Minimum Path Length Research Articles

Shortest-path recovery from signature with an optimal control approach

AbstractIn this paper, we consider the signature-to-path reconstruction problem from the control-theoretic perspective. Namely, we design an optimal control problem whose solution leads to the minimal-length path that generates a given signature. In order to do that, we minimize a cost functional consisting of two competing terms, i.e., a weighted final-time cost combined with the $$L^2$$ L 2 -norm squared of the controls. Moreover, we can show that, by taking the limit to infinity of the parameter that tunes the final-time cost, the problem $$\Gamma $$ Γ -converges to the problem of finding a sub-Riemannian geodesic connecting two signatures. Finally, we provide an alternative reformulation of the latter problem, which is particularly suitable for the numerical implementation.

Modeling the trajectories of a group of unmanned aerial vehicles based on the ADRRT-Connect algorithm in the problem of placing seismic sensors

Optimal route planning is a key aspect of successfully delivering geosensors using unmanned aerial vehicles (UAVs) to geographically distributed targets. The optimality of the route depends on the time required to plan the route and execute the flight to a target or group of targets, considering traffic safety and dynamic constraints. The trajectory calculation algorithm must always find a route, if one exists, and if it is impossible to find one, inform the operator about this circumstance. This article proposes a method based on a set of algorithms that ensure efficient distribution of targets among group members based on information about the targets and characteristics of the unmanned aerial vehicles used. The method involves constructing optimal routes considering minimizing path length, avoiding sharp turns and loops, as well as avoiding obstacles and avoiding collisions with other unmanned aerial vehicles within the group. To test the proposed method, software was developed using the ROS/Gazebo en-vironment. The proposed method is a comprehensive solution to the problem of optimal route planning for UAVs with an emphasis on efficiency, safety, and efficiency in the context of geosensor delivery using unmanned aerial vehicles.

Optimized structural inspection path planning for automated unmanned aerial systems

Automation in Unmanned Aerial Systems (UAS)-based structural inspections has gained significant traction given the scale and complexity of infrastructure. A core problem in UAS-based inspection is electing an optimal flight path to achieve the mission objectives while minimizing flight time. This paper presents an effective two-stage method that guarantees coverage as a constraint to ensure damage detectability, while minimizing path length as an objective. A genetic algorithm first determines viewpoint positions, and a greedy algorithm calculates the camera poses, as opposed to directly optimizing all degrees of freedom (DOF) simultaneously. A sensitivity analysis demonstrates the range of applicability and superiority of this formulation over direct 5-DOF optimization by at least 30 % shorter path length. Applied examples, including focused and partial space inspections, are also presented, demonstrating the flexibility of the proposed method to meet real-world requirements. The results highlight the feasibility of the approach and contribute to incorporating automation into UAS-based structural inspections.

Simple olfactory navigation in air and water

Two simple algorithms based on combining odor concentration differences across time and space along with information on the flow direction are tested for their ability to locate an odor source in four different odor landscapes. Image data taken from air plumes in three different regimes and a water plume are used as test environments for a bilateral (“stereo sampling”) algorithm using concentration differences across two sensors and a “casting” algorithm that uses successive samples to decide orientation. Agents are started at random locations and orientations in the landscape and allowed to move until they reach the source of the odor (success) or leave the imaged area (failure). Parameters for the algorithm are chosen to optimize success and to minimize path length to the source. Success rates over 90% are consistently obtained with path lengths that can be as low as twice the starting distance from the source in air and four times the distance in the highly turbulent water plumes. We find that parameters that optimize success often lead to more exploratory pathways to the source. Information about the direction from which the odor is coming is necessary for successful navigation in the water plume and reduces the path length in the three tested air plumes.

An Adaptive Multi-Objective Genetic Algorithm for Solving Heterogeneous Green City Vehicle Routing Problem

Intelligent scheduling plays a crucial role in minimizing transportation expenses and enhancing overall efficiency. However, most of the existing scheduling models fail to comprehensively account for the requirements of urban development, as exemplified by the vehicle routing problem with time windows (VRPTW), which merely specifies the minimization of path length. This paper introduces a new model of the heterogeneous green city vehicle routing problem with time windows (HGCVRPTW), addressing challenges in urban logistics. The HGCVRPTW model considers carriers with diverse attributes, recipients with varying tolerance for delays, and fluctuating road congestion levels impacting carbon emissions. To better deal with the HGCVRPTW, an adaptive multi-objective genetic algorithm based on the greedy initialization strategy (AMoGA-GIS) is proposed, which includes the following three advantages. Firstly, considering the impact of initial information on the search process, a greedy initialization strategy (GIS) is proposed to guide the overall evolution during the initialization phase. Secondly, the adaptive multiple mutation operators (AMMO) are introduced to improve the diversity of the population at different evolutionary stages according to their success rate of mutation. Moreover, we built a more tailored testing dataset that better aligns with the challenges faced by the HGCVRPTW. Our extensive experiments affirm the competitive performance of the AMoGA-GIS by comparing it with other state-of-the-art algorithms and prove that the GIS and AMMO play a pivotal role in advancing algorithmic capabilities tailored to the HGCVRPTW.

