Related papers: A Discrete Topological Complexity of Discrete Moti…
This paper presents a novel planning method that achieves navigation of multi-robot formations in cluttered environments, while maintaining the formation throughout the robots motion. The method utilises a decentralised approach to find…
How do we move a robot efficiently from one position to another? To answer this question, we need to understand its configuration space, a 'map' where we can find every possible position of the robot. Unfortunately, these maps are very…
This paper presents a motion planning algorithm for quadruped locomotion based on density functions. We decompose the locomotion problem into a high-level density planner and a model predictive controller (MPC). Due to density functions…
We study discrete dynamical systems through the topological concepts of limit set, which consists of all points that can be reached arbitrarily late, and asymptotic set, which consists of all adhering values of orbits. In particular, we…
An integration of distributionally robust risk allocation into sampling-based motion planning algorithms for robots operating in uncertain environments is proposed. We perform non-uniform risk allocation by decomposing the distributionally…
The present paper aims at analyzing the topological content of the complex trajectories that weeder-autonomous robots follow in operation. We will prove that the topological descriptors of these trajectories are affected by the robot…
Finding asymptotically-optimal paths in multi-robot motion planning problems could be achieved, in principle, using sampling-based planners in the composite configuration space of all of the robots in the space. The dimensionality of this…
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.…
Developing robust locomotion for humanoid robots is a complex task due to the unstable nature of these robots and also to the unpredictability of the terrain. A robust locomotion planner is one of the fundamental components for generating…
Task and motion planning represents a powerful set of hybrid planning methods that combine reasoning over discrete task domains and continuous motion generation. Traditional reasoning necessitates task domain models and enough information…
Discrete Morse theory emerged as an essential tool for computational geometry and topology. Its core structures are discrete gradient fields, defined as acyclic matchings on a complex $C$, from which topological and geometrical informations…
Sampling-based algorithms are widely used for motion planning in high-dimensional configuration spaces. However, due to low sampling efficiency, their performance often diminishes in complex configuration spaces with narrow corridors.…
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…
We study the categories of discrete modules for topological rings arising as the rings of operations in various kinds of topological K-theory. We prove that for these rings the discrete modules coincide with those modules which are locally…
This paper investigates the online motion coordination problem for a group of mobile robots moving in a shared workspace. Based on the realistic assumptions that each robot is subject to both velocity and input constraints and can have only…
A central problem in topological data analysis is that of computing the homology of a given simplicial complex. Said complexes can have arbitrary large number of simplices, as can happen, for example, if the space is the Rips-Vietoris or…
We present a homotopic approach to solving challenging, optimization-based motion planning problems. The approach uses Homotopy Optimization, which, unlike standard continuation methods for solving homotopy problems, solves a sequence of…
Integrated Task and Motion Planning (ITMP) for mobile robots in a dynamic environment with moving obstacles is a challenging research question and attracts more and more attentions recently. Most existing methods either restrict to static…
In general relativity, the motion of an extended body moving in a given spacetime can be described by a particle on a (generally non-geodesic) worldline. In first approximation, this worldline is a geodesic of the underlying spacetime, and…
Autonomous navigation of a mobile robot is a challenging task which requires ability of mapping, localization, path planning and path following. Conventional mapping methods build a dense metric map like an occupancy grid, which is affected…