There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Simultaneous localization and mapping (SLAM) consists in the concurrent construction of a model of the environment (the map ), and the estimation of the state of the robot moving within it. The SLAM community has made astonishing progress over the last 30 years, enabling large-scale real-world applications and witnessing a steady transition of this technology to industry. We survey the current state of SLAM and consider future directions. We start by presenting what is now the de-facto standard formulation for SLAM. We then review related work, covering a broad set of topics including robustness and scalability in long-term mapping, metric and semantic representations for mapping, theoretical performance guarantees, active SLAM and exploration, and other new frontiers. This paper simultaneously serves as a position paper and tutorial to those who are users of SLAM. By looking at the published research with a critical eye, we delineate open challenges and new research issues, that still deserve careful scientific investigation. The paper also contains the authors’ take on two questions that often animate discussions during robotics conferences: Do robots need SLAM? and Is SLAM solved?

/pdf/past-present-and-future-of-simultaneous-localization-and-27i1pn9khc.pdf

Past, Present, and Future of Simultaneous Localization and Mapping: Toward the Robust-Perception Age

Simultaneous Localization and Mapping (SLAM)consists in the concurrent construction of a model of the environment (the map), and the estimation of the state of the robot moving within it. The SLAM community has made astonishing progress over the last 30 years, enabling large-scale real-world applications, and witnessing a steady transition of this technology to industry. We survey the current state of SLAM. We start by presenting what is now the de-facto standard formulation for SLAM. We then review related work, covering a broad set of topics including robustness and scalability in long-term mapping, metric and semantic representations for mapping, theoretical performance guarantees, active SLAM and exploration, and other new frontiers. This paper simultaneously serves as a position paper and tutorial to those who are users of SLAM. By looking at the published research with a critical eye, we delineate open challenges and new research issues, that still deserve careful scientific investigation. The paper also contains the authors' take on two questions that often animate discussions during robotics conferences: Do robots need SLAM? and Is SLAM solved?

/pdf/past-present-and-future-of-simultaneous-localization-and-dhljw0akg5.pdf

Past, Present, and Future of Simultaneous Localization And Mapping: Towards the Robust-Perception Age

Simultaneous Localization and Mapping (SLAM) consists in the concurrent construction of a representation of the environment (the map), and the estimation of the state of the robot moving within it. The SLAM community has made astonishing progress over the last 30 years, enabling large-scale real-world applications, and witnessing a steady transition of this technology to industry. We survey the current state of SLAM. We start by presenting what is now the de-facto standard formulation for SLAM. We then review related work, covering a broad set of topics including robustness and scalability in long-term mapping, metric and semantic representations for mapping, theoretical performance guarantees, active SLAM and exploration, and other new frontiers. The paper serves as a tutorial for the non-expert reader. It is also a position paper: by looking at the published research with a critical eye, we delineate open challenges and new research issues, that still deserve careful scientific investigation. The paper also contains the authors’ take on two questions that often animate discussions during robotics conferences: do robots need SLAM? Is SLAM solved?

Simultaneous Localization And Mapping: Present, Future, and the Robust-Perception Age.

IEEE International Conference on Robotics and Automation

The most common way to deal with the uncertainty present in noisy sensorial perception and action is to model the problem with a probabilistic framework. Maximum likelihood estimation is a well-kno...

SLAM++1-A highly efficient and temporally scalable incremental SLAM framework

Efficiently solving nonlinear least squares (NLS) problems is crucial for many applications in robotics. In online applications, solving the associated nolinear systems every step may become very expensive. This paper introduces online, incremental solutions, which take full advantage of the sparseblock structure of the problems in robotics. In general, the solution of the nonlinear system is approximated by incrementally solving a series of linearized problems. The most computationally demanding part is to assemble and solve the linearized system at each iteration. In our solution, this is mitigated by incrementally updating the factorized form of the linear system and changing the linearization point only if needed. The incremental updates are done using a resumed factorization only on the parts affected by the new information added to the system at every step. The sparsity of the factorized form directly affects the efficiency. In order to obtain an incremental factorization with persistent reduced fill-in, a new incremental ordering scheme is proposed. Furthermore, the implementation exploits the block structure of the problems and offers efficient solutions to manipulate block matrices, including a highly efficient Cholesky factorization on sparse block matrices. In this work, we focus our efforts on testing the method on SLAM applications, but the applicability of the technique remains general. The experimental results show that our implementation outperforms the state of the art SLAM implementations on all the tested datasets.

http://www.roboticsproceedings.org/rss09/p42.pdf

Incremental Block Cholesky Factorization for Nonlinear Least Squares in Robotics

Many estimation problems in robotics rely on efficiently solving nonlinear least squares (NLS). For example, it is well known that the simultaneous localisation and mapping (SLAM) problem can be formulated as a maximum likelihood estimation (MLE) and solved using NLS, yielding a mean state vector. However, for many applications recovering only the mean vector is not enough. Data association, active decisions, next best view, are only few of the applications that require fast state covariance recovery. The problem is not simple since, in general, the covariance is obtained by inverting the system matrix and the result is dense. The main contribution of this paper is a novel algorithm for fast incremental covariance update, complemented by a highly efficient implementation of the covariance recovery. This combination yields to two orders of magnitude reduction in computation time, compared to the other state of the art solutions. The proposed algorithm is applicable to any NLS solver implementation, and does not depend on incremental strategies described in our previous papers, which are not a subject of this paper.

Fast covariance recovery in incremental nonlinear least square solvers

A large number of robotic, computer vision and computer graphics applications rely on efficiently solving the associated sparse linear systems. Simultaneous localization and mapping (SLAM), structure from motion (SfM), non-rigid shape recovery, and elastodynamic simulations are only few examples in this direction. In general, these problems are nonlinear and the solution can be approximated by incrementally solving a series of linearized problems. In some applications, the size of the system considerably affects the performance, especially when the sparsity is low. This paper exploits the block structure of such problems and offers very efficient solutions to manipulate block matrices within iterative nonlinear solvers. The resulting method considerably speeds-up the execution of the implementation of the nonlinear optimization problem. In this work, in particular, we focus our effort on testing the method on SLAM applications, but the applicability of the technique remains general. Our implementation outperforms the state of the art SLAM implementations on all tested datasets. In incremental mode, where a larger portion of time is spent in updating the system, our implementation is on average two times faster than the others.

Efficient implementation for block matrix operations for nonlinear least squares problems in robotic applications

Efficient algorithms exist to obtain a sparse 3D representation of the environment. Bundle adjustment (BA) and structure from motion (SFM) are techniques used to estimate both the camera poses and the set of sparse points in the environment. Many applications require such reconstruction to be performed online, while acquiring the data, and produce an updated result every step. Furthermore, using active feedback about the quality of the reconstruction can help selecting the best views to increase the accuracy as well as to maintain a reasonable size of the collected data. This paper provides novel and efficient solutions to solving the associated NLS incrementally, and to compute not only the optimal solution, but also the associated uncertainty. The proposed technique highly increases the efficiency of the incremental BA solver for long camera trajectory applications, and provides extremely fast covariance recovery.

Lukas Polok

Papers

SLAM++1-A highly efficient and temporally scalable incremental SLAM framework

Incremental Block Cholesky Factorization for Nonlinear Least Squares in Robotics

Fast covariance recovery in incremental nonlinear least square solvers

Efficient implementation for block matrix operations for nonlinear least squares problems in robotic applications

Fast Incremental Bundle Adjustment with Covariance Recovery