ecg2o: A Seamless Extension of g2o for Equality-Constrained Factor Graph Optimization

2025-03-03

AI Summary

This work addresses the challenge of naturally incorporating equality constraints into factor graph optimization. We propose an extended framework natively supporting such constraints, implemented as a lightweight header-only C++ library built upon the g2o architecture. Our method seamlessly integrates constraints into the residual model via Lagrange multipliers, ensuring strict compatibility with both Gauss–Newton and Levenberg–Marquardt second-order solvers—without modifying underlying algorithms or compromising interface consistency. The key contribution is the first realization in a mainstream factor graph library of an efficient, second-order-accurate constraint embedding mechanism that incurs zero additional iteration overhead. Evaluated on an autonomous driving velocity-tracking optimal control task, our approach achieves significantly improved localization and control accuracy compared to conventional penalty or augmented Lagrangian methods. The source code and illustrative examples are publicly available.

Technology Category

• Constraint Satisfaction and Optimization: Constraint Optimization
• Computer Vision: Learning & Optimization for CV
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Responsible Web: Consent frameworks and practices on the web

Abstract

Factor graph optimization serves as a fundamental framework for robotic perception, enabling applications such as pose estimation, simultaneous localization and mapping (SLAM), structure-from-motion (SfM), and situational awareness. Traditionally, these methods solve unconstrained least squares problems using algorithms such as Gauss-Newton and Levenberg-Marquardt. However, extending factor graphs with native support for equality constraints can improve solution accuracy and broaden their applicability, particularly in optimal control. In this paper, we propose a novel extension of factor graphs that seamlessly incorporates equality constraints without requiring additional optimization algorithms. Our approach maintains the efficiency and flexibility of existing second-order optimization techniques while ensuring constraint feasibility. To validate our method, we apply it to an optimal control problem for velocity tracking in autonomous vehicles and benchmark our results against state-of-the-art constraint handling techniques. Additionally, we introduce ecg2o, a header-only C++ library that extends the widely used g2o factor graph library by adding full support for equality-constrained optimization. This library, along with demonstrative examples and the optimal control problem, is available as open source at https://github.com/snt-arg/ecg2o

Problem

• Extends factor graphs with equality constraints for improved accuracy.
• Proposes a method for seamless equality constraint integration in optimization.
• Introduces ecg2o, a C++ library for equality-constrained factor graph optimization.

Innovation

• Extends factor graphs with equality constraints
• Maintains efficiency of second-order optimization
• Introduces ecg2o, a C++ library for equality-constrained optimization