Related papers: Shortest Path to Boundary for Self-Intersecting Me…
Global optimisation problems in networks often require shortest path length computations to determine the most efficient route. The simplest and most common problem with a shortest path solution is perhaps that of a traditional labyrinth or…
In this paper, a new fast algorithm for path planning and a collision prediction framework for two dimensional dynamically changing environments are introduced. The method is called Time Distance (TD) and benefits from the space-time space…
The need to compute the intersections between a line and a high-order curve or surface arises in a large number of finite element applications. Such intersection problems are easy to formulate but hard to solve robustly. We introduce a…
We propose a neural network-based approach for collision detection with deformable objects. Unlike previous approaches based on bounding volume hierarchies, our neural approach does not require an update of the spatial data structure when…
This paper proposes vehicle motion planning methods with obstacle avoidance in tight spaces by incorporating polygonal approximations of both the vehicle and obstacles into a model predictive control (MPC) framework. Representing these…
We present a new framework for expressing finite element methods on multiple intersecting meshes: multimesh finite element methods. The framework enables the use of separate meshes to discretize parts of a computational domain that are…
Trajectory planning in dense, interactive traffic scenarios presents significant challenges for autonomous vehicles, primarily due to the uncertainty of human driver behavior and the non-convex nature of collision avoidance constraints.…
This work presents a motion planning framework for robotic manipulators that computes collision-free paths directly in image space. The generated paths can then be tracked using vision-based control, eliminating the need for an explicit…
The determination of time-dependent collision-free shortest paths has received a fair amount of attention. Here, we study the problem of computing a time-dependent shortest path among growing discs which has been previously studied for the…
Boundary detection is essential for a variety of computer vision tasks such as segmentation and recognition. In this paper we propose a unified formulation and a novel algorithm that are applicable to the detection of different types of…
The quadratic shortest path problem is the problem of finding a path in a directed graph such that the sum of interaction costs over all pairs of arcs on the path is minimized. We derive several semidefinite programming relaxations for the…
The shortest path problem in graphs is a cornerstone of AI theory and applications. Existing algorithms generally ignore edge weight computation time. We present a generalized framework for weighted directed graphs, where edge weight can be…
This paper addresses the problem of finding shortest paths homotopic to a given disjoint set of paths that wind amongst point obstacles in the plane. We present a faster algorithm than previously known.
We derive exact expressions for the shortest path length to a point of a Poisson line Cox process (PLCP) from the typical point of the PLCP and from the typical intersection of the underlying Poisson line process (PLP), restricted to a…
In this paper we consider the problem of coordinating autonomous vehicles approaching an intersection. We cast the problem in the distributed optimisation framework and propose an algorithm to solve it in real time. We extend previous work…
The question of representation of 3D geometry is of vital importance when it comes to leveraging the recent advances in the field of machine learning for geometry processing tasks. For common unstructured surface meshes state-of-the-art…
We propose a technique called Rotate-and-Kill for solving the polygon inclusion and circumscribing problems. By applying this technique, we obtain $O(n)$ time algorithms for computing (1) the maximum area triangle in a given $n$-sided…
In this article, we present an approximation algorithm for solving the Weighted Region Problem amidst a set of $ n $ non-overlapping weighted disks in the plane. For a given parameter $ \varepsilon \in (0,1]$, the length of the approximate…
The Shortest-Path Problem in Graph of Convex Sets (SPP in GCS) is a recently developed optimization framework that blends discrete and continuous decision making. Many relevant problems in robotics, such as collision-free motion planning,…
We consider the problem of cooperative intersection management. It arises in automated transportation systems for people or goods but also in multi-robots environment. Therefore many solutions have been proposed to avoid collisions. The…