UAV Search & Capture of a Moving Ground Target
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Transcript of 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
UGS Sensor Range
UGS Communication Range
Valid Intruder PathScenarioUAV Communication Range
BASE
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
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
System Dynamics
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)
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)
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]
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]
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.
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
Out of sequence Estimation Process
Set of safe UAV locations
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.
Sufficient condition
The condition is however not necessary for guaranteed capture due to the dual control aspect of the problem.
2x2 Grid Example Problem
UAV starting location 1 satisfies sufficient condition (see entry 0 in table)
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).
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).
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).
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
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
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
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
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)
Search & Capture Video