An incremental trust-region method for Robust online sparse least-squares estimation

Many online inference problems in computer vision and robotics are characterized by probability distributions whose factor graph representations are sparse and whose factors are all Gaussian functions of error residuals. Under these conditions, maximum likelihood estimation corresponds to solving a sequence of sparse least-squares minimization problems in which additional summands are added to the objective function over time. In this paper we present Robust Incremental least-Squares Estimation (RISE), an incrementalized version of the Powell's Dog-Leg trust-region method suitable for use in online sparse least-squares minimization. As a trust-region method, Powell's Dog-Leg enjoys excellent global convergence properties, and is known to be considerably faster than both Gauss-Newton and Levenberg-Marquardt when applied to sparse least-squares problems. Consequently, RISE maintains the speed of current state-of-the-art incremental sparse least-squares methods while providing superior robustness to objective function nonlinearities.United States. Office of Naval Research (Grant N00014-06-1-0043)United States. Office of Naval Research (Grant N00014-10-1-0936)United States. Air Force Research Laboratory (Contract FA8650-11-C-7137

A convex relaxation for approximate global optimization in simultaneous localization and mapping

Modern approaches to simultaneous localization and mapping (SLAM) formulate the inference problem as a high-dimensional but sparse nonconvex M-estimation, and then apply general first- or second-order smooth optimization methods to recover a local minimizer of the objective function. The performance of any such approach depends crucially upon initializing the optimization algorithm near a good solution for the inference problem, a condition that is often difficult or impossible to guarantee in practice. To address this limitation, in this paper we present a formulation of the SLAM M-estimation with the property that, by expanding the feasible set of the estimation program, we obtain a convex relaxation whose solution approximates the globally optimal solution of the SLAM inference problem and can be recovered using a smooth optimization method initialized at any feasible point. Our formulation thus provides a means to obtain a high-quality solution to the SLAM problem without requiring high-quality initialization.Google (Firm) (Software Engineering Internship)United States. Office of Naval Research (Grants N00014-10-1-0936, N00014-11-1-0688 and N00014- 13-1-0588)National Science Foundation (U.S.) (Award IIS-1318392

RISE: An Incremental Trust-Region Method for Robust Online Sparse Least-Squares Estimation

Many point estimation problems in robotics, computer vision, and machine learning can be formulated as instances of the general problem of minimizing a sparse nonlinear sum-of-squares objective function. For inference problems of this type, each input datum gives rise to a summand in the objective function, and therefore performing online inference corresponds to solving a sequence of sparse nonlinear least-squares minimization problems in which additional summands are added to the objective function over time. In this paper, we present Robust Incremental least-Squares Estimation (RISE), an incrementalized version of the Powell's Dog-Leg numerical optimization method suitable for use in online sequential sparse least-squares minimization. As a trust-region method, RISE is naturally robust to objective function nonlinearity and numerical ill-conditioning and is provably globally convergent for a broad class of inferential cost functions (twice-continuously differentiable functions with bounded sublevel sets). Consequently, RISE maintains the speed of current state-of-the-art online sparse least-squares methods while providing superior reliability.United States. Office of Naval Research (Grant N00014-12-1-0093)United States. Office of Naval Research (Grant N00014-11-1-0688)United States. Office of Naval Research (Grant N00014-06-1-0043)United States. Office of Naval Research (Grant N00014-10-1-0936)United States. Air Force Research Laboratory (Contract FA8650-11-C-7137

OASIS: Optimal Arrangements for Sensing in SLAM

The number and arrangement of sensors on an autonomous mobile robot dramatically influence its perception capabilities. Ensuring that sensors are mounted in a manner that enables accurate detection, localization, and mapping is essential for the success of downstream control tasks. However, when designing a new robotic platform, researchers and practitioners alike usually mimic standard configurations or maximize simple heuristics like field-of-view (FOV) coverage to decide where to place exteroceptive sensors. In this work, we conduct an information-theoretic investigation of this overlooked element of mobile robotic perception in the context of simultaneous localization and mapping (SLAM). We show how to formalize the sensor arrangement problem as a form of subset selection under the E-optimality performance criterion. While this formulation is NP-hard in general, we further show that a combination of greedy sensor selection and fast convex relaxation-based post-hoc verification enables the efficient recovery of certifiably optimal sensor designs in practice. Results from synthetic experiments reveal that sensors placed with OASIS outperform benchmarks in terms of mean squared error of visual SLAM estimates

Alterations of neural activity in the prefrontal cortex associated with deficits in working memory performance

