arXiv subjects

Alan Papalia

Publications and source records attributed to Alan Papalia.

14 recordsLinked to original sources

arXiv2026

$(\text{DNN})^2$: Doubly Non-Negative Relaxations for Deep Neural Networks

Existing linear program (LP) and semidefinite program (SDP) relaxations for rectified linear unit (ReLU) neural network (NN) verification yield overly-conservative safety guarantees due to significant relaxation gaps. While the completely positive program (CPP) formulation closes this gap, it is NP-hard to solve. Its cheapest tractable relaxation, the doubly non-negative program (DNN), retains critical constraints as an SDP, but one whose size exceeds the reach of interior-point methods at practical scale. While Burer-Monteiro (BM) factorization has been applied to make SDP-based verification scalable, no such result exists for the strictly tighter DNN formulation. A key obstacle is that additional non-negativity constraints in the DNN cause dual multipliers for optimality certification to be non-unique, making standard certification methods inapplicable. We propose a novel eigenvalue maximization procedure that searches the non-unique multiplier space for a valid certificate, i.e. a global optimality guarantee. Experiments demonstrate that our approach $(\text{DNN})^2$ produces bounds consistently tighter than the standard SDP method, often matching the exact solution, and that our certification procedure confirms global optimality when a valid certificate exists. These results are a key step toward providing tight, certifiable, and computationally scalable verification guarantees needed to deploy neural network controllers and perception modules in safety-critical autonomous systems.

cs.LG↗

arXiv2025

Sparse Variable Projection in Robotic Perception: Exploiting Separable Structure for Efficient Nonlinear Optimization

Robotic perception often requires solving large nonlinear least-squares (NLS) problems. While sparsity has been well-exploited to scale solvers, a complementary and underexploited structure is \emph{separability} -- where some variables (e.g., visual landmarks) appear linearly in the residuals and, for any estimate of the remaining variables (e.g., poses), have a closed-form solution. Variable projection (VarPro) methods are a family of techniques that exploit this structure by analytically eliminating the linear variables and presenting a reduced problem in the remaining variables that has favorable properties. However, VarPro has seen limited use in robotic perception; a major challenge arises from gauge symmetries (e.g., cost invariance to global shifts and rotations), which are common in perception and induce specific computational challenges in standard VarPro approaches. We present a VarPro scheme designed for problems with gauge symmetries that jointly exploits separability and sparsity. Our method can be applied as a one-time preprocessing step to construct a \emph{matrix-free Schur complement operator}. This operator allows efficient evaluation of costs, gradients, and Hessian-vector products of the reduced problem and readily integrates with standard iterative NLS solvers. We provide precise conditions under which our method applies, and describe extensions when these conditions are only partially met. Across synthetic and real benchmarks in SLAM, SNL, and SfM, our approach achieves up to \textbf{2$\times$--35$\times$ faster runtimes} than state-of-the-art methods while maintaining accuracy. We release an open-source C++ implementation and all datasets from our experiments.

cs.RO↗

arXiv2025

Practical and Performant Enhancements for Maximization of Algebraic Connectivity

Long-term state estimation over graphs remains challenging as current graph estimation methods scale poorly on large, long-term graphs. To address this, our work advances a current state-of-the-art graph sparsification algorithm, maximizing algebraic connectivity (MAC). MAC is a sparsification method that preserves estimation performance by maximizing the algebraic connectivity, a spectral graph property that is directly connected to the estimation error. Unfortunately, MAC remains computationally prohibitive for online use and requires users to manually pre-specify a connectivity-preserving edge set. Our contributions close these gaps along three complementary fronts: we develop a specialized solver for algebraic connectivity that yields an average 2x runtime speedup; we investigate advanced step size strategies for MAC's optimization procedure to enhance both convergence speed and solution quality; and we propose automatic schemes that guarantee graph connectivity without requiring manual specification of edges. Together, these contributions make MAC more scalable, reliable, and suitable for real-time estimation applications.

