Related papers: Sequential parametrized topological complexity of …
Despite the attention that the problem of path planning for tethered robots has garnered in the past few decades, the approaches proposed to solve it typically rely on a discrete representation of the configuration space and do not exploit…
We numerically investigate and experimentally demonstrate an in-situ topological band transition in a highly tunable mechanical system made of cylindrical granular particles. This system allows us to tune its inter-particle stiffness in a…
Parametrized motion planning algorithms have high degrees of universality and flexibility, as they are designed to work under a variety of external conditions, which are viewed as parameters and form part of the input of the underlying…
We present a novel method for computing slow manifolds and their fast fibre bundles in geometric singular perturbation problems. This coordinate-independent method is inspired by the parametrisation method introduced by Cabr\'e, Fontich and…
It has been observed that the very important motion planning problem of robotics mathematically speaking boils down to the problem of finding a section to the path-space fibration, raising the notion of topological complexity, as introduced…
A topological theory initiated recently by the author uses methods of algebraic topology to estimate numerically the character of instabilities arising in motion planning algorithms. The present paper studies random motion planning…
Topological complexity $\TC{B}$ of a space $B$ is introduced by M. Farber to measure how much complex the space is, which is first considered on a configuration space of a motion planning of a robot arm. We also consider a stronger version…
We study certain topological problems that are inspired by applications to autonomous robot manipulation. Consider a continuous map $f\colon X\to Y$, where $f$ can be a kinematic map from the configuration space $X$ to the working space $Y$…
In Coordinated Motion Planning (CMP), we are given a rectangular-grid on which $k$ robots occupy $k$ distinct starting gridpoints and need to reach $k$ distinct destination gridpoints. In each time step, any robot may move to a neighboring…
We use topological data analysis and machine learning to study a seminal model of collective motion in biology [D'Orsogna et al., Phys. Rev. Lett. 96 (2006)]. This model describes agents interacting nonlinearly via attractive-repulsive…
Multi-robot motion planning (MRMP) is the problem of finding collision-free paths for a set of robots in a continuous state space. The difficulty of MRMP increases with the number of robots and is exacerbated in environments with narrow…
When planning motions in a configuration space that has underlying symmetries (e.g. when manipulating one or multiple symmetric objects), the ideal planning algorithm should take advantage of those symmetries to produce shorter…
We introduce a sequential learning algorithm to address a robust controller tuning problem, which in effect, finds (with high probability) a candidate solution satisfying the internal performance constraint to a chance-constrained program…
We introduce and study the sequential analogue of Grant's parametrized topological complexity of group epimorphisms, which generalizes the sequential topological complexity of groups. We derive bounds for sequential parametrized topological…
We describe an algorithm for motion planning based on expert demonstrations of a skill. In order to teach robots to perform complex object manipulation tasks that can generalize robustly to new environments, we must (1) learn a…
Many remarkably robust, rapid and spontaneous self-assembly phenomena in nature can be modeled geometrically starting from a collection of rigid bunches of spheres. This paper highlights the role of symmetry in sphere-based assembly…
In this paper we generalize the discrete r-homotopy to the discrete (s, r)-homotopy. Then by this notion, we introduce the discrete motion planning for robots which can move discreetly. Moreover, in this case the number of motion planning,…
We study an elementary problem of topological robotics: rotation of a line, which is fixed by a revolving joint at a base point: one wants to bring the line from its initial position to a final position by a continuous motion in the space.…
Topological phenomena typically govern the behavior of delocalized waves, giving rise to robust transport in electronic, photonic, and mechanical systems. Whether similar principles can directly control the motion of a localized particle,…
This paper deals with shape irregularity issues in discrete topology optimization algorithms whereby the design is created using the automated distribution of material in the design region. Graph theory is employed to derive appropriate…