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Dellaert, Frank

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Author: Indelman, Vadim × Has files: Yes × search.filters.applied.f.resourcesubtype: Article ×

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    Planning in the Continuous Domain: a Generalized Belief Space Approach for Autonomous Navigation in Unknown Environments
    (Georgia Institute of Technology, 2015) Indelman, Vadim ; Carlone, Luca ; Dellaert, Frank
    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.
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    Incremental Light Bundle Adjustment for Structure From Motion and Robotics
    (Georgia Institute of Technology, 2015) Indelman, Vadim ; Roberts, Richard ; Dellaert, Frank
    Bundle adjustment (BA) is essential in many robotics and structure-from-motion applications. In robotics, often a bundle adjustment solution is desired to be available incrementally as new poses and 3D points are observed. Similarly in batch structure from motion, cameras are typically added incrementally to allow good initializations. Current incremental BA methods quickly become computationally expensive as more camera poses and 3D points are added into the optimization. In this paper we introduce incremental light bundle adjustment (iLBA), an efficient optimization framework that substantially reduces computational complexity compared to incremental bundle adjustment. First, the number of variables in the optimization is reduced by algebraic elimination of observed 3D points, leading to a structureless BA. The resulting cost function is formulated in terms of three-view constraints instead of re-projection errors and only the camera poses are optimized. Second, the optimization problem is represented using graphical models and incremental inference is applied, updating the solution using adaptive partial calculations each time a new camera is incorporated into the optimization. Typically, only a small fraction of the camera poses are recalculated in each optimization step. The 3D points, although not explicitly optimized, can be reconstructed based on the optimized camera poses at any time. We study probabilistic and computational aspects of iLBA and compare its accuracy against incremental BA and another recent structureless method using real-imagery and synthetic datasets. Results indicate iLBA is 2-10 times faster than incremental BA, depending on number of image observations per frame.
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    Concurrent 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, Frank
    We 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.
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    Information Fusion in Navigation Systems via Factor Graph Based Incremental Smoothing
    (Georgia Institute of Technology, 2013-08) Indelman, Vadim ; Williams, Stephen ; Kaess, Michael ; Dellaert, Frank
    This paper presents a new approach for high-rate information fusion in modern inertial navigation systems, that have a variety of sensors operating at different frequencies. Optimal information fusion corresponds to calculating the maximum a posteriori estimate over the joint probability distribution function (pdf) of all states, a computationally-expensive process in the general case. Our approach consists of two key components, which yields a flexible, high-rate, near-optimal inertial navigation system. First, the joint pdf is represented using a graphical model, the factor graph, that fully exploits the system sparsity and provides a plug and play capability that easily accommodates the addition and removal of measurement sources. Second, an efficient incremental inference algorithm over the factor graph is applied, whose performance approaches the solution that would be obtained by a computationally-expensive batch optimization at a fraction of the computational cost. To further aid high-rate performance, we introduce an equivalent IMU factor based on a recently developed technique for IMU pre-integration, drastically reducing the number of states that must be added to the system. The proposed approach is experimentally validated using real IMU and imagery data that was recorded by a ground vehicle, and a statistical performance study is conducted in a simulated aerial scenario. A comparison to conventional fixed-lag smoothing demonstrates that our method provides a considerably improved trade-off between computational complexity and performance.