49Th Ieee Conference on Decision and Control, 2010
This work investigates the problem of distributed estimation of the position of agents in a netwo... more This work investigates the problem of distributed estimation of the position of agents in a networked system, from pairwise distance measurements between them. Although the underlying geometrical problem has been studied quite extensively, most of the state-of-the-art algorithms for network localization presuppose a central unit, capable of collecting agents' measurements and retrieving the configuration of the whole network. Here, we explore decentralized, or distributed, approaches for range localization, and we develop two algorithms in which distributed optimization techniques are applied for localization, namely a distributed gradient method with Barzilai-Borwein stepsizes and a distributed Gauss-Newton approach. The advantage of these approaches is that each agent may autonomously compute its position estimate, exchanging information only with its neighbors, without need of communicating with a central station and without needing complete knowledge of the network structure. The proposed algorithms are proved to converge, under an hypothesis of network connectivity, to the same solution of their centralized counterparts.
Exactly sparse memory efficient SLAM using the multi-block alternating direction method of multipliers
2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2015
Large-scale SLAM demands for scalable techniques in which the computational burden and the memory... more Large-scale SLAM demands for scalable techniques in which the computational burden and the memory consumption is shared among many processing units. While recent literature offers competitive approaches for scalable mapping, these usually involve approximations to preserve sparsity of the resulting subproblems. We present an approach to scalable SLAM that is exactly sparse. The main insight is that rather than eliminating variables (which induces dense cliques), we split the separators connecting subgraphs. Then, we enforce consistency of the separators in different subgraphs using hard constraints. The resulting constrained optimization problem can be solved in a decentralized manner using the multiblock Alternating Direction Method of Multipliers (ADMM). Our framework is appealing since (i) it preserves the sparsity structure of the original problem, (ii) it has a straightforward implementation, (iii) it allows to easily trade-off between computation time and accuracy. While our approach is currently slower than competitors, it is more accurate than other memory efficient alternatives. Moreover, we believe that the proposed framework can be of interest on its own as it draws connections with recent literature on decentralized optimization.
This article investigates the problem of Simultaneous Localization and Mapping (SLAM) from the pe... more This article investigates the problem of Simultaneous Localization 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.
We propose an anchorless distributed technique for estimating the centroid of a network of agents... more We propose an anchorless distributed technique for estimating the centroid of a network of agents from noisy relative measurements. The positions of the agents are then obtained relative to the estimated centroid. The usual approach to multi-agent localization assumes instead that one anchor agent exists in the network, and the other agents positions are estimated with respect to the anchor.
When dealing with a network with a large number of nodes a manual configuration of node positions... more When dealing with a network with a large number of nodes a manual configuration of node positions during system set up, when possible, is an expensive and time consuming task. Moreover, in many applications, such as mobile robotics, nodes can move autonomously, thus positions need be tracked as time evolves. A possible solution consists in equipping each node with a GPS sensor, hence allowing the nodes to directly measure their location. Such an approach is often infeasible in terms of cost, weight burden, power consumption, or when the network is deployed in GPS-denied areas. As the above mentioned factors could be technological barriers, a wide variety of solutions for computing node locations through effective and efficient procedures was proposed in the last decade. The so-called indirects methods are finalized at determining absolute node positions (with respect to a local or global reference frame) from partial relative measurements between nodes, that is, each node may measure the relative position (angle and distance, angle only or distance only) from a set of neighbor nodes, and the global absolute positions of all nodes need be retrieved. This problem is generically known as network localization. If all relative measurements are gathered to some "central elaboration unit" which performs estimation over the whole network, the corresponding localization technique is said to be centralized. This is the approach that one implicitly assumes when writing and solving a problem: all the data that is relevant for the problem description is available to the problem solver. In a distributed setup, however, each node communicates only with its neighbors, and performs local computations in order to obtain an estimate of its own position. As a consequence, the communication burden is equally spread among the network, the computation is decentralized and entrusted to each agent, improving both efficiency and robustness of the estimation process. In the most usual situation of planar networks, i.e., networks with nodes displaced in twodimensional space, three main variations of the localization problem are typically considered in the literature, depending on the type of relative measurements available to the nodes. A first case is when nodes may take noisy measurements of the full relative position (coordinates or, equivalently, range and angle) of neighbors; this setup has been recently surveyed in . The localization problem with full position measurements is a linear estimation problem that can be solved efficiently via a standard least-squares approach, and the networked nature of the problem can also be exploited to devise distributed algorithms (such as the Jacobi algorithm proposed in ). A second case arises, instead, when only angle measurements between nodes are available. This case, which is often referred to as bearing localization, can be attacked via maximum likelihood estimation as described in . This localization setup was pioneered by Stanfield , and further studied in . In the last case, which is probably the most common situation in practice, each node can measure only distances from a subset of other nodes in the formation. This setup that we shall
Pose Graph Optimization (PGO) is the problem of estimating a set of poses from pairwise relative ... more Pose Graph Optimization (PGO) is the problem of estimating a set of poses from pairwise relative measurements. PGO is a nonconvex problem, and currently no known technique can guarantee the computation of an optimal solution. In this paper, we show that Lagrangian duality allows computing a globally optimal solution, under certain conditions that are satisfied in many practical cases. Our first contribution is to frame the PGO problem in the complex domain. This makes analysis easier and allows drawing connections with the recent literature on unit gain graphs. Exploiting this connection we prove non-trival results about the spectrum of the matrix underlying the problem. The second contribution is to formulate and analyze the dual problem in the complex domain. Our analysis shows that the duality gap is connected to the number of eigenvalues of the penalized pose graph matrix, which arises from the solution of the dual. We prove that if this matrix has a single eigenvalue in zero, t...