Working memory (WM), a core cognitive function, enables the temporary holding and manipulation of information in mind to support ongoing behavior. Neurophysiological recordings conducted in nonhuman primates have revealed neural correlates of this process in a network of higher-order cortical regions, particularly the prefrontal cortex (PFC). Here, we review the circuit mechanisms and functional importance of WM-related activity in these areas. Recent neurophysiological data indicates that the absence of these neural correlates at different stages of WM is accompanied by distinct behavioral deficits, which are characteristic of various disease states/normal aging and which we review here. Finally, we discuss emerging evidence of electrical stimulation ameliorating these WM deficits in both humans and non-human primates. These results are important for a basic understanding of the neural mechanisms supporting WM, as well as for translational efforts to developing therapies capable of enhancing healthy WM ability or restoring WM from dysfunction

SE-Sync: a certifiably correct algorithm for synchronization over the special Euclidean group

Many important geometric estimation problems naturally take the form of synchronization over the special Euclidean group: estimate the values of a set of unknown group elements (Formula presented.) given noisy measurements of a subset of their pairwise relative transforms (Formula presented.). Examples of this class include the foundational problems of pose-graph simultaneous localization and mapping (SLAM) (in robotics), camera motion estimation (in computer vision), and sensor network localization (in distributed sensing), among others. This inference problem is typically formulated as a non-convex maximum-likelihood estimation that is computationally hard to solve in general. Nevertheless, in this paper we present an algorithm that is able to efficiently recover certifiably globally optimal solutions of the special Euclidean synchronization problem in a non-adversarial noise regime. The crux of our approach is the development of a semidefinite relaxation of the maximum-likelihood estimation (MLE) whose minimizer provides an exact maximum-likelihood estimate so long as the magnitude of the noise corrupting the available measurements falls below a certain critical threshold; furthermore, whenever exactness obtains, it is possible to verify this fact a posteriori, thereby certifying the optimality of the recovered estimate. We develop a specialized optimization scheme for solving large-scale instances of this semidefinite relaxation by exploiting its low-rank, geometric, and graph-theoretic structure to reduce it to an equivalent optimization problem defined on a low-dimensional Riemannian manifold, and then design a Riemannian truncated-Newton trust-region method to solve this reduction efficiently. Finally, we combine this fast optimization approach with a simple rounding procedure to produce our algorithm, SE-Sync. Experimental evaluation on a variety of simulated and real-world pose-graph SLAM datasets shows that SE-Sync is capable of recovering certifiably globally optimal solutions when the available measurements are corrupted by noise up to an order of magnitude greater than that typically encountered in robotics and computer vision applications, and does so significantly faster than the Gauss–Newton-based approach that forms the basis of current state-of-the-art techniques

A Smooth Representation of Belief over SO(3) for Deep Rotation Learning with Uncertainty

Accurate rotation estimation is at the heart of robot perception tasks such as visual odometry and object pose estimation. Deep neural networks have provided a new way to perform these tasks, and the choice of rotation representation is an important part of network design. In this work, we present a novel symmetric matrix representation of the 3D rotation group, SO(3), with two important properties that make it particularly suitable for learned models: (1) it satisfies a smoothness property that improves convergence and generalization when regressing large rotation targets, and (2) it encodes a symmetric Bingham belief over the space of unit quaternions, permitting the training of uncertainty-aware models. We empirically validate the benefits of our formulation by training deep neural rotation regressors on two data modalities. First, we use synthetic point-cloud data to show that our representation leads to superior predictive accuracy over existing representations for arbitrary rotation targets. Second, we use image data collected onboard ground and aerial vehicles to demonstrate that our representation is amenable to an effective out-of-distribution (OOD) rejection technique that significantly improves the robustness of rotation estimates to unseen environmental effects and corrupted input images, without requiring the use of an explicit likelihood loss, stochastic sampling, or an auxiliary classifier. This capability is key for safety-critical applications where detecting novel inputs can prevent catastrophic failure of learned models.Comment: In Proceedings of Robotics: Science and Systems (RSS'20), Corvallis , Oregon, USA, Jul. 12-16, 202

Distributed functions of prefrontal and parietal cortices during sequential categorical decisions

Comparing sequential stimuli is crucial for guiding complex behaviors. To understand mechanisms underlying sequential decisions, we compared neuronal responses in the prefrontal cortex (PFC), the lateral intraparietal (LIP), and medial intraparietal (MIP) areas in monkeys trained to decide whether sequentially presented stimuli were from matching (M) or nonmatching (NM) categories. We found that PFC leads M/NM decisions, whereas LIP and MIP appear more involved in stimulus evaluation and motor planning, respectively. Compared to LIP, PFC showed greater nonlinear integration of currently visible and remembered stimuli, which correlated with the monkeys’ M/NM decisions. Furthermore, multi-module recurrent networks trained on the same task exhibited key features of PFC and LIP encoding, including nonlinear integration in the PFC-like module, which was causally involved in the networks’ decisions. Network analysis found that nonlinear units have stronger and more widespread connections with input, output, and within-area units, indicating putative circuit-level mechanisms for sequential decisions