Alan Papalia

Alan Papalia, Nikolas Sanderson, Haoyu Han et al.

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.

Alan Papalia, Yulun Tian, David M. Rosen et al.

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.

Zihao Dong, Alan Papalia, Leonard Jung et al.

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.

Leonard Jung, Alan Papalia, Kevin Doherty et al.

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.

Alan Papalia, Charles Dawson, Laurentiu L. Anton et al. · mit

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.

Qiangqiang Huang, Alan Papalia, John J. Leonard

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.

Alan Papalia, Nicole Thumma, John Leonard

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.

Alan Papalia, John Leonard

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.