scholarly journals Dynamical Analysis of a Navigation Algorithm

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3139
Author(s):  
Mireya Cabezas-Olivenza ◽  
Ekaitz Zulueta ◽  
Ander Sánchez-Chica ◽  
Adrian Teso-Fz-Betoño ◽  
Unai Fernandez-Gamiz
Keyword(s):  
Lyapunov Method ◽  
Autonomous Vehicle ◽  
Artificial Vision ◽  
Dynamical Analysis ◽  
Longitudinal Control ◽  
Navigation Algorithm ◽  
Localization And Mapping ◽  
Navigation Algorithms ◽  
The Stability ◽  
Adequate Reliability

There is presently a need for more robust navigation algorithms for autonomous industrial vehicles. These have reasonably guaranteed the adequate reliability of the navigation. In the current work, the stability of a modified algorithm for collision-free guiding of this type of vehicle is ensured. A lateral control and a longitudinal control are implemented. To demonstrate their viability, a stability analysis employing the Lyapunov method is carried out. In addition, this mathematical analysis enables the constants of the designed algorithm to be determined. In conjunction with the navigation algorithm, the present work satisfactorily solves the localization problem, also known as simultaneous localization and mapping (SLAM). Simultaneously, a convolutional neural network is managed, which is used to calculate the trajectory to be followed by the AGV, by implementing the artificial vision. The use of neural networks for image processing is considered to constitute the most robust and flexible method for realising a navigation algorithm. In this way, the autonomous vehicle is provided with considerable autonomy. It can be regarded that the designed algorithm is adequate, being able to trace any type of path.

scholarly journals Solution of problem of returning to the starting point of autonomously flying UAV by visual navigation

Informatics ◽  
2020 ◽  
Vol 17 (2) ◽  
pp. 17-24
Author(s):  
R. S. Zhuk ◽  
B. A. Zalesky ◽  
Ph. S. Trotski
Keyword(s):  
Visual Odometry ◽  
Video Camera ◽  
Visual Navigation ◽  
Navigation Algorithm ◽  
Localization And Mapping ◽  
Starting Point ◽  
Navigation Algorithms ◽  
Aerial Vehicle ◽  
Navigation Signals ◽  
The Moment

An autonomous visual navigation algorithm is considered, designed for “home“ return of unmanned aerial vehicle (UAV) equipped with on-board video camera and on-board computer, out of GPS and GLONASS navigation signals. The proposed algorithm is similar to the well-known visual navigation algorithms such as V-SLAM (simultaneous localization and mapping) and visual odometry, however, it differs in separate implementation of mapping and localization processes. It calculates the geographical coordinates of the features on the frames taken by on-board video camera during the flight from the start point until the moment of GPS and GLONASS signals loss. After the loss of the signal the return mission is launched, which provides estimation of the position of UAV relatively the map created by previously found features. Proposed approach does not require such complex calculations as V-SLAM and does not accumulate errors over time, in contrast to visual odometry and traditional methods of inertial navigation. The algorithm was implemented and tested with use of DJI Phantom 3 Pro quadcopter.

scholarly journals Dynamics of the rumor-spreading model with hesitation mechanism in heterogenous networks and bilingual environment

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shuai Yang ◽  
Haijun Jiang ◽  
Cheng Hu ◽  
Juan Yu ◽  
Jiarong Li
Keyword(s):  
Lyapunov Method ◽  
Reproduction Number ◽  
Model Parameters ◽  
Rumor Spreading ◽  
Spreading Model ◽  
Reductio Ad Absurdum ◽  
The Stability ◽  
The Impact ◽  
Theoretical Results ◽  
The Basic Reproduction Number

Abstract In this paper, a novel rumor-spreading model is proposed under bilingual environment and heterogenous networks, which considers that exposures may be converted to spreaders or stiflers at a set rate. Firstly, the nonnegativity and boundedness of the solution for rumor-spreading model are proved by reductio ad absurdum. Secondly, both the basic reproduction number and the stability of the rumor-free equilibrium are systematically discussed. Whereafter, the global stability of rumor-prevailing equilibrium is explored by utilizing Lyapunov method and LaSalle’s invariance principle. Finally, the sensitivity analysis and the numerical simulation are respectively presented to analyze the impact of model parameters and illustrate the validity of theoretical results.

