Motion Planning for Example Finding Evasive Targets in a Cluttered - - PDF document

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Motion Planning for Finding Evasive Targets in a Cluttered Environment

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+ Map Building

Example

robot’s visibility region hidin cleared region robot

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hiding region

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Problem

A target is hiding in an environment cluttered with obstacles A robot or multiple robots with vision

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m p sensor must find the target Compute a motion strategy with minimal number of robot(s)

Assumptions

Target is unpredictable and can move arbitrarily fast Environment is polygonal B th th t t d b t d l d

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Both the target and robots are modeled as points A robot finds the target when the straight line joining them intersects no

• bstacles (omni-directional vision)

Animated Target-Finding Strategy

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Does a solution always exist for a single robot?

No !

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Hard to test: No “hole” in the workspace Easy to test: “Hole” in the workspace

2 Effect of Geometry on the Number of Robots

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Two robots are needed

Effect of Number n of Edges

Minimal number of robots N = Θ(log n)

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Effect of Number h of Holes

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N=Θ( h)

Information State

(x ) a = 0 or 1 c = 0 or 1 b = 0 or 1

visibility region

• bstacle edge

free edge

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Example of an information state = (x,y,a=1,b=1,c=0) An initial state is of the form (x,y,a=1,b=1,...,u=1) A goal state is any state of the form (x,y,a=0,b=0,..., u=0)

(x,y) 0 cleared region 1 contaminated region

Critical Line

a=0 b=1

(x,y,a=0,b=1)

contaminated area

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( ,y,a , )

Information state is unchanged

(x,y,a=0,b=1)

a=0 b=1 a=0 b=0

(x,y,a=0,b=0)

Critical line

cleared area

Grid-Based Discretization

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Ignores critical lines Visits many “equivalent” states Many information states per grid point Potentially very inefficient

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Discretization into Conservative Cells

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In each conservative cell, the “topology” of the visibility region remains constant, i.e., the robot keeps seeing the same obstacle edges

Discretization into Conservative Cells

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In each conservative cell, the “topology” of the visibility region remains constant, i.e., the robot keeps seeing the same obstacle edges

Discretization into Conservative Cells

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In each conservative cell, the “topology” of the visibility region remains constant, i.e., the robot keeps seeing the same obstacle edges

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Search Graph

{Nodes} = {Conservative Cells} X {Information States} Node (c,i) is connected to (c’,i’) iff:

• Cells c and c’ share an edge (i.e., are adjacent)
• Moving from c, with state i, into c’ yields state i’

Initial node (c,i) is such that:

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Initial node (c,i) is such that

• c is the cell where the robot is initially located
• i = (1, 1, …, 1)

Goal node is any node where the information state is (0, 0, …, 0) Size is exponential in the number of edges

Example

A

(C,a=1,b=1) (D,a=1) (B,b=1)

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B C D E

a b

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A

(C,a=1,b=1) (D,a=1) (B,b=1)

Example

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B C D E

(E,a=1) (C,a=1,b=0)

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(C,a=1,b=1) (D,a=1) (B,b=1)

Example

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B C D E

(E,a=1) (C,a=1,b=0) (B,b=0) (D,a=1)

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(C,a=1,b=1) (D,a=1) (B,b=1)

Example

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C D E

(E,a=1) (C,a=1,b=0) (B,b=0) (D,a=1) Much smaller search tree than with grid-based discretization !

B

Example of Target-Finding Strategy

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Visible Cleared Contaminated

More Complex Example

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1 2 3

Example with Recontaminations

3 2 1

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6 5 4

5 Example with Linear Number

• f Recontaminations

Recontaminated area 2 1

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4 3

Example with Two Robots

(Greedy algorithm)

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Example with Two Robots

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Example with Three Robots

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Robot with Cone of Vision

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Other Topics

Dimensioned targets and robots, three- dimensional environments Non-guaranteed strategies C t d l t ti d

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Concurrent model construction and target finding Planning the escape strategy of the target

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Map Building

Laser range finder

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Sensing

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Alignment of Contours

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Merging of Four Partial Models

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Dealing with Uncertainty

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1. Simultaneous Localization and Mapping (SLAM)

• 2. Next-Best View (NBV) Planning

Next-Best View Planning

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NBV Example 1

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NBV Example 2

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Map Building with NBV

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3D Mapping

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