uav search & capture of a moving ground target

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K. KRISHNA, D. CASBEER, P. CHANDLER & M. PACHTER AFRL CONTROL SCIENCE CENTER OF EXCELLENCE MACCCS REVIEW APRIL 19, 2012 UAV Search & Capture of a Moving Ground Target Approved for public release; distribution unlimited; case number: 88ABW-2012-2747

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UAV Search & Capture of a Moving Ground Target. K. Krishna, D. Casbeer , P. Chandler & M. Pachter AFRL control science Center of excellence MACCCS Review April 19, 2012. Scenario. UGS Sensor Range. Valid Intruder Path. UAV Communication Range. UGS Communication Range. BASE. - PowerPoint PPT Presentation

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Page 1: UAV Search & Capture of a Moving Ground  Target

K . K R I S H N A , D . C A S B E E R , P. C H A N D L E R & M . PA C H T E R

A F R L C O N T R O L S C I E N C E C E N T E R O F E XC E L L E N C E

MA C C C S R E V I E W A P R I L 1 9 , 2 0 1 2

UAV Search & Capture of a Moving Ground Target

Approved for public release; distribution unlimited; case number: 88ABW-2012-2747

Page 2: UAV Search & Capture of a Moving Ground  Target

UGS Sensor Range

UGS Communication Range

Valid Intruder PathScenarioUAV Communication Range

BASE

Page 3: UAV Search & Capture of a Moving Ground  Target

UAV/UGS Framework• UAV engaged in search and capture of intruder on

a road network• Intersections in road instrumented with

Unattended Ground Sensors (UGSs)• Intruder is a goal oriented random walker • UAV has a speed advantage over the intruder• Passing intruder triggers UGS and the event is

time-stamped and stored in the UGS• UAV has no sensing capability• Capture occurs when UAV and intruder are at an

UGS location at the same time

Page 4: UAV Search & Capture of a Moving Ground  Target

Manhattan Grid

All edges of the grid are of same length Intruder starts at node S and proceeds towards goal nodes marked G UAV also starts at node S and observes red UGS with delay d Intruder dynamics - randomly move North, East or South but cannot retrace

path UAV actions - move North, East or South or Loiter at current location

G

G

G

S

Page 5: UAV Search & Capture of a Moving Ground  Target

System Dynamics

Page 6: UAV Search & Capture of a Moving Ground  Target

Solution MethodPose the problem as a POMDP

unconventional POMDP since observations give delayed intruder location information with random time delays!

Use observations to compute the current intruder position probabilities

Dual control problem choose UAV action that minimizes the

uncertainty associated with intruder location (localization) or choose action that gets the UAV closest to the most probable intruder location (“end game”/ capture)

Page 7: UAV Search & Capture of a Moving Ground  Target

A few notes

Assumptions: The intruder finishes in finite time and can not retrace his steps (no cycles).

Guaranteed intruder capture is hard because Incomplete, out-of-sequence, and delayed information (Unconventional POMDP formulation)

Page 8: UAV Search & Capture of a Moving Ground  Target

Worst Case Guaranteed Capture(Perfect Information)

Related to control with uncertainty modeled as bounded sets [Witsenhausen 68, Bertsekas and Rhodes 73]

Guaranteed capture is related to reachable sets [Bertsekas and Rhodes 71]

Page 9: UAV Search & Capture of a Moving Ground  Target

Full Information Scenario

From end of finite horizon Find set of UAV “safe’’ locations that guarantee

capture Proceed backwards in time looking for “safe locations”

Under full information, we have a necessary and sufficient condition for guaranteed capture [Bertsekas and Rhodes 71]

Page 10: UAV Search & Capture of a Moving Ground  Target

Full Information strategy

Case 1: Intruder is at a goal The UAV must be at the same goal

locationCase 2: Intruder is not at the

goal Safe locations:

1. Capture now OR2. Ensure that UAV is in a position to

capture the intruder in the future regardless of intruder’s moves.

Page 11: UAV Search & Capture of a Moving Ground  Target

Proceed in a fashion similar to the full information case except using (estimate) set of intruder locations instead of the true (unknown) intruder location.

Partial and Delayed observation

Page 12: UAV Search & Capture of a Moving Ground  Target

Out of sequence Estimation Process

Page 13: UAV Search & Capture of a Moving Ground  Target

Set of safe UAV locations

Page 14: UAV Search & Capture of a Moving Ground  Target

Backward (DP) recursion

Either the UAV is at the current intruder location leading to immediate capture or the UAV can take action such that it goes to a favorable location in the next time step; leading to eventual capture.

Page 15: UAV Search & Capture of a Moving Ground  Target

Sufficient condition

The condition is however not necessary for guaranteed capture due to the dual control aspect of the problem.

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2x2 Grid Example Problem

UAV starting location 1 satisfies sufficient condition (see entry 0 in table)

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b1b2

Min-Max Optimal Paths For bottom row delays 1 and 2. Intruder path is orange and corresponding optimal UAV path is in green (dotted circle represents loiter).

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c1

b1

Min-Max Optimal (End Game) For middle row delay 1. Intruder path is orange and corresponding optimal UAV path is in green (dotted circle represents loiter).

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c1

b1b3

Min-Max Optimal Paths For bottom row delay 3. Intruder path is orange and corresponding optimal UAV path is in green (dotted circle represents loiter).

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c1

b1

c2

For middle row delay 2. Intruder path is orange and corresponding optimal UAV path is in green (dotted circle represents loiter).

Min-Max Optimal Paths

Page 21: UAV Search & Capture of a Moving Ground  Target

c1

b1

cD cD-1

(D-2) steps

For middle row delay D>0 - Induction argument (to prove optimality) leading to the “End Game”

Min-Max Optimal Paths

Page 22: UAV Search & Capture of a Moving Ground  Target

c1

b1bD

cD-2

(D-3) steps

For bottom row delay D>2 - Induction argument (to prove optimality) leading to the “End Game”

Min-Max Optimal Paths

Page 23: UAV Search & Capture of a Moving Ground  Target

Min-Max optimal Steps to capture

Case Number steps Number columns needed

bottom row - delay 1 (b1)

5 1

middle row - delay 1 (c1)

11 3

bottom row - delay 2 (b2)

6 2

middle row - delay 2 (c2)

12 4

bottom row - delay 3 (b3)

13 4

middle row - delay 3 (c3)

13 5

Page 24: UAV Search & Capture of a Moving Ground  Target

Conclusions

Sufficient condition for guaranteed capture in partial information case

Currently trying to tighten the gap between necessity and sufficiency Include possible future observations to reduce the

predicted future uncertainty setAn induction argument for guaranteed

capture on longer horizons (exploit structure in the graph)

Page 25: UAV Search & Capture of a Moving Ground  Target

Search & Capture Video