This work investigates the problem of planning under uncertainty, with application to mobile robo... more This work investigates the problem of planning under uncertainty, with application to mobile robotics. We propose a probabilistic framework in which the robot bases its decisions on the generalized belief, which is a probabilistic description of its own state and of external variables of interest. The approach naturally leads to a dual-layer architecture: an inner estimation layer, which performs inference to predict the outcome of possible decisions, and an outer decisional layer which is in charge of deciding the best action to undertake. The approach does not discretize the state or control space, and allows planning in continuous domain. Moreover, it allows to relax the assumption of maximum likelihood observations: predicted measurements are treated as random variables and are not considered as given. Experimental results show that our planning approach produces smooth trajectories while maintaining uncertainty within reasonable bounds.
The International Journal of Robotics Research, 2015
We investigate the problem of planning under uncertainty, with application to mobile robotics. We... more We investigate the problem of planning under uncertainty, with application to mobile robotics. We propose a probabilistic framework in which the robot bases its decisions on the generalized belief, which is a probabilistic description of its own state and of external variables of interest. The approach naturally leads to a dual-layer architecture: an inner estimation layer, which performs inference to predict the outcome of possible decisions, and an outer decisional layer which is in charge of deciding the best action to undertake. Decision making is entrusted to a Model Predictive Control (MPC) scheme. The formulation is valid for general cost functions and does not discretize the state or control space, enabling planning in continuous domain. Moreover, it allows to relax the assumption of maximum likelihood observations: predicted measurements are treated as random variables, and binary random variables are used to model the event that a measurement is actually taken by the robot. We successfully apply our approach to the problem of uncertainty-constrained exploration, in which the robot has to perform tasks in an unknown environment, while maintaining localization uncertainty within given bounds. We present an extensive numerical analysis of the proposed approach and compare it against related work. In practice, our planning approach produces smooth and natural trajectories and is able to impose soft upper bounds on the uncertainty. Finally, we exploit the results of this analysis to identify current limitations and show that the proposed framework can accommodate several desirable extensions.
2014 IEEE International Conference on Robotics and Automation (ICRA), 2014
This work investigates the problem of planning under uncertainty, with application to mobile robo... more This work investigates the problem of planning under uncertainty, with application to mobile robotics. We propose a probabilistic framework in which the robot bases its decisions on the generalized belief, which is a probabilistic description of its own state and of external variables of interest. The approach naturally leads to a dual-layer architecture: an inner estimation layer, which performs inference to predict the outcome of possible decisions, and an outer decisional layer which is in charge of deciding the best action to undertake. The approach does not discretize the state or control space, and allows planning in continuous domain. Moreover, it allows to relax the assumption of maximum likelihood observations: predicted measurements are treated as random variables and are not considered as given. Experimental results show that our planning approach produces smooth trajectories while maintaining uncertainty within reasonable bounds.
Position estimation from relative distance measurements in multi-agents formations
18th Mediterranean Conference on Control and Automation, MED'10, 2010
The problem of reconstructing the geometric position of nodes in a networked formation from inter... more The problem of reconstructing the geometric position of nodes in a networked formation from inter-nodal distance measurements is a complex computational task that involves the minimization of a non-convex and highly multi-modal cost criterion. In this paper, we examine three numerical techniques for attacking this problem, namely an iterative Least-Squares (LS) approach, a Trust-Region (TR) approach, and a Global Continuation
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Papers by Luca Carlone