Related papers: Oriented robot motion planning in Riemannian manif…
Computational optimal transport (OT) offers a principled framework for generative modeling. Neural OT methods, which use neural networks to learn an OT map (or potential) from data in an amortized way, can be evaluated out of sample after…
The general construction of self-adjoint configuration space representations of the Heisenberg algebra over an arbitrary manifold is considered. All such inequivalent representations are parametrised in terms of the topology classes of flat…
Recent advancements in robotics have transformed industries such as manufacturing, logistics, surgery, and planetary exploration. A key challenge is developing efficient motion planning algorithms that allow robots to navigate complex…
We determine the cup-length of some oriented Grassmann manifolds by finding a Groebner basis associated with a certain subring of the cohomology of them. As its applications, we provide not only a lower but also an upper bound for the…
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…
Optimization on Hadamard manifolds -- the natural Riemannian setting for globally geodesically convex problems -- relies on exponential maps to retract tangent vectors and parallel transport to connect tangent spaces across the manifold.…
Optimal transport (OT) has recently found widespread interest in machine learning. It allows to define novel distances between probability measures, which have shown promise in several applications. In this work, we discuss how to…
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…
Off-diagonal upper bounds are established away from the diagonal for the Bergman kernels associated to high powers of holomorphic line bundles over compact complex manifolds, asymptotically as the power tends to infinity. The line bundle is…
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…
Articulated robots such as manipulators increasingly must operate in uncertain and dynamic environments where interaction (with human coworkers, for example) is necessary. In these situations, the capacity to quickly adapt to unexpected…
How hard is it to program $n$ robots to move about a long narrow aisle such that only $w$ of them can fit across the width of the aisle? In this paper, we answer that question by calculating the topological complexity of $\text{conf}(n,w)$,…
The aim of this paper is to give some existence results of optimal control of robotic systems with a Riemannian geometric view, and derive a formulation of the PMP using the intrinsic geometry of the configuration space. Applying this…
This work studies rearrangement problems involving the sorting of robots or objects in stack-like containers, which can be accessed only from one side. Two scenarios are considered: one where every robot or object needs to reach a…
This paper presents a minimum displacement motion planning problem wherein obstacles are displaced by a minimum amount to find a feasible path. We define a metric for robot-obstacle intersection that measures the extent of the intersection…
In the realm of robotics, numerous downstream robotics tasks leverage machine learning methods for processing, modeling, or synthesizing data. Often, this data comprises variables that inherently carry geometric constraints, such as the…
The motion planning problem is a fundamental problem in robotics, so that every autonomous robot should be able to deal with it. A number of solutions have been proposed and a probabilistic one seems to be quite reasonable. However, here we…
Motion Planning (MP) is a critical challenge in robotics, especially pertinent with the burgeoning interest in embodied artificial intelligence. Traditional MP methods often struggle with high-dimensional complexities. Recently neural…
We use rewriting systems to spell out cup-products in the (twisted) cohomology groups of a product of surface groups. This allows us to detect a non-trivial obstruction bounding from below the effective topological complexity of an…
We present a modular framework for solving a motion planning problem among a group of robots. The proposed framework utilizes a finite set of low level motion primitives to generate motions in a gridded workspace. The constraints on…