Frank Dellaert

Avinash Subramanian, Connor Holmes, Timothy D. Barfoot et al.

Robust and efficient state estimation is crucial for perception, navigation, and control in robotics. State estimation problems are conveniently modeled using the factor-graph framework as enabled by modern software packages such as GTSAM or g2o. However, the standard solvers included in such frameworks are local and may converge to poor local minima, posing significant safety concerns. Conversely, techniques based on convex relaxations have been shown to provide a means of globally solving or certifying many state estimation problems. However, these relaxations 1) often require substantial effort to formulate, and 2) may incur significantly higher cost compared to efficient local solvers, as they require solving a large semidefinite program (SDP). In this work, we address both shortcomings by 1) creating a new procedure within the GTSAM framework for automatically constructing convex SDP relaxations for any factor graphs with common factor and variable types, and by 2) exploiting the Bayes tree constructions native to GTSAM to decompose the SDP problem, leading to significant speedup in solver time for chordally sparse problems. We demonstrate the favorable scaling of this structure-exploiting global estimator compared to standard local solvers for two case studies: A 3D pose-graph SLAM problem with a ring factor graph and a 2D localization problem with a chain factor graph. The software framework is available at https://github.com/borglab/gtsam.

Lu Mi, Abhijit Kundu, David Ross et al. · deepmind

We propose im2nerf, a learning framework that predicts a continuous neural object representation given a single input image in the wild, supervised by only segmentation output from off-the-shelf recognition methods. The standard approach to constructing neural radiance fields takes advantage of multi-view consistency and requires many calibrated views of a scene, a requirement that cannot be satisfied when learning on large-scale image data in the wild. We take a step towards addressing this shortcoming by introducing a model that encodes the input image into a disentangled object representation that contains a code for object shape, a code for object appearance, and an estimated camera pose from which the object image is captured. Our model conditions a NeRF on the predicted object representation and uses volume rendering to generate images from novel views. We train the model end-to-end on a large collection of input images. As the model is only provided with single-view images, the problem is highly under-constrained. Therefore, in addition to using a reconstruction loss on the synthesized input view, we use an auxiliary adversarial loss on the novel rendered views. Furthermore, we leverage object symmetry and cycle camera pose consistency. We conduct extensive quantitative and qualitative experiments on the ShapeNet dataset as well as qualitative experiments on Open Images dataset. We show that in all cases, im2nerf achieves the state-of-the-art performance for novel view synthesis from a single-view unposed image in the wild.

Yuhao Zhang, Yifu Tao, Frank Dellaert et al.

Recent works have explored unifying SLAM with geometric foundation models (GFMs). However, directly using GFM predictions for tracking is highly sensitive to model capability and uncertainty, as geometric inaccuracies in the predictions can adversely affect pose estimation. To address this limitation, we present a decoupled framework that integrates classical feature-based SLAM with GFMs, which achieves higher quality and more consistent dense reconstruction. In brief, we use classical visual SLAM for robust low-latency tracking and use GFMs exclusively for mapping. By anchoring mapping to poses produced by the SLAM module and optimizing across depth scales, the proposed design avoids propagating inaccuracies from GFM predictions into pose estimation while imposing geometric constraints on the reconstruction. The system builds submaps from multiple posed keyframes and enforces scale consistency via lightweight frame and submap scale optimization. It also performs projection-based point cloud fusion within each submap, and updates submaps online to reflect trajectory updates from the feature-based SLAM. To evaluate tracking and reconstruction of our method, we introduce a loop-rich, building-scale indoor dataset with accurate sensor trajectories and LiDAR ground-truth. Experiments show that our approach achieves superior trajectory accuracy while improving reconstruction precision by 10%-20% over existing methods, with about 2 cm reconstruction error per 10 m chunk on building-scale dataset. On large-scale outdoor datasets, it attains 10 cm error per 30 m chunk (w.r.t LiDAR ground-truth models).

Abhijit Kundu, Kyle Genova, Xiaoqi Yin et al.

We present Panoptic Neural Fields (PNF), an object-aware neural scene representation that decomposes a scene into a set of objects (things) and background (stuff). Each object is represented by an oriented 3D bounding box and a multi-layer perceptron (MLP) that takes position, direction, and time and outputs density and radiance. The background stuff is represented by a similar MLP that additionally outputs semantic labels. Each object MLPs are instance-specific and thus can be smaller and faster than previous object-aware approaches, while still leveraging category-specific priors incorporated via meta-learned initialization. Our model builds a panoptic radiance field representation of any scene from just color images. We use off-the-shelf algorithms to predict camera poses, object tracks, and 2D image semantic segmentations. Then we jointly optimize the MLP weights and bounding box parameters using analysis-by-synthesis with self-supervision from color images and pseudo-supervision from predicted semantic segmentations. During experiments with real-world dynamic scenes, we find that our model can be used effectively for several tasks like novel view synthesis, 2D panoptic segmentation, 3D scene editing, and multiview depth prediction.

