Sensor Assignment Algorithms to Improve Observability while Tracking Targets

We study two sensor assignment problems for multi-target tracking with the goal of improving the observability of the underlying estimator. We consider various measures of the observability matrix as the assignment value function. We first study the general version where the sensors must form teams to track individual targets. If the value function is monotonically increasing and submodular then a greedy algorithm yields a 1/2-approximation. We then study a restricted version where exactly two sensors must be assigned to each target. We present a 1/3-approximation algorithm for this problem which holds for arbitrary value functions (not necessarily submodular or monotone). In addition to approximation algorithms, we also present various properties of observability measures. We show that the inverse of the condition number of the observability matrix is neither monotone nor submodular, but present other measures which are. Specifically, we show that the trace and rank of the symmetric observability matrix are monotone and submodular and the log determinant of the symmetric observability matrix is monotone and submodular when the matrix is non-singular. If the target's motion model is not known, the inverse cannot be computed exactly. Instead, we present a lower bound for distance sensors. In addition to theoretical results, we evaluate our results empirically through simulations.Comment: Second version submission. Accidental submission as new article. Please see arXiv:1706.0087

Distributed Active State Estimation with User-Specified Accuracy

In this paper, we address the problem of controlling a network of mobile sensors so that a set of hidden states are estimated up to a user-specified accuracy. The sensors take measurements and fuse them online using an Information Consensus Filter (ICF). At the same time, the local estimates guide the sensors to their next best configuration. This leads to an LMI-constrained optimization problem that we solve by means of a new distributed random approximate projections method. The new method is robust to the state disagreement errors that exist among the robots as the ICF fuses the collected measurements. Assuming that the noise corrupting the measurements is zero-mean and Gaussian and that the robots are self localized in the environment, the integrated system converges to the next best positions from where new observations will be taken. This process is repeated with the robots taking a sequence of observations until the hidden states are estimated up to the desired user-specified accuracy. We present simulations of sparse landmark localization, where the robotic team achieves the desired estimation tolerances while exhibiting interesting emergent behavior.Comment: IEEE Transactions on Automatic Control, June 201

Technical Report: Scalable Active Information Acquisition for Multi-Robot Systems

This paper proposes a novel highly scalable non-myopic planning algorithm for multi-robot Active Information Acquisition (AIA) tasks. AIA scenarios include target localization and tracking, active SLAM, surveillance, environmental monitoring and others. The objective is to compute control policies for multiple robots which minimize the accumulated uncertainty of a static hidden state over an a priori unknown horizon. The majority of existing AIA approaches are centralized and, therefore, face scaling challenges. To mitigate this issue, we propose an online algorithm that relies on decomposing the AIA task into local tasks via a dynamic space-partitioning method. The local subtasks are formulated online and require the robots to switch between exploration and active information gathering roles depending on their functionality in the environment. The switching process is tightly integrated with optimizing information gathering giving rise to a hybrid control approach. We show that the proposed decomposition-based algorithm is probabilistically complete for homogeneous sensor teams and under linearity and Gaussian assumptions. We provide extensive simulation results that show that the proposed algorithm can address large-scale estimation tasks that are computationally challenging to solve using existing centralized approaches

Distributed State Estimation Using Intermittently Connected Robot Networks

This paper considers the problem of distributed state estimation using multi-robot systems. The robots have limited communication capabilities and, therefore, communicate their measurements intermittently only when they are physically close to each other. To decrease the distance that the robots need to travel only to communicate, we divide them into small teams that can communicate at different locations to share information and update their beliefs. Then, we propose a new distributed scheme that combines (i) communication schedules that ensure that the network is intermittently connected, and (ii) sampling-based motion planning for the robots in every team with the objective to collect optimal measurements and decide a location for those robots to communicate. To the best of our knowledge, this is the first distributed state estimation framework that relaxes all network connectivity assumptions, and controls intermittent communication events so that the estimation uncertainty is minimized. We present simulation results that demonstrate significant improvement in estimation accuracy compared to methods that maintain an end-to-end connected network for all time