Related papers: Ergodic Exploration over Meshable Surfaces
We present a computational study of a visualization method for invariant sets based on ergodic partition theory, first proposed in [1,2]. The algorithms for computation of the time averages of observables on phase space are developed and…
Efficient motion planning for high-dimensional robotic systems, such as manipulators and mobile manipulators, is critical for real-time operation and reliable deployment. Although advances in planning algorithms have enhanced scalability to…
A method is proposed for constraining the Galactic gravitational potential from high precision observations of the phase space coordinates of a system of relaxed tracers. The method relies on an "ergodic" assumption that the observations…
Inspired by the classical fractional cascading technique, we introduce new techniques to speed up the following type of iterated search in 3D: The input is a graph $\mathbf{G}$ with bounded degree together with a set $H_v$ of 3D hyperplanes…
Finding the diameter of a dataset in multidimensional Euclidean space is a well-established problem, with well-known algorithms. However, most of the algorithms found in the literature do not scale well with large values of data dimension,…
We develop an algorithm to explore an environment to generate a measurement model for use in future localization tasks. Ergodic exploration with respect to the likelihood of a particular class of measurement (e.g., a contact detection…
Although wheeled robots have been predominant for planetary exploration, their geometry limits their capabilities when traveling over steep slopes, through rocky terrains, and in microgravity. Legged robots equipped with grippers are a…
Suppose a target is hidden in one of the vertices of an edge-weighted graph according to a known probability distribution. The expanding search problem asks for a search sequence of the vertices so as to minimize the expected time for…
Recent advances in Large Language Models (LLMs) have helped facilitate exciting progress for robotic planning in real, open-world environments. 3D scene graphs (3DSGs) offer a promising environment representation for grounding such…
This paper concerns electromagnetic 3D subsurface imaging in connection with sparsity of signal sources. We explored an imaging approach that can be implemented in situations that allow obtaining a large amount of data over a surface or a…
A single nonholonomic under-actuated mobile robot with a bounded control range travels in a 3D workspace. This workspace also hosts a compact unknown domain with a smooth boundary. The robot has access to the horizontal distance to this…
This paper contributes a novel strategy for semantics-aware autonomous exploration and inspection path planning. Attuned to the fact that environments that need to be explored often involve a sparse set of semantic entities of particular…
A searcher is tasked with exploring a graph with edge lengths and vertex weights, starting from a designated vertex. Initially, only the starting vertex is considered explored. At each step, the searcher adds an edge to the solution,…
"Looking for things" is a mundane but critical task we repeatedly carry on in our daily life. We introduce a method to develop a human character capable of searching for a randomly located target object in a detailed 3D scene using its…
We consider a search problem where a robot has one or more types of sensors, each suited to detecting different types of targets or target information. Often, information in the form of a distribution of possible target locations, or…
Exploration systems are critical for enhancing the autonomy of robots. Due to the unpredictability of the future planning space, existing methods either adopt an inefficient greedy strategy or require a lot of resources to obtain a global…
Enabling robots to efficiently search for and identify objects in complex, unstructured environments is critical for diverse applications ranging from household assistance to industrial automation. However, traditional scene representations…
We are witnessing significant progress on perception models, specifically those trained on large-scale internet images. However, efficiently generalizing these perception models to unseen embodied tasks is insufficiently studied, which will…
We study the arithmetic analogue of maximal functions on diagonal hypersurfaces. This paper is a natural step following the papers of \cite{Magyar_dyadic}, \cite{Magyar_ergodic} and \cite{MSW}. We combine more precise knowledge of…
This paper derives an infinite-horizon ergodic controller based on kernel mean embeddings for long-duration coverage tasks on general domains. While existing kernel-based ergodic control methods provide strong coverage guarantees on general…