Varun Agrawal, Frank Dellaert

Many problems in robotics involve both continuous and discrete components, and modeling them together for estimation tasks has been a long standing and difficult problem. Hybrid Factor Graphs give us a mathematical framework to model these types of problems, however existing approaches for solving them are based on approximations. In this work, we propose a new framework for hybrid factor graphs along with a novel variable elimination algorithm to produce a hybrid Bayes network, which can be used for exact Maximum A Posteriori estimation and marginalization over both sets of variables. Our approach first develops a novel hybrid Gaussian factor which can connect to both discrete and continuous variables, and a hybrid conditional which can represent multiple continuous hypotheses conditioned on the discrete variables. Using these representations, we derive the process of hybrid variable elimination under the Conditional Linear Gaussian scheme, giving us exact posteriors as a hybrid Bayes network. To bound the number of discrete hypotheses, we use a tree-structured representation of the factors coupled with a simple pruning and probabilistic assignment scheme, which allows for tractable inference. We demonstrate the applicability of our framework on a large scale SLAM dataset and a real world pose graph optimization problem, both with ambiguous measurements which require discrete choices to be made for the most likely measurements. Our demonstrated results showcase the accuracy, generality, and simplicity of our hybrid factor graph framework.

Ayush Baid, John Lambert, Travis Driver et al.

While initial approaches to Structure-from-Motion (SfM) revolved around both global and incremental methods, most recent applications rely on incremental systems to estimate camera poses due to their superior robustness. Though there has been tremendous progress in SfM `front-ends' powered by deep models learned from data, the state-of-the-art (incremental) SfM pipelines still rely on classical SIFT features, developed in 2004. In this work, we investigate whether leveraging the developments in feature extraction and matching helps global SfM perform on par with the SOTA incremental SfM approach (COLMAP). To do so, we design a modular SfM framework that allows us to easily combine developments in different stages of the SfM pipeline. Our experiments show that while developments in deep-learning based two-view correspondence estimation do translate to improvements in point density for scenes reconstructed with global SfM, none of them outperform SIFT when comparing with incremental SfM results on a range of datasets. Our SfM system is designed from the ground up to leverage distributed computation, enabling us to parallelize computation on multiple machines and scale to large scenes.

Shangjie Xue, Jesse Dill, Dhruv Ahuja et al.

We present Gaussian Splatting Anisotropic Visibility Field (GAVIS), a novel framework for uncertainty quantification and active mapping in 3DGS. Our key insight is that regions unseen from the training views yield unreliable predictions from the 3DGS. To address this, we introduce a principled and efficient method for quantifying the visibility field in 3DGS, defined as the anisotropic visibility of each particle with respect to the training views, and represented using spherical harmonics. The resulting visibility field is integrated into a Bayesian Network-based uncertainty-aware 3DGS rasterizer, enabling real-time (200 FPS) uncertainty quantification for synthesized views. Active mapping is further performed within a maximum information gain framework building on this formulation. Extensive experiments across diverse environments demonstrate that GAVIS consistently and significantly outperforms prior approaches in both accuracy and efficiency. Moreover, beyond standalone use, our method can be applied post-hoc to improve the performance of existing approaches.

Frank Dellaert, Chiyun Noh, Varun Agrawal et al.

Legged robots carry an IMU, but the inertial solution drifts because consumer-grade IMUs are noisy. However, the feet create intermittent contacts with the environment that can be used to mitigate that drift. This report develops a sequence of increasingly expressive legged robot state estimators that leverage this. In all cases, the floating-base state comprises attitude, position, velocity, and IMU biases. To model foot contacts, we start from the contact-aided invariant EKF of Hartley et al., albeit at a reduced contact update rate. This is then augmented by replacing the measurement update by a small factor graph. Finally, we turn the same factors into a fixed-lag smoother with contact-episode footholds, with and without an evolving IMU bias. To facilitate reproducibility and further research in proprioceptive legged odometry, all four variants are available in GTSAM (Dellaert et. al), and we additionally provide a ROS2-compatible implementation.

Yetong Zhang, Frank Dellaert

We introduce a manifold-based framework for addressing optimization problems with equality and inequality constraints found in robotics. Our approach transforms the original problem into an unconstrained optimization problem directly on the constrained state space. To achieve this, we introduce ``constraint manifolds with corners" to represent the state space satisfying mixed nonlinear equality and inequality constraints. We further extend manifold optimization algorithms to operate on this new topological structure. We demonstrate the power and robustness of our framework in the context of a large-scale kinodynamic planning problem, successfully generating dynamically feasible trajectories where standard methods fail.

John Lambert, Yuguang Li, Ivaylo Boyadzhiev et al.

We propose a new system for automatic 2D floorplan reconstruction that is enabled by SALVe, our novel pairwise learned alignment verifier. The inputs to our system are sparsely located 360$^\circ$ panoramas, whose semantic features (windows, doors, and openings) are inferred and used to hypothesize pairwise room adjacency or overlap. SALVe initializes a pose graph, which is subsequently optimized using GTSAM. Once the room poses are computed, room layouts are inferred using HorizonNet, and the floorplan is constructed by stitching the most confident layout boundaries. We validate our system qualitatively and quantitatively as well as through ablation studies, showing that it outperforms state-of-the-art SfM systems in completeness by over 200%, without sacrificing accuracy. Our results point to the significance of our work: poses of 81% of panoramas are localized in the first 2 connected components (CCs), and 89% in the first 3 CCs. Code and models are publicly available at https://github.com/zillow/salve.

Connor Holmes, Sven Lilge, Zi Cong Guo et al.

Continuous-time state estimation is gaining in popularity due to its abilities to provide smooth solutions, handle asynchronous sensors, and interpolate between data points. While there are two main paradigms, parametric (e.g., temporal basis functions, splines) and nonparametric (Gaussian processes), the latter has seen less adoption despite its technical advantages and relative ease of implementation. In this article, we seek to rectify this situation by providing a new simplified explanation of GP continuous-time estimation rooted in the language of factor graphs, which have become the de facto estimation paradigm in much of robotics. To simplify onboarding, we also provide three working examples implemented in the popular GTSAM estimation framework.

Shangjie Xue, Jesse Dill, Pranay Mathur et al.

This paper presents Neural Visibility Field (NVF), a novel uncertainty quantification method for Neural Radiance Fields (NeRF) applied to active mapping. Our key insight is that regions not visible in the training views lead to inherently unreliable color predictions by NeRF at this region, resulting in increased uncertainty in the synthesized views. To address this, we propose to use Bayesian Networks to composite position-based field uncertainty into ray-based uncertainty in camera observations. Consequently, NVF naturally assigns higher uncertainty to unobserved regions, aiding robots to select the most informative next viewpoints. Extensive evaluations show that NVF excels not only in uncertainty quantification but also in scene reconstruction for active mapping, outperforming existing methods.

Fan Jiang, Andrew Marmon, Ildebrando De Courten et al.

In many applications of computer vision it is important to accurately estimate the trajectory of an object over time by fusing data from a number of sources, of which 2D and 3D imagery is only one. In this paper, we show how to use a deep feature encoding in conjunction with generative densities over the features in a factor-graph based, probabilistic tracking framework. We present a likelihood model that combines a learned feature encoder with generative densities over them, both trained in a supervised manner. We also experiment with directly inferring probability through the use of image classification models that feed into the likelihood formulation. These models are used to implement deep factors that are added to the factor graph to complement other factors that represent domain-specific knowledge such as motion models and/or other prior information. Factors are then optimized together in a non-linear least-squares tracking framework that takes the form of an Extended Kalman Smoother with a Gaussian prior. A key feature of our likelihood model is that it leverages the Lie group properties of the tracked target's pose to apply the feature encoding on an image patch, extracted through a differentiable warp function inspired by spatial transformer networks. To illustrate the proposed approach we evaluate it on a challenging social insect behavior dataset, and show that using deep features does outperform these earlier linear appearance models used in this setting.

Russell Buchanan, Marco Camurri, Frank Dellaert et al.

This paper introduces a novel proprioceptive state estimator for legged robots based on a learned displacement measurement from IMU data. Recent research in pedestrian tracking has shown that motion can be inferred from inertial data using convolutional neural networks. A learned inertial displacement measurement can improve state estimation in challenging scenarios where leg odometry is unreliable, such as slipping and compressible terrains. Our work learns to estimate a displacement measurement from IMU data which is then fused with traditional leg odometry. Our approach greatly reduces the drift of proprioceptive state estimation, which is critical for legged robots deployed in vision and lidar denied environments such as foggy sewers or dusty mines. We compared results from an EKF and an incremental fixed-lag factor graph estimator using data from several real robot experiments crossing challenging terrains. Our results show a reduction of relative pose error by 37% in challenging scenarios when compared to a traditional kinematic-inertial estimator without learned measurement. We also demonstrate a 22% reduction in error when used with vision systems in visually degraded environments such as an underground mine.

Gerry Chen, Sereym Baek, Juan-Diego Florez et al.

We present GTGraffiti, a graffiti painting system from Georgia Tech that tackles challenges in art, hardware, and human-robot collaboration. The problem of painting graffiti in a human style is particularly challenging and requires a system-level approach because the robotics and art must be designed around each other. The robot must be highly dynamic over a large workspace while the artist must work within the robot's limitations. Our approach consists of three stages: artwork capture, robot hardware, and planning & control. We use motion capture to capture collaborator painting motions which are then composed and processed into a time-varying linear feedback controller for a cable-driven parallel robot (CDPR) to execute. In this work, we will describe the capturing process, the design and construction of a purpose-built CDPR, and the software for turning an artist's vision into control commands. Our work represents an important step towards faithfully recreating human graffiti artwork by demonstrating that we can reproduce artist motions up to 2m/s and 20m/s$^2$ within 9.3mm RMSE to paint artworks. Changes to the submitted manuscript are colored in blue.

Mandy Xie, Anqi Li, Karl Van Wyk et al.

Imitation learning (IL) is a frequently used approach for data-efficient policy learning. Many IL methods, such as Dataset Aggregation (DAgger), combat challenges like distributional shift by interacting with oracular experts. Unfortunately, assuming access to oracular experts is often unrealistic in practice; data used in IL frequently comes from offline processes such as lead-through or teleoperation. In this paper, we present a novel imitation learning technique called Collocation for Demonstration Encoding (CoDE) that operates on only a fixed set of trajectory demonstrations. We circumvent challenges with methods like back-propagation-through-time by introducing an auxiliary trajectory network, which takes inspiration from collocation techniques in optimal control. Our method generalizes well and more accurately reproduces the demonstrated behavior with fewer guiding trajectories when compared to standard behavioral cloning methods. We present simulation results on a 7-degree-of-freedom (DoF) robotic manipulator that learns to exhibit lifting, target-reaching, and obstacle avoidance behaviors.

Roshan Pradhan, Shuo Yang, Frank Dellaert et al.

Dynamical systems with a distributed yet interconnected structure, like multi-rigid-body robots or large-scale multi-agent systems, introduce valuable sparsity into the system dynamics that can be exploited in an optimal control setting for speeding up computation and improving numerical conditioning. Conventional approaches for solving the Optimal Control Problem (OCP) rarely capitalize on such structural sparsity, and hence suffer from a cubic computational complexity growth as the dimensionality of the system scales. In this paper, we present an OCP formulation that relies on graphical models to capture the sparsely-interconnected nature of the system dynamics. Such a representational choice allows the use of contemporary graphical inference algorithms that enable our solver to achieve a linear time complexity in the state and control dimensions as well as the time horizon. We demonstrate the numerical and computational advantages of our approach on a canonical dynamical system in simulation.

Fan Jiang, Varun Agrawal, Russell Buchanan et al.

State estimation of multi-modal hybrid systems is an important problem with many applications in the field robotics. However, incorporating discrete modes in the estimation process is hampered by a potentially combinatorial growth in computation. In this paper we present a novel incremental multi-hypothesis smoother based on eliminating a hybrid factor graph into a multi-hypothesis Bayes tree, which represents possible discrete state sequence hypotheses. Following iSAM, we enable incremental inference by conditioning the past on the future but we add to that the capability of maintaining multiple discrete mode histories, exploiting the temporal structure of the problem to obtain a simplified representation that unifies the multiple hypothesis tree with the Bayes tree. In the results section we demonstrate the generality of the algorithm with examples in three problem domains: lane change detection (1D), aircraft maneuver detection (2D), and contact detection in legged robots (3D).

Varun Agrawal, Frank Dellaert

We present a novel continuous time trajectory representation based on a Chebyshev polynomial basis, which when governed by known dynamics models, allows for full trajectory and robot dynamics estimation, particularly useful for high-performance robotics applications such as unmanned aerial vehicles. We show that we can gracefully incorporate model dynamics to our trajectory representation, within a factor-graph based framework, and leverage ideas from pseudo-spectral optimal control to parameterize the state and the control trajectories as interpolating polynomials. This allows us to perform efficient optimization at specifically chosen points derived from the theory, while recovering full trajectory estimates. Through simulated experiments we demonstrate the applicability of our representation for accurate flight dynamics estimation for multirotor aerial vehicles. The representation framework is general and can thus be applied to a multitude of high-performance applications beyond multirotor platforms.

Frank Dellaert, Lin Yen-Chen

Besides the COVID-19 pandemic and political upheaval in the US, 2020 was also the year in which neural volume rendering exploded onto the scene, triggered by the impressive NeRF paper by Mildenhall et al. (2020). Both of us have tried to capture this excitement, Frank on a blog post (Dellaert, 2020) and Yen-Chen in a Github collection (Yen-Chen, 2020). This note is an annotated bibliography of the relevant papers, and we posted the associated bibtex file on the repository.

Mandy Xie, Alejandro Escontrela, Frank Dellaert

In this paper, we introduce dynamics factor graphs as a graphical framework to solve dynamics problems and kinodynamic motion planning problems with full consideration of whole-body dynamics and contacts. A factor graph representation of dynamics problems provides an insightful visualization of their mathematical structure and can be used in conjunction with sparse nonlinear optimizers to solve challenging, high-dimensional optimization problems in robotics. We can easily formulate kinodynamic motion planning as a trajectory optimization problem with factor graphs. We demonstrate the flexibility and descriptive power of dynamics factor graphs by applying them to control various dynamical systems, ranging from a simple cart pole to a 12-DoF quadrupedal robot.

Shuo Yang, Gerry Chen, Yetong Zhang et al.

This paper presents a novel factor graph-based approach to solve the discrete-time finite-horizon Linear Quadratic Regulator problem subject to auxiliary linear equality constraints within and across time steps. We represent such optimal control problems using constrained factor graphs and optimize the factor graphs to obtain the optimal trajectory and the feedback control policies using the variable elimination algorithm with a modified Gram-Schmidt process. We prove that our approach has the same order of computational complexity as the state-of-the-art dynamic programming approach. Furthermore, current dynamic programming approaches can only handle equality constraints between variables at the same time step, but ours can handle equality constraints among any combination of variables at any time step while maintaining linear complexity with respect to trajectory length. Our approach can be used to efficiently generate trajectories and feedback control policies to achieve periodic motion or repetitive manipulation.

Frank Dellaert, David M. Rosen, Jing Wu et al.

Shonan Rotation Averaging is a fast, simple, and elegant rotation averaging algorithm that is guaranteed to recover globally optimal solutions under mild assumptions on the measurement noise. Our method employs semidefinite relaxation in order to recover provably globally optimal solutions of the rotation averaging problem. In contrast to prior work, we show how to solve large-scale instances of these relaxations using manifold minimization on (only slightly) higher-dimensional rotation manifolds, re-using existing high-performance (but local) structure-from-motion pipelines. Our method thus preserves the speed and scalability of current SFM methods, while recovering globally optimal solutions.

Mandy Xie, Frank Dellaert

This paper presents a kinodynamic motion planner that is able to produce energy efficient motions by taking the full robot dynamics into account, and making use of gravity, inertia, and momentum to reduce the effort. Given a specific goal state for the robot, we use factor graphs and numerical optimization to solve for an optimal trajectory, which meets not only the requirements of collision avoidance, but also all kinematic and dynamic constraints, such as velocity, acceleration and torque limits. By exploiting the sparsity in factor graphs, we can solve a kinodynamic motion planning problem efficiently, on par with existing optimal control methods, and use incremental elimination techniques to achieve an order of magnitude faster replanning.

Sen Wang, Jiaqi Chen, Xuanliang Deng et al.

Chinese calligraphy is a unique art form with great artistic value but difficult to master. In this paper, we formulate the calligraphy writing problem as a trajectory optimization problem, and propose an improved virtual brush model for simulating the real writing process. Our approach is inspired by pseudospectral optimal control in that we parameterize the actuator trajectory for each stroke as a Chebyshev polynomial. The proposed dynamic virtual brush model plays a key role in formulating the objective function to be optimized. Our approach shows excellent performance in drawing aesthetically pleasing characters, and does so much more efficiently than previous work, opening up the possibility to achieve real-time closed-loop control.

