Grid Path Research Articles

Optimization Study on Indoor Robot Path Planning based on Improved Differential Evolution Algorithm

Aiming at the problem that there are many obstacles indoor and the situation is complex, and the traditional robot path planning algorithm is ineffective, this paper proposes a grid path planning algorithm based on the improved differential evolution algorithm for the robot in the building. Firstly, the grid model is used to construct the path planning model of the robot in the building, and the running direction model of the robot indoor is obtained. On this basis, the intelligent algorithm optimization model of the path planning of the robot indoor is given. Secondly, the differential evolution algorithm is introduced to optimize the structural optimization index, and the Q learning method is used to improve the optimization algorithm to realize the building. Finally, the performance advantages of the proposed algorithm in obstacle avoidance and optimization planning of robot path are verified by the simulation of an example of robot path planning in building.

Square grid Path Planning for Mobile Anchor-Based Localization in Wireless Sensor Networks

Localization is to provide all sensor nodes with their geographical positions. A mobile anchor-based localization in WSNs uses a mobile anchor equipped with GPS, which travels along a predetermined path. At each specified beacon point, it broadcasts its current known position to help other sensor nodes with unknown locations estimate their positions. In this paper, we analyze the determination of beacon points based on a square grid. We propose an improved path planning model named Union-curve. Our proposed model incorporates all beacon points of five previously developed paths, namely, SCAN, HILBERT, S-type, Z-curve, and $\Sigma$-Scan on the commonly used square grid decomposition of area. Unknown sensor nodes estimate their positions using two techniques, APT and WCWCL-RSSI. Simulation results show that the proposed model has higher accuracy, with a big difference in error rate compared to the other models. In addition, this model guarantees maximum coverage with less path resolution value.

High-quality fabrication of diamond straight microchannels heat sink with large aspect ratio microchannels using UV nanosecond laser based on multi-feed method

The high heat flux density of modern chips presents a major challenge to their development. Single-phase or two-phase flow heat dissipation techniques using high thermal conductivity materials are seen as a potential solution. However, creating microfluidic channels from ultra-high thermal conductivity diamond materials is a significant challenge. In this paper, we present an experimental study on the fabrication of diamond heat sinks with high aspect ratio microchannels using a UV-nanosecond laser processing system, along with two multi-feed processing techniques for the collecting grooves and microchannels. We used a 1 μm spacing grid path combined with a polished multi-feed process to fabricate a 1600 μm deep collecting groove with a smooth bottom morphology. We also proposed a multi-area multi-feed fabrication technique for microchannels with an aspect ratio of 8:1 and a depth of 1600 μm. Finally, we have successfully fabricated a diamond straight microchannels heat sink, featuring a high aspect ratio and low phase change damage.

Fast parallel algorithms for finding the longest flow paths in flow direction grids

In hydrological modeling, the longest flow path is an important feature used to characterize a catchment. Many existing GIS platforms offer dedicated software tools for its identification and delineation, generally implementing methods based on searching through the flow direction data. Unfortunately, currently available algorithms for this task often turn out to be inefficient, especially when working with modern large datasets. Moreover, existing methods often rely on incorrect assumptions or perform calculations in a way that can lead to precision issues. In this work, new parallel algorithms were developed, tested and presented. Measurements show that two of the newly proposed implementations are able to identify the longest flow paths in significantly less time compared with other existing methods.

On approximating shortest paths in weighted triangular tessellations

We study the quality of weighted shortest paths when a continuous 2-dimensional space is discretized by a weighted triangular tessellation. In order to evaluate how well the tessellation approximates the 2-dimensional space, we study three types of shortest paths: a weighted shortest path SPw(s,t), which is a shortest path from s to t in the space; a weighted shortest vertex path SVPw(s,t), which is an any-angle shortest path; and a weighted shortest grid path SGPw(s,t), which is a shortest path whose edges are edges of the tessellation. Given any arbitrary weight assignment to the faces of a triangular tessellation, thus extending recent results by Bailey et al. (2021) [6], we prove upper and lower bounds on the ratios ‖SGPw(s,t)‖‖SPw(s,t)‖, ‖SVPw(s,t)‖‖SPw(s,t)‖, ‖SGPw(s,t)‖‖SVPw(s,t)‖, which provide estimates on the quality of the approximation. It turns out, surprisingly, that our worst-case bounds are independent of any weight assignment. Our main result is that ‖SGPw(s,t)‖‖SPw(s,t)‖=23≈1.15 in the worst case, and this is tight. As a corollary, for the weighted any-angle path SVPw(s,t) we obtain the approximation result ‖SVPw(s,t)‖‖SPw(s,t)‖⪅1.15.

