heuristic estimate f (n):
                        f(n) = [g(n) + h(n)] / 2
    With : g (n) = pathdd (ngoal, n) / (1 + γ. pathCost (ngoal, n))
           h (n) = pathdd (n, nstart) / (1 + γ. pathCost (n, nstart))
           0 ≤ γ ≤ 1.
       The quality of a path is a combination of its dd and its cost in
        terms of distance (the Euclidian distance for example)

   γ determines the influence of the dd on f (n)

   With γ = 1 and all dds = 1s, nodes with least cost to goal
    privileged (if Euclidean distance, admissible heuristic and
    optimal solution guaranteed)
FADPRM - Detailed Algorithm

Experimental Results
           FADPRM - Implementation

                                 MPK                FADPRM

    (Proximity Query Package)

MPK : Motion Planning Kit (J-C. Latombe et al, Stanford University)
COIN 3D: C++ Library for 3D graphics software development
PQP: Proximity Query Package (Larsen et al)
     FADPRM - Canadarm II on ISS
γ = 0.7, dd neutral = 0.5
FADPRM - Puma Robot
FADPRM within Roman Tutor
Roman Tutor
              The learner interface
              with three monitors :
              • Each monitor is
              mapped to a camera
              (selected among 14
              • Each camera can
              be rotated and
              zoomed in/out
              • Canadarm is
              manipulated in two
              modes : FOR mode
              or Joint by Joint
              • On the bottom we
              have a trace window
FADPRM within Roman Tutor
                                  Go To Task

                                                                    Goal Config.

     Start Config.

•   Corridors
     – for sequences of displacements
     – To recognize and qualify a path
•   Elementary spaces: visibility through cameras
•   Corridors are assigned a degree of desirability. Function of:
     – Visibility through cameras (stored into Elementary spaces)
     – Relevency of the corridor/zone in the current task.
   Continuous Tutoring Assistance

 FADPRM Path planner : the central
  component of the tutor
 The tutor uses the anytime capability of
  FADPRM to :
   Validate incrementally student’s actions
   Give information about next relevant action or
    sequence of actions
   Generate relevant task demonstration
    resources using the movie generator
Goto Task

            • In Goto tasks
              the learner is
              asked to move
              the robot from
              configuration to

            • Here the
              learner is
              provided with
              an animation
              illustrating the
              requested task
Ask - How to Go To ?
                       •   At any time
                           during a task
                           the learner can
                           ask for help
                           about how to
                           achieve his task

                       •   FADPRM path-
                           planner is
                           invoked to
                           calculate a path
                           from the current
                           configuration to
                           a given goal

                       •   The path can be
                           animated for a
                           illustration of
                           the task
FADPRM: Anytime Dynamic Path-Planner

                               • FADPRM takes
                                 into account the
                                 field of view of
                                 cameras on the

                               • Here we illustrate a
                                 path calculated by
                                 FADPRM taking
                                 into account the
                                 disposition of
                                 cameras on
                                 monitor 2 &
                                 monitor 3.

 We Just explained improvement to PRM path
  planning along three dimensions:
     Modeling zones with degrees of desirability
     Re-computing paths in dynamic environments
     Anytime planning capability for real-time application

 We showed that there is no need to plan in
  advance what feedback to give to the learner or to
  explicitly create a complex task graph to support
  the tutoring process

 K. Belghith, F. Kabanza, L. Hartman and R. Nkambou. “Anytime Dynamic Path-Planning
with Flexible Probabilistic Roadmaps”. In Proc. of IEEE International Conference on Robotics
and Automation (ICRA), 2006.
 R. Nkambou, K. Belghith and F. Kabanza. “An Approach to Intelligent Training on a
Robotic Simulator using an Innovative Path-Planner”. Proc. of the 8th International
Conference on Intelligent Tutoring Systems (ITS), 2006.
 Nkambou R, Belghith K., and Kabanza F. “Generating Tutoring Feedback in an Intelligent
Training System on a Robotic Simulator”. Proc of 19th International Conference on Industrial
Engineering & Other Applications of Applied Intelligent Systems (IEA/AIE), 2006.
 F. Kabanza, R. Nkambou and K. Belghith. “Path-Planning for Autonomous Training on
Robot Manipulators in Space”. Proc. of International Joint Conference on Artificial
Intelligence (IJCAI), 2005.
 K. Belghith, F. Kabanza, R. Nkambou, M. Khan, and L. Hartman. “Roman Tutor: A Robot
Manipulation Tutoring Simulator”. System demonstration. 15th International Conference on
Automated Planning and Scheduling (ICAPS), 2005.
Questions ???

Shared By: