Person:
Dellaert,
Frank
Dellaert,
Frank
Permanent Link
Associated Organization(s)
Organizational Unit
ORCID
ArchiveSpace Name Record
Publication Search Results
Now showing
1 - 10 of 57
-
ItemDuality-based Verification Techniques for 2D SLAM(Georgia Institute of Technology, 2015-05) Carlone, Luca ; Dellaert, FrankWhile iterative optimization techniques for Simultaneous Localization and Mapping (SLAM) are now very efficient and widely used, none of them can guarantee global convergence to the maximum likelihood estimate. Local convergence usually implies artifacts in map reconstruction and large localization errors, hence it is very undesirable for applications in which accuracy and safety are of paramount importance. We provide a technique to verify if a given 2D SLAM solution is globally optimal. The insight is that, while computing the optimal solution is hard in general, duality theory provides tools to compute tight bounds on the optimal cost, via convex programming. These bounds can be used to evaluate the quality of a SLAM solution, hence providing a “sanity check” for state-of-the-art incremental and batch solvers. Experimental results show that our technique successfully identifies wrong estimates (i.e., local minima) in large-scale SLAM scenarios. This work, together with [1], represents a step towards the objective of having SLAM techniques with guaranteed performance, that can be used in safety-critical applications.
-
ItemMonocular Image Space Tracking on a Computationally Limited MAV(Georgia Institute of Technology, 2015-05) Ok, Kyel ; Gamage, Dinesh ; Drummond, Tom ; Dellaert, Frank ; Roy, NicholasWe propose a method of monocular camera-inertial based navigation for computationally limited micro air vehicles (MAVs). Our approach is derived from the recent development of parallel tracking and mapping algorithms, but unlike previous results, we show how the tracking and mapping processes operate using different representations.The separation of representations allows us not only to move the computational load of full map inference to a ground station, but to further reduce the computational cost of on-board tracking for pose estimation. Our primary contribution is to show how the cost of tracking the vehicle pose on-board can be substantially reduced by estimating the camera motion directly in the image frame, rather than in the world co-ordinate frame. We demonstrate our method on an Ascending Technologies Pelican quad-rotor, and show that we can track the vehicle pose with reduced on-board computation but without compromised navigation accuracy.
-
ItemDifferential Dynamic Programming for Optimal Estimation(Georgia Institute of Technology, 2015-05) Kobilarov, Marin ; Ta, Duy-Nguyen ; Dellaert, FrankThis paper studies an optimization-based approach for solving optimal estimation and optimal control problems through a unified computational formulation. The goal is to perform trajectory estimation over extended past horizons and model-predictive control over future horizons by enforcing the same dynamics, control, and sensing constraints in both problems, and thus solving both problems with identical computational tools. Through such systematic estimation-control formulation we aim to improve the performance of autonomous systems such as agile robotic vehicles. This work focuses on sequential sweep trajectory optimization methods, and more specifically extends the method known as differential dynamic programming to the parameter-dependent setting in order to enable the solutions to general estimation and control problems.
-
ItemDistributed Navigation with Unknown Initial Poses and Data Association via Expectation Maximization(Georgia Institute of Technology, 2015-02) Indelman, Vadim ; Michael, Nathan ; Dellaert, FrankWe present a novel approach for multi-robot distributed and incremental inference over variables of interest, such as robot trajectories, considering the initial relative poses between the robots and multi-robot data association are both unknown. Assuming robots share with each other informative observations, this inference problem is formulated within an Expectation-Maximization (EM) optimization, performed by each robot separately, alternating between inference over variables of interest and multi-robot data association. To facilitate this process, a common reference frame between the robots should first be established. We show the latter is coupled with determining multi-robot data association, and therefore concurrently infer both using a separate EM optimization. This optimization is performed by each robot starting from several promising initial solutions, converging to locally-optimal hypotheses regarding data association and reference frame transformation. Choosing the best hypothesis in an incremental problem setting is in particular challenging due to high sensitivity to measurement aliasing and possibly insufficient amount of data. Selecting an incorrect hypothesis introduces outliers and can lead to catastrophic results. To address these challenges we develop a model-selection based approach to choose the most probable hypothesis, while resorting to Chinese Restaurant Process to represent statistical knowledge regarding hypothesis prior probabilities. We evaluate our approach in real-data experiments.
-
ItemRigid Components Identification and Rigidity Enforcement in Bearing-Only Localization using the Graph Cycle Basis(Georgia Institute of Technology, 2015) Tron, Roberto ; Carlone, Luca ; Dellaert, Frank ; Daniilidis, KostasBearing-only localization can be formulated in terms of optimal graph embedding: one has to assign a 2-D or 3-D position to each node in a graph while satisfying as close as possible all the bearing-only constraints on the edges. If the graph is parallel rigid, this can be done via spectral methods. When the graph is not rigid the reconstruction is ambiguous, as different subsets of vertices can be scaled differently. It is therefore important to first identify a partition of the problem into maximal rigid components. In this paper we show that the cycle basis matrix of the graph not only translates into an algorithm to identify all rigid sub-graphs, but also provides a more intuitive way to look at graph rigidity, showing, for instance, why triangulated graphs are rigid and why graphs with long cycles may loose this property. Furthermore, it provides practical tools to enforce rigidity by adding a minimal number of measurements.
-
ItemLinear-Time Estimation with Tree Assumed Density Filtering and Low-Rank Approximation(Georgia Institute of Technology, 2014-09) Ta, Duy-Nguyen ; Dellaert, FrankWe present two fast and memory-efficient approximate estimation methods, targeting obstacle avoidance applications on small robot platforms. Our methods avoid a main bottleneck of traditional filtering techniques, which creates densely correlated cliques of landmarks, leading to expensive time and space complexity. We introduce a novel technique to avoid the dense cliques by sparsifying them into a tree structure and maintain that tree structure efficiently over time. Unlike other edge removal graph sparsification methods, our methods sparsify the landmark cliques by introducing new variables to de-correlate them. The first method projects the current density onto a tree rooted at the same variable at each step. The second method improves upon the first one by carefully choosing a new low-dimensional root variable at each step to replace such that the independence and conditional densities of the landmarks given the trajectory are optimally preserved. Our experiments show a significant improvement in time and space complexity of the methods compared to other standard filtering techniques in worst-case scenarios, with small trade-offs in accuracy due to low-rank approximation errors.
-
ItemConcurrent Filtering and Smoothing: A Parallel Architecture for Real-Time Navigation and Full Smoothing(Georgia Institute of Technology, 2014) Williams, Stephen ; Indelman, Vadim ; Kaess, Michael ; Roberts, Richard ; Leonard, John J. ; Dellaert, FrankWe present a parallelized navigation architecture that is capable of running in real-time and incorporating long-term loop closure constraints while producing the optimal Bayesian solution. This architecture splits the inference problem into a low-latency update that incorporates new measurements using just the most recent states (filter), and a high-latency update that is capable of closing long loops and smooths using all past states (smoother). This architecture employs the probabilistic graphical models of Factor Graphs, which allows the low-latency inference and high-latency inference to be viewed as sub-operations of a single optimization performed within a single graphical model. A specific factorization of the full joint density is employed that allows the different inference operations to be performed asynchronously while still recovering the optimal solution produced by a full batch optimization. Due to the real-time, asynchronous nature of this algorithm, updates to the state estimates from the high-latency smoother will naturally be delayed until the smoother calculations have completed. This architecture has been tested within a simulated aerial environment and on real data collected from an autonomous ground vehicle. In all cases, the concurrent architecture is shown to recover the full batch solution, even while updated state estimates are produced in real-time.
-
ItemModern MAP Inference Methods for Accurate and Fast Occupancy Grid Mapping on Higher Order Factor Graphs(Georgia Institute of Technology, 2014) Dhiman, Vikas ; Kundu, Abhijit ; Dellaert, Frank ; Corso, Jason J.Using the inverse sensor model has been popular in occupancy grid mapping. However, it is widely known that applying the inverse sensor model to mapping requires certain assumptions that are not necessarily true. Even the works that use forward sensor models have relied on methods like expectation maximization or Gibbs sampling which have been succeeded by more effective methods of maximum a posteriori (MAP) inference over graphical models. In this paper, we propose the use of modern MAP inference methods along with the forward sensor model. Our implementation and experimental results demonstrate that these modern inference methods deliver more accurate maps more efficiently than previously used methods.
-
ItemEliminating Conditionally Independent Sets in Factor Graphs: A Unifying Perspective based on Smart Factors(Georgia Institute of Technology, 2014) Carlone, Luca ; Kira, Zsolt ; Beall, Chris ; Indelman, Vadim ; Dellaert, FrankFactor graphs are a general estimation framework that has been widely used in computer vision and robotics. In several classes of problems a natural partition arises among variables involved in the estimation. A subset of the variables are actually of interest for the user: we call those target variables. The remaining variables are essential for the formulation of the optimization problem underlying maximum a posteriori (MAP) estimation; however these variables, that we call support variables, are not strictly required as output of the estimation problem. In this paper, we propose a systematic way to abstract support variables, defining optimization problems that are only defined over the set of target variables. This abstraction naturally leads to the definition of smart factors, which correspond to constraints among target variables. We show that this perspective unifies the treatment of heterogeneous problems, ranging from structureless bundle adjustment to robust estimation in SLAM. Moreover, it enables to exploit the underlying structure of the optimization problem and the treatment of degenerate instances, enhancing both computational efficiency and robustness.
-
ItemTowards Planning in Generalized Belief Space(Georgia Institute of Technology, 2013-12) Indelman, Vadim ; Carlone, Luca ; Dellaert, FrankWe investigate the problem of planning under uncertainty, which is of interest in several robotic applications, ranging from autonomous navigation to manipulation. Recent effort from the research community has been devoted to design planning approaches working in a continuous domain, relaxing the assumption that the controls belong to a finite set. In this case robot policy is computed from the current robot belief (planning in belief space), while the environment in which the robot moves is usually assumed to be known or partially known. We contribute to this branch of the literature by relaxing the assumption of known environment; for this purpose we introduce the concept of generalized belief space (GBS), in which the robot maintains a joint belief over its state and the state of the environment. We use GBS within a Model Predictive Control (MPC) scheme; our formulation is valid for general cost functions and incorporates a dual-layer optimization: the outer layer computes the best control action, while the inner layer computes the generalized belief given the action. The resulting approach does not require prior knowledge of the environment and does not assume maximum likelihood observations. We also present an application to a specific family of cost functions and we elucidate on the theoretical derivation with numerical examples.