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E-motion-planning

# E-motion-planning - (Its all in the discretization R&N Chap...

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1 1 Motion Planning (It’s all in the discretization) R&N: Chap. 25 gives some background 2 Motion planning is the ability for an agent to compute its own motions in order to achieve certain goals. All autonomous robots and digital actors should eventually have this ability 3 Digital Actors video 1 video 2 4 Basic problem Point robot in a 2-dimensional workspace with obstacles of known shape and position Find a collision-free path between a start and a goal position of the robot 5 Basic problem Each robot position (x,y) can be seen as a state Continuous state space Then each state has an infinity of successors We need to discretize the state space (x,y) 6 Two Possible Discretizations Grid-based Criticality-based

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2 7 Two Possible Discretizations Grid-based Criticality-based But this problem is very simple How do these discretizations scale up? 8 Intruder Finding Problem A moving intruder is hiding in a 2-D workspace The robot must “sweep” the workspace to find the intruder Both the robot and the intruder are points robot’s visibility region hiding region 1 cleared region 2 3 4 5 6 robot 9 Does a solution always exist? Easy to test: “Hole” in the workspace Hard to test: No “hole” in the workspace No ! Information State Example of an information state = (x,y,a=1,b=1,c=0) An initial state is of the form (x,y,1, 1, ..., 1) A goal state is any state of the form (x,y,0,0, ..., 0) (x,y) a = 0 or 1 c = 0 or 1 b = 0 or 1 0 Æ cleared region 1 Æ hidding region 11 Critical Line a=0 b=1 a=0 b=1 Information state is unchanged a=0 b=0 Critical line 12 A B C D E Criticality-Based Discretization Each of the regions A, B, C, D, and E consists of “equivalent” positions of the robot, so it’s sufficient to consider a single position per region
3 13 Criticality-Based Discretization A B C D E (C, 1, 1) (D, 1) (B, 1) 14 Criticality-Based Discretization A B C D E (C, 1, 1) (D, 1) (B, 1) (E, 1) (C, 1, 0) 15 Criticality-Based Discretization A B C D E (C, 1, 1) (D, 1) (B, 1) (E, 1) (C, 1, 0) (B, 0) (D, 1) 16 Criticality-Based Discretization A C D E (C, 1, 1) (D, 1) (B, 1) (E, 1) (C, 1, 0) (B, 0) (D, 1) Much smaller search tree than with grid-based discretization ! B 17 Grid-Based Discretization Ignores critical lines Æ Visits many “equivalent” states Many information states per grid point Potentially very inefficient 18 Example of Solution

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