Fused deposition modeling of Si3N4 ceramics: A cost-effective 3D-printing route for dense and high performance non-oxide ceramic materials

Dense Si3N4 ceramics were prepared by fused deposition molding method accompanied by gas pressure sintering. In this study, the surface steps, inter layer bonding and microstructure evolution were characterized and dense Si3N4 ceramics without obvious defects were obtained. It was verified that layer thickness and nozzle diameter have little impact on the density and flexural strength of both green and sintered parts. As to the filling strategy, contour offset path was more effective to obtain sintered part with higher flexural strength than parallel lines and grid path, which was due to the possible voids appeared at the intersection of print paths with different directions. The highest flexure strength 824.74 ± 85 MPa was obtained with layer thickness 0.15 mm, nozzle size 0.6 mm and contour offset path. The reliability of the obtained Si3N4 ceramics was also investigated and complex shaped Si3N4 ceramic parts with good shape keeping was prepared successfully.

A Novel Green Logistics Technique for Planning Merchandise Deliveries: A Case Study

Background: The health crisis due to COVID-19 has changed the habits of social coexistence and therefore has had a significant impact on several economic sectors, including logistics. Nowadays, this sector faces one of the most difficult challenges in history and hence has carried out innovative strategies to adjust to the new normal and guarantee the permanence of the supply chain. In this paper, a novel green logistics technique for planning merchandise deliveries is introduced herein. Methods: This technique is based on a modified version of the Resistive Grid Path Planning Methodology (RGPPM) to establish a path through georeferential locations for delivering merchandise to customers. To do this, multi-connected resistive grids are based at customer locations for searching the path connecting the positions through electronic circuit analysis techniques. Results: Experimental results reveal that the proposed method can find a minimum spanning tree that connects all hand-over points by a continuous path. This finding has represented a reduction of around 45% in the length of the path with respect to the longest path. Conclusions: Finally, this technique is capable of addressing different optimization strategies, locating a merchandise distribution center and exploring environmental standards to reduce fuel consumption.

The JPS Pathfinding System in 3D

The ability to quickly compute shortest paths in 3D grids is a technological enabler for several applications such as pipe routing and computer video games. The main challenge is how to deal with the many symmetric permutations of each shortest path. We tackle this problem by adapting Jump Point Search (JPS), a well-known symmetry breaking technique developed for fast pathfinding in 2D grids. We give a rigorous reformulation of the JPS pathfinding system into 3D and we prove that our new algorithm, JPS-3D, is optimality preserving. We also develop a novel method for limiting scan depth during jump operations, which can further reduce search time. Experimental results show significant improvements versus online A* search and previous attempts at generalising JPS. We demonstrate that searching with adaptive scan limits can yield additional speedups of over an order of magnitude.

Path Counting for Grid-Based Navigation

Counting the number of shortest paths on a grid is a simple procedure with close ties to Pascal’s triangle. We show how path counting can be used to select relatively direct grid paths for AI-related applications involving navigation through spatial environments. Typical implementations of Dijkstra’s algorithm and A* prioritize grid moves in an arbitrary manner, producing paths which stray conspicuously far from line-of-sight trajectories. We find that by counting the number of paths which traverse each vertex, then selecting the vertices with the highest counts, one obtains a path that is reasonably direct in practice and can be improved by refining the grid resolution. Central Dijkstra and Central A* are introduced as the basic methods for computing these central grid paths. Theoretical analysis reveals that the proposed grid-based navigation approach is related to an existing grid-based visibility approach, and establishes that central grid paths converge on clear sightlines as the grid spacing approaches zero. A more general property, that central paths converge on direct paths, is formulated as a conjecture.

