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Diffusion models excel at creating images and videos thanks to their multimodal generative capabilities. These same capabilities have made diffusion models increasingly popular in robotics research, where they are used for generating robot…

Sensor coverage is the critical multi-robot problem of maximizing the detection of events in an environment through the deployment of multiple robots. Large multi-robot systems are often composed of simple robots that are typically not…

The robotic assembly task poses a key challenge in building generalist robots due to the intrinsic complexity of part interactions and the sensitivity to noise perturbations in contact-rich settings. The assembly agent is typically designed…

We introduce the heat equation relative to a positive dd-bar-closed current and apply it to the invariant currents associated with Riemann surface laminations possibly with singularities. The main examples are holomorphic foliations by…

We demonstrate the non-ergodicity of a simple Markovian stochastic processes with space-dependent diffusion coefficient $D(x)$. For power-law forms $D(x) \simeq|x|^{\alpha}$, this process yield anomalous diffusion of the form $\ < x^2(t)\ >…

We study the long time behavior of an advection-diffusion equation with a random shear flow which depends on a stationary Ornstein-Uhlenbeck (OU) process in parallel-plate channels enforcing the no-flux boundary conditions. We derive a…

We consider the ergodicity and consensus problem for a discrete-time linear dynamic model driven by random stochastic matrices, which is equivalent to studying these concepts for the product of such matrices. Our focus is on the model where…

Motion retargeting for specific robot from existing motion datasets is one critical step in transferring motion patterns from human behaviors to and across various robots. However, inconsistencies in topological structure, geometrical…

Transient diffusion equations arise in many branches of engineering and applied sciences (e.g., heat transfer and mass transfer), and are parabolic partial differential equations. It is well-known that, under certain assumptions on the…

We research adaptive maximum likelihood-type estimation for an ergodic diffusion process where the observation is contaminated by noise. This methodology leads to the asymptotic independence of the estimators for the variance of observation…

We present a hybrid model/model-free data-driven approach to solve poroelasticity problems. Extending the data-driven modeling framework originated from Kirchdoerfer and Ortiz (2016), we introduce one model-free and two hybrid…

It is a common problem in robotics to specify the position of each joint of the robot so that the endpoint reaches a certain target in space. This can be solved in two ways, forward kinematics method and inverse kinematics method. However,…

In communication restricted environments, a multi-robot system can be deployed to either: i) maintain constant communication but potentially sacrifice operational efficiency due to proximity constraints or ii) allow disconnections to…

Diffusion models have recently emerged as powerful tools for robot motion planning by capturing the multi-modal distribution of feasible trajectories. However, their extension to multi-robot settings with flexible, language-conditioned task…

We propose a novel autonomous robotic palpation framework for real-time elastic mapping during tissue exploration using a viscoelastic tissue model. The method combines force-based parameter estimation using a commercial force/torque sensor…

Diffusion models have risen as a powerful tool in robotics due to their flexibility and multi-modality. While some of these methods effectively address complex problems, they often depend heavily on inference-time obstacle detection and…

Motivated by the design of fast reinforcement learning algorithms, we study the diffusive limit of a class of pure jump ergodic stochastic control problems. We show that, whenever the intensity of jumps is large enough, the approximation…

This work focuses on determining the coefficient of thermal diffusivity in a one-dimensional heat transfer process along a homogeneous and isotropic bar, embedded in a moving fluid with heat generation. A first type (Dirichlet) condition is…

Here, we adapt the concept of transformational thermodynamics, whereby the flux of temperature is controlled via anisotropic heterogeneous diffusivity, for the diffusion and transport of mass concentration. The n-dimensional,…

Using a model Hamiltonian for a single-mode electromagnetic field interacting with a nonlinear medium, we show that quantum expectation values of subsystem observables can exhibit remarkably diverse ergodic properties even when the dynamics…