Related papers: Motion planning in tori
We study the problem of motion planning for a collection of $n$ labeled unit disc robots in a polygonal environment. We assume that the robots have revolving areas around their start and final positions: that each start and each final is…
Using the notion of contiguity of simplicial maps, we adapt Farber's topological complexity to the realm of simplicial complexes. We show that, for a finite simplicial complex $K$, our discretized concept recovers the topological complexity…
We show that the discrete Sinkhorn algorithm - as applied in the setting of Optimal Transport on a compact manifold - converges to the solution of a fully non-linear parabolic PDE of Monge-Ampere type, in a large-scale limit. The latter…
Motion path planning is an intrinsically geometric problem which is central for design of robot systems. Since the early years of AI, robotics together with computer vision have been the areas of computer science that drove its development.…
In this paper we present efficient algorithms for the computation of several invariant objects for Hamiltonian dynamics. More precisely, we consider KAM tori (i.e diffeomorphic copies of the torus such that the motion on them is conjugated…
We systematically produce algebraic varieties with torus action by constructing them as suitably embedded subvarieties of toric varieties. The resulting varieties admit an explicit treatment in terms of toric geometry and graded ring…
A motion planning algorithm computes the motion of a robot by computing a path through its configuration space. To improve the runtime of motion planning algorithms, we propose to nest robots in each other, creating a nested quotient-space…
Motion planning for multi-jointed robots is challenging. Due to the inherent complexity of the problem, most existing works decompose motion planning as easier subproblems. However, because of the inconsistent performance metrics, only…
We introduce toric arrangements, essentially finite families of codimension 1 subtori of a torus or of their cosets, as a periodic generalization of hyperplane arrangements, compute cohomology of the complement of such an arrangement and…
We study a generalized motion planning problem involving multiple autonomous robots navigating in a $d$-dimensional Euclidean space in the presence of a set of obstacles whose positions are unknown a priori. Each robot is required to visit…
Motion planning in the configuration space (C-space) induces benefits, such as smooth trajectories. It becomes more complex as the degrees of freedom (DOF) increase. This is due to the direct relation between the dimensionality of the…
Planning for multi-robot teams in complex environments is a challenging problem, especially when these teams must coordinate to accomplish a common objective. In general, optimal solutions to these planning problems are computationally…
Task and motion planning under Signal Temporal Logic constraints is known to be NP-hard. A common class of approaches formulates these hybrid problems, which involve discrete task scheduling and continuous motion planning, as mixed-integer…
Planning whole-body motions while taking into account the terrain conditions is a challenging problem for legged robots since the terrain model might produce many local minima. Our coupled planning method uses stochastic and…
We present a decoupled algorithm for motion planning for a collection of unit-balls moving among polyhedral obstacles in $\mathbb{R}^d$, for any $d \ge 2$. We assume that the robots have revolving areas in the vicinity of their start and…
This paper presents motion planning algorithms for underactuated systems evolving on rigid rotation and displacement groups. Motion planning is transcribed into (low-dimensional) combinatorial selection and inverse-kinematics problems. We…
In this paper, we deal with the robot motion planning problem in multi-valued function theory. We first enrich the multi-homotopy studies by introducing a multi-homotopy lifting property and a multi-fibration. Then we compute both a…
In this paper, we introduce the notion of maximal actions of compact tori on smooth manifolds and study compact connected complex manifolds equipped with maximal actions of compact tori. We give a complete classification of such manifolds,…
In this paper, we approach the challenging problem of motion planning for knot tying. We propose a hierarchical approach in which the top layer produces a topological plan and the bottom layer translates this plan into continuous robot…
We propose a novel method for planning shortest length piecewise-linear motions through complex environments punctured with static, moving, or even morphing obstacles. Using a moment optimization approach, we formulate a hierarchy of…