cs685-motion-planning-2

# cs685-motion-planning-2 - Motion Planning Jana Kosecka...

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1 Motion Planning Jana Kosecka Department of Computer Science Probabilistic motion planning Slides thanks to http://cs.cmu.edu/~motionplanning , Jyh-Ming Lien Hard Motion Planning Configuration Space methods – complex even for low dimensional configuration spaces Plus – always guarantee finding a plan if it exists in finite time (or answer no) Idea behind sampling cased motion planning – sacrifice completeness for efficiency – weaker guarantee – notion on probabilistic completeness

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2 General motion planning problem is PSPACE-hard [Reif 79, Hopcroft et al. 84 & 86] PSPACE-complete [Canny 87] The best deterministic algorithm known has running time that is exponential in the dimension of the robot’s C- space [Canny 86] C-space has high dimension - 6D for rigid body in 3D space simple obstacles have complex C-obstacles impractical to compute explicit representation of free space for more than 4 or 5 dof The Complexity of Motion Planning PSPACE NP P robot obst obst obst obst x y C-obst C-obst C-obst C-obst robot Path is swept volume Motion Planning in C-space Path is 1D curve Workspace C-space Simple workspace obstacle transformed Into complicated C-obstacle!!
3 The Alpha Puzzle Hard Motion Planning Problems Swapping Cubes Puzzle Separate two shapes (one considered robot) – another obstacle Exchange the positions of two cubes (one needs move to empty space) All these planning problems are considered in continuous spaces Polyhedron: 25 dof Hard Motion Planning Problems Highly Articulated (Constrained) Systems Paper Folding Articulated robot Line: 30 dof

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4 Hard Motion Planning Problems Highly Articulated (Constrained) Systems Digital Actors Reaching and grasping Hard Motion Planning Problems Flocking: Covering, Homing, Shepherding Motion for coordinated entities Control the motion of coordinated entities Interactive Navigation of Multiple Agents in Crowded Environments. Jur van den Berg, Sachin Patil, Jason Sewall, Dinesh Manocha, Ming Lin, i3D 2008
5 Hard Motion Planning Problems Deformable Objects Find a path for a deformable object that can deform to avoid collision with obstacles move a mattress in a house, elastic or air-filled objects, metal sheets or long flexible tubes virtual surgery applications computer animation and games Issue: difficult to find natural deformation efficiently Hard Motion Planning Problems Movable Objects M. Stilman and J.J. Kuffner Planning Among Movable Obstacles with Artificial Constraints Workshop on the Algorithmic Foundations of Robotics, July, 2006

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6 Hard Motion Planning Problems Intelligent CAD Applications Using Motion Planning to Test Design Requirements : – Accessibility for servicing/assembly tested on physical “mock ups” – Digital testing saves time and money, is more accurate, enables more extensive testing, and is useful for training (VR or e-manuals) Maintainability Problems: Mechanical Designs from GE flange Airplane engine
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cs685-motion-planning-2 - Motion Planning Jana Kosecka...

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