cs.RO↗

arXiv2025

A Roadmap for Climate-Relevant Robotics Research

Climate change is one of the defining challenges of the 21st century, and many in the robotics community are looking for ways to contribute. This paper presents a roadmap for climate-relevant robotics research, identifying high-impact opportunities for collaboration between roboticists and experts across climate domains such as energy, the built environment, transportation, industry, land use, and Earth sciences. These applications include problems such as energy systems optimization, construction, precision agriculture, building envelope retrofits, autonomous trucking, and large-scale environmental monitoring. Critically, we include opportunities to apply not only physical robots but also the broader robotics toolkit - including planning, perception, control, and estimation algorithms - to climate-relevant problems. A central goal of this roadmap is to inspire new research directions and collaboration by highlighting specific, actionable problems at the intersection of robotics and climate. This work represents a collaboration between robotics researchers and domain experts in various climate disciplines, and it serves as an invitation to the robotics community to bring their expertise to bear on urgent climate priorities.

cs.RO↗

arXiv2025

Learning Smooth State-Dependent Traversability from Dense Point Clouds

A key open challenge in off-road autonomy is that the traversability of terrain often depends on the vehicle's state. In particular, some obstacles are only traversable from some orientations. However, learning this interaction by encoding the angle of approach as a model input demands a large and diverse training dataset and is computationally inefficient during planning due to repeated model inference. To address these challenges, we present SPARTA, a method for estimating approach angle conditioned traversability from point clouds. Specifically, we impose geometric structure into our network by outputting a smooth analytical function over the 1-Sphere that predicts risk distribution for any angle of approach with minimal overhead and can be reused for subsequent queries. The function is composed of Fourier basis functions, which has important advantages for generalization due to their periodic nature and smoothness. We demonstrate SPARTA both in a high-fidelity simulation platform, where our model achieves a 91\% success rate crossing a 40m boulder field (compared to 73\% for the baseline), and on hardware, illustrating the generalization ability of the model to real-world settings. Our code will be available at https://github.com/neu-autonomy/SPARTA.

cs.RO↗

arXiv2025

Distributed Certifiably Correct Range-Aided SLAM

Reliable simultaneous localization and mapping (SLAM) algorithms are necessary for safety-critical autonomous navigation. In the communication-constrained multi-agent setting, navigation systems increasingly use point-to-point range sensors as they afford measurements with low bandwidth requirements and known data association. The state estimation problem for these systems takes the form of range-aided (RA) SLAM. However, distributed algorithms for solving the RA-SLAM problem lack formal guarantees on the quality of the returned estimate. To this end, we present the first distributed algorithm for RA-SLAM that can efficiently recover certifiably globally optimal solutions. Our algorithm, distributed certifiably correct RA-SLAM (DCORA), achieves this via the Riemannian Staircase method, where computational procedures developed for distributed certifiably correct pose graph optimization are generalized to the RA-SLAM problem. We demonstrate DCORA's efficacy on real-world multi-agent datasets by achieving absolute trajectory errors comparable to those of a state-of-the-art centralized certifiably correct RA-SLAM algorithm. Additionally, we perform a parametric study on the structure of the RA-SLAM problem using synthetic data, revealing how common parameters affect DCORA's performance.

cs.RO↗

arXiv2024

An Overview of the Burer-Monteiro Method for Certifiable Robot Perception

This paper presents an overview of the Burer-Monteiro method (BM), a technique that has been applied to solve robot perception problems to certifiable optimality in real-time. BM is often used to solve semidefinite programming relaxations, which can be used to perform global optimization for non-convex perception problems. Specifically, BM leverages the low-rank structure of typical semidefinite programs to dramatically reduce the computational cost of performing optimization. This paper discusses BM in certifiable perception, with three main objectives: (i) to consolidate information from the literature into a unified presentation, (ii) to elucidate the role of the linear independence constraint qualification (LICQ), a concept not yet well-covered in certifiable perception literature, and (iii) to share practical considerations that are discussed among practitioners but not thoroughly covered in the literature. Our general aim is to offer a practical primer for applying BM towards certifiable perception.