scholarly journals Exploring the Distribution of Traffic Flow for Shared Human and Autonomous Vehicle Roads

Energies ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 3425
Author(s):  
Huanping Li ◽  
Jian Wang ◽  
Guopeng Bai ◽  
Xiaowei Hu
Keyword(s):  
Traffic Flow ◽  
Autonomous Vehicles ◽  
Flow Model ◽  
Road Traffic ◽  
Autonomous Vehicle ◽  
Transformation Model ◽  
Hydrodynamic Theory ◽  
Traffic Flow Model ◽  
Traffic System ◽  
The Stability

In order to explore the changes that autonomous vehicles would bring to the current traffic system, we analyze the car-following behavior of different traffic scenarios based on an anti-collision theory and establish a traffic flow model with an arbitrary proportion (p) of autonomous vehicles. Using calculus and difference methods, a speed transformation model is established which could make the autonomous/human-driven vehicles maintain synchronized speed changes. Based on multi-hydrodynamic theory, a mixed traffic flow model capable of numerical calculation is established to predict the changes in traffic flow under different proportions of autonomous vehicles, then obtain the redistribution characteristics of traffic flow. Results show that the reaction time of autonomous vehicles has a decisive influence on traffic capacity; the q-k curve for mixed human/autonomous traffic remains in the region between the q-k curves for 100% human and 100% autonomous traffic; the participation of autonomous vehicles won’t bring essential changes to road traffic parameters; the speed-following transformation model minimizes the safety distance and provides a reference for the bottom program design of autonomous vehicles. In general, the research could not only optimize the stability of transportation system operation but also save road resources.

Global stability analysis of fractional-order gene regulatory networks with time delay

2019 ◽  
Vol 12 (06) ◽  
pp. 1950067 ◽  
Author(s):  
Zhaohua Wu ◽  
Zhiming Wang ◽  
Tiejun Zhou
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Gene Regulatory Networks ◽  
Existence And Uniqueness ◽  
Regulatory Networks ◽  
Lyapunov Method ◽  
Regulation Mechanism ◽  
Global Stability Analysis ◽  
Gene Regulatory ◽  
The Stability

Fractional-order gene regulatory networks with time delay (DFGRNs) have proven that they are more suitable to model gene regulation mechanism than integer-order. In this paper, a novel DFGRN is proposed. The existence and uniqueness of the equilibrium point for the DFGRN are proved under certain conditions. On this basis, the conditions on the global asymptotic stability are established by using the Lyapunov method and comparison theorem for the DFGRN, and the stability conditions are dependent on the fractional-order [Formula: see text]. Finally, numerical simulations show that the obtained results are reasonable.

A novel path tracking approach considering safety of the intended functionality for autonomous vehicles

2021 ◽  
pp. 095440702110205
Author(s):  
Huiran Wang ◽  
Qidong Wang ◽  
Wuwei Chen ◽  
Linfeng Zhao ◽  
Dongkui Tan
Keyword(s):  
Autonomous Vehicles ◽  
Autonomous Vehicle ◽  
Coordinated Control ◽  
Steering System ◽  
Front Wheel ◽  
Path Tracking ◽  
Hierarchical Architecture ◽  
Automatic Steering ◽  
The Stability ◽  
Control Layer

To reduce the adverse effect of the functional insufficiency of the steering system on the accuracy of path tracking, a path tracking approach considering safety of the intended functionality is proposed by coordinating automatic steering and differential braking in this paper. The proposed method adopts a hierarchical architecture consisting of a coordinated control layer and an execution control layer. In coordinated control layer, an extension controller considering functional insufficiency of the steering system, tire force characteristics and vehicle driving stability is proposed to determine the weight coefficients of automatic steering and the differential braking, and a model predictive controller is designed to calculate the desired front wheel angle and additional yaw moment. In execution control layer, a H∞ steering angle controller considering external disturbances and parameter uncertainty is designed to track desired front wheel angle, and a braking force distribution module is used to determine the wheel cylinder pressure of the controlled wheels. Both simulation and experiment results show that the proposed method can overcome the functional insufficiency of the steering system and improve the accuracy of path tracking while maintaining the stability of the autonomous vehicle.