Mandy Xie, Frank Dellaert

This paper describes a unified method solving for inverse, forward, and hybrid dynamics problems for robotic manipulators with either open kinematic chains or closed kinematic loops based on factor graphs. Manipulator dynamics is considered to be a well studied problem, and various different algorithms have been developed to solve each type of dynamics problem. However, they are not easily explained in a unified and intuitive way. In this paper, we introduce factor graphs as a unifying graphical language in which not only to solve all types of dynamics problems, but also explain the classical dynamics algorithms in a unified framework.

Sen Wang, Jiaqi Chen, Xuanliang Deng et al.

Chinese calligraphy is a unique art form with great artistic value but difficult to master. In this paper, we formulate the calligraphy writing problem as a trajectory optimization problem, and propose an improved virtual brush model for simulating the real writing process. Our approach is inspired by pseudospectral optimal control in that we parameterize the actuator trajectory for each stroke as a Chebyshev polynomial. The proposed dynamic virtual brush model plays a key role in formulating the objective function to be optimized. Our approach shows excellent performance in drawing aesthetically pleasing characters, and does so much more efficiently than previous work, opening up the possibility to achieve real-time closed-loop control.

Abhinav Jain, Seth Hutchinson, Frank Dellaert

In this paper, we explore the task of robot sculpting. We propose a search based planning algorithm to solve the problem of sculpting by material removal with a multi-axis manipulator. We generate collision free trajectories for a manipulator using best-first search in voxel space. We also show significant speedup of our algorithm by using octrees to decompose the voxel space. We demonstrate our algorithm on a multi-axis manipulator in simulation by sculpting Michelangelo's Statue of David, evaluate certain metrics of our algorithm and discuss future goals for the project.

Abhinav Jain, Frank Dellaert

Pose estimation is a vital step in many robotics and perception tasks such as robotic manipulation, autonomous vehicle navigation, etc. Current state-of-the-art pose estimation methods rely on deep neural networks with complicated structures and long inference times. While highly robust, they require computing power often unavailable on mobile robots. We propose a CNN-based pose refinement system which takes a coarsely estimated 3D pose from a computationally cheaper algorithm along with a bounding box image of the object, and returns a highly refined pose. Our experiments on the YCB-Video dataset show that our system can refine 3D poses to an extremely high precision with minimal training data.

Zhaoyang Lv, Frank Dellaert, James M. Rehg et al.

In this paper, we provide a modern synthesis of the classic inverse compositional algorithm for dense image alignment. We first discuss the assumptions made by this well-established technique, and subsequently propose to relax these assumptions by incorporating data-driven priors into this model. More specifically, we unroll a robust version of the inverse compositional algorithm and replace multiple components of this algorithm using more expressive models whose parameters we train in an end-to-end fashion from data. Our experiments on several challenging 3D rigid motion estimation tasks demonstrate the advantages of combining optimization with learning-based techniques, outperforming the classic inverse compositional algorithm as well as data-driven image-to-pose regression approaches.

Jing Dong, Byron Boots, Frank Dellaert et al.

Image alignment tasks require accurate pixel correspondences, which are usually recovered by matching local feature descriptors. Such descriptors are often derived using supervised learning on existing datasets with ground truth correspondences. However, the cost of creating such datasets is usually prohibitive. In this paper, we propose a new approach to align two images related by an unknown 2D homography where the local descriptor is learned from scratch from the images and the homography is estimated simultaneously. Our key insight is that a siamese convolutional neural network can be trained jointly while iteratively updating the homography parameters by optimizing a single loss function. Our method is currently weakly supervised because the input images need to be roughly aligned. We have used this method to align images of different modalities such as RGB and near-infra-red (NIR) without using any prior labeled data. Images automatically aligned by our method were then used to train descriptors that generalize to new images. We also evaluated our method on RGB images. On the HPatches benchmark, our method achieves comparable accuracy to deep local descriptors that were trained offline in a supervised setting.

Mustafa Mukadam, Jing Dong, Frank Dellaert et al.

We present a unified probabilistic framework for simultaneous trajectory estimation and planning (STEAP). Estimation and planning problems are usually considered separately, however, within our framework we show that solving them simultaneously can be more accurate and efficient. The key idea is to compute the full continuous-time trajectory from start to goal at each time-step. While the robot traverses the trajectory, the history portion of the trajectory signifies the solution to the estimation problem, and the future portion of the trajectory signifies a solution to the planning problem. Building on recent probabilistic inference approaches to continuous-time localization and mapping and continuous-time motion planning, we solve the joint problem by iteratively recomputing the maximum a posteriori trajectory conditioned on all available sensor data and cost information. Our approach can contend with high-degree-of-freedom (DOF) trajectory spaces, uncertainty due to limited sensing capabilities, model inaccuracy, the stochastic effect of executing actions, and can find a solution in real-time. We evaluate our framework empirically in both simulation and on a mobile manipulator.

