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

On robust estimation of the location parameter

One camera and one low-cost inertial measurement unit (IMU) form a monocular visual-inertial system (VINS), which is the minimum sensor suite (in size, weight, and power) for the metric six degrees-of-freedom (DOF) state estimation. In this paper, we present VINS-Mono: a robust and versatile monocular visual-inertial state estimator. Our approach starts with a robust procedure for estimator initialization. A tightly coupled, nonlinear optimization-based method is used to obtain highly accurate visual-inertial odometry by fusing preintegrated IMU measurements and feature observations. A loop detection module, in combination with our tightly coupled formulation, enables relocalization with minimum computation. We additionally perform 4-DOF pose graph optimization to enforce the global consistency. Furthermore, the proposed system can reuse a map by saving and loading it in an efficient way. The current and previous maps can be merged together by the global pose graph optimization. We validate the performance of our system on public datasets and real-world experiments and compare against other state-of-the-art algorithms. We also perform an onboard closed-loop autonomous flight on the microaerial-vehicle platform and port the algorithm to an iOS-based demonstration. We highlight that the proposed work is a reliable, complete, and versatile system that is applicable for different applications that require high accuracy in localization. We open source our implementations for both PCs ( https://github.com/HKUST-Aerial-Robotics/VINS-Mono ) and iOS mobile devices ( https://github.com/HKUST-Aerial-Robotics/VINS-Mobile ).

VINS-Mono: A Robust and Versatile Monocular Visual-Inertial State Estimator

IEEE Transactions on Pattern Analysis and Machine Intelligence

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

We present a novel data structure, the Bayes tree, that provides an algorithmic foundation enabling a better understanding of existing graphical model inference algorithms and their connection to sparse matrix factorization methods. Similar to a clique tree, a Bayes tree encodes a factored probability density, but unlike the clique tree it is directed and maps more naturally to the square root information matrix of the simultaneous localization and mapping (SLAM) problem. In this paper, we highlight three insights provided by our new data structure. First, the Bayes tree provides a better understanding of the matrix factorization in terms of probability densities. Second, we show how the fairly abstract updates to a matrix factorization translate to a simple editing of the Bayes tree and its conditional densities. Third, we apply the Bayes tree to obtain a completely novel algorithm for sparse nonlinear incremental optimization, named iSAM2, which achieves improvements in efficiency through incremental variable re-ordering and fluid relinearization, eliminating the need for periodic batch steps. We analyze various properties of iSAM2 in detail, and show on a range of real and simulated datasets that our algorithm compares favorably with other recent mapping algorithms in both quality and efficiency.

/pdf/isam2-incremental-smoothing-and-mapping-using-the-bayes-tree-3ixkuyhnhk.pdf

iSAM2: Incremental smoothing and mapping using the Bayes tree

We present iSAM2, a fully incremental, graph-based version of incremental smoothing and mapping (iSAM). iSAM2 is based on a novel graphical model-based interpretation of incremental sparse matrix factorization methods, afforded by the recently introduced Bayes tree data structure. The original iSAM algorithm incrementally maintains the square root information matrix by applying matrix factorization updates. We analyze the matrix updates as simple editing operations on the Bayes tree and the conditional densities represented by its cliques. Based on that insight, we present a new method to incrementally change the variable ordering which has a large effect on efficiency. The efficiency and accuracy of the new method is based on fluid relinearization, the concept of selectively relinearizing variables as needed. This allows us to obtain a fully incremental algorithm without any need for periodic batch steps. We analyze the properties of the resulting algorithm in detail, and show on various real and simulated datasets that the iSAM2 algorithm compares favorably with other recent mapping algorithms in both quality and efficiency.

