Related papers: Anisotropic Diffusion-Driven Ergodic Coverage in M…
In this work, we consider the problem of multi-agent informative path planning (IPP) for robots whose sensor visibility continuously changes as a consequence of a time-varying natural phenomenon. We leverage ergodic trajectory optimization…
The nature of diffusion is usually studied for particles or time-evolving systems. Similar in principle, such studies can be conducted by tracking how a given function of observable properties evolves over time-akin to the evolution of…
Considerable research has led to ergodic isothermal dynamics which can replicate Gibbs' canonical distribution for simple ( small ) dynamical problems. Adding one or two thermostat forces to the Hamiltonian motion equations can give an…
Autonomous exploration is an application of growing importance in robotics. A promising strategy is ergodic trajectory planning, whereby an agent spends in each area a fraction of time which is proportional to its probability information…
We present a novel formulation of ergodic trajectory optimization that can be specified over general domains using kernel maximum mean discrepancy. Ergodic trajectory optimization is an effective approach that generates coverage paths for…
Continuous exploration without interruption is important in scenarios such as search and rescue and precision agriculture, where consistent presence is needed to detect events over large areas. Ergodic search already derives continuous…
We study a simple stochastic differential equation that models the dispersion of close heavy particles moving in a turbulent flow. In one and two dimensions, the model is closely related to the one-dimensional stationary Schroedinger…
This paper develops KL-Ergodic Exploration from Equilibrium ($\text{KL-E}^3$), a method for robotic systems to integrate stability into actively generating informative measurements through ergodic exploration. Ergodic exploration enables…
Designing continuous trajectories whose time-averaged occupancy provably matches a prescribed spatial density (the \emph{ergodic coverage} problem) is central to UAV-assisted data collection and sensing, robotic exploration, and mobile…
Recent methods in ergodic coverage planning have shown promise as tools that can adapt to a wide range of geometric coverage problems with general constraints, but are highly sensitive to the numerical scaling of the problem space. The…
In this article we consider the ergodic risk-sensitive control problem for a large class of multidimensional controlled diffusions on the whole space. We study the minimization and maximization problems under either a blanket stability…
This paper investigates performance guarantees on coverage-based ergodic exploration methods in environments containing disturbances. Ergodic exploration methods generate trajectories for autonomous robots such that time spent in each area…
This research addresses the challenge of executing multi-UAV survey missions over diverse terrains characterized by varying elevations. The approach integrates advanced two-dimensional ergodic search technique with model predictive control…
Robots with the ability to balance time against the thoroughness of search have the potential to provide time-critical assistance in applications such as search and rescue. Current advances in ergodic coverage-based search methods have…
Modeling multimodal human behavior has been a key barrier to increasing the level of interaction between human and robot, particularly for collaborative tasks. Our key insight is that an effective, learned robot policy used for human-robot…
We consider elliptic diffusion problems with a random anisotropic diffusion coefficient, where, in a notable direction given by a random vector field, the diffusion strength differs from the diffusion strength perpendicular to this notable…
A random-walk Metropolis sampler is geometrically ergodic if its equilibrium density is super-exponentially light and satisfies a curvature condition [Stochastic Process. Appl. 85 (2000) 341-361]. Many applications, including Bayesian…
The paper considers an Euler discretization based numerical scheme for approximating functionals of invariant distribution of an ergodic diffusion. Convergence of the numerical scheme is shown for suitably chosen discretization step, and a…
In this paper we find nonasymptotic exponential upper bounds for the deviation in the ergodic theorem for families of homogeneous Markov processes. We find some sufficient conditions for geometric ergodicity uniformly over a parametric…
Canonical characterization techniques that rely upon mean squared displacement ($\mathrm{MSD}$) break down for non-ergodic processes, making it challenging to characterize anomalous diffusion from an individual time-series measurement.…