Mustafa Mukadam, Jing Dong, Xinyan Yan et al.

We introduce a novel formulation of motion planning, for continuous-time trajectories, as probabilistic inference. We first show how smooth continuous-time trajectories can be represented by a small number of states using sparse Gaussian process (GP) models. We next develop an efficient gradient-based optimization algorithm that exploits this sparsity and GP interpolation. We call this algorithm the Gaussian Process Motion Planner (GPMP). We then detail how motion planning problems can be formulated as probabilistic inference on a factor graph. This forms the basis for GPMP2, a very efficient algorithm that combines GP representations of trajectories with fast, structure-exploiting inference via numerical optimization. Finally, we extend GPMP2 to an incremental algorithm, iGPMP2, that can efficiently replan when conditions change. We benchmark our algorithms against several sampling-based and trajectory optimization-based motion planning algorithms on planning problems in multiple environments. Our evaluation reveals that GPMP2 is several times faster than previous algorithms while retaining robustness. We also benchmark iGPMP2 on replanning problems, and show that it can find successful solutions in a fraction of the time required by GPMP2 to replan from scratch.

Jing Dong, Byron Boots, Frank Dellaert

Continuous-time trajectory representations are a powerful tool that can be used to address several issues in many practical simultaneous localization and mapping (SLAM) scenarios, like continuously collected measurements distorted by robot motion, or during with asynchronous sensor measurements. Sparse Gaussian processes (GP) allow for a probabilistic non-parametric trajectory representation that enables fast trajectory estimation by sparse GP regression. However, previous approaches are limited to dealing with vector space representations of state only. In this technical report we extend the work by Barfoot et al. [1] to general matrix Lie groups, by applying constant-velocity prior, and defining locally linear GP. This enables using sparse GP approach in a large space of practical SLAM settings. In this report we give the theory and leave the experimental evaluation in future publications.

Siddharth Choudhary, Luca Carlone, Carlos Nieto et al.

We consider the following problem: a team of robots is deployed in an unknown environment and it has to collaboratively build a map of the area without a reliable infrastructure for communication. The backbone for modern mapping techniques is pose graph optimization, which estimates the trajectory of the robots, from which the map can be easily built. The first contribution of this paper is a set of distributed algorithms for pose graph optimization: rather than sending all sensor data to a remote sensor fusion server, the robots exchange very partial and noisy information to reach an agreement on the pose graph configuration. Our approach can be considered as a distributed implementation of the two-stage approach of Carlone et al., where we use the Successive Over-Relaxation (SOR) and the Jacobi Over-Relaxation (JOR) as workhorses to split the computation among the robots. As a second contribution, we extend %and demonstrate the applicability of the proposed distributed algorithms to work with object-based map models. The use of object-based models avoids the exchange of raw sensor measurements (e.g., point clouds) further reducing the communication burden. Our third contribution is an extensive experimental evaluation of the proposed techniques, including tests in realistic Gazebo simulations and field experiments in a military test facility. Abundant experimental evidence suggests that one of the proposed algorithms (the Distributed Gauss-Seidel method or DGS) has excellent performance. The DGS requires minimal information exchange, has an anytime flavor, scales well to large teams, is robust to noise, and is easy to implement. Our field tests show that the combined use of our distributed algorithms and object-based models reduces the communication requirements by several orders of magnitude and enables distributed mapping with large teams of robots in real-world problems.

Jing Dong, John Gary Burnham, Byron Boots et al.

Autonomous crop monitoring at high spatial and temporal resolution is a critical problem in precision agriculture. While Structure from Motion and Multi-View Stereo algorithms can finely reconstruct the 3D structure of a field with low-cost image sensors, these algorithms fail to capture the dynamic nature of continuously growing crops. In this paper we propose a 4D reconstruction approach to crop monitoring, which employs a spatio-temporal model of dynamic scenes that is useful for precision agriculture applications. Additionally, we provide a robust data association algorithm to address the problem of large appearance changes due to scenes being viewed from different angles at different points in time, which is critical to achieving 4D reconstruction. Finally, we collected a high quality dataset with ground truth statistics to evaluate the performance of our method. We demonstrate that our 4D reconstruction approach provides models that are qualitatively correct with respect to visual appearance and quantitatively accurate when measured against the ground truth geometric properties of the monitored crops.