Shortest-Path Percolation on Random Networks.

We propose a bond-percolation model intended to describe the consumption, and eventual exhaustion, of resources in transport networks. Edges forming minimum-length paths connecting demanded origin-destination nodes are removed if below a certain budget. As pairs of nodes are demanded and edges are removed, the macroscopic connected component of the graph disappears, i.e., the graph undergoes a percolation transition. Here, we study such a shortest-path-percolation transition in homogeneous random graphs where pairs of demanded origin-destination nodes are randomly generated, and fully characterize it by means of finite-size scaling analysis. If budget is finite, the transition is identical to the one of ordinary percolation, where a single giant cluster shrinks as edges are removed from the graph; for infinite budget, the transition becomes more abrupt than the one of ordinary percolation, being characterized by the sudden fragmentation of the giant connected component into a multitude of clusters of similar size.

An Integrated Route and Path Planning Strategy for Skid–Steer Mobile Robots in Assisted Harvesting Tasks with Terrain Traversability Constraints

This article presents a combined route and path planning strategy to guide Skid–Steer Mobile Robots (SSMRs) in scheduled harvest tasks within expansive crop rows with complex terrain conditions. The proposed strategy integrates: (i) a global planning algorithm based on the Traveling Salesman Problem under the Capacitated Vehicle Routing approach and Optimization Routing (OR-tools from Google) to prioritize harvesting positions by minimum path length, unexplored harvest points, and vehicle payload capacity; and (ii) a local planning strategy using Informed Rapidly-exploring Random Tree (IRRT*) to coordinate scheduled harvesting points while avoiding low-traction terrain obstacles. The global approach generates an ordered queue of harvesting locations, maximizing the crop yield in a workspace map. In the second stage, the IRRT* planner avoids potential obstacles, including farm layout and slippery terrain. The path planning scheme incorporates a traversability model and a motion model of SSMRs to meet kinematic constraints. Experimental results in a generic fruit orchard demonstrate the effectiveness of the proposed strategy. In particular, the IRRT* algorithm outperformed RRT and RRT* with 96.1% and 97.6% smoother paths, respectively. The IRRT* also showed improved navigation efficiency, avoiding obstacles and slippage zones, making it suitable for precision agriculture.

Robot Motion Planning Based on an Adaptive Slime Mold Algorithm and Motion Constraints

The rapid advancement of artificial intelligence technology has significantly enhanced the intelligence of mobile robots, facilitating their widespread utilization in unmanned driving, smart home systems, and various other domains. As the scope, scale, and complexity of robot deployment continue to expand, there arises a heightened demand for enhanced computational power and real-time performance, with path planning emerging as a prominent research focus. In this study, we present an adaptive Lévy flight–rotation slime mold algorithm (LRSMA) for global robot motion planning, which incorporates LRSMA with the cubic Hermite interpolation. Unlike traditional methods, the algorithm eliminates the need for a priori knowledge of appropriate interpolation points. Instead, it autonomously detects the convergence status of LRSMA, dynamically increasing interpolation points to enhance the curvature of the motion curve when it surpasses the predefined threshold. Subsequently, it compares path lengths resulting from two different objective functions to determine the optimal number of interpolation points and the best path. Compared to LRSMA, this algorithm reduced the minimum path length and average processing time by (2.52%, 3.56%) and (38.89%, 62.46%), respectively, along with minimum processing times. Our findings demonstrate that this method effectively generates collision-free, smooth, and curvature-constrained motion curves with the least processing time.

Route planning of mobile robot based on improved RRT star and TEB algorithm

This paper presents a fusion algorithm based on the enhanced RRT* TEB algorithm. The enhanced RRT* algorithm is utilized for generating an optimal global path. Firstly, proposing an adaptive sampling function and extending node bias to accelerate global path generation and mitigate local optimality. Secondly, eliminating path redundancy to minimize path length. Thirdly, imposing constraints on the turning angle of the path to enhance path smoothness. Conducting kinematic modeling of the mobile robot and optimizing the TEB algorithm to align the trajectory with the mobile robot's kinematics. The integration of these two algorithms culminates in the development of a fusion algorithm. Simulation and experimental results demonstrate that, in contrast to the traditional RRT* algorithm, the enhanced RRT* algorithm achieves a 5.8% reduction in path length and a 62.5% decrease in the number of turning points. Utilizing the fusion algorithm for path planning, the mobile robot generates a superior, seamlessly smooth global path, adept at circumventing obstacles. Furthermore, the local trajectory meticulously conforms to the kinematic constraints of the mobile robot.

