Geeks Shall Inherit the Earth
Sampling Your Way Out of the Curse of Dimensionality This post is an exposition of the recent paper HJ-Gauss: A Monte Carlo HJ Reachability Scheme (Molu, Renganathan, Cho). The full implementation with solver, examples, and tests is at the monte_carlo folder of my levelsetpy repo. The reliability 1 of the modern automation algorithms that we design (e.g., in AI, modern cyberphysical systems etc.)…
Mr. Kolmogorov Reinforces Diffusion This exposition develops the backward Kolmogorov equation (BKE) for diffusion processes on an infinite-dimensional Hilbert space \(\mathcal{H}\), with particular attention to the Ornstein-Uhlenbeck (OU) process that underlies modern diffusion generative models. This note is a theoretical compendium to the results presented in the paper: Kolmogorov Reggression…
This post accompanies my recent work, Visuomotor Diffusion Policies via Inverse PDEs ( RoboDiff ). It distills two companion notes — a first-principles derivation of the backward Kolmogorov equation (BKE) in infinite dimensions, and a hands-on PushT exposition notebook — into one narrative. The claim in a sentence: for long-horizon planning, don’t diffuse points — diffuse functions. Why…
Denoising Diffusion Probabilistic Models, Jonathan Ho, Ajay Jain, Pieter Abbeel Diffusion Policy: Visuomotor Policy Learning via Action Diffusion, Cheng Chi, Zhenjia Xu, Siyuan Feng, Eric Cousineau, Yilun Du, Benjamin Burchfiel, Russ Tedrake 2,3, Shuran Song Flow Matching Imitation Learning for Multi-Support Manipulation, Quentin Rouxel, Andrea Ferrari, Serena Ivaldi, and Jean-Baptiste Mouret Flow…
Table of Contents Introduction Stability vs optimality Optimality Intro The question of the connection between optimality and stability is a curious thing. On the one hand, we are led to believe that if we can find an optimal control law, that can execute a plan, with the least amount of energy possible, then we are satisfied to know we have fulfilled the specifications posed in our objective…
Table of Contents Introduction Definitions, Theorems, Lemmas etc Nonlinear Control Theory Stability Intro Here are a few control theorems, concepts and diagrams that I think every control student should know. I keep updating this post, so please check back from time to time. Definitions, Theorems, Lemmas and such. Nonlinear Control Theory A differential equation of the form \begin{align} dx/dt =…
This post includes curated links to advice on doing good research from people I respect. I hope you find time to enjoy reading them. How to write a good research paper ~ Bill Freiman . Many readers will skim over formulas on their first reading of your exposition. Therefore, your sentences should flow smoothly when all but the simplest formulas are replaced by “blah” or some other grunting noise.…
Through the looking-glass, tired of working my brain out while familiarizing myself with a giant codebase I was reverse-engineering to prove a theory for an upcoming conference, I started asking myself why I was doing what I was doing? Just to get a paper out? Or to make a great contribution to science and my field? I googled something along the lines of “ How to write a best IEEE RAS conference…
Optimal Controllers: --> This post deals with understanding the necessary and sufficient conditions, fundamental Lipschitz continuity assumptions and the terminal boundary conditions imposed on the Hamilton-Jacobi equation to assure that the problem of minimizing an integral performance index is well-posed. Problem Statement Suppose we have the following nonlinear dynamical system \begin{equation}…
This was my answer to a question posted in an email thread to our research group’s email lists. The question goes like this: QUESTION __ __ __ __ __ __ __ From: XXX@uni-x.edu Sent: Sunday, May 14, 2017 9:29 AM To: XXX@lists.uni-x.edu Subject: RE: [robotec] MuJoCo From the documentation, looks like MuJoCo is faster and therefore better to simulate computational intensive controllers like MPC.…