Factor Graph Optimization

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Overview

Factor graph optimization represents unknown poses, biases, landmarks, or object states as variables linked by measurements and priors, turning estimation into sparse nonlinear inference. Common approaches include Gauss–Newton and Levenberg–Marquardt solvers, incremental smoothing with fixed-lag windows, robust M-estimation, and belief propagation; newer work adds learned weighting, distributed optimization, and semidefinite relaxations that can certify global solutions. It underpins SLAM, visual and inertial navigation, mapping, and robot state estimation, and is commonly evaluated on pose-graph, bundle-adjustment, and sensor-fusion benchmarks as well as with field robots. A central challenge is balancing accuracy and robustness to outliers with runtime and memory, while global guarantees and calibrated uncertainty remain difficult to scale beyond local optimization.

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Feb 18, 2026

Decentralized and Fully Onboard: Range-Aided Cooperative Localization and Navigation on Micro Aerial Vehicles

Controlling a team of robots in a coordinated manner is challenging because centralized approaches (where all computation is performed on a central machine) scale poorly, and globally referenced external localization systems may not always be available. In this work, we consider the problem of range-aided decentralized localization and formation control. In such a setting, each robot estimates its relative pose by combining data only from onboard odometry sensors and distance measurements to other robots in the team. Additionally, each robot calculates the control inputs necessary to collaboratively navigate an environment to accomplish a specific task, for example, moving in a desired formation while monitoring an area. We present a block coordinate descent approach to localization that does not require strict coordination between the robots. We present a novel formulation for formation control as inference on factor graphs that takes into account the state estimation uncertainty and can be solved efficiently. Our approach to range-aided localization and formation-based navigation is completely decentralized, does not require specialized trajectories to maintain formation, and achieves decimeter-level positioning and formation control accuracy. We demonstrate our approach through multiple real experiments involving formation flights in diverse indoor and outdoor environments.

Abhishek Goudar, Angela P. Schoellig

The authors are with the Learning Systems and Robotics Lab at the Technical University of Munich, Germany, and the University of Toronto Institute for Aerospace Studies, Canada. They are also affiliated with the University of Toronto Robotics Institute, the Munich Institute of Robotics and Machine Intelligence (MIRMI), and the Vector Institute for Artificial Intelligence.

Cooperative LocalizationRobot NavigationMulti-Robot Formation ControlAerial RoboticsFactor Graph Optimization
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