Polynomial and Multinomial Coefficients in Terms of Number of Shortest Paths

The binomial coefficients show, in fact, the number of shortest paths in the square grid if only grid paths, i.e., paths on the grid lines, are allowed, and they also give the number of shortest paths in the hexagonal grid. When diagonal steps are also allowed in the square grid, the number of shortest paths can be described by trinomial coefficients. They form a triangle where three neighbour elements in the previous row are summed. We consider also further generalisations of such triangles and their elements, quadrinomial and n-nomial coefficients. In this context, n-nomial coefficients of n-nomial expansions represent the numbers of paths between the top and the actual position when n different types of steps are allowed to use, e.g., at trinomial coefficients three types of steps. Formulae to calculate trinomial, quadrominal and n-nomial coefficients are shown based on trinomial, quadrominal and n-nomial expansions, where the power of the sum of more than two items is computed, respectively. Multinomial expansions are also related. We give also a comparison of those values known as various ways of generalizations of the binomial coefficients.

Path Planning on Grids: The Effect of Vertex Placement on Path Length

Video-game designers often tessellate continuous 2-dimensional terrain into a grid of blocked and unblocked square cells. The three main ways to calculate short paths on such a grid are to determine truly shortest paths, shortest vertex paths and shortest grid paths, listed here in decreasing order of computation time and increasing order of resulting path length. We show that, for both vertex and grid paths on both 4-neighbor and 8-neighbor grids, placing vertices at cell corners rather than at cell centers tends to result in shorter paths. We quantify the advantage of cell corners over cell centers theoretically with tight worst-case bounds on the ratios of path lengths, and empirically on a large set of benchmark test cases. We also quantify the advantage of 8-neighbor grids over 4-neighbor grids.

Fusing tie points' RGB and thermal information for mapping large areas based on aerial images: A study of fusion performance under different flight configurations and experimental conditions

Three-dimensional thermal mapping from aerial images can be used in energy audits. Tie points that define the location of object points in a 3D space for reconstructing a 3D model, also include thermal information, which plays an important role in energy audits. However, it is often harder and less accurate to extract common features and determine tie points from low-resolution thermal images. It is more effective and accurate to use high-definition RGB images to determine tie points and fuse the RGB and thermal information. In this study, we investigate how to utilize high-definition RGB images that allow for more accurate tie point detection, how different flight configurations affect tie point data fusion, and how tie point data fusion performance can be improved. We propose a tie points' thermal and RGB data-fusion framework to create district-level thermal mapping to solve such problems. This paper aims to evaluate how different flight configurations affect the results of the proposed data fusion approach. Flight configurations include different camera altitudes (60 m and 35 m), distinct camera angles (45 degrees and 30 degrees), diverse flight path designs (mesh grid and Y path), and various building styles (campus buildings and city buildings).We find the following results in this paper: (1) higher flight altitude is not suggested for our data fusion approach; (2) a 30-degree thermal camera angle is suggested for roof inspection, while a 45-degree thermal camera angle is suggested for façade inspection when using the tie point data fusion approach; (3) a Y flight path performs better than a mesh grid path; and (4) our tie point data fusion approach performs better in traditional European city buildings than in modern campus buildings. We also demonstrate that pixels in the thermal images' central area can more accurately represent thermal information than pixels around the image edges for tie point data fusion. Additionally, our studies show that images taken at the edges of mapping areas have more errors. Thus, it is crucial to enlarge the survey area to obtain more accurate possible results.

Parallel Swarm Intelligent Motion Planning with Energy‐Balanced for Multirobot in Obstacle Environment