cs.RO↗

arXiv2024

MAC: Graph Sparsification by Maximizing Algebraic Connectivity

Simultaneous localization and mapping (SLAM) is a critical capability in autonomous navigation, but memory and computational limits make long-term application of common SLAM techniques impractical; a robot must be able to determine what information should be retained and what can safely be forgotten. In graph-based SLAM, the number of edges (measurements) in a pose graph determines both the memory requirements of storing a robot's observations and the computational expense of algorithms deployed for performing state estimation using those observations, both of which can grow unbounded during long-term navigation. Motivated by these challenges, we propose a new general purpose approach to sparsify graphs in a manner that maximizes algebraic connectivity, a key spectral property of graphs which has been shown to control the estimation error of pose graph SLAM solutions. Our algorithm, MAC (for maximizing algebraic connectivity), is simple and computationally inexpensive, and admits formal post hoc performance guarantees on the quality of the solution that it provides. In application to the problem of pose-graph SLAM, we show on several benchmark datasets that our approach quickly produces high-quality sparsification results which retain the connectivity of the graph and, in turn, the quality of corresponding SLAM solutions.

cs.RO↗

arXiv2023

Certifiably Correct Range-Aided SLAM

We present the first algorithm to efficiently compute certifiably optimal solutions to range-aided simultaneous localization and mapping (RA-SLAM) problems. Robotic navigation systems increasingly incorporate point-to-point ranging sensors, leading to state estimation problems in the form of RA-SLAM. However, the RA-SLAM problem is significantly more difficult to solve than traditional pose-graph SLAM: ranging sensor models introduce non-convexity and single range measurements do not uniquely determine the transform between the involved sensors. As a result, RA-SLAM inference is sensitive to initial estimates yet lacks reliable initialization techniques. Our approach, certifiably correct RA-SLAM (CORA), leverages a novel quadratically constrained quadratic programming (QCQP) formulation of RA-SLAM to relax the RA-SLAM problem to a semidefinite program (SDP). CORA solves the SDP efficiently using the Riemannian Staircase methodology; the SDP solution provides both (i) a lower bound on the RA-SLAM problem's optimal value, and (ii) an approximate solution of the RA-SLAM problem, which can be subsequently refined using local optimization. CORA applies to problems with arbitrary pose-pose, pose-landmark, and ranging measurements and, due to using convex relaxation, is insensitive to initialization. We evaluate CORA on several real-world problems. In contrast to state-of-the-art approaches, CORA is able to obtain high-quality solutions on all problems despite being initialized with random values. Additionally, we study the tightness of the SDP relaxation with respect to important problem parameters: the number of (i) robots, (ii) landmarks, and (iii) range measurements. These experiments demonstrate that the SDP relaxation is often tight and reveal relationships between graph connectivity and the tightness of the SDP relaxation.

cs.RO↗

arXiv2022

SCORE: A Second-Order Conic Initialization for Range-Aided SLAM

We present a novel initialization technique for the range-aided simultaneous localization and mapping (RA-SLAM) problem. In RA-SLAM we consider measurements of point-to-point distances in addition to measurements of rigid transformations to landmark or pose variables. Standard formulations of RA-SLAM approach the problem as non-convex optimization, which requires a good initialization to obtain quality results. The initialization technique proposed here relaxes the RA-SLAM problem to a convex problem which is then solved to determine an initialization for the original, non-convex problem. The relaxation is a second-order cone program (SOCP), which is derived from a quadratically constrained quadratic program (QCQP) formulation of the RA-SLAM problem. As a SOCP, the method is highly scalable. We name this relaxation Second-order COnic RElaxation for RA-SLAM (SCORE). To our knowledge, this work represents the first convex relaxation for RA-SLAM. We present real-world and simulated experiments which show SCORE initialization permits the efficient recovery of quality solutions for a variety of challenging single- and multi-robot RA-SLAM problems with thousands of poses and range measurements.

