Abstract — In this paper, we consider the problem of multicentralized Cooperative Localization (CL) under severe communication constraints, i.e., when each robot can communicate only a single bit per real-valued (analog) measurement. Existing approaches, such as those based on the Sign-of-Innovation Kalman filter (SOI-KF) and its variants, require each robot to process quantized versions of both its local (i.e., recorded by its own sensors) and remote (i.e., collected by other robots) measurements. This results in suboptimal performance since each robot has to discard information that is available in its own analog measurements. To address this limitation, we introduce a novel hybrid estimation scheme that enables each robot to process both quantized (from remote sensors) and analog (from its own sensors) measurements. Specifically, we first present the hybrid (H)-SOI-KF, a direct extension of the

Abstract—In this paper, we study the problem of optimal trajectory generation for a team of heterogeneous robots moving in a plane and tracking a moving target by processing relative observations, i.e., distance and/or bearing. Contrary to previous approaches, we explicitly consider limits on the robots ’ speed and impose constraints on the minimum distance at which the robots are allowed to approach the target. We first address the case of a single tracking sensor and seek the next sensing location in order to minimize the uncertainty about the target’s position. We show that although the corresponding optimization problem involves a non-convex objective function and a non-convex constraint, its global optimal solution can be determined analytically. We then extend the approach to the case of multiple sensors and propose an iterative algorithm, Gauss-Seidel-relaxation (GSR), for determining the next best sensing location for each sensor. Extensive simulation results demonstrate that the GSR algorithm, whose computational complexity is linear in the number of sensors, achieves higher tracking accuracy than gradient descent methods, and has performance indistinguishable from that of a grid-based exhaustive search, whose cost is exponential in the number of sensors. Finally, through experiments we demonstrate that the proposed GSR algorithm is robust and applicable to real systems.

Abstract — This paper focuses on reducing the computational complexity of the extended Kalman filter (EKF)-based multirobot cooperative localization (CL) by taking advantage of the sparse structure of the measurement Jacobian matrix H. In contrast to the standard EKF update, whose complexity is up to O(N 4) (N is the number of robots in a team), we introduce a Modified Householder QR algorithm which fully exploits the sparse structure of the matrix H, and prove that the overall complexity of the EKF update, based on our QR factorization scheme, reduces to O(N 3). Finally, we validate the Modified Householder QR algorithm through extensive simulations, and demonstrate its superior performance both in terms of accuracy and CPU runtime, as compared to the current state-of-the-art QR decomposition algorithm for sparse matrices. I.