Related papers: Generating Plane Quadrangulations and Symmetry-pre…
In the classical context of robotic mapping and localization, map matching is typically defined as the task of finding a rigid transformation (i.e., 3DOF rotation/translation on the 2D moving plane) that aligns the query and reference maps…
Computing a morph between two drawings of a graph is a classical problem in computational geometry and graph drawing. While this problem has been widely studied in the context of planar graphs, very little is known about the existence of…
Manipulators can be added to legged robots, allowing them to interact with and change their environment. Legged mobile manipulation planners must consider how contact forces generated by these manipulators affect the system. Current…
We have formulated the problem of generating periodic dense paritcle packings as an optimization problem called the Adaptive Shrinking Cell (ASC) formulation [S. Torquato and Y. Jiao, Phys. Rev. E {\bf 80}, 041104 (2009)]. Because the…
We extend to $p$-uniformly convex spaces tools from the analysis of fixed point iterations in linear spaces. This study is restricted to an appropriate generalization of single-valued, pointwise $\alpha$-averaged mappings. Our main…
We investigate multiple fundamental variants of the classic coordinated motion planning (CMP) problem for unit square robots in the plane under the $L_1$ metric. In coordinated motion planning, we are given two arrangements of $k$ robots…
We calculate the generating functions for the number of tilings of rectangles of various widths by the right tromino, the $L$ tetromino, and the $T$ tetromino. This allows us to place lower bounds on the entropy of tilings of the plane by…
In this paper we propose a method that uses Lagrange multipliers and numerical algebraic geometry to find all critical points, and therefore globally solve, polynomial optimization problems. We design a polyhedral homotopy algorithm that…
Polyhedral Lyapunov functions can approximate any norm arbitrarily well. Because of this, they are used to study the stability of linear time varying and linear parameter varying systems without being conservative. However, the…
Triangle strips have been widely used for efficient rendering. It is NP-complete to test whether a given triangulated model can be represented as a single triangle strip, so many heuristics have been proposed to partition models into few…
Scattering amplitudes for colored theories have recently been formulated in a new way, in terms of curves on surfaces. In this note we describe a canonical set of functions we call surface functions, associated to all orders in the…
We compute the distance-dependent two-point function of vertex-bicolored planar maps, i.e., maps whose vertices are colored in black and white so that no adjacent vertices have the same color. By distance-dependent two-point function, we…
We provide "growth schemes" for inductively generating uniform random $2p$-angulations of the sphere with $n$ faces, as well as uniform random simple triangulations of the sphere with $2n$ faces. In the case of $2p$-angulations, we provide…
This paper implements Simultaneous Localization and Mapping (SLAM) technique to construct a map of a given environment. A Real Time Appearance Based Mapping (RTAB-Map) approach was taken for accomplishing this task. Initially, a 2d…
Multi-Angled Parallelism (MAP) is a method to recognize lines in binary images. It is suitable to be implemented in parallel processing and image processing hardware. The binary image is transformed into directional planes, upon which,…
We present a mechanism for the creation of gaps in the spectra of self-adjoint operators defined over a Hilbert space of functions on a graph, which is based on the process of graph decoration. The resulting Hamiltonians can be viewed as…
Rectangulations are partitions of a square into axis-aligned rectangles. A number of results provide bijections between combinatorial equivalence classes of rectangulations and families of pattern-avoiding permutations. Other results deal…
This paper generalizes a previously-conceived, continuation-based optimization technique for scalar objective functions on constraint manifolds to cases of periodic and quasiperiodic solutions of delay-differential equations. A Lagrange…
A typical manipulation task consists of a manipulator equipped with a gripper to grasp and move an object with constraints on the motion of the hand-held object, which may be due to the nature of the task itself or from object-environment…
Symmetry is the essential element of lifted inference that has recently demon- strated the possibility to perform very efficient inference in highly-connected, but symmetric probabilistic models models. This raises the question, whether…