Related papers: Topological complexity of motion planning
Finding the Time-Optimal Parameterization of a Path (TOPP) subject to second-order constraints (e.g. acceleration, torque, contact stability, etc.) is an important and well-studied problem in robotics. In comparison, TOPP subject to…
In arXiv:1711.10132 a new approximating invariant ${\mathsf{TC}}^{\mathcal{D}}$ for topological complexity was introduced called $\mathcal{D}$-topological complexity. In this paper, we explore more fully the properties of…
Mathematical morphology is a theory concerned with non-linear operators for image processing and analysis. The underlying framework for mathematical morphology is a partially ordered set with well-defined supremum and infimum operations.…
We present a method for effectively planning the motion trajectory of robots in manufacturing tasks, the tool-paths of which are usually complex and have a large number of discrete-time constraints as waypoints. Kinematic redundancy also…
The presence of task constraints imposes a significant challenge to motion planning. Despite all recent advancements, existing algorithms are still computationally expensive for most planning problems. In this paper, we present Constrained…
We consider the problem of finding collision-free paths for curvature-constrained systems in the presence of obstacles while minimizing execution time. Specifically, we focus on the setting where a planar system can travel at some range of…
We study the parameterized complexity of a generalization of the coordinated motion planning problem on graphs, where the goal is to route a specified subset of a given set of $k$ robots to their destinations with the aim of minimizing the…
Trusses are load-carrying light-weight structures consisting of bars connected at joints ubiquitously applied in a variety of engineering scenarios. Designing optimal trusses that satisfy functional specifications with a minimal amount 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…
Motion planning in the presence of multiple dynamic obstacles is an important research problem from the perspective of autonomous vehicles as well as space-constrained multi-robot work environment. In this paper, we address the motion…
We propose a novel, multi-layered planning approach for computing paths that satisfy both kinodynamic and spatiotemporal constraints. Our three-part framework first establishes potential sequences to meet spatial constraints, using them to…
In many robot motion planning problems, task objectives and physical constraints induce non-Euclidean geometry on the configuration space, yet many planners operate using Euclidean distances that ignore this structure. We address the…
Living systems exhibit complex yet organized behavior on multiple spatiotemporal scales. To investigate the nature of multiscale coordination in living systems, one needs a meaningful and systematic way to quantify the complex dynamics, a…
Motion planning and control are key problems in a collection of robotic applications including the design of autonomous agile vehicles and of minimalist manipulators. These problems can be accurately formalized within the language of affine…
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…
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…
Modern methods of graph theory describe a graph up to isomorphism, which makes it difficult to create mathematical models for visualizing graph drawings on a plane. The topological drawing of the planar part of a graph allows representing…
We consider the makespan minimization coupled-tasks problem in presence of compatibility constraints with a specified topology. In particular, we focus on stretched coupled-tasks, i.e. coupled-tasks having the same sub-tasks execution time…
Topological data analysis is a powerful tool for describing topological signatures in real world data. An important challenge in topological data analysis is matching significant topological signals across distinct systems. In geometry and…
We study a variant of the Coordinated Motion Planning problem on undirected graphs, referred to herein as the \textsc{Coordinated Sliding-Motion Planning} (CSMP) problem. In this variant, we are given an undirected graph $G$, $k$ robots…