SPARSER: Sparse Variable Projection by Exploiting Separable Structure in Robotic Perception

2026-09-21

AI Summary

本文提出SPARSER方法，通过利用可分离结构和稀疏性解决机器人感知中的大规模非线性最小二乘问题，提高计算效率。

Abstract

Robotic perception often requires solving large nonlinear least-squares (NLS) problems. While sparsity has been widely exploited to scale solvers, a complementary and underused structure is \emph{separability}: some variables, such as visual landmarks, appear linearly in the residuals and admit a closed-form solution once the remaining variables, such as poses, are fixed. Variable projection (VarPro) exploits this structure by analytically eliminating the linear variables, yielding a reduced problem with favorable computational properties. However, its use in robotic perception has been limited by gauge symmetries, such as invariance to global translations and rotations, which introduce challenges for standard VarPro methods. We present SPARSER (\textbf{S}parsity \textbf{P}reserving \textbf{A}nalytic \textbf{R}eduction for \textbf{S}eparable \textbf{R}obotic \textbf{P}erception), a VarPro framework for gauge-symmetric problems that jointly exploits separability and sparsity. Our method constructs a \emph{matrix-free Schur complement operator} for efficient evaluation of reduced costs, gradients, and Hessian-vector products, enabling integration with iterative NLS solvers. We characterize the applicable problem class, identify common cases admitting further analytical simplifications, and show that IRLS-based robust costs preserve most of the exploitable structure. Across synthetic and real SLAM, SNL, and SfM benchmarks, SPARSER is on average $5\times$--$7\times$ faster than state-of-the-art baselines on CPU and GPU, with gains exceeding $40\times$ on individual datasets. On outlier-corrupted multi-robot SLAM data, the robust variant is $2\times$--$16\times$ faster than a state-of-the-art GNC solver. We release open-source C++ code and all datasets.

Problem

• separability
• sparsity
• gauge symmetries
• robotic perception
• nonlinear least-squares

Innovation

• Variable Projection
• Separability
• Sparsity
• Gauge Symmetry
• Matrix-free Schur Complement Operator