Related papers: Optimal Path in Two and Three Dimensions
Consider the problem of distributing two conducting materials in a ball with fixed proportion in order to minimize the first eigenvalue of a Dirichlet operator. It was conjectured that the optimal distribution consists of putting the…
It is shown that optimal network plans can be obtained, naturally, as a limit of easier problems of point allocations. These problems are obtained by minimizing the mass transportation on the set of atomic measures of prescribed number of…
Optimal path planning is prone to convergence to local, rather than global, optima. This is often the case for mobile manipulators due to nonconvexities induced by obstacles, robot kinematics and constraints. This paper focuses on planning…
Driving energy consumption plays a major role in the navigation of mobile robots in challenging environments, especially if they are left to operate unattended under limited on-board power. This paper reports on first results of an…
This paper proposes coordination laws for optimal energy generation and distribution in energy network, which is composed of physical flow layer and cyber communication layer. The physical energy flows through the physical layer; but all…
How do we search for the entire family tree without unwanted random guesses, starting from a high-index and high-energy stationary state on the energy landscape? Here we introduce a general numerical method that constructs the pathway map…
This review is devoted to the detailed consideration of the universal statistical properties of one-dimensional directed polymers in a random potential. In terms of the replica Bethe ansatz technique we derive several exact results for…
We study the statistics of the optimal path in both random and scale free networks, where weights $w$ are taken from a general distribution $P(w)$. We find that different types of disorder lead to the same universal behavior. Specifically,…
UAV trajectory planning is often done in a two-step approach, where a low-dimensional path is refined to a dynamic trajectory. The resulting trajectories are only locally optimal, however. On the other hand, direct planning in…
An effective method for optimizing path planning for a specific model of a 6-degree-of-freedom (6-DOF) robot manipulator is presented as part of the motion planning of the manipulator using computer algebra. We assume that we are given a…
We present an optimal strategy having finite outcomes for estimating a single parameter of the displacement operator on an arbitrary finite dimensional system using a finite number of identical samples. Assuming the uniform {\it a priori}…
The manner in which probability amplitudes of paths sum up to form wave functions of a harmonic oscillator, as well as other, simple 1-dimensional problems, is described. Using known, closed-form, path-based propagators for each problem, an…
Molecules with complex internal structure in time-dependent periodic potentials are studied by using short Rubinstein-Duke model polymers as an example. We extend our earlier work on transport in stochastically varying potentials to cover…
We present a novel algorithm for dynamic routing with dedicated path protection which, as the presented simulation results suggest, can be efficient and exact. We present the algorithm in the setting of optical networks, but it should be…
Many exciting robotic applications require multiple robots with many degrees of freedom, such as manipulators, to coordinate their motion in a shared workspace. Discovering high-quality paths in such scenarios can be achieved, in principle,…
In this work we consider the HYBRID model of distributed computing, introduced recently by Augustine, Hinnenthal, Kuhn, Scheideler, and Schneider (SODA 2020), where nodes have access to two different communication modes: high-bandwidth…
Path finding is a well-studied problem in AI, which is often framed as graph search. Any-angle path finding is a technique that augments the initial graph with additional edges to build shorter paths to the goal. Indeed, optimal algorithms…
We consider the problem of finding the global optimum of a real-valued complex polynomial on a compact set defined by real-valued complex polynomial inequalities. It reduces to solving a sequence of complex semidefinite programming…
This paper proposes earliest and latest path algorithms based on binary weight allocation, assigning weights of 2(i-1) and 2(m-i) to the i-th arc in a network. While traditional shortest path algorithms optimize only distance, our approach…
In this letter, we propose a new routing strategy to improve the transportation efficiency on complex networks. Instead of using the routing strategy for shortest path, we give a generalized routing algorithm to find the so-called {\it…