1 / 34

CS 326A: Motion Planning

This motion planning approach uses trapezoidal decomposition to decompose the configuration space into "regular" regions and find targets in cluttered environments. It addresses issues such as property definition and decomposition usage. The approach is applicable in low-dimensional spaces but sensitive to floating point errors.

lillies
Download Presentation

CS 326A: Motion Planning

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. CS 326A: Motion Planning Criticality-Based Motion Planning: Target Finding

  2. Trapezoidal decomposition

  3. Criticality-Based Planning • Define a property P • Decompose the configuration space into “regular” regions (cells) over which P is constant. • Use this decomposition for planning • Issues: - What is P? It depends on the problem- How to use the decomposition? • Approach is practical only in low-dimensional spaces:- Complexity of the arrangement of cells- Sensitivity to floating point errors

  4. Topics of this class and the next one • Target finding Information (or belief) state/space • Assembly planning Path space

  5. cleared region 2 4 5 6 Example robot robot’s visibilityregion hiding region 1 3

  6. Problem • A target is hiding in an environment cluttered with obstacles • A robot or multiple robots with vision sensor must find the target • Compute a motion strategy with minimal number of robot(s)

  7. Assumptions • Target is unpredictable and can move arbitrarily fast • Environment is polygonal • Both the target and robots are modeled as points • A robot finds the target when the straight line joining them intersects no obstacles (omni-directional vision)

  8. Animated Target-Finding Strategy

  9. No ! Easy to test: “Hole” in the workspace Does a solution always existfor a single robot? Hard to test: No “hole” in the workspace

  10. Two robots are needed Effect of Geometry on the Number of Robots

  11. Effect of Number n of Edges Minimal number of robots N = Q(log n)

  12. Effect of Number h of Holes

  13. a = 0 or 1 c = 0 or 1 b = 0 or 1 (x,y) 0  cleared region 1  contaminated region Information State • 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) visibility region free edge obstacle edge

  14. b=1 b=0 a=0 a=0 cleared area b=1 a=0 Critical line Information state is unchanged (x,y,a=0,b=0) (x,y,a=0,b=1) Critical Line contaminated area (x,y,a=0,b=1)

  15. Grid-Based Discretization • Ignores critical lines  Visits many “equivalent” states • Many information states per grid point • Potentially very inefficient

  16. Discretization into Conservative Cells In each conservative cell, the “topology” of the visibilityregion remains constant, i.e., the robot keeps seeing the same obstacle edges

  17. Discretization into Conservative Cells In each conservative cell, the “topology” of the visibilityregion remains constant, i.e., the robot keeps seeing the same obstacle edges

  18. Discretization into Conservative Cells In each conservative cell, the “topology” of the visibilityregion remains constant, i.e., the robot keeps seeing the same obstacle edges

  19. 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: • 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

  20. A (C,a=1,b=1) (B,b=1) (D,a=1) E B C D Example a b

  21. A (C,a=1,b=1) (B,b=1) (D,a=1) E B C D (C,a=1,b=0) (E,a=1) Example

  22. A (C,a=1,b=1) (B,b=1) (D,a=1) E B C D (C,a=1,b=0) (E,a=1) (B,b=0) (D,a=1) Example

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

  24. Visible Cleared Contaminated Example of Target-Finding Strategy

  25. More Complex Example 2 1 3

  26. Example with Recontaminations 3 1 2 6 4 5

  27. Recontaminatedarea Example with Linear Number of Recontaminations 1 2 3 4

  28. Example with Two Robots (Greedy algorithm)

  29. Example with Two Robots

  30. Example with Three Robots

  31. Robot with Cone of Vision

  32. Other Topics • Dimensioned targets and robots, three-dimensional environments • Non-guaranteed strategies • Concurrent model construction and target finding • Planning the escape strategy of the target

More Related