Related papers: Proximity Queries for Absolutely Continuous Parame…
In this paper, an algorithm to compute a certified $G^1$ rational parametric approximation for algebraic space curves is given by extending the local generic position method for solving zero dimensional polynomial equation systems to the…
Many robotics applications benefit from being able to compute multiple locally optimal paths in a given configuration space. Examples include path planning for of tethered robots with cable-length constraints, systems involving cables,…
We study the navigation problem for a robot moving amidst static and dynamic obstacles and rely on a hierarchical approach to solve it. First, the reference trajectory is planned by the safe interval path planning algorithm that is capable…
We present a certified algorithm based on subdivision for computing an isotopic approximation to any number of curves in the plane. Our algorithm is based on the certified curve approximation algorithm of Plantinga and Vegter. The main…
We present a certified algorithm based on subdivision for computing an isotopic approximation to any number of curves in the plane. Our algorithm is based on the certified curve approximation algorithm of Plantinga and Vegter. The main…
The Fr\'echet distance is a popular similarity measure that is well-understood for polygonal curves in $\mathbb{R}^d$: near-quadratic time algorithms exist, and conditional lower bounds suggest that these results cannot be improved…
We present a new method for visualizing implicit real algebraic curves inside a bounding box in the $2$-D or $3$-D ambient space based on numerical continuation and critical point methods. The underlying techniques work also for tracing…
Given a non-rational real space curve and a tolerance $\epsilon>0$, we present an algorithm to approximately parametrize the curve. The algorithm checks whether a planar projection of the space curve is $\epsilon$-rational and, in the…
We study two fundamental problems dealing with curves in the plane, namely, the nearest-neighbor problem and the center problem. Let $\mathcal{C}$ be a set of $n$ polygonal curves, each of size $m$. In the nearest-neighbor problem, the goal…
A central aspect of robotic motion planning is collision avoidance, where a multitude of different approaches are currently in use. Optimization-based motion planning is one method, that often heavily relies on distance computations between…
Accurate prediction of surrounding road users' trajectories is essential for safe and efficient autonomous driving. While deep learning models have improved performance, challenges remain in preventing off-road predictions and ensuring…
Finding paths in graphs is a fundamental graph-theoretic task. In this work, we we are concerned with finding a path with some constraints on its length and the number of vertices neighboring the path, that is, being outside of and incident…
We propose a simple subsampling scheme for fast randomized approximate computation of optimal transport distances. This scheme operates on a random subset of the full data and can use any exact algorithm as a black-box back-end, including…
Balancing the trade-off between safety and efficiency is of significant importance for path planning under uncertainty. Many risk-aware path planners have been developed to explicitly limit the probability of collision to an acceptable…
In many robotics applications, it is necessary to compute not only the distance between the robot and the environment, but also its derivative - for example, when using control barrier functions. However, since the traditional Euclidean…
This work presents proximally optimal predictive control algorithm, which is essentially a model-based lateral controller for steered autonomous vehicles that selects an optimal steering command within the neighborhood of previous steering…
This research addresses the increasing demand for advanced navigation systems capable of operating within confined surroundings. A significant challenge in this field is developing an efficient planning framework that can generalize across…
As mobile robots and autonomous vehicles become increasingly prevalent in human-centred environments, there is a need to control the risk of collision. Perceptual modules, for example machine vision, provide uncertain estimates of object…
We consider a general model for representing and manipulating parametric curves, in which a curve is specified by a black box mapping a parameter value between 0 and 1 to a point in Euclidean d-space. In this model, we consider the…
We analyse the convergence of an approximate, fully inexact, ADMM algorithm under additive, deterministic and probabilistic error models. We consider the generalized ADMM scheme that is derived from generalized Lagrangian penalty with…