Zhaoyang Lv, Chris Beall, Pablo F. Alcantarilla et al.

We propose a continuous optimization method for solving dense 3D scene flow problems from stereo imagery. As in recent work, we represent the dynamic 3D scene as a collection of rigidly moving planar segments. The scene flow problem then becomes the joint estimation of pixel-to-segment assignment, 3D position, normal vector and rigid motion parameters for each segment, leading to a complex and expensive discrete-continuous optimization problem. In contrast, we propose a purely continuous formulation which can be solved more efficiently. Using a fine superpixel segmentation that is fixed a-priori, we propose a factor graph formulation that decomposes the problem into photometric, geometric, and smoothing constraints. We initialize the solution with a novel, high-quality initialization method, then independently refine the geometry and motion of the scene, and finally perform a global non-linear refinement using Levenberg-Marquardt. We evaluate our method in the challenging KITTI Scene Flow benchmark, ranking in third position, while being 3 to 30 times faster than the top competitors.

Christian Forster, Luca Carlone, Frank Dellaert et al.

Current approaches for visual-inertial odometry (VIO) are able to attain highly accurate state estimation via nonlinear optimization. However, real-time optimization quickly becomes infeasible as the trajectory grows over time, this problem is further emphasized by the fact that inertial measurements come at high rate, hence leading to fast growth of the number of variables in the optimization. In this paper, we address this issue by preintegrating inertial measurements between selected keyframes into single relative motion constraints. Our first contribution is a \emph{preintegration theory} that properly addresses the manifold structure of the rotation group. We formally discuss the generative measurement model as well as the nature of the rotation noise and derive the expression for the \emph{maximum a posteriori} state estimator. Our theoretical development enables the computation of all necessary Jacobians for the optimization and a-posteriori bias correction in analytic form. The second contribution is to show that the preintegrated IMU model can be seamlessly integrated into a visual-inertial pipeline under the unifying framework of factor graphs. This enables the application of incremental-smoothing algorithms and the use of a \emph{structureless} model for visual measurements, which avoids optimizing over the 3D points, further accelerating the computation. We perform an extensive evaluation of our monocular \VIO pipeline on real and simulated datasets. The results confirm that our modelling effort leads to accurate state estimation in real-time, outperforming state-of-the-art approaches.

Luca Carlone, David Rosen, Giuseppe Calafiore et al.

State-of-the-art techniques for simultaneous localization and mapping (SLAM) employ iterative nonlinear optimization methods to compute an estimate for robot poses. While these techniques often work well in practice, they do not provide guarantees on the quality of the estimate. This paper shows that Lagrangian duality is a powerful tool to assess the quality of a given candidate solution. Our contribution is threefold. First, we discuss a revised formulation of the SLAM inference problem. We show that this formulation is probabilistically grounded and has the advantage of leading to an optimization problem with quadratic objective. The second contribution is the derivation of the corresponding Lagrangian dual problem. The SLAM dual problem is a (convex) semidefinite program, which can be solved reliably and globally by off-the-shelf solvers. The third contribution is to discuss the relation between the original SLAM problem and its dual. We show that from the dual problem, one can evaluate the quality (i.e., the suboptimality gap) of a candidate SLAM solution, and ultimately provide a certificate of optimality. Moreover, when the duality gap is zero, one can compute a guaranteed optimal SLAM solution from the dual problem, circumventing non-convex optimization. We present extensive (real and simulated) experiments supporting our claims and discuss practical relevance and open problems.

Giuseppe Calafiore, Luca Carlone, Frank Dellaert

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, then (i) the duality gap is zero, (ii) the primal PGO problem has a unique solution, and (iii) the primal solution can be computed by scaling an eigenvector of the penalized pose graph matrix. The third contribution is algorithmic: we exploit the dual problem and propose an algorithm that computes a guaranteed optimal solution for PGO when the penalized pose graph matrix satisfies the Single Zero Eigenvalue Property (SZEP). We also propose a variant that deals with the case in which the SZEP is not satisfied. The fourth contribution is a numerical analysis. Empirical evidence shows that in the vast majority of cases (100% of the tests under noise regimes of practical robotics applications) the penalized pose graph matrix does satisfy the SZEP, hence our approach allows computing the global optimal solution. Finally, we report simple counterexamples in which the duality gap is nonzero, and discuss open problems.