scholarly journals An Iterative Method Based on the Marginalized Particle Filter for Nonlinear B-Spline Data Approximation and Trajectory Optimization

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 355 ◽  
Author(s):  
Jens Jauch ◽  
Felix Bleimund ◽  
Michael Frey ◽  
Frank Gauterin
Keyword(s):  
Trajectory Optimization ◽  
Spline Function ◽  
Nonlinear Approximation ◽  
Computational Effort ◽  
Optimization Approach ◽  
Data Approximation ◽  
B Spline ◽  
Marquardt Algorithm ◽  
Trajectory Length ◽  
Data Points

The B-spline function representation is commonly used for data approximation and trajectory definition, but filter-based methods for NWLS approximation are restricted to a bounded definition range. We present an algorithm termed NRBA for an iterative NWLS approximation of an unbounded set of data points by a B-spline function. NRBA is based on a MPF, in which a KF solves the linear subproblem optimally while a PF deals with nonlinear approximation goals. NRBA can adjust the bounded definition range of the approximating B-spline function during run-time such that, regardless of the initially chosen definition range, all data points can be processed. In numerical experiments, NRBA achieves approximation results close to those of the Levenberg–Marquardt algorithm. An NWLS approximation problem is a nonlinear optimization problem. The direct trajectory optimization approach also leads to a nonlinear problem. The computational effort of most solution methods grows exponentially with the trajectory length. We demonstrate how NRBA can be applied for a multiobjective trajectory optimization for a BEV in order to determine an energy-efficient velocity trajectory. With NRBA, the effort increases only linearly with the processed data points and the trajectory length.

The Relationship between the Letters of Al-Iḫlāṣ (Q 112:1-4) and Their Iterations Using B-Spline Function

2019 ◽  
Vol 17 (1) ◽  
pp. 60-86
Author(s):  
Faoziya S.M. Musbah
Keyword(s):  
Spline Function ◽  
Piecewise Linear ◽  
Two Dimensional ◽  
B Spline ◽  
Holy Quran ◽  
Data Points ◽  
The Holy Quran ◽  
The Absolute ◽  
Unity Of God ◽  
The Relationship

Abstract Al-Iḫlāṣ is an important chapter within the Holy Quran (words of God) because it is a brief declaration of the absolute unity of God (Allah). This paper analyzes al-Iḫlāṣ mathematically in order to gain an understanding of the relationship between the letters of this chapter and their iterations. The analyzed two-dimensional data points (xi,yi) define a piecewise linear curve that is shaped like Allah’s name as it is written in Arabic. The B-spline function is used to analyze this data so as to obtain a second degree curve.

Locally Adaptive Online Trajectory Optimization in Unknown Environments With RRTs

2018 ◽  
Author(s):  
Ethan N. Evans ◽  
Patrick Meyer ◽  
Samuel Seifert ◽  
Dimitri N. Mavris ◽  
Evangelos A. Theodorou
Keyword(s):  
Trajectory Optimization ◽  
Adaptive Sampling ◽  
Low Cost ◽  
Asymptotic Optimality ◽  
Computational Effort ◽  
Random Trees ◽  
Optimization Approach ◽  
Trade Offs ◽  
Locally Adaptive ◽  
Local Sampling

Rapidly Exploring Random Trees (RRTs) have gained significant attention due to provable properties such as completeness and asymptotic optimality. However, offline methods are only useful when the entire problem landscape is known a priori. Furthermore, many real world applications have problem scopes that are orders of magnitude larger than typical mazes and bug traps that require large numbers of samples to match typical sample densities, resulting in high computational effort for reasonably low-cost trajectories. In this paper we propose an online trajectory optimization algorithm for uncertain large environments using RRTs, which we call Locally Adaptive Rapidly Exploring Random Tree (LARRT). This is achieved through two main contributions. We use an adaptive local sampling region and adaptive sampling scheme which depend on states of the dynamic system and observations of obstacles. We also propose a localized approach to planning and re-planning through fixing the root node to the current vehicle state and adding tree update functions. LARRT is designed to leverage local problem scope to reduce computational complexity and obtain a total lower-cost solution compared to a classical RRT of a similar number of nodes. Using this technique we can ensure that popular variants of RRT will remain online even for prohibitively large planning problems by transforming a large trajectory optimization approach to one that resembles receding horizon optimization. Finally, we demonstrate our approach in simulation and discuss various algorithmic trade-offs of the proposed approach.