scholarly journals Stability of thin-shell wormholes from noncommutative BTZ black hole

2015 ◽  
Vol 24 (05) ◽  
pp. 1550034 ◽  
Author(s):  
Piyali Bhar ◽  
Ayan Banerjee
Keyword(s):  
Black Hole ◽  
Thin Shell ◽  
Static Solution ◽  
Dynamical Analysis ◽  
Energy Conditions ◽  
Btz Black Hole ◽  
Wormhole Throat ◽  
Radial Perturbation ◽  
Thin Shell Wormholes ◽  
The Stability

In this paper, we construct thin-shell wormholes in (2 + 1)-dimensions from noncommutative BTZ black hole by applying the cut-and-paste procedure implemented by Visser. We calculate the surface stresses localized at the wormhole throat by using the Darmois–Israel formalism and we find that the wormholes are supported by matter violating the energy conditions. In order to explore the dynamical analysis of the wormhole throat, we consider that the matter at the shell is supported by dark energy equation of state (EoS) p = ωρ with ω < 0. The stability analysis is carried out of these wormholes to linearized spherically symmetric perturbations around static solutions. Preserving the symmetry we also consider the linearized radial perturbation around static solution to investigate the stability of wormholes which was explored by the parameter β (speed of sound).

On the stability of a mathematical model for HIV(AIDS) - cancer dynamics

2021 ◽  
Vol 8 (4) ◽  
pp. 783-796
Author(s):  
H. W. Salih ◽  
◽  
A. Nachaoui ◽  
Keyword(s):  
Mathematical Model ◽  
Highly Active Antiretroviral Therapy ◽  
Lyapunov Method ◽  
Equilibrium Points ◽  
Hiv Treatment ◽  
Biochemical Processes ◽  
Highly Active ◽  
Biological Phenomena ◽  
The Stability ◽  
The Impact

In this work, we study an impulsive mathematical model proposed by Chavez et al. [1] to describe the dynamics of cancer growth and HIV infection, when chemotherapy and HIV treatment are combined. To better understand these complex biological phenomena, we study the stability of equilibrium points. To do this, we construct an appropriate Lyapunov function for the first equilibrium point while the indirect Lyapunov method is used for the second one. None of the equilibrium points obtained allow us to study the stability of the chemotherapeutic dynamics, we then propose a bifurcation of the model and make a study of the bifurcated system which contributes to a better understanding of the underlying biochemical processes which govern this highly active antiretroviral therapy. This shows that this mathematical model is sufficiently realistic to formulate the impact of this treatment.

scholarly journals Performance Analysis of NDT-based Graph SLAM for Autonomous Vehicle in Diverse Typical Driving Scenarios of Hong Kong

Sensors ◽  
2018 ◽  
Vol 18 (11) ◽  
pp. 3928 ◽  
Author(s):  
Weisong Wen ◽  
Li-Ta Hsu ◽  
Guohao Zhang
Keyword(s):  
New York ◽  
Hong Kong ◽  
Autonomous Vehicles ◽  
Autonomous Vehicle ◽  
Tall Buildings ◽  
Point Clouds ◽  
Reliability Estimation ◽  
Traffic Condition ◽  
Localization And Mapping ◽  
Graph Slam

Robust and lane-level positioning is essential for autonomous vehicles. As an irreplaceable sensor, Light detection and ranging (LiDAR) can provide continuous and high-frequency pose estimation by means of mapping, on condition that enough environment features are available. The error of mapping can accumulate over time. Therefore, LiDAR is usually integrated with other sensors. In diverse urban scenarios, the environment feature availability relies heavily on the traffic (moving and static objects) and the degree of urbanization. Common LiDAR-based simultaneous localization and mapping (SLAM) demonstrations tend to be studied in light traffic and less urbanized area. However, its performance can be severely challenged in deep urbanized cities, such as Hong Kong, Tokyo, and New York with dense traffic and tall buildings. This paper proposes to analyze the performance of standalone NDT-based graph SLAM and its reliability estimation in diverse urban scenarios to further evaluate the relationship between the performance of LiDAR-based SLAM and scenario conditions. The normal distribution transform (NDT) is employed to calculate the transformation between frames of point clouds. Then, the LiDAR odometry is performed based on the calculated continuous transformation. The state-of-the-art graph-based optimization is used to integrate the LiDAR odometry measurements to implement optimization. The 3D building models are generated and the definition of the degree of urbanization based on Skyplot is proposed. Experiments are implemented in different scenarios with different degrees of urbanization and traffic conditions. The results show that the performance of the LiDAR-based SLAM using NDT is strongly related to the traffic condition and degree of urbanization. The best performance is achieved in the sparse area with normal traffic and the worse performance is obtained in dense urban area with 3D positioning error (summation of horizontal and vertical) gradients of 0.024 m/s and 0.189 m/s, respectively. The analyzed results can be a comprehensive benchmark for evaluating the performance of standalone NDT-based graph SLAM in diverse scenarios which is significant for multi-sensor fusion of autonomous vehicle.

scholarly journals Dynamical Analysis of a Viral Infection Model with Delays in Computer Networks

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Zizhen Zhang ◽  
Huizhong Yang
Keyword(s):  
Hopf Bifurcation ◽  
Propagation Model ◽  
Dynamical Analysis ◽  
Infection Model ◽  
Virus Propagation ◽  
Normal Form Theory ◽  
Center Manifold Theorem ◽  
Form Theory ◽  
Two Delays ◽  
The Stability

This paper is devoted to the study of an SIRS computer virus propagation model with two delays and multistate antivirus measures. We demonstrate that the system loses its stability and a Hopf bifurcation occurs when the delay passes through the corresponding critical value by choosing the possible combination of the two delays as the bifurcation parameter. Moreover, the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by means of the center manifold theorem and the normal form theory. Finally, some numerical simulations are performed to illustrate the obtained results.

scholarly journals Real - Time Trajectory and Velocity Planning for Autonomous Vehicles

2021 ◽  
Vol 10 (5) ◽  
pp. 439-448
Author(s):  
Hrishikesh Dey ◽  
Rithika Ranadive ◽  
Abhishek Chaudhari
Keyword(s):  
Path Planning ◽  
Velocity Profile ◽  
Real Time ◽  
Autonomous Vehicle ◽  
Optimal Path ◽  
Autonomous Driving ◽  
Navigation Algorithm ◽  
Velocity Planning ◽  
Planning Algorithm ◽  
Path Planner

Path planning algorithm integrated with a velocity profile generation-based navigation system is one of the most important aspects of an autonomous driving system. In this paper, a real-time path planning solution to obtain a feasible and collision-free trajectory is proposed for navigating an autonomous car on a virtual highway. This is achieved by designing the navigation algorithm to incorporate a path planner for finding the optimal path, and a velocity planning algorithm for ensuring a safe and comfortable motion along the obtained path. The navigation algorithm was validated on the Unity 3D Highway-Simulated Environment for practical driving while maintaining velocity and acceleration constraints. The autonomous vehicle drives at the maximum specified velocity until interrupted by vehicular traffic, whereas then, the path planner, based on the various constraints provided by the simulator using µWebSockets, decides to either decelerate the vehicle or shift to a more secure lane. Subsequently, a splinebased trajectory generation for this path results in continuous and smooth trajectories. The velocity planner employs an analytical method based on trapezoidal velocity profile to generate velocities for the vehicle traveling along the precomputed path. To provide smooth control, an s-like trapezoidal profile is considered that uses a cubic spline for generating velocities for the ramp-up and ramp-down portions of the curve. The acceleration and velocity constraints, which are derived from road limitations and physical systems, are explicitly considered. Depending upon these constraints and higher module requirements (e.g., maintaining velocity, and stopping), an appropriate segment of the velocity profile is deployed. The motion profiles for all the use-cases are generated and verified graphically.

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