Agenda Motivation Introduction Introduction (contd.) Previous Work

Agenda Motivation Introduction Introduction (contd.) Previous Work www.phwiki.com

Agenda Motivation Introduction Introduction (contd.) Previous Work

Martin, James, Contributing Editor has reference to this Academic Journal, PHwiki organized this Journal Probabilistic Roadmaps as long as Path Planning in High-Dimensional Configuration Spaces Authors: Lydia E. Kavraki, Petr Svestka, Jean-Claude Latombe, in addition to Mark H. Overmars Presented By: Aninoy Mahapatra Agenda Motivation Introduction Previous Work The Method Experiments Results References Motivation Applications: Car assembly lines Nuclear plant cooling pipes Cleaning airplane fuselages Complex workspaces Tedious programming Efficient, reliable planner required to reduce burden

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Introduction Motion planning in static workspaces Holonomic robots, with many degrees of freedom Static obstacles, avoid collision Problem definition: “Compute a collision-free path as long as a holonomic object (virtually any type of robot, with many degrees of freedom) among static obstacles” Introduction (contd.) Inputs: Geometry of robot in addition to obstacles Kinematics of robot (degrees of freedom) Initial in addition to goal robot configurations (placements) Outputs: Continuous sequence of collision-free robot configurations connecting the initial in addition to goal configurations Robotic Arm Video Source: http://ai.stan as long as d.edu/~latombe/projects/motion-planning.ppt Previous Work Potential Fields: http://www.youtube.com/watchv=r9FD7P76zJs Potential field / cell decomposition based methods RPP (fails as long as several examples, falling into local minima bounded by obstacles) variational dynamic programming Use of genetic algorithms Roadmap based methods Visibility graph (low dimension C-spaces) Voronoi diagram (low dimension C-spaces) Silhouette method (any dimension but complex, hence impractical)

The Method Learning Phase Construction: reasonably connected graph covering C-space Expansion: improve connectivity Local paths not memorized (cheap to re-compute) The Method (contd.) Construction step algorithm: Source: Probabilistic roadmaps as long as path planning in high-dimensional configuration spaces.pdf The Method (contd.) Query Phase Connect start in addition to goal configurations to roadmap (say, in addition to ) Find path between in addition to in roadmap in addition to should be in same connected component, else failure If too many failures, increase learning time

Principle of Probabilistic Roadmaps free space Source: [Kavraki, Svestka, Latombe, Overmars, 95] (http://ai.stan as long as d.edu/~latombe/projects/motion-planning.ppt) Probabilistic Roadmaps (contd.) Source: [Kavraki, Latombe, Motwani, Raghavan, 95] (http://ai.stan as long as d.edu/~latombe/projects/motion-planning.ppt) Properties of PRM Planners Is probabilistically complete, i.e., whenever a solution exists, the probability that it finds one tends toward 1 as the number N of milestones increases Under rather general hypotheses, the rate of convergence is exponential in the number N of milestones, i.e.: Prob[failure] ~ exp(-N) Source: http://ai.stan as long as d.edu/~latombe/projects/motion-planning.ppt

Properties of PRM Planners (contd.) Are fast Deal effectively with many – dof robots Are easy to implement Have solved complex problems Experiments Customized planner used Parameters adjusted TC , time as long as construction step TE , time as long as expansion step maxdist, distance between nodes e ps, constant as long as discretization of local paths maxneighbours, no. of calls to local planner TRB-EXPAND , duration as long as each r in addition to om bounce walk NRB-QUERY , max no. of r in addition to om bounce walks TRB-QUERY , duration as long as each r in addition to om bounce walk Experiments (contd.) Experimental Planar Articulated Robot Experimental Setup 1: For 7-revolute-joint fixed base robot Source: Probabilistic roadmaps as long as path planning in high-dimensional configuration spaces.pdf

Experiments (contd.) Experimental Setup 2: For 5-revolute-joint free base robot (7 dof) Source: Probabilistic roadmaps as long as path planning in high-dimensional configuration spaces.pdf Results For experimental setup 1 (with expansion) For experimental setup 1 (without expansion) Source: Probabilistic roadmaps as long as path planning in high-dimensional configuration spaces.pdf Results (contd.) For experimental setup 2 (with expansion) For experimental setup 2 (without expansion) Source: Probabilistic roadmaps as long as path planning in high-dimensional configuration spaces.pdf

References http://ai.stan as long as d.edu/~latombe/projects/motion-planning.ppt http://ai.stan as long as d.edu/~latombe/projects/grenoble2000.ppt http://ai.stan as long as d.edu/~latombe/projects/wafr06.ppt http://ai.stan as long as d.edu/~latombe/projects/prm-strategies.ppt http://www.cs.cmu.edu/~biorobotics/papers/sbp-papers/b/barraqu in addition to -langlois-latombe-potential.pdf http://ai.stan as long as d.edu/~mitul/mpk/index.html

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