Berth Allocation in a Bulk Terminal with Overall Quay Length Constraint

Motivated by the operation of bulk terminal in the Pearl River Delta, we study a berth allocation problem (BAP) with 2 berths and overall quay length constraint. The quay length occupied by a vessel depends on its berthing directions. The feasible berthing direction changes in a tide cycle. The objective is to minimize the total service of all vessels. We develop a mixed integer programming (MIP) model for the problem. We also propose an efficient genetic algorithm to tackle the problem. Our computational experiments show that the mixed integral programming model can only be solved by CPLEX for small-size instances, the genetic algorithm obtains good approximation solutions for large-size instances.

Tangle-Free Exploration with a Tethered Mobile Robot

Exploration and remote sensing with mobile robots is a well known field of research, but current solutions cannot be directly applied for tethered robots. In some applications, tethers may be very important to provide power or allow communication with the robot. This paper presents an exploration algorithm that guarantees complete exploration of arbitrary environments within the length constraint of the tether, while keeping the tether tangle-free at all times. While we also propose a generalized algorithm that can be used with several exploration strategies, our implementation uses a modified frontier-based exploration approach, where the robot chooses its next goal in the frontier between explored and unexplored regions of the environment. The basic idea of the algorithm is to keep an estimate of the tether configuration, including length and homotopy, and decide the next robot path based on the difference between the current tether length and the shortest tether length at the next goal position. Our algorithm is provable correct and was tested and evaluated using both simulations and real-world experiments.

On the regularity of critical points for O’Hara’s knot energies: From smoothness to analyticity

We prove the analyticity of smooth critical points for O’Hara’s knot energies [Formula: see text], with [Formula: see text] and [Formula: see text], subject to a fixed length constraint. This implies, together with the already established regularity results for O’Hara’s knot energies, that bounded energy critical points of [Formula: see text] subject to a fixed length constraint are not only [Formula: see text] but also analytic. Our approach is based on Cauchy’s method of majorants and a decomposition of the gradient that was adapted from the Möbius energy case [Formula: see text].

Effect of Nonlinear Baseline Length Constraint on Global Navigation Satellite System Compass: A Theoretical Analysis

GNSS (global navigation satellite system) compass is a low-cost, high-precision, and temporally stable north-finding technique. While the nonlinear baseline length constraint is widely known to be important in ambiguity resolution of GNSS compass, its direct effect on yaw angle estimation is theoretically analyzed in this work. Four different methods are considered with different ways in which the length constraint is made use of as follows: one without considering the constraints, one with simple scaling, one with indirect statistical scaling, and one with direct statistical scaling. It is found that simple scaling does not have any effect on yaw estimation; indirect and direct statistical scalings are equivalent to each other with both being able to increase the precision. The analysis and the conclusion developed in this work can go in parallel for the case of the tilt angle estimation.