scholarly journals Trajectory planning in UAV emergency networks with potential underlaying D2D communication based on K-means

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Shuo Zhang ◽  
Shuo Shi ◽  
Tianming Feng ◽  
Xuemai Gu
Keyword(s):  
Trajectory Planning ◽  
Trajectory Optimization ◽  
Communication Systems ◽  
Complete Coverage ◽  
Wireless System ◽  
Fifth Generation ◽  
Emergency Communications ◽  
Trajectory Length ◽  
Post Disaster ◽  
Joint Evaluation

AbstractAt present, unmanned aerial vehicles (UAVs) have been widely used in communication systems, and the fifth-generation wireless system (5G) has further promoted the vigorous development of them. The trajectory planning of UAV is an important factor that affects the timeliness and completion of missions, especially in scenarios such as emergency communications and post-disaster rescue. In this paper, we consider an emergency communication network where a UAV aims to achieve complete coverage of potential underlaying device-to-device (D2D) users. Trajectory planning issues are grouped into clustering and supplementary phases for optimization. Aiming at trajectory length and sum throughput, two trajectory planning algorithms based on K-means are proposed, respectively. In addition, in order to balance sum throughput with trajectory length, we present a joint evaluation index. Then relying on this index, a third trajectory optimization algorithm is further proposed. Simulation results show the validity of the proposed algorithms which have advantages over the well-known benchmark scheme in terms of trajectory length and sum throughput.

scholarly journals Strategies for Improving Optimal Positioning of Quality Sensors in Urban Drainage Systems for Non-Conservative Contaminants

Water ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 934
Author(s):  
Mariacrocetta Sambito ◽  
Gabriele Freni
Keyword(s):  
Treatment Plant ◽  
Optimal Solution ◽  
Monitoring Network ◽  
Computational Effort ◽  
Bayesian Optimization ◽  
Urban Drainage ◽  
Optimization Approach ◽  
Sensor Location ◽  
Contamination Source ◽  
Monitoring Point

In the urban drainage sector, the problem of polluting discharges in sewers may act on the proper functioning of the sewer system, on the wastewater treatment plant reliability and on the receiving water body preservation. Therefore, the implementation of a chemical monitoring network is necessary to promptly detect and contain the event of contamination. Sensor location is usually an optimization exercise that is based on probabilistic or black-box methods and their efficiency is usually dependent on the initial assumption made on possible eligibility of nodes to become a monitoring point. It is a common practice to establish an initial non-informative assumption by considering all network nodes to have equal possibilities to allocate a sensor. In the present study, such a common approach is compared with different initial strategies to pre-screen eligible nodes as a function of topological and hydraulic information, and non-formal 'grey' information on the most probable locations of the contamination source. Such strategies were previously compared for conservative xenobiotic contaminations and now they are compared for a more difficult identification exercise: the detection of nonconservative immanent contaminants. The strategies are applied to a Bayesian optimization approach that demonstrated to be efficient in contamination source location. The case study is the literature network of the Storm Water Management Model (SWMM) manual, Example 8. The results show that the pre-screening and ‘grey’ information are able to reduce the computational effort needed to obtain the optimal solution or, with equal computational effort, to improve location efficiency. The nature of the contamination is highly relevant, affecting monitoring efficiency, sensor location and computational efforts to reach optimality.

scholarly journals B-splines Algorithms for Solving Fredholm Linear Integro-Differential Equations