cs.RO↗

arXiv2022

Nested Sampling for Non-Gaussian Inference in SLAM Factor Graphs

We present nested sampling for factor graphs (NSFG), a novel nested sampling approach to approximate inference for posterior distributions expressed over factor-graphs. Performing such inference is a key step in simultaneous localization and mapping (SLAM). Although the Gaussian approximation often works well, in other more challenging SLAM situations, the posterior distribution is non-Gaussian and cannot be explicitly represented with standard distributions. Our technique applies to settings where the posterior distribution is substantially non-Gaussian (e.g., multi-modal) and thus needs a more expressive representation. NSFG exploits nested sampling methods to directly sample the posterior to represent the distribution without parametric density models. While nested sampling methods are known for their powerful capability in sampling multi-modal distributions, the application of the methods to SLAM factor graphs is not straightforward. NSFG leverages the structure of factor graphs to construct informative prior distributions which are efficiently sampled and provide notable computational benefits for nested sampling methods. We present simulated experiments which demonstrate that NSFG is more robust and computes solutions over an order of magnitude faster than state-of-the-art sampling techniques. Similarly, we compare NSFG to state-of-the-art Gaussian and non-Gaussian SLAM approaches and demonstrate that NSFG is notably more robust in describing non-Gaussian posteriors.

cs.RO↗

arXiv2021

Prioritized Planning for Cooperative Range-Only Localization in Multi-Robot Networks

We present a novel path-planning algorithm to reduce localization error for a network of robots cooperatively localizing via inter-robot range measurements. The quality of localization with range measurements depends on the configuration of the network, and poor configurations can cause substantial localization errors. To reduce the effect of network configuration on localization error for moving networks we consider various optimality measures of the Fisher information matrix (FIM), which have well-studied relationships with the localization error. In particular, we pose a trajectory planning problem with constraints on the FIM optimality measures. By constraining these optimality measures we can control the statistical properties of the localization error. To efficiently generate trajectories which satisfy these FIM constraints we present a prioritized planner which leverages graph-based planning and unique properties of the range-only FIM. We show results in simulated experiments that demonstrate the trajectories generated by our algorithm reduce worst-case localization error by up to 42\% in comparison to existing planning approaches and can scalably plan distance-efficient trajectories in complicated environments for large numbers of robots.

cs.RO↗

arXiv2020

Network Localization Based Planning for Autonomous Underwater Vehicles with Inter-Vehicle Ranging

Localization between a swarm of AUVs can be entirely estimated through the use of range measurements between neighboring AUVs via a class of techniques commonly referred to as sensor network localization. However, the localization quality depends on network topology, with degenerate topologies, referred to as low-rigidity configurations, leading to ambiguous or highly uncertain localization results. This paper presents tools for rigidity-based analysis, planning, and control of a multi-AUV network which account for sensor noise and limited sensing range. We evaluate our long-term planning framework in several two-dimensional simulated environments and show we are able to generate paths in feasible time and guarantee a minimum network rigidity over the full course of the paths.

cs.RO↗

arXiv2020

Inter-Mobile-Device Distance Estimation using Network Localization Algorithms for Digital Contact Logging Applications

Mobile applications are being developed for automated logging of contacts via Bluetooth to help scale up digital contact tracing efforts in the context of the ongoing COVID-19 pandemic. A useful component of such applications is inter-device distance estimation, which can be formulated as a network localization problem. We survey several approaches and evaluate the performance of each on real and simulated Bluetooth Low Energy (BLE) measurement datasets with respect to both distance estimate accuracy and the proximity detection problem. We investigate the effects of obstructions like pockets, differences between device models, and the environment (i.e. indoors or outdoors) on performance. We conclude that while direct estimation can provide the best proximity detection when Received Signal Strength Indicator (RSSI) measurements are available, network localization algorithms like Isomap, Local Linear Embedding, and the spring model outperform direct estimation in the presence of missing or very noisy measurements. The spring model consistently achieves the best distance estimation accuracy.

eess.SP↗