A comprehensive network meta-analysis: comparison of long-term outcomes between intravascular ultrasound, optical coherence tomography, and angiography-guided stent implantation

Abstract Background Intravascular ultrasonography (IVUS) and optical coherence tomography (OCT) guided stent implantations are alternative techniques that are adjunct to angiography-guided (ANG) percutaneous coronary interventions in patients with coronary artery disease (CAD), especially for optimal stent deployment. We aimed to conduct a network meta-analysis including studies comparing those three techniques. Methods We searched PubMed, Scopus, and Cochrane libraries for eligible studies that compared IVUS, OCT, and angiography-guided stent implantation in patients with CAD. After excluding studies, which were irrelevant, duplicated, and had inappropriate results, 54 randomized, propensity-score matched, and observational studies with 232.181 patients were included in this meta-analysis. Results Number of studies compared ANG and IVUS was higher than the other two comparisons. Indirect evidence of network estimates between OCT and IVUS was higher than direct estimate (60% vs. 40%). Minimal parallelism and mean path length of each estimation was suitable with numbers low than 2 for both for comparisons. ANG had higher MACE (RR =1.30; 1.22-1.39, p<0.001), all cause-death (RR=1.45;1.30-1.61, p<0.001), cardiac death (RR=1.72;1.54-1.92, p<0.001), myocardial infarction (RR=1.34; 1.23-1.45, p<0.001), target lesion revascularization (RR=1.20; 1.13-1.26, p<0.001), and stent thrombosis (RR=1.58;1.34-1.85, p<0.001) risks compared to IVUS. There was no difference between OCT and IVUS regarding all outcomes. MACE (RR=1.51;1.26-1.81, p<0.001), cardiac death (RR=2.13;1.41-3.21, p<0.001), and myocardial infarction (RR=1.42;1.05-1.93, p<0.001) risks were higher in ANG groups than in OCT group. Highest benefit was established with OCT for MACE (p-score = 0.973), with IVUS for all-cause death (p-score= 0.792), with OCT for cardiac death (p-score=0.921), with OCT for myocardial infarction (p-score =0.823), with IVUS for target lesion revascularization (p-score=0.865), and with IVUS for stent thrombosis (p-score=0.930). Heterogeneity was appropriate for all outcomes (I2 <70%). There was no publication bias for all outcomes. Conclusion This comprehensive network meta-analysis indicated that angiography-guided stent implantation had higher risk of MACE, cardiac death, myocardial infarction, target lesion-revascularization, and stent thrombosis when compared to IVUS and had higher risk of MACE, cardiac death, and myocardial infarction than OCT.

Optimal Coverage Path Planning for Agricultural Vehicles with Curvature Constraints

Complete coverage path planning (CCPP) is vital in mobile robot applications. Optimizing CCPP is particularly significant in precision agriculture, where it enhances resource utilization, reduces soil compaction, and boosts crop yields. This work offers a comprehensive approach to CCPP for agricultural vehicles with curvature constraints. Our methodology comprises four key stages. First, it decomposes complex agricultural areas into simpler cells, each equipped with guidance tracks, forming a fixed track system. The subsequent route planning and smooth path planning stages compute a path that adheres to path constraints, optimally traverses the cells, and aligns with the track system. We use the generalized traveling salesman problem (GTSP) to determine the optimal traversing sequence. Additionally, we introduce an algorithm for calculating paths that are both smooth and curvature-constrained within individual cells, as well as paths that enable seamless transitions between cells, resulting in a smooth, curvature-constraint coverage path. Our modular approach allows method flexibility at each step. We evaluate our method on real agricultural fields, demonstrating its effectiveness in minimizing path length, ensuring efficient coverage, and adhering to curvature constraints. This work establishes a strong foundation for precise and efficient agricultural coverage path planning, with potential for further real-world applications and enhancements.

