Related papers: A Decomposition-Based Approach to Reasoning about …

In two-dimensional geometric knapsack problem, we are given a set of n axis-aligned rectangular items and an axis-aligned square-shaped knapsack. Each item has integral width, integral height and an associated integral profit. The goal is…

Mobile robots navigating in indoor and outdoor environments must be able to identify and avoid unsafe terrain. Although a significant amount of work has been done on the detection of standing obstacles (solid obstructions), not much work…

In this work, we present scalable balancing domain decomposition by constraints methods for linear systems arising from arbitrary order edge finite element discretizations of multi-material and heterogeneous 3D problems. In order to enforce…

We consider generalizations of the familiar fifteen-piece sliding puzzle on the 4 by 4 square grid. On larger grids with more pieces and more holes, asymptotically how fast can we move the puzzle into the solved state? We also give a…

This work establishes a solution to the problem of assessing the capacity of multi-object assemblies to withstand external forces without becoming unstable. Our physically-grounded approach handles arbitrary structures made from rigid…

This paper presents an enhanced direct-method-based approach for the real-time solution of optimal control problems to handle path constraints, such as obstacles. The principal contributions of this work are twofold: first, the existing…

This paper studies path synthesis for nonholonomic mobile robots moving in two-dimensional space. We first address the problem of interpolating paths expressed as sequences of straight line segments, such as those produced by some planning…

We study an optimization problem related to the approximation of given data by a linear combination of transformed modes. In the simplest case, the optimization problem reduces to a minimization problem well-studied in the context of proper…

The representation of a Configuration Space C plays a vital role in accelerating the finding of a collision-free path for sampling-based motion planners where the majority of computation time is spent in collision checking of states.…

The free space diagram is a popular tool to compute the well-known Fr\'echet distance. As the Fr\'echet distance is used in many different fields, many variants have been established to cover the specific needs of these applications. Often,…

Decomposition spaces are a class of function spaces constructed out of well-behaved coverings and partitions of unity of a set. The structure of the covering of the set determines the properties of the decomposition space. Besov spaces,…

For configurations of point-sets that are pairwise constrained by distance intervals, the EASAL software implements a suite of algorithms that characterize the structure and geometric properties of the configuration space. The algorithms…

Reasoning 3D shapes from 2D images is an essential yet challenging task, especially when only single-view images are at our disposal. While an object can have a complicated shape, individual parts are usually close to geometric primitives…

We study the geometric knapsack problem in which we are given a set of $d$-dimensional objects (each with associated profits) and the goal is to find the maximum profit subset that can be packed non-overlappingly into a given…

We consider the problem of finding a continuous and non-rigid matching between a 2D contour and a 3D mesh. While such problems can be solved to global optimality by finding a shortest path in the product graph between both shapes, existing…

This paper addresses the problem of distance- and orientation-based formation control of a class of second-order nonlinear multi-agent systems in 3D space, under static and undirected communication topologies. More specifically, we design a…

A two-dimensional configuration is a coloring of the infinite grid Z^2 with finitely many colors. For a finite subset D of Z^2, the D-patterns of a configuration are the colored patterns of shape D that appear in the configuration. The…

3D object detection is one of the most important tasks in 3D vision perceptual system of autonomous vehicles. In this paper, we propose a novel two stage 3D object detection method aimed at get the optimal solution of object location in 3D…

Achieving collision avoidance between moving objects is an important objective while determining robot trajectories. In performing collision avoidance maneuvers, the relative shapes of the objects play an important role. The literature…

Developing safe autonomous driving systems is a major scientific and technical challenge. Existing AI-based end-to-end solutions do not offer the necessary safety guarantees, while traditional systems engineering approaches are defeated by…