scholarly journals On Determining the Optimal Lifting Law of the Walking Propulsion Device Foot of an Underwater Robot from the Bottom

2021 ◽  
Author(s):  
E.S. Briskin ◽  
Ya.V. Kalinin ◽  
L.D. Smirnaya
Keyword(s):  
Mathematical Model ◽  
Mobile Robot ◽  
Analytical Solutions ◽  
Center Of Mass ◽  
Underwater Robot ◽  
Compression Force ◽  
Fluid Filtration ◽  
Linearized Model ◽  
Gas Expansion ◽  
Dissolved Air

The problem of lifting the foot of the walking propulsion device of an underwater mobile robot is considered, taking into account the additional “compression” force acting on it. A mathematical model has been developed for the detachment of a propulsion foot from the ground, based on Henry's laws establishing the concentration of dissolved air in a liquid, the law of gas expansion at a constant temperature, Darcy's law on fluid filtration and the theorem on the motion of the center of mass of a solid body. The linearized model allows to obtain and analytical solutions. Based on the solution of the variational problem, optimal modes of lifting the foot of the walking propulsion of an underwater mobile robot are established.

scholarly journals The application of virtual prototyping methods to determine the dynamic parameters of mobile robot

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Krzysztof Kurc ◽  
Dariusz Szybicki ◽  
Andrzej Burghardt ◽  
Magdalena Muszyńska
Keyword(s):  
Mathematical Model ◽  
Mobile Robot ◽  
Virtual Prototyping ◽  
Design Stage ◽  
Kinematics And Dynamics ◽  
Underwater Robot ◽  
Design Tools ◽  
Dynamic Parameters ◽  
Mechatronic Design

Abstract The paper presents methods used to determine the parameters necessary to build a mathematical model of an underwater robot with a crawler drive. The parameters present in the dynamics equation will be determined by means of advanced mechatronic design tools, including: CAD/CAE software andMES modules. The virtual prototyping process is described as well as the various possible uses (design adaptability) depending on the optional accessories added to the vehicle. A mathematical model is presented to show the kinematics and dynamics of the underwater crawler robot, essential for the design stage.

TO THE STABILITY OF TANK VEHICLES IN THE BRAKE MODE

2019 ◽  
pp. 27-32
Author(s):  
Denys Popelysh ◽  
Yurii Seluk ◽  
Sergyi Tomchuk
Keyword(s):  
Mathematical Model ◽  
Control Systems ◽  
Distribution Systems ◽  
Traffic Accidents ◽  
Road Traffic ◽  
Center Of Mass ◽  
Dynamic Processes ◽  
Course Stability ◽  
The Stability ◽  
Tank Vehicles

This article discusses the question of the possibility of improving the roll stability of partially filled tank vehicles while braking. We consider the dangers associated with partially filled tank vehicles. We give examples of the severe consequences of road traffic accidents that have occurred with tank vehicles carrying dangerous goods. We conducted an analysis of the dynamic processes of fluid flow in the tank and their influence on the basic parameters of the stability of vehicle. When transporting a partially filled tank due to the comparability of the mass of the empty tank with the mass of the fluid being transported, the dynamic qualities of the vehicle change so that they differ significantly from the dynamic characteristics of other vehicles. Due to large displacements of the center of mass of cargo in the tank there are additional loads that act vehicle and significantly reduce the course stability and the drivability. We consider the dynamics of liquid sloshing in moving containers, and give examples of building a mechanical model of an oscillating fluid in a tank and a mathematical model of a vehicle with a tank. We also considered the method of improving the vehicle’s stability, which is based on the prediction of the moment of action and the nature of the dynamic processes of liquid cargo and the implementation of preventive actions by executive mechanisms. Modern automated control systems (anti-lock brake system, anti-slip control systems, stabilization systems, braking forces distribution systems, floor level systems, etc.) use a certain list of elements for collecting necessary parameters and actuators for their work. This gives the ability to influence the course stability properties without interfering with the design of the vehicle only by making changes to the software of these systems. Keywords: tank vehicle, roll stability, mathematical model, vehicle control systems.

Zur Lösung der BETHE-GOLDSTONE-Gleichung bei nicht-verschwindendem Gesamtimpuls I

1963 ◽  
Vol 18 (4) ◽  
pp. 531-538
Author(s):  
Dallas T. Hayes
Keyword(s):  
Approximate Solution ◽  
Analytical Solution ◽  
Nuclear Matter ◽  
Analytical Solutions ◽  
Projection Operator ◽  
Center Of Mass ◽  
Separable Potential ◽  
Localized Solutions ◽  
Non Local ◽  
Square Well

Localized solutions of the BETHE—GOLDSTONE equation for two nucleons in nuclear matter are examined as a function of the center-of-mass momentum (c. m. m.) of the two nucleons. The equation depends upon the c. m. m. as parameter due to the dependence upon the c. m. m. of the projection operator appearing in the equation. An analytical solution of the equation is obtained for a non-local but separable potential, whereby a numerical solution is also obtained. An approximate solution for small c. m. m. is calculated for a square-well potential. In the range of the approximation the two analytical solutions agree exactly.

Identification and Model Predictive Position Control of Two Wheeled Inverted Pendulum Mobile Robot

2015 ◽  
Vol 73 (6) ◽  
Author(s):  
Amir A. Bature ◽  
Salinda Buyamin ◽  
Mohamad N. Ahmad ◽  
Mustapha Muhammad ◽  
Auwalu A. Muhammad
Keyword(s):  
Mathematical Model ◽  
System Identification ◽  
Mobile Robot ◽  
Inverted Pendulum ◽  
Position Control ◽  
Superior Performance ◽  
System A ◽  
Wheeled Inverted Pendulum ◽  
Simulation Results ◽  
Real Plant

In order to predict and analyse the behaviour of a real system, a simulated model is needed. The more accurate the model the better the response is when dealing with the real plant. This paper presents a model predictive position control of a Two Wheeled Inverted Pendulum robot. The model was developed by system identification using a grey box technique. Simulation results show superior performance of the gains computed using the grey box model as compared to common linearized mathematical model. 

scholarly journals SYNTHESIS OF PROGRAM AND FINITE LAWS OF MOTION IN ANALYTICAL MODELS OF CONTROL OF THE FINAL STATE OF BIOMECHANICAL SYSTEMS

2019 ◽  
Vol 19 (1) ◽  
pp. 93-99
Author(s):  
V Zagrevskiy ◽  
O Zagrevskiy
Keyword(s):  
Mathematical Model ◽  
Computer Program ◽  
Center Of Mass ◽  
Material Point ◽  
Object Motion ◽  
Reference Points ◽  
Analytical Models ◽  
Final State ◽  
Finite Control ◽  
The Mathematical Model

Aim. The article deals with developing a computer program to simulate the movement of the object with a given initial and final speed and fixed travel time. Materials and methods. The analysis, as a method of biomechanics, allows us to assess the biomechanical state of the athlete in real sports exercises. The function of motion synthesis is the ability to predict