Related papers: The grasshopper problem
Building on the results of Ma, Trudinger and Wang \cite{MTW}, and of the author \cite{L5}, we study two problems of optimal transportation on the sphere: the first corresponds to the cost function $d^2(x,y)$, where $d(\cdot,\cdot)$ is the…
A planar herding problem is considered, where a superior pursuer herds a flock of non-cooperative, inferior evaders around a predefined target point. An inverse square law of repulsion is assumed between the pursuer and each evader. Two…
This paper studies the motion planning problem of the pick-and-place of an aerial manipulator that consists of a quadcopter flying base and a Delta arm. We propose a novel partially decoupled motion planning framework to solve this problem.…
Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of motions are thoroughly analyzed. A variational system around a grazing solution which depends…
Robot motion planning involves computing a sequence of valid robot configurations that take the robot from its initial state to a goal state. Solving a motion planning problem optimally using analytical methods is proven to be PSPACE-Hard.…
We propose a machine learning enhanced algorithm for solving the optimal landing problem. Using Pontryagin's minimum principle, we derive a two-point boundary value problem for the landing problem. The proposed algorithm uses deep learning…
Ratcheting surfaces are a common motif in nature and appear in plant awns and grasses. They are known to profer selective advantages for seed dispersion and burial. In two simple model experiments we show that these anisotropically toothed…
An important goal in algorithm design is determining the best running time for solving a problem (approximately). For some problems, we know the optimal running time, assuming certain conditional lower bounds. In this work, we study the…
We consider random translation-invariant frustration-free quantum spin Hamiltonians on $\mathbb Z^D$ in which the nearest-neighbor interaction in every direction is randomly sampled and then distributed across the lattice. Our main result…
We consider a shape optimization problem for the persistence threshold of a biological species dispersing in a periodically fragmented environment, the unknown shape corresponding to the portion of the habitat which is favorable to the…
We study a very general four dimensional Field Theory model describing the dynamics of a massless higher spin $N$ symmetric tensor field particle interacting with a geometrical background.This model is invariant under the action of an…
Thanks to the rapid evolvement of robotic technologies, robot mowing is emerging to liberate humans from the tedious and time-consuming landscape work. Traditionally, robot mowing is perceived as a "Coverage Path Planning" problem, with a…
When setting up field experiments, to test and compare a range of genotypes (e.g. maize hybrids), it is important to account for any possible field effect that may otherwise bias performance estimates of genotypes. To do so, we propose a…
This paper is a continuation of our ongoing efforts to solve a number of geometric problems and their extensions by using advanced tools of variational analysis and generalized differentiation. Here we propose and study, from both…
Quantum annealing offers a promising strategy for solving complex optimization problems by encoding the solution into the ground state of a problem Hamiltonian. While most implementations rely on spin-$1/2$ systems, we explore the…
Frustrated magnetic interactions in a quasi-two-dimensional [111] slab of pyrochlore lattice were studied. For uniform nearest neighbor (NN) interactions, we show that the complex magnetic problem can be mapped onto a model with two…
With the development of robotics, ground robots are no longer limited to planar motion. Passive height variation due to complex terrain and active height control provided by special structures on robots require a more general navigation…
In this article, a new model for 3D motion planning, applicable to aerial vehicles, is proposed to connect an initial and final configuration subject to pitch rate and yaw rate constraints. The motion planning problem for a…
We present a decoupled algorithm for motion planning for a collection of unit-balls moving among polyhedral obstacles in $\mathbb{R}^d$, for any $d \ge 2$. We assume that the robots have revolving areas in the vicinity of their start and…
The moving sofa problem, posed by L. Moser in 1966, asks for the planar shape of maximal area that can move around a right-angled corner in a hallway of unit width, and is conjectured to have as its solution a complicated shape derived by…