Related papers: On the Targeted Complexity of a Map
This research is motivated by studying image processing algorithms through a topological lens. The images we focus on here are those that have been segmented by digital Jordan curves as a means of image compression. The algorithms of…
We perform a refined complexity-theoretic analysis of three classical problems in the context of Hierarchical Task Network Planning: the verification of a provided plan, whether an executable plan exists, and whether a given state can be…
Among the several topological properties of complex networks, the shortest path represents a particularly important characteristic because of its potential impact not only on other topological properties, but mainly for its influence on…
In this paper, we study instances of complex neural networks, i.e. neural netwo rks with complex topologies. We use Self-Organizing Map neural networks whose n eighbourhood relationships are defined by a complex network, to classify handwr…
This work presents a new path classification criterion to distinguish paths geometrically and topologically from the workspace, which is divided through cell decomposition, generating a medial-axis-like skeleton structure. We use this…
Systems of networked mobile robots, such as unmanned aerial or ground vehicles, will play important roles in future military and commercial applications. The communications for such systems will typically be over wireless links and may…
Traditional multi-robot motion planning (MMP) focuses on computing trajectories for multiple robots acting in an environment, such that the robots do not collide when the trajectories are taken simultaneously. In safety-critical…
Sequential parametrized topological complexity is a numerical homotopy invariant of a fibration, which arose in the robot motion planning problem with external constraints. In this paper, we study sequential parametrized topological…
Multi-robot planning and coordination in uncertain environments is a fundamental computational challenge, since the belief space increases exponentially with the number of robots. In this paper, we address the problem of planning in…
We provide a short introduction to the field of topological data analysis and discuss its possible relevance for the study of complex systems. Topological data analysis provides a set of tools to characterise the shape of data, in terms of…
Visual robot navigation within large-scale, semi-structured environments deals with various challenges such as computation intensive path planning algorithms or insufficient knowledge about traversable spaces. Moreover, many…
Mapping operator motions to a robot is a key problem in teleoperation. Due to differences between workspaces, such as object locations, it is particularly challenging to derive smooth motion mappings that fulfill different goals (e.g.…
Motion planning techniques for quadrotors have advanced significantly over the past decade. Most successful planners have two stages: a front-end that determines a path that incorporates geometric (or kinematic or input) constraints and…
In this study, we delve into the discrete TC of surjective simplicial fibrations, aiming to unravel the interplay between topological complexity, discrete geometric structures, and computational efficiency. Moreover, we examine the…
Soft robotics holds transformative potential for enabling adaptive and adaptable systems in dynamic environments. However, the interplay between morphological and control complexities and their collective impact on task performance remains…
This paper aims to improve the computational efficiency of motion planning for mobile robots with non-trivial dynamics through the use of learned controllers. Offline, a system-specific controller is first trained in an empty environment.…
We present a new approach to equivariant version of the topological complexity, called a symmetric topological complexity. It seems that the presented approach is more adequate for the analysis of an impact of symmetry on the the motion…
Schematic maps are in daily use to show the connectivity of subway systems and to facilitate travellers to plan their journeys effectively. This study surveys up-to-date algorithmic approaches in order to give an overview of the state of…
A significant challenge in motion planning is to avoid being in or near \emph{singular configurations} (\textit{singularities}), that is, joint configurations that result in the loss of the ability to move in certain directions in task…
In this paper, we introduce relative LS category of a map and study some of its properties. Then we introduce `higher topological complexity' of a map, a homotopy invariant. We give a cohomological lower bound and compare it with previously…