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...dependence on the team’s trajectory, cτ for brevity. The expression is a sum over devices because devices and their associated measurements are pairwise independent, p(x, zτ (cτ )) = ∏ d p(x d, zdτ ) =-=[8]-=-. Calculating the entropy, H[zdτ ], is difficult because the distribution over future measurements to device d is a Gaussian mixture model (GMM): p(zdτ ) =∑N i=1 wi ∏t+T j=t+1 ∏R r=1 p(z d,r j | xd = ...

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...dividual positions are independent of each other, that measurements arrive at discrete time steps, and that multiple measurements to a device are conditionally independent given the device’s location =-=[21]-=-. 2.2 Adaptive Sequential Information Planning We are interested in a general control policy for a team of robots which maximizes mutual information over a finite time horizon. This is difficult for t...

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...ery A general approach for devising a unified from control policy form multiple information-theoretic objectives is to normalize them, and introduce a parameter for trading off between the objectives =-=[3]-=-. Specifically, we propose using ASIP with the objectives for localizing and discovering all devices: I(x, zτ ) = α MI[x, zτ ] max MI[x, zτ ] + (1− α) MI[g, qτ ] max MI[g, qτ ] (7) Where the maximums ...

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... Planning paths that minimize the total distance traveled by the entire team is a variant of the multiple traveling salesman problem, and it is unlikely that an exact polynomial time algorithm exists =-=[1]-=-. Instead, we use the nearest neighbor heuristic, and at each planning step assign robots to unvisited waypoints such that the maximum distance any robot travels is minimized. Calculating each assignm...

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...ider multiple trajectories (black arrows) and the finite range of their sensors (orange circles). planning algorithms that maximize mutual information for environmental monitoring. Hoffman and Tomlin =-=[11]-=- localize a single static device using a team of robots by maximizing mutual information with a particle filter. Hook et al. [22] develops a greedy algorithm to localize a discovered device with a sin...

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...f interest are known a priori. Hollinger and Sukhatme [12] develop a sampling based strategy for maximizing a variety of information metrics with strong asymptotic optimality guarantees. Singh et al. =-=[19]-=- and Binney et al. [2] develop offline Fig. 1. Problem overview. A robotic team must discover and localize an unknown number of devices (shown as beacons) using range-only sensors. The team must consi...

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...nsors. Despite this simplification, p(zdτ ) is still a GMM, whose entropy cannot be evaluated analytically. We approximate it using the 2nd order Taylor-series approximation developed by Huber et al. =-=[13]-=-. This approach has a time complexity of O(N2RT ). Using the conditional independence assumption, the conditional entropy is H[zdτ | xd] = ∑N i=1 wi ∑t+T j=t+1 ∑R r=1 H[z d,r j | xd = x̃di ]. Re-apply...

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...ary filter to discover targets throughout an environment and maximize mutual information to control an individual robot. Pursuit-evasion games where a team must find or maintain visibility to targets =-=[7]-=- are also quite relevant. While we model range-only sensors as binary when trying to discover devices, the team must consider the geometric information range-only sensors provide in order to accuratel...

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...In the near future, automated buildings will use a large numbers of devices for a variety of services including power and water monitoring, building security, and indoor localization for smart phones =-=[18]-=-. Effectively using and maintaining this many devices will require knowing where each of them is located. A costeffective way of getting this information would be to equip each device with RF or audio...

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...intaining this many devices will require knowing where each of them is located. A costeffective way of getting this information would be to equip each device with RF or audio based range-only sensors =-=[14,17]-=-. This approach could even work when sensors are embedded in a building’s walls [10]. However, range-only sensors only provide limited information about a device’s location and having humans localize ...

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...scribes a strategy for actively localizing a known number of devices with prior estimates using range-only sensors. In previous work, we presented a similar approach for localizing individual devices =-=[5,6]-=-. In comparison, here we model the finite range of the sensors. 3.1 Estimating Devices’ Locations Because devices are independent of each other and measurements have a known data association, we estim...

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...certainty in the team’s position. We expect that incorporating this uncertainty would not significantly affect the selected control actions as range-only sensors typically have errors of a few meters =-=[6]-=- whereas robot localization solutions are substantially more accurate. We further assume that each measurement has a unique identifier (e.g., MAC address), which is typically the case for range-only s...

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...sider a similar scenario, but assume measurements have an unknown association requiring their control law to only consider whether or not any measurement to any target will be received. Carpin et al. =-=[4]-=- use a variable resolution binary filter to discover targets throughout an environment and maximize mutual information to control an individual robot. Pursuit-evasion games where a team must find or m...

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...duce the uncertainty of position estimates of devices and seek to discover all of them. Research on multi-target tracking using binary measurement models also relates to our approach. Dames and Kumar =-=[9]-=- consider a similar scenario, but assume measurements have an unknown association requiring their control law to only consider whether or not any measurement to any target will be received. Carpin et ...

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...h that the maximum distance any robot travels is minimized. Calculating each assignment can be done in O(max{R,W}4) time by repeatedly solving linear assignment problems using the Hungarian algorithm =-=[20]-=-. 6 Evaluation In this section we evaluate the strategies in Sect. 5 and examine their ability to discover and localize devices. To evaluate an approach, we measure the wall clock time – including pla...

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...ze mutual information for environmental monitoring. Hoffman and Tomlin [11] localize a single static device using a team of robots by maximizing mutual information with a particle filter. Hook et al. =-=[22]-=- develops a greedy algorithm to localize a discovered device with a single bearingonly sensor, and provides a lower bound on the time for any active control policy to localize it. In contrast to these...

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...intaining this many devices will require knowing where each of them is located. A costeffective way of getting this information would be to equip each device with RF or audio based range-only sensors =-=[14,17]-=-. This approach could even work when sensors are embedded in a building’s walls [10]. However, range-only sensors only provide limited information about a device’s location and having humans localize ...

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...l policies that maximize mutual information to reduce the uncertainty of estimates have been successfully applied in robotics when the variables of interest are known a priori. Hollinger and Sukhatme =-=[12]-=- develop a sampling based strategy for maximizing a variety of information metrics with strong asymptotic optimality guarantees. Singh et al. [19] and Binney et al. [2] develop offline Fig. 1. Problem...

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...priori. Hollinger and Sukhatme [12] develop a sampling based strategy for maximizing a variety of information metrics with strong asymptotic optimality guarantees. Singh et al. [19] and Binney et al. =-=[2]-=- develop offline Fig. 1. Problem overview. A robotic team must discover and localize an unknown number of devices (shown as beacons) using range-only sensors. The team must consider multiple trajector...