Multirobot motion planning is always one of the critical techniques in edge intelligent systems, which involve a variety of algorithms, such as map modeling, path search, and trajectory optimization and smoothing. To overcome the slow running speed and imbalance of energy consumption, a swarm intelligence solution based on parallel computing is proposed to plan motion paths for multirobot with many task nodes in a complex scene that have multiple irregularly‐shaped obstacles, which objective is to find a smooth trajectory under the constraints of the shortest total distance and the energy‐balanced consumption for all robots to travel between nodes. In a practical scenario, the imbalance of task allocation will inevitably lead to some robots stopping on the way. Thus, we firstly model a gridded scene as a weighted MTSP (multitraveling salesman problem) in which the weights are the energies of obstacle constraints and path length. Then, a hybridization of particle swarm and ant colony optimization (GPSO‐AC) based on a platform of Compute Unified Device Architecture (CUDA) is presented to find the optimal path for the weighted MTSPs. Next, we improve the A∗ algorithm to generate a weighted obstacle avoidance path on the gridded map, but there are still many sharp turns on it. Therefore, an improved smooth grid path algorithm is proposed by integrating the dynamic constraints in this paper to optimize the trajectory smoothly, to be more in line with the law of robot motion, which can more realistically simulate the multirobot in a real scene. Finally, experimental comparisons with other methods on the designed platform of GPUs demonstrate the applicability of the proposed algorithm in different scenarios, and our method strikes a good balance between energy consumption and optimality, with significantly faster and better performance than other considered approaches, and the effects of the adjustment coefficient q on the performance of the algorithm are also discussed in the experiments.

The Application of Fractal Transform and Entropy for Improving Fault Tolerance and Load Balancing in Grid Computing Environments

This paper applies the entropy-based fractal indexing scheme that enables the grid environment for fast indexing and querying. It addresses the issue of fault tolerance and load balancing-based fractal management to make computational grids more effective and reliable. A fractal dimension of a cloud of points gives an estimate of the intrinsic dimensionality of the data in that space. The main drawback of this technique is the long computing time. The main contribution of the suggested work is to investigate the effect of fractal transform by adding R-tree index structure-based entropy to existing grid computing models to obtain a balanced infrastructure with minimal fault. In this regard, the presented work is going to extend the commonly scheduling algorithms that are built based on the physical grid structure to a reduced logical network. The objective of this logical network is to reduce the searching in the grid paths according to arrival time rate and path’s bandwidth with respect to load balance and fault tolerance, respectively. Furthermore, an optimization searching technique is utilized to enhance the grid performance by investigating the optimum number of nodes extracted from the logical grid. The experimental results indicated that the proposed model has better execution time, throughput, makespan, latency, load balancing, and success rate.

From generalized Tamari intervals to non-separable planar maps

Let v be a grid path made of north and east steps. The lattice TAM(v), based on all grid paths weakly above the grid path v sharing the same endpoints as v, was introduced by Pre ́ville-Ratelle and Viennot (2014) and corresponds to the usual Tamari lattice in the case v = (NE)n. They showed that TAM(v) is isomorphic to the dual of TAM(←−v ), where ←−v is the reverse of v with N and E exchanged. Our main contribution is a bijection from intervals in TAM(v) to non-separable planar maps. It follows that the number of intervals in TAM(v) over all v of length n is 2(3n+3)! (n+2)!(2n+3)! . This formula was first obtained by Tutte(1963) for non-separable planar maps.

The 2^k Neighborhoods for Grid Path Planning

Grid path planning is an important problem in AI. Its understanding has been key for the development of autonomous navigation systems. An interesting and rather surprising fact about the vast literature on this problem is that only a few neighborhoods have been used when evaluating these algorithms. Indeed, only the 4- and 8-neighborhoods are usually considered, and rarely the 16-neighborhood. This paper describes three contributions that enable the construction of effective grid path planners for extended 2k-neighborhoods; that is, neighborhoods that admit 2k neighbors per state, where k is a parameter. First, we provide a simple recursive definition of the 2k-neighborhood in terms of the 2k-1-neighborhood. Second, we derive distance functions, for any k ≥ 2, which allow us to propose admissible heuristics that are perfect for obstacle-free grids, which generalize the well-known Manhattan and Octile distances. Third, we define the notion of canonical path for the 2k-neighborhood; this allows us to incorporate our neighborhoods into two versions of A*, namely Canonical A* and Jump Point Search (JPS), whose performance, we show, scales well when increasing k. Our empirical evaluation shows that, when increasing k, the cost of the solution found improves substantially. Used with the 2k-neighborhood, Canonical A* and JPS, in many configurations, are also superior to the any-angle path planner Theta* both in terms of solution quality and runtime. Our planner is competitive with one implementation of the any-angle path planner, ANYA in some configurations. Our main practical conclusion is that standard, well-understood grid path planning technology may provide an effective approach to any-angle grid path planning.

