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Robot motion planning


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Piano mover’s problem …

Piano mover’s problem
Combinatorial planning
sampling-based planning

Published in: Design
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  • 1.  getting a robot to automatically determine how to move while avoiding collisions with mover’s problem  getting robots to reason geometrically about their environments and synthesize such plans.
  • 2.  For a two-dimensional world,W═R2 and O is the obstacle region.  For a three-dimensional world, the only differences are that W═R3 & O is polyhedra.  Basic path planning: Inputs are given and corresponding outputs are produced.
  • 4.  set of all rigid body transformations that can be applied to the robot is called the configuration space or C-space.  C-space in physics and control theory is usually called a Lie group.  C-space used in motion planning requires no calculus; therefore, it is described as a topological manifold.
  • 5.  2-D world: A<R2 denotes polygonal robot. • Position of robot q=(xt,yt,θ) called configuration • Matrix used for finding co-ordinates is: • By this C space is given by R2*S’
  • 6.  3-D World: • 3 translational parameters xt,yt,zt for translation only robot. • C space is C=R3, q=(xt,yt,zt). • If rotation is considered θ=[0,2π),forms a sphere • Each position corresponds to a circle. • These circles glued together arround the sphere is called Hopf fibration.
  • 7.  Set of points where A(q)nC≠0  Set of all non colliding configuration is called free space Cfree.  Compliment is obstacle region Cobs=C/Cfree.
  • 8. 2 types:  Combinatorial planning  sampling-based planning
  • 9.  Constructs structures in the C-space that discretely and completely capture all information needed to perform planning.  Steps : 1)By vertical segments, decompose Cfree into trapezoids
  • 10. 2) Choose centroid in each trapezoid. 3) Place one vertex at each vertical segment. 4)Connect each vertex gives obstacle free path
  • 11. Plane sweep principle:  Sort polygon vertices from left to right  At each step edge list is updated.  If edges are on the left of vertex, they are deleted.  If they are on the right of vertex, inserted in the list.
  • 12. 1) Each cell should be easy to traverse 2) Decomposition of cells should be easily compatable. 3) Adjacencies between cells should be straight forward. Properties of Roadmap: 1) Accessibility 2) Connectivity preserving
  • 13.  Translation only robot, cobs is constructed as a polygonal boundary.  The edge to edge contact between A & O is connected to obtain it, if A & O are convex.  If A & O are non convex, then convert them to convex.
  • 14.  Most common choice for industrial grade problem.  Here without completely exploring Cfree , finding a solution.  Rapidly Exploring Random Trees(RRT) algorithm is used.  Idea is to add leaf vertex and edge between 2 configuration in each iteration.
  • 15. 1) Initialises G to contain a single vertex q0 2) Random config generator is used to find random configuration qrand. 3) Finds qnear between G & qrand. 4) Extends the tree.
  • 16.  Collision detection algorithm makes sure that path is in Cfree.  Not be able to reach qrand without hitting Cobs. So new vertex is placed.
  • 17.  The task is to pull apart the twisted nails.  Solution is shown in above figure.
  • 18.  Produced paths are jagged as they traverse Cfree. This makes the solution animation jumpy.  Path smoothening is done to cleanup solution path.  To avoid this problem take a pair of points in path & try to replace it with straight line.
  • 19.  Medical Applications  Autonomous Vehicles  Robot Navigation, Automation, Robotic surgery
  • 20.  Combinatorial planning solves simpler problems in a clean, elegant way, but the running time is too high for industrial-grade problems.  Sampling-based planning provides practical solutions for real-world problems but offers weaker guarantees