发表机构
University of Michigan; Northeastern University; Massachusetts Institute of Technology; Harvard University（密歇根大学; 东北大学; 麻省理工学院; 哈佛大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对机器人感知中的大规模非线性最小二乘问题，提出SPARSER框架，联合利用可分离性和稀疏性，通过无矩阵Schur补算子实现高效变量投影，在SLAM、SNL和SfM基准上平均加速5-7倍，鲁棒变体加速2-16倍。
AI 中文摘要
机器人感知通常需要求解大规模非线性最小二乘（NLS）问题。虽然稀疏性已被广泛用于扩展求解器的规模，但一种互补且未被充分利用的结构是\u201c可分离性\u201d：某些变量（如视觉地标）在残差中线性出现，一旦其余变量（如位姿）被固定，它们便具有闭式解。变量投影（VarPro）通过解析地消除线性变量来利用这一结构，从而产生一个具有良好计算特性的降阶问题。然而，其在机器人感知中的应用一直受到规范对称性（如对全局平移和旋转的不变性）的限制，这为标准VarPro方法带来了挑战。我们提出SPARSER（\textbf{S}parsity \textbf{P}reserving \textbf{A}nalytic \textbf{R}eduction for \textbf{S}eparable \textbf{R}obotic \textbf{P}erception），一个针对规范对称问题的VarPro框架，它联合利用可分离性和稀疏性。我们的方法构建了一个\u201c无矩阵Schur补算子\u201d，用于高效评估降阶成本、梯度和Hessian-向量乘积，从而能够与迭代NLS求解器集成。我们刻画了适用的问题类别，识别了可进一步解析简化的常见情形，并表明基于IRLS的鲁棒成本保留了大部分可利用的结构。在合成和真实的SLAM、SNL和SfM基准测试中，SPARSER在CPU和GPU上平均比最先进的基线快$5\ imes$--$7\ imes$，在个别数据集上的加速比超过$40\ imes$。在受异常值污染的多机器人SLAM数据上，鲁棒变体比最先进的GNC求解器快$2\ imes$--$16\ imes$。我们发布了开源C++代码和所有数据集。
英文摘要
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.
