Related papers: Shortest Path to Boundary for Self-Intersecting Me…

We demonstrate that challenging shortest path problems can be solved via direct spline regression from a neural network, trained in an unsupervised manner (i.e. without requiring ground truth optimal paths for training). To achieve this, we…

This paper presents a modeling and optimization framework to compute the minimum-lap-time spatial trajectory and powertrain operation of racing cars in a computationally efficient fashion. Specifically, we first derive a quasi-steady-state…

In this paper, we look into the minimum obstacle displacement (MOD) planning problem from a mobile robot motion planning perspective. This problem finds an optimal path to goal by displacing movable obstacles when no path exists due to…

In this work, we introduce a collision model specifically tailored for the simulation of inextensible textiles. The model considers friction, contacts, and inextensibility constraints all at the same time without any decoupling.…

We introduce a new technique, which we call the boundary method, for solving semi-discrete optimal transport problems with a wide range of cost functions. The boundary method reduces the effective dimension of the problem, thus improving…

In computer vision and graphics, various types of symmetries are extensively studied since symmetry present in objects is a fundamental cue for understanding the shape and the structure of objects. In this work, we detect the intrinsic…

The collision avoidance constraints are prominent as non-convex, non-differentiable, and challenging when defined in optimization-based motion planning problems. To overcome these issues, this paper presents a novel non-conservative…

We consider a suboptimal solution path algorithm for the Support Vector Machine. The solution path algorithm is an effective tool for solving a sequence of a parametrized optimization problems in machine learning. The path of the solutions…

Continuous 2-dimensional space is often discretized by considering a mesh of weighted cells. In this work we study how well a weighted mesh approximates the space, with respect to shortest paths. We consider a shortest path $…

This paper proposes collision-free optimal trajectory planning for autonomous vehicles in highway traffic, where vehicles need to deal with the interaction among each other. To address this issue, a novel optimal control framework is…

This work proposes an algorithm to bound the minimum distance between points on trajectories of a dynamical system and points on an unsafe set. Prior work on certifying safety of trajectories includes barrier and density methods, which do…

We present a continuous-time collision detection algorithm for quickly detecting whether certain polynomial trajectories in time intersect with convex obstacles. The algorithm is used in conjunction with an existing multicopter trajectory…

The detection of curved lanes is still challenging for autonomous driving systems. Although current cutting-edge approaches have performed well in real applications, most of them are based on strict model assumptions. Similar to other…

In this paper, we tackle the problem of planning an optimal coverage path for a robot operating indoors. Many existing approaches attempt to discourage turns in the path by covering the environment along the least number of coverage lines,…

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…

Model reduction methods are relevant when the computation time of a full convection-diffusion-reaction simulation based on detailed chemical reaction mechanisms is too large. In this article, we review a model reduction approach based on…

We propose a space mapping-based optimization algorithm for microscopic interacting particle dynamics which are inappropriate for direct optimization. This is of relevance for example in applications with bounded domains such that the…

We study the problem of computing the minimum area triangle that circumscribes a given $n$-sided convex polygon touching edge-to-edge. In other words, we compute the minimum area triangle that is the intersection of 3 half-planes out of $n$…

We show via examples that, when solving optimal control problems, representing the optimal state and input trajectory directly using interpolation schemes may not be the best choice. Due to the lack of considerations for solution…

Reducing the triangle count in complex 3D models is a basic geometry preprocessing step in graphics pipelines such as efficient rendering and interactive editing. However, most existing mesh simplification methods exhibit a few issues.…