Riemannian optimization

Distributed Riemannian Optimization with Lazy Communication for Collaborative Geometric Estimation

The first distributed optimization algorithm with *lazy communication* for large-scale collaborative geometric estimation.

Distributed Certifiably Correct Pose-Graph Optimization

The first *distributed* algorithm provably capable of recovering correct (*globally optimal*) solutions of SLAM and rotation averaging. Honorable Mention, IEEE Transactions on Robotics King-Sun Fu Memorial Best Paper Award

Shonan Rotation Averaging: Global Optimality by Surfing $SO(p)^n$

A fast algorithm for *certifiably globally optimal* rotation averaging. Implemented in the GTSAM library. ECCV 2020 spotlight talk (top 5%)

SE-Sync: A Certifiably Correct Algorithm for Synchronization over the Special Euclidean Group

The first practical algorithm *provably* capable of recovering correct (*globally optimal*) solutions of the SLAM problem. Invited article (IJRR Special Issue)

Computational Enhancements for Certifiably Correct SLAM

We investigate numerical and computational aspects of the use of convex relaxation for simultaneous localization and mapping (SLAM). Recent work has shown that convex relaxation provides an effective tool for computing, and certifying the correctness …

SE-Sync: A Certifiably Correct Algorithm for Synchronization over the Special Euclidean Group

Many important geometric estimation problems naturally take the form of *synchronization over the special Euclidean group*: estimate the values of a set of unknown poses given noisy measurements of a subset of their pairwise relative transforms. …

A Certifiably Correct Algorithm for Synchronization over the Special Euclidean Group

The first practical algorithm *provably* capable of recovering correct (*globally optimal*) solutions of the SLAM problem. Best Paper Award (WAFR 2016)