Structural Assessment of Large Membrane Structures Using an Unmanned Aerial Vehicle Aided Photogrammetry: Determination of Flight Parameters and Trials at the Western Treatment Plant

Abstract Floating covers are examples of a large membrane structure used at sewage treatment plants. At the Western Treatment Plant (WTP), Werribee, Melbourne, Australia, floating covers are used in the anaerobic lagoons. They are deployed to assist with the anaerobic treatment of the raw sewage beneath, to harness the methane-rich biogas generated, and for odor control. In this respect, these floating covers are important assets for harnessing a sustainable and renewable energy source, as well as protecting the environment from the release of the damaging greenhouse methane-rich biogas from the treatment plant. Given the continuous nature of the biological process beneath the cover, the forces imposed on the floating cover will change with time. Hence, the monitoring and the assessment of the structural integrity of the floating cover are of paramount importance. These floating covers are made from high-density polyethylene (HDPE), a polymeric material. The size of these covers, the hazardous environment, and the expected life span demand a novel, remotely piloted, unmanned aerial vehicle based noncontact technique for the structural health assessment. This assessment methodology will utilize photogrammetry as the basis for determining the surface deformation of the membrane. This paper reports on an experimental study to determine the flight parameters and to assess the accuracy of the measurement technique. It was conducted over an area having similar dimensions to the large covers at the WTP. There are also features in this area, which are of similar scale to those expected in the floating cover. A total of nine test flights were used to investigate the parameters for optimal definition of the significant features to describe the deformation of the floating cover. The findings inform the selection of the unmanned aerial vehicle assisted photogrammetry parameters for optimal flight altitude, photogrammetry image overlap, and flight grid path for future integrity assessment of the floating covers. Two trial flights at WTP are also discussed to demonstrate the effectiveness of this noncontact technique for the future structural health assessment and in assisting with the operation of this large high-value asset.

A Novel Collision-Free Path Planning Modeling and Simulation Methodology for Robotical Arms Using Resistive Grids

SUMMARYPath planning represents planning collision-free strategies to move from starting point to ending point. These strategies can be carried out for known and unknown environments. Recently, a novel and reduced CPU-time modeling and simulation methodology for path planning in known environment based on resistive grids (RGs) has been introduced. In this work, a novel modified version of Resistive Grid Path Planning Methodology (RGPPM) methodology is presented with the purpose of exploring collision-free path planning for robotic arms. This extension of the methodology allows to numerically relate positions in the RG with angular values of the robotic systems. In addition, it is possible to include obstacles in the configuration space, and therefore collision detection can be established for RGs. Finally, the variation of links for robotic arms and obstacles for configuration space is explored by simulating different scenarios.

FFLV-type monomial bases for type $B$

We present a combinatorial monomial basis (or, more precisely, a family of monomial bases) in every finite-dimensional irreducible $\mathfrak{so}_{2n+1}$-module. These bases are in many ways similar to the FFLV bases for types $A$ and $C$. They are also defined combinatorially via sums over Dyck paths in certain triangular grids. Our sums, however, involve weights depending on the length of the corresponding root. Accordingly, our bases also induce bases in certain degenerations of the modules but these degenerations are obtained not from the filtration by PBW degree but by a weighted version thereof.

Cooperative Path Planning for Multiple Robots With Motion Constraints in Obstacle-Strewn Environment

A cooperative path searching approach is proposed to decouple cooperative path planning for multiple robots into the path planning phase and the trajectory tracking phase. Unexpected local environment changes or failures for some robots will not affect the regular running of other robots. The collision between robots and the motion constraints of robots are not considered in the first phase. A new connection point method suitable for the trap-like map is used to find the shortest path for every robot. Connection point method does not require much computation cost even if the grid map is zoomed in. In the second phase, a cooperative search tracking approach based on modified coevolution pigeon-inspired optimization algorithm is proposed to enable every robot to track the grid path obtained by the connection point method. A competition mechanism with serial number priority is used to cope with collisions between robots. The numerical simulations are performed to verify the effectiveness of the proposed approach.