13 citations · 34 across the 28 of their papers we have counts for
33 papers
Noise-Induced Navigation in Non-convex Domains and Compact Manifolds
Karthik Elamvazhuthi
In this note, we study the problem of designing a feedback law that globally steers a system to a prescribed target configuration. Even if the system is fully actuated, topological…
Notes on Generative Modeling for Feedback Control and Planning
Karthik Elamvazhuthi
In these notes, we view control as a dynamically constrained sampling problem on the state-space of a control system. With this viewpoint, we extend methods from generative modelin…
From Schrodinger Bridge to Optimal Transport over Sub-Riemannian Manifolds
Daniel Owusu Adu, Karthik Elamvazhuthi, Bahman Gharesifard
We study the least-energy way to reshape a probability distribution when motion is constrained to a horizontal bundle, that is, optimal transport and distribution steering in sub-R…
Discrete Diffusion with Sample-Efficient Estimators for Conditionals
Karthik Elamvazhuthi, Abhijith Jayakumar, Andrey Y. Lokhov
We study a discrete denoising diffusion framework that integrates a sample-efficient estimator of single-site conditionals with round-robin noising and denoising dynamics for gener…
Geometry-Preserving Neural Architectures on Manifolds with Boundary
Karthik Elamvazhuthi, Shiba Biswal, Kian Rosenblum +4
A growing number of neural architectures have been proposed to enforce geometric constraints, including projection-based networks, exponential-map updates, constrained output layer…
Flow Matching for Measure Transport and Feedback Stabilization of Control-Affine Systems
Karthik Elamvazhuthi
We develop a \emph{flow-matching framework} for transporting probability measures under control-affine dynamics and for steering systems to points or target sets. Starting from the…
Uniform Sampling from the Reachable Set Using Optimal Transport
Karthik Elamvazhuthi, Sachin Shivakumar
Estimating the reachable set of a dynamical system is a fundamental problem in control theory, particularly when control inputs are bounded. Direct simulation using randomly sample…
Score Matching Diffusion Based Feedback Control and Planning of Nonlinear Systems
Karthik Elamvazhuthi, Darshan Gadginmath, Fabio Pasqualetti
In this paper, we propose a deterministic diffusion-based framework for controlling the probability density of nonlinear control-affine systems, with theoretical guarantees for dri…
The Ground Cost for Optimal Transport of Angular Velocity
Karthik Elamvazhuthi, Abhishek Halder
We revisit the optimal transport problem over angular velocity dynamics given by the controlled Euler equation. The solution of this problem enables stochastic guidance of spin sta…
Quantitative Flow Approximation Properties of Narrow Neural ODEs
Karthik Elamvazhuthi
In this note, we revisit the problem of flow approximation properties of neural ordinary differential equations (NODEs). The approximation properties have been considered as a flow…
Universal Approximation of Mean-Field Models via Transformers
Shiba Biswal, Karthik Elamvazhuthi, Rishi Sonthalia
This paper investigates the use of transformers to approximate the mean-field dynamics of interacting particle systems exhibiting collective behavior. Such systems are fundamental…
Benamou-Brenier Formulation of Optimal Transport for Nonlinear Control Systems on Rd
Karthik Elamvazhuthi
In this paper we consider the Benamou-Brenier formulation of optimal transport for nonlinear control affine systems on $\Rd$, removing the compactness assumption of the underlying…
A Linear Test for Global Nonlinear Controllability
Karthik Elamvazhuthi
It is known that if a nonlinear control affine system without drift is bracket generating, then its associated sub-Laplacian is invertible under some conditions on the domain. In t…
A Blob Method for Mean Field Control With Terminal Constraints
Katy Craig, Karthik Elamvazhuthi, Harlin Lee
In the present work, we develop a novel particle method for a general class of mean field control problems, with source and terminal constraints. Specific examples of the problems…
Denoising Diffusion-Based Control of Nonlinear Systems
Karthik Elamvazhuthi, Darshan Gadginmath, Fabio Pasqualetti
We propose a novel approach based on Denoising Diffusion Probabilistic Models (DDPMs) to control nonlinear dynamical systems. DDPMs are the state-of-art of generative models that h…
Optimal Transport of Linear Systems over Equilibrium Measures
Karthik Elamvazhuthi, Matt Jacobs
We consider the optimal transport problem over convex costs arising from optimal control of linear time-invariant(LTI) systems when the initial and target measures are assumed to b…
Noise in the reverse process improves the approximation capabilities of diffusion models
Karthik Elamvazhuthi, Samet Oymak, Fabio Pasqualetti
In Score based Generative Modeling (SGMs), the state-of-the-art in generative modeling, stochastic reverse processes are known to perform better than their deterministic counterpar…
Density Stabilization Strategies for Nonholonomic Agents on Compact Manifolds
Karthik Elamvazhuthi, Spring Berman
In this article, we consider the problem of stabilizing stochastic processes, which are constrained to a bounded Euclidean domain or a compact smooth manifold, to a given target pr…
Learning on Manifolds: Universal Approximations Properties using Geometric Controllability Conditions for Neural ODEs
Karthik Elamvazhuthi, Xuechen Zhang, Samet Oymak +1
In numerous robotics and mechanical engineering applications, among others, data is often constrained on smooth manifolds due to the presence of rotational degrees of freedom. Comm…
Neural ODE Control for Trajectory Approximation of Continuity Equation
Karthik Elamvazhuthi, Bahman Gharesifard, Andrea Bertozzi +1
We consider the controllability problem for the continuity equation, corresponding to neural ordinary differential equations (ODEs), which describes how a probability measure is pu…
A blob method for inhomogeneous diffusion with applications to multi-agent control and sampling
Katy Craig, Karthik Elamvazhuthi, Matt Haberland +1
As a counterpoint to classical stochastic particle methods for linear diffusion equations, we develop a deterministic particle method for the weighted porous medium equation (WPME)…
Multi-Robot Target Search using Probabilistic Consensus on Discrete Markov Chains
Aniket Shirsat, Karthik Elamvazhuthi, Spring Berman
In this paper, we propose a probabilistic consensus-based multi-robot search strategy that is robust to communication link failures, and thus is suitable for disaster affected area…
Using Reinforcement Learning to Herd a Robotic Swarm to a Target Distribution
Zahi M. Kakish, Karthik Elamvazhuthi, Spring Berman
In this paper, we present a reinforcement learning approach to designing a control policy for a "leader" agent that herds a swarm of "follower" agents, via repulsive interactions,…
Optimal Transport over Deterministic Discrete-time Nonlinear Systems using Stochastic Feedback Laws
Karthik Elamvazhuthi, Piyush Grover, Spring Berman
This paper considers the relaxed version of the transport problem for general nonlinear control systems, where the objective is to design time-varying feedback laws that transport…