Self-Directed Mobile Robot Navigation Based on Functional Firefly Algorithm (FFA)

This paper proposes an optimized mobile robot navigation strategy using a functional firefly algorithm (FFA) and choice function. This approach has two key advantages: first, the linear objective function performs efficiently with the single degree and finite-order polynomial time operation, and second, the cartesian constraint performs compactly with the chosen degree of freedom on the finite interval. This functional approach optimizes the size of operational parameters in context with key size, operation time, and a finite range of verification. The choice function achieves parameter order (size) reduction. The attraction characteristic of fireflies is represented by the choice function for optimizing the choice between low and high intensities of fireflies. In 2D and 3D environments, the proposed robot navigation performs well in an uncertain environment with static and dynamic obstacles. This efficiency includes the robot’s speed as determined by the choice function’s minimum path lengths. The collision-free path is achieved by the non-void family of non-void sets. The obtained results are optimal in terms of path length and navigational time. The proposed controller is also compared with the other existing controllers, and it is observed that the FFA gives the shortest path in less time for the same environmental condition.

An autonomous mobile robot path planning strategy using an enhanced slime mold algorithm.

Autonomous mobile robot encompasses modules such as perception, path planning, decision-making, and control. Among these modules, path planning serves as a prerequisite for mobile robots to accomplish tasks. Enhancing path planning capability of mobile robots can effectively save costs, reduce energy consumption, and improve work efficiency. The primary slime mold algorithm (SMA) exhibits characteristics such as a reduced number of parameters, strong robustness, and a relatively high level of exploratory ability. SMA performs well in path planning for mobile robots. However, it is prone to local optimization and lacks dynamic obstacle avoidance, making it less effective in real-world settings. This paper presents an enhanced SMA (ESMA) path-planning algorithm for mobile robots. The ESMA algorithm incorporates adaptive techniques to enhance global search capabilities and integrates an artificial potential field to improve dynamic obstacle avoidance. Compared to the SMA algorithm, the SMA-AGDE algorithm, which combines the Adaptive Guided Differential Evolution algorithm, and the Lévy Flight-Rotation SMA (LRSMA) algorithm, resulted in an average reduction in the minimum path length of (3.92%, 8.93%, 2.73%), along with corresponding reductions in path minimum values and processing times. Experiments show ESMA can find shortest collision-free paths for mobile robots in both static and dynamic environments.

Neuronal branching is increasingly asymmetric near synapses, potentially enabling plasticity while minimizing energy dissipation and conduction time.

Neurons' primary function is to encode and transmit information in the brain and body. The branching architecture of axons and dendrites must compute, respond and make decisions while obeying the rules of the substrate in which they are enmeshed. Thus, it is important to delineate and understand the principles that govern these branching patterns. Here, we present evidence that asymmetric branching is a key factor in understanding the functional properties of neurons. First, we derive novel predictions for asymmetric scaling exponents that encapsulate branching architecture associated with crucial principles such as conduction time, power minimization and material costs. We compare our predictions with extensive data extracted from images to associate specific principles with specific biophysical functions and cell types. Notably, we find that asymmetric branching models lead to predictions and empirical findings that correspond to different weightings of the importance of maximum, minimum or total path lengths from the soma to the synapses. These different path lengths quantitatively and qualitatively affect energy, time and materials. Moreover, we generally observe that higher degrees of asymmetric branching-potentially arising from extrinsic environmental cues and synaptic plasticity in response to activity-occur closer to the tips than the soma (cell body).

A Fuzzy Logic Approach and Path Algorithm for Time and Energy Management of Smart Cleaning Robots

Smart home technologies (SHM) or devices provide some degree of digitally connected, automated, or enhanced services to building occupants in residential areas and have been becoming increasingly popular in recent years. SHM have the potential to improve home comfort, convenience, security, and energy management. Different technologies are used to equip household parts for smarter monitoring, movement, and remote control and to allow effective harmonic interaction between them. Especially, energy management and path-planning algorithms are some of the important problems for such technologies to get optimum efficiency and benefit. Smart vacuum cleaning robot is one of the applications of such devices with various functions. These cleaning robots have limited battery power and battery sizes, thus effective cleaning is critical. Additionally, the shortest / optimal path planning is essential for the efficient operation of effective cleaning based on the battery time. In this article, two distinct algorithms, which are Search algorithm and CSP algorithm are utilized to obtain distinct optimal minimum path lengths for keeping the home's total dirt level as low as possible. Depending on various types of linguistic, abstract, or perceptual variables, these algorithms are not enough for the energy management of the battery. Therefore, the fuzzy logic-based inference system is proposed for obtaining the charge durability of battery of the cleaning robot, in addition to these algorithms. The inputs affecting the charge durability are considered as floor type, dirt level and the width of area for the fuzzy approach.

Measuring lattices

Unit cells are used to represent crystallographic lattices. Calculations measuring the differences between unit cells are used to provide metrics for measuring meaningful distances between three-dimensional crystallographic lattices. This is a surprisingly complex and computationally demanding problem. A review is presented of the current best practice using Delaunay-reduced unit cells in the six-dimensional real space of Selling scalar cells S 6 and the equivalent three-dimensional complex space C 3. The process is a simplified version of the process needed when working with the more complex six-dimensional real space of Niggli-reduced unit cells G 6. Obtaining a distance begins with identification of the fundamental region in the space, continues with conversion to primitive cells and reduction, analysis of distances to the boundaries of the fundamental unit, and is completed by a comparison of direct paths with boundary-interrupted paths, looking for a path of minimal length.

Intelligent Object Avoidance Method Design of Railroad Inspection Robot Based on Particle Swarm Algorithm

<p>In order to make the railroad inspection robot better adapt to its complex working environment, it is especially important to study the robot object avoidance algorithm. The WOA algorithm has simple and understandable structure and strong optimization ability but is prone to local convergence. IWOA-PSO is used for railway inspection robots. The performance of IWOA-PSO in the experimental results is better than that of WOA and PSO, and the average accuracy and standard deviation of the IWOA-PSO can better reach the theoretical optimal value in the function tests, and it has performance close to the theoretical value. In the simple environment object avoidance route planning, the minimum path length of IWOA-PSO is 850 mm, which is 53.6% less than that of the PSO algorithm, and the search time is 13.12 seconds, which is 5.11 seconds less than that of PSO algorithm; in the ordinary environment object avoidance route planning, the minimum path length of IWOA-PSO is 830 mm, while the path length of PSO algorithm is 1339 mm, the former is 38% less than the latter, and the search time of IWOA-PSO is 14.05 seconds less than PSO algorithm, so the method has better effect on object avoidance.</p> <p> </p>

Hybrid UWB-Inertial TDoA-Based Target Tracking With Concentrated Anchors

In this paper, hybrid radio/inertial mobile target tracking for accurate and smooth path estimation is considered. The proposed tracking approach builds upon an Ultra WideBand (UWB)-based positioning algorithm, based on the Linear Hyperbolic Positioning System (LinHPS), with Time Difference of Arrival (TDoA) processing and anchors concentrated on a single hotspot at the center of the environment where the target moves. First, we design an Adaptive Radio-based Extended Kalman Filter (AREKF), which does not require a priori statistical knowledge of the noise in the target movement model and estimates the measurement noise covariance, at each sampling time, according to a proper LookUp Table (LUT). In order to improve the performance of AREKF, we incorporate inertial data collected from the target and propose three “hybrid” radio/inertial algorithms, denoted as Hybrid Inertial Measurement Unit (IMU)-aided Radio-based EKF (HIREKF), Hybrid Noisy Control EKF (HNCEKF), and Hybrid Control EKF (HCEKF). Our results on experimentally acquired paths show that the proposed algorithms achieve an average instantaneous position estimation error on the order of a few centimeters. Moreover, the minimum target path length estimation error, obtained with HCEKF, is on the order of 6% and 1% for two paths with lengths equal to approximately 17 m and 46 m, respectively.

Qubit geodesics on the Bloch sphere from optimal-speed Hamiltonian evolutions

In the geometry of quantum evolutions, a geodesic path is viewed as a path of minimal statistical length connecting two pure quantum states along which the maximal number of statistically distinguishable states is minimum. In this paper, we present an explicit geodesic analysis of the dynamical trajectories that emerge from the quantum evolution of a single-qubit quantum state. The evolution is governed by an Hermitian Hamiltonian operator that achieves the fastest possible unitary evolution between given initial and final pure states. Furthermore, in addition to viewing geodesics in ray space as paths of minimal length, we also verify the geodesicity of paths in terms of unit geometric efficiency and vanishing geometric phase. Finally, based on our analysis, we briefly address the main hurdles in moving to the geometry of quantum evolutions for open quantum systems in mixed quantum states.

Circular Planar Electrical Networks, Split Systems, and Phylogenetic Networks

Two well-known generalizations of phylogenetic trees are split systems and phylogenetic networks. Distances for both are typically calculated as the minimum path weight. Relatedly, a tree-shaped electrical network has effective resistance between its leaf nodes found as the minimum path resistance. This latter fact raises the question of comparing the effective resistance on electrical networks to the minimum path length on split systems. Surprisingly, it turns out that circular planar electrical networks correspond to unique weighted circular split systems. This crucial result is found precisely by showing that the resistance metric of the Kron reduction of a circular planar electrical network obeys the Kalmanson condition. We demonstrate how this fact allows interchange of methods: primarily circuit reconstruction using phylogenetic techniques.