/pdf/isam2-incremental-smoothing-and-mapping-with-fluid-180l42zslx.pdf

iSAM2: Incremental smoothing and mapping with fluid relinearization and incremental variable reordering

Pose SLAM is the variant of simultaneous localization and map building (SLAM) is the variant of SLAM, in which only the robot trajectory is estimated and where landmarks are only used to produce relative constraints between robot poses. To reduce the computational cost of the information filter form of Pose SLAM and, at the same time, to delay inconsistency as much as possible, we introduce an approach that takes into account only highly informative loop-closure links and nonredundant poses. This approach includes constant time procedures to compute the distance between poses, the expected information gain for each potential link, and the exact marginal covariances while moving in open loop, as well as a procedure to recover the state after a loop closure that, in practical situations, scales linearly in terms of both time and memory. Using these procedures, the robot operates most of the time in open loop, and the cost of the loop closure is amortized over long trajectories. This way, the computational bottleneck shifts to data association, which is the search over the set of previously visited poses to determine good candidates for sensor registration. To speed up data association, we introduce a method to search for neighboring poses whose complexity ranges from logarithmic in the usual case to linear in degenerate situations. The method is based on organizing the pose information in a balanced tree whose internal levels are defined using interval arithmetic. The proposed Pose-SLAM approach is validated through simulations, real mapping sessions, and experiments using standard SLAM data sets.

/pdf/information-based-compact-pose-slam-198ml58i76.pdf

Information-Based Compact Pose SLAM

We present a novel data structure, the Bayes tree, that provides an algorithmic foundation enabling a better understanding of existing graphical model inference algorithms and their connection to sparse matrix factorization methods. Similar to a clique tree, a Bayes tree encodes a factored probability density, but unlike the clique tree it is directed and maps more naturally to the square root information matrix of the simultaneous localization and mapping (SLAM) problem. In this paper, we highlight three insights provided by our new data structure. First, the Bayes tree provides a better understanding of batch matrix factorization in terms of probability densities. Second, we show how the fairly abstract updates to a matrix factorization translate to a simple editing of the Bayes tree and its conditional densities. Third, we apply the Bayes tree to obtain a completely novel algorithm for sparse nonlinear incremental optimization, that combines incremental updates with fluid relinearization of a reduced set of variables for efficiency, combined with fast convergence to the exact solution. We also present a novel strategy for incremental variable reordering to retain sparsity.We evaluate our algorithmon standard datasets in both landmark and pose SLAM settings.

/pdf/the-bayes-tree-an-algorithmic-foundation-for-probabilistic-4ydws88183.pdf

The Bayes Tree: An Algorithmic Foundation for Probabilistic Robot Mapping

Environmental change is a growing international concern, calling for the regular monitoring, studying and preserving of detailed information about the evolution of underwater ecosystems. For example, fragile coral reefs are exposed to various sources of hazards and potential destruction, and need close observation. Computer vision offers promising technologies to build 3D models of an environment from two-dimensional images. The state of the art techniques have enabled high-quality digital reconstruction of large-scale structures, e.g., buildings and urban environments, but only sparse representations or dense reconstruction of small objects have been obtained from underwater video and still imagery. The application of standard 3D reconstruction methods to challenging underwater environments typically produces unsatisfactory results. Accurate, full camera trajectories are needed to serve as the basis for dense 3D reconstruction. A highly accurate sparse 3D reconstruction is the ideal foundation on which to base subsequent dense reconstruction algorithms. In our application the models are constructed from synchronized high definition videos collected using a wide baseline stereo rig. The rig can be hand-held, attached to a boat, or even to an autonomous underwater vehicle. We solve this problem by employing a smoothing and mapping toolkit developed in our lab specifically for this type of application. The result of our technique is a highly accurate sparse 3D reconstruction of underwater structures such as corals.

/pdf/3d-reconstruction-of-underwater-structures-d3c046zsmm.pdf

Viorela Ila

Papers

iSAM2: Incremental smoothing and mapping using the Bayes tree

iSAM2: Incremental smoothing and mapping with fluid relinearization and incremental variable reordering

Information-Based Compact Pose SLAM

The Bayes Tree: An Algorithmic Foundation for Probabilistic Robot Mapping

3D reconstruction of underwater structures