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**1 - 4**of**4**### Multi-Robot Localization via GPS and Relative Measurements in the Presence of Asynchronous and Lossy Communication

"... Abstract — This work addresses the problem of distributed multi-agent localization in presence of heterogeneous measure-ments and wireless communication. The proposed algorithm integrates low precision global sensors, like GPS and compasses, with more precise relative position (i.e., range plus bear ..."

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Abstract — This work addresses the problem of distributed multi-agent localization in presence of heterogeneous measure-ments and wireless communication. The proposed algorithm integrates low precision global sensors, like GPS and compasses, with more precise relative position (i.e., range plus bearing) sensors. Global sensors are used to reconstruct the absolute position and orientation, while relative sensors are used to retrieve the shape of the formation. A fast distributed and asynchronous linear least-squares algorithm is proposed to solve an approximated version of the non-linear Maximum Likelihood problem. The algorithm is provably shown to be robust to communication losses and random delays. The use of ACK-less broadcast-based communication protocols ensures an efficient and easy implementation in real world scenarios. If the relative measurement errors are sufficiently small, we show that the algorithm attains a solution which is very close to the maximum likelihood solution. The theoretical findings and the algorithm performances are extensively tested by means of Monte-Carlo simulations. I.

### Curve-Graph odometry: Removing the orientation in loop closure optimisation problems

"... Abstract. In robot odometry and SLAM applications the real trajec-tory is estimated incrementally. This produces an accumulation of errors which gives raise to a drift in the trajectory. When revisiting a previous position this drift becomes observable and thus it can be corrected by ap-plying loop ..."

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Abstract. In robot odometry and SLAM applications the real trajec-tory is estimated incrementally. This produces an accumulation of errors which gives raise to a drift in the trajectory. When revisiting a previous position this drift becomes observable and thus it can be corrected by ap-plying loop closing techniques. Ultimately a loop closing process leads to an optimisation problem where new constraints between poses obtained from loop detection are applied to the initial incremental estimate of the trajectory. Typically this optimisation is jointly applied on the position and orientation of each pose of the robot using the state-of-the-art pose graph optimisation scheme on the manifold of the rigid body motions. In this paper we propose to address the loop closure problem using only the positions and thus removing the orientations from the optimisation vector. The novelty in our approach is that, instead of treating trajectory as a set of poses, we look at it as a curve in its pure mathematical mean-ing. We define an observation function which computes the estimate of one constraint in a local reference frame using only the robot positions. Our proposed method is compared against state-of-the-art pose graph optimisation algorithms in 2 and 3 dimensions. The main advantages of our method are the elimination of the need of mixing the orientation and position in the optimisation and the savings in computational cost due to the reduction of the dimension of the optimisation vector. 1

### Selecting Good Measurements via `1 Relaxation: a Convex Approach for Robust Estimation over Graphs

"... Abstract — Pose graph optimization is an elegant and efficient formulation for robot localization and mapping. Experimental evidence suggests that, in real problems, the set of measure-ments used to estimate robot poses is prone to contain outliers, due to perceptual aliasing and incorrect data asso ..."

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Abstract — Pose graph optimization is an elegant and efficient formulation for robot localization and mapping. Experimental evidence suggests that, in real problems, the set of measure-ments used to estimate robot poses is prone to contain outliers, due to perceptual aliasing and incorrect data association. While several related works deal with the rejection of outliers during pose estimation, the goal of this paper is to propose a grounded strategy for measurements selection, i.e., the output of our approach is a set of “reliable ” measurements, rather than pose estimates. Because the classification in inliers/outliers is not observable in general, we pose the problem as finding the maximal subset of the measurements that is internally coherent. In the linear case, we show that the selection of the maximal coherent set can be (conservatively) relaxed to obtain a linear programming problem with `1 objective. We show that this approach can be extended to (nonlinear) planar pose graph optimization using similar ideas as our previous work on linear approaches to pose graph optimization. We evaluate our method on standard datasets, and we show that it is robust to a large number of outliers and different outlier generation models, while entailing the advantages of linear programming (fast computation, scalability). I.