Related papers: Towards Constructing Finer then Homotopy Path Clas…
Fast and accurate path planning is important for ground robots to achieve safe and efficient autonomous navigation in unstructured outdoor environments. However, most existing methods exploiting either 2D or 2.5D maps struggle to balance…
In this paper, we propose a new method for path planning to a point for robot in environment with obstacles. The resulting algorithm is implemented as a simple variation of Dijkstra's algorithm. By adding a constraint to the shortest-path,…
We introduce the topological complexity of the work map associated to a robot system. In broad terms, this measures the complexity of any algorithm controlling, not just the motion of the configuration space of the given system, but the…
At modern warehouses, mobile robots transport packages and drop them into collection bins/chutes based on shipping destinations grouped by, e.g., the ZIP code. System throughput, measured as the number of packages sorted per unit of time,…
Classification of large and dense networks based on topology is very difficult due to the computational challenges of extracting meaningful topological features from real-world networks. In this paper we present a computationally tractable…
Robot pick and place systems have traditionally decoupled grasp, placement, and motion planning to build sequential optimization pipelines with the assumption that the individual components will be able to work together. However, this…
Multi-agent trajectory planning requires ensuring both safety and efficiency, yet deadlocks remain a significant challenge, especially in obstacle-dense environments. Such deadlocks frequently occur when multiple agents attempt to traverse…
In this study we want to connect our previously proposed context-relevant topographical maps with the deep learning community. Our architecture is a classifier with hidden layers that are hierarchical two-dimensional topographical maps.…
We consider path planning for a rigid spatial robot with 6 degrees of freedom (6 DOFs), moving amidst polyhedral obstacles. A correct, complete and practical path planner for such a robot has never been achieved, although this is widely…
We examine configurations of finite subsets of manifolds within the homotopy-theoretic context of $\infty$-categories by way of stratified spaces. Through these higher categorical means, we identify the homotopy types of such configuration…
High-dimensional neural activity often reside in a low-dimensional subspace, referred to as neural manifolds. Grid cells in the medial entorhinal cortex provide a periodic spatial code that are organized near a toroidal manifold,…
We study the topological complexity of work maps with respect to some subspaces of the configuration space and a workspace considered as the target set of the motion of robots. The motivation is to optimize and reduce the number of motion…
Besides per-pixel accuracy, topological correctness is also crucial for the segmentation of images with fine-scale structures, e.g., satellite images and biomedical images. In this paper, by leveraging the theory of digital topology, we…
This work serves as an opening and basis of an ongoing program investigating topological and geometric aspects of the moduli space of smooth fiberings on a manifold. The present paper focuses on the algebraic and differential topology of…
Topological strategies for navigation meaningfully reduce the space of possible actions available to a robot, allowing use of heuristic priors or learning to enable computationally efficient, intelligent planning. The challenges in…
The pattern formation task is commonly seen in a multi-robot system. In this paper, we study the problem of forming complex shapes with functionally limited mobile robots, which have to rely on other robots to precisely locate themselves.…
Ordered phases resulting from spontaneously broken continuous symmetries are effectively described by sigma models of maps to the coset space of Goldstone modes. A classic problem is to classify the topological sectors of the sigma model.…
We are dealing with the problem of space layout planning here. We present an architectural conceptual CAD approach. Starting with design specifications in terms of constraints over spaces, a specific enumeration heuristics leads to a…
The complexity of algorithms solving the motion planning problem is measured by a homotopy invariant TC(X) of the configuration space X of the system. Previously known lower bounds for TC(X) use the structure of the cohomology algebra of X.…
We utilize classical facts from topology to show that the classification problem in machine learning is always solvable under very mild conditions. Furthermore, we show that a softmax classification network acts on an input topological…