Alan Papalia

Distributed Certifiably Correct Range-Aided SLAM Alexander Thoms, @PapaliaAlan, Jared Velasquez, @david_m_rosen, Sriram Narasimhan tl;dr: RA-SLAM->QCQP->SDR->Riemannian Staircase arxiv.org/abs/2503.03192

@KasraKhosoussi @eemensch Asymptotic convergence to an isotropic Gaussian would make sense (I think @david_m_rosen had some fun math in an SE-Sync appendix that agrees that). Thanks for the thoughts!

@KasraKhosoussi @eemensch Oh interesting, I didn't think about the importance of having an analytical form for the normalization constant (partition function) but it makes sense...

In robotics & computer vision estimation problems (SLAM, bundle adjustment, etc.), we often assume zero-mean Gaussian noise. But where does the noise covariance matrix come from? Ideally: calibration with ground truth. In practice: arbitrary (often isotropic) guesses / ad hoc trial-and-error tuning😅 Well, no more tuning!

@KasraKhosoussi @eemensch Fun read, thanks for sharing! The analytical solutions were nice surprises. How would this generalize to other distributional assumptions (e.g. Langevin-distributed noise on rotations or other maximum entropy distributions)? Have Bayesian statistics people figured that all out?

In our new preprint (arxiv.org/pdf/2502.04584), @eemensch and I show show how to *jointly* estimate the noise covariance matrix and system states directly from noisy measurements. Our algorithm is easy to implement in your favorite nonlinear least squares solver (g2o, GTSAM, ceres - we did it in g2o): After every n iterations of Gauss-Newton/etc, update the noise covariance matrix using the expressions provided in Theorem 1. These expression depend on the sample noise covariance, Wishart prior (in the case of MAP when a prior estimate is available), and optional structural constraints (diagonal covariance, bounds on min/max eigenvalue).

@zhenjun_zhao @TianYulun @david_m_rosen @jleonardmit For any interested there's a number of other people (beyond my great co-authors here) also doing solid work in efficient global optimization / certifiably correct perception. Some names to know: @FrederikeD37988, Tim Barfoot, @newtype511, @hankyang94, @lucacarlone1

@zhenjun_zhao @TianYulun @david_m_rosen @jleonardmit Thanks for the kind words @zhenjun_zhao! We wrote this paper to try to demystify a technique (the Burer-Monteiro method) which we've found to be amazingly powerful in our research.

An Overview of the Burer-Monteiro Method for Certifiable Robot Perception @PapaliaAlan, @TianYulun, @david_m_rosen, Jonathan P. How, @jleonardmit tl;dr: in title good paper! arxiv.org/pdf/2410.00117

The MIT Robotics & Climate Working Group, led by @PapaliaAlan, @ch_dawson, @sywang2, and @jingnanshi, hosted a workshop bringing together researchers in robotics, climate science, and the built environment to discuss how roboticists can contribute ... [1/n]

@shortstein Is this (partially) because a series of papers is more accessible? Slicing ideas across multiple papers can help make it more apparent how several distinct contributions fit into a bigger picture? Not to disregard the signal-boosting effect from more works floating around.

An Energy-based Perspective on Learning Observation Models – Machine Learning Blog | ML@CMU | Carnegie Mellon University blog.ml.cmu.edu/2021/12/17/lea…

Thrilled to finally finish the Ph.D.! It was a lot of fun talking about my work on learning in factor graphs and tactile perception youtu.be/6ILCBoo16NA It's been a rather strange and wonderful journey these last few years at CMU. Excited to set off on a new adventure 🚀