Abstract-This article investigates the problem of SimultaneousLocalization and Mapping (SLAM) from the perspective of linear estimation theory. The problem is first formulated in terms of graph embedding: a graph describing robot poses at subsequent instants of time needs be embedded in a three-dimensional space, assuring that the estimated configuration maximizes measurement likelihood. Combining tools belonging to linear estimation and graph theory, a closed-form approximation to the full SLAM problem is proposed, under the assumption that the relative position and the relative orientation measurements are independent. The approach needs no initial guess for optimization and is formally proven to admit solution under the SLAM setup. The resulting estimate can be used as an approximation of the actual nonlinear solution or can be further refined by using it as an initial guess for nonlinear optimization techniques. Finally, the experimental analysis demonstrates that such refinement is often unnecessary, since the linear estimate is already accurate.

This work investigates the pose graph optimization problem, which arises in maximum likelihood approaches to simultaneous localization and mapping (SLAM). State-of-the-art approaches have been demonstrated to be very efficient in mediumand large-sized scenarios; however, their convergence to the maximum likelihood estimate heavily relies on the quality of the initial guess. We show that, in planar scenarios, pose graph optimization has a very peculiar structure. The problem of estimating robot orientations from relative orientation measurements is a quadratic optimization problem (after computing suitable regularization terms); moreover, given robot orientations, the overall optimization problem becomes quadratic. We exploit these observations to design an approximation of the maximum likelihood estimate, which does not require the availability of an initial guess. The approximation, named LAGO (Linear Approximation for pose Graph Optimization), can be used as a stand-alone tool or can bootstrap state-of-the-art techniques, reducing the risk of being trapped in local minima. We provide analytical results on existence and sub-optimality of LAGO, and we discuss the factors influencing its quality. Experimental results demonstrate that LAGO is accurate in common SLAM problems. Moreover, it is remarkably faster than state-of-the-art techniques, and is able to solve very large-scale problems in a few seconds.

Abstract-We study the feature-based map merging problem in robot networks. Along its operation, each robot observes the environment and builds and maintains a local map. Simultaneously, each robot communicates and computes the global map of the environment. The communication between the robots is rangelimited. We propose a dynamic strategy based on consensus algorithms that is fully distributed and does not rely on any particular communication topology. Under mild connectivity conditions on the communication graph, our merging algorithm asymptotically converges to the global map. We present a formal analysis of its convergence rate and provide accurate characterizations of the errors as a function of the timestep. The proposed approach has been experimentally validated using real visual information.

Abstract-In this paper we address the data association problem of features observed by a robot team with limited communications. At every time instant, each robot can only exchange data with a subset of the robots, its neighbors. Initially, each robot solves a local data association with each of its neighbors. After that, the robots execute the proposed algorithm to agree on a data association between all their local observations which is globally consistent. One inconsistency appears when chains of local associations give rise to two features from one robot being associated among them. The contribution of this work is the decentralized detection and resolution of these inconsistencies. We provide a fully decentralized solution to the problem. This solution does not rely on any particular communication topology. Every robot plays the same role, making the system robust to individual failures. Information is exchanged exclusively between neighbors. In a finite number of iterations, the algorithm finishes with a data association which is free of inconsistent associations.In the experiments, we show the performance of the algorithm under two scenarios. In the first one, we apply the resolution and detection algorithm for a set of stochastic visual maps. In the second, we solve the feature matching between a set of images taken by a robotic team.

Abstract-In this paper we address the problem of estimating the poses of a team of agents when they do not share any common reference frame. Each agent is capable of measuring the relative position and orientation of its neighboring agents, however these measurements are not exact but they are corrupted with noises. The goal is to compute the pose of each agent relative to the anchor node from noisy relative pose measurements. We present an strategy where, first of all, the agents compute their orientations relative to an anchor node. After that, they update the relative position measurements according to these orientations, to finally compute their positions. As contribution we discuss the proposed strategy, that has the interesting property that can be executed in a distributed fashion. The distributed implementation allows each agent to recover its pose using exclusively local information and local interactions with its neighbors. Besides, it only requires each node to maintain an estimate of its own orientation and position. Thus, the memory load of the algorithm is low compared to methods where each agent must also estimate the positions and orientations of any other agent.

Abstract-In several multi agent control problems, the convergence properties and the convergence speed of the system depend on the algebraic connectivity of the graph. We present a novel distributed algorithm where the agents estimate this algebraic connectivity, obtaining a more accurate estimate at each iteration. This algorithm relies on the distributed computation of the powers of the adjacency matrix. We provide proofs of convergence and convergence rate of the algebraic connectivity estimation algorithm. In addition, we give upper and lower bounds at each iteration of the estimated algebraic connectivity. We apply this method to an event-triggered consensus scenario, where the most recent estimate of the algebraic connectivity is used for adapting the behavior of the average consensus algorithm. We show that both processes can be executed in parallel, i.e., the nodes do not need to wait for obtaining a good estimate of the algebraic connectivity before starting the averaging algorithm.

The algebraic connectivity of the graph Laplacian plays an essential role in various multi-agent control systems. In many cases a lower bound of this algebraic connectivity is necessary in order to achieve a certain performance. Lately, several methods based on distributed Power Iteration have been proposed for computing the algebraic connectivity of a symmetric Laplacian matrix. However, these methods cannot give any lower bound of the algebraic connectivity and their convergence rates are often unclear. In this paper, we present a distributed algorithm for estimating the algebraic connectivity for undirected graphs with symmetric Laplacian matrices. Our method relies on the distributed computation of the powers of the adjacency matrix and its main interest is that, at each iteration, agents obtain both upper and lower bounds for the true algebraic connectivity. It was proven that both bounds successively approach the true algebraic connectivity with the convergence speed no slower than O(1/k).

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