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Efficient Touch Based Localization through Submodularity

Presentation from ICRA 2013. For more details, see:
by Shervin Javdani on 14 May 2013

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Transcript of Efficient Touch Based Localization through Submodularity

Efficient Touch Based Localization through Submodularity Information Gain (Reduction of Shannon Entropy) [Hebert et al. '12] [Bourgault et al. '02] [Fox et al. '98] [Mutlu et al. '07] [Krause and Guestrin '05] [Erickson et al. '08] [Fu et al. '07] [Hsiao et al. '08] Many More! Plan vs. Policy Submodular Cannot React to Observations [Nemhauser et al. '78]
Ex: Chair sensors [Mutlu et al. '07] Adaptive Submodular React Online to Observations Near-optimal offline plan Near-optimal online policy Adaptive Submodularity Implications Monotonicty: More is better Submodularity: Early is better Mild Implication: Actions cannot increase uncertainty Strong Implication: Actions cannot setup future actions Shervin Javdani, Matt Klingensmith, J. Andrew Bagnell, Nancy Pollard, Siddhartha S. Srinivasa
Robotics Institute, Carnegie Mellon University Goal: Efficient Automation of Touch Localization Select a Sequence of Information Gathering Actions Motivation Need to account for uncertainty Find minimum-time sequence which achieves sufficient localization Intractable! Limit actions and depth
Unclear how this affects performance Recent Advance: If the problem is adaptive submodular [1] greedy is near-optimal! Touch Localization is Adaptive Submodular Efficient lazy-greedy algorithm comparable to optimal solution { seconds days { Method Guarded moves can be effective Touch Localization as Set Cover Objective: Maximize Coverage
(Maximally Disprove Hypotheses) Problem Formulation [1] Golovin and Krause '11 Computing Action Utilities Related Work:
Generalized Binary Search [Nowak '08]
Multiple Outcomes [Guillory and Bilmes '09] Computing Action Utilities After Update Adaptive Submodularity Requirements Strong Adaptive Monotonicity Adaptive Submodularity More is Better Any action, observation pair can only remove hypotheses Early is Better Easy to see: Utility does not increase for fixed observation
Less obvious: Expected utility does not increase. Proof in paper!
Observation Probabilities and Utilities change with updates Hypotheses: Object Pose Actions: Guarded Moves
(Straight motion until contact) Observations: Distance until contact Properties imply greedy is near-optimal policy [Golovin and Krause '11] Use Adaptive Submodularity to skip re-evaluations Efficiency Boost: Lazy-Greedy Results Results and Discussion Not adaptive submodular, stills work well with greedy [Golovin and Krause '11]
Ex: Touch based Localization Take Away: Touch Localization is Adaptive Submodular Efficient lazy-greedy algorithm comparable to optimal solution speedup theoretical bound Overview Partially Observable Markov Decision Process (POMDP) [Kaelbling '98]
POMDP for Touch Localization [Hsiao '09]
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