2004 ◽  
Vol 1 (2) ◽  
pp. 340-346
Author(s):  
Baghdad Science Journal
Keyword(s):  
Differential Equations ◽  
Spline Function ◽  
Cubic Spline ◽  
Second Order ◽  
Third Order ◽  
B Spline ◽  
Numerical Examples ◽  
B Splines ◽  
The Third ◽  
New Procedures

Algorithms using the second order of B -splines [B (x)] and the third order of B -splines [B,3(x)] are derived to solve 1' , 2nd and 3rd linear Fredholm integro-differential equations (F1DEs). These new procedures have all the useful properties of B -spline function and can be used comparatively greater computational ease and efficiency.The results of these algorithms are compared with the cubic spline function.Two numerical examples are given for conciliated the results of this method.

Parametric Generation of Planing Hulls with NURBS Surfaces

2013 ◽  
Vol 57 (04) ◽  
pp. 241-261
Author(s):  
Francisco L. Perez-Arribas ◽  
Erno Peter-Cosma
Keyword(s):  
Maximum Deviation ◽  
Geometric Features ◽  
Surface Geometry ◽  
Orthogonal Projections ◽  
Parametric Generation ◽  
B Spline ◽  
Spline Curves ◽  
Hull Design ◽  
Data Points ◽  
Control Curves

This article presents a mathematical method for producing hard-chine ship hulls based on a set of numerical parameters that are directly related to the geometric features of the hull and uniquely define a hull form for this type of ship. The term planing hull is used generically to describe the majority of hard-chine boats being built today. This article is focused on unstepped, single-chine hulls. B-spline curves and surfaces were combined with constraints on the significant ship curves to produce the final hull design. The hard-chine hull geometry was modeled by decomposing the surface geometry into boundary curves, which were defined by design constraints or parameters. In planing hull design, these control curves are the center, chine, and sheer lines as well as their geometric features including position, slope, and, in the case of the chine, enclosed area and centroid. These geometric parameters have physical, hydrodynamic, and stability implications from the design point of view. The proposed method uses two-dimensional orthogonal projections of the control curves and then produces three-dimensional (3-D) definitions using B-spline fitting of the 3-D data points. The fitting considers maximum deviation from the curve to the data points and is based on an original selection of the parameterization. A net of B-spline curves (stations) is then created to match the previously defined 3-D boundaries. A final set of lofting surfaces of the previous B-spline curves produces the hull surface.

scholarly journals Adaptive Droop Based Virtual Slack Control of Multiple DGs in Practical DC Distribution System to Improve Voltage Profile

Energies ◽  
2019 ◽  
Vol 12 (8) ◽  
pp. 1541
Author(s):  
Soo Hyoung Lee
Keyword(s):  
Distribution System ◽  
Voltage Regulation ◽  
Optimal Operation ◽  
Computational Effort ◽  
Current Control ◽  
Voltage Profile ◽  
Dc System ◽  
Dc Distribution ◽  
Real Distribution ◽  
Marquardt Algorithm

This paper proposes an adaptive droop based virtual slack (ADVS) control for multiple distributed generations (DGs) to improve voltage stability of a practical DC distribution system. Although there have been many researches for optimal sizes of multiple DGs, their solutions are valid only in the particular operating point. Additionally, a previous study proposed a voltage control based optimal operation method, its performance depends on measurement accuracy in practice. The proposed ADVS control operates the system based on the current sensitivities between the DGs and loads, so that it can regulate the system voltages without a large computational effort. This is effective even if measurements are noisy and biased. All DGs contribute to voltage regulation by current control even though they do not directly control voltages. As an additional effect, they effectively share the load. To verify the proposed method, the DC system is modeled based on the real distribution system of the Do-gok area in Seoul, Korea. Then, the Levenberg-Marquardt algorithm determines its operation point. The proposed method is verified based on the electromagnetic transient (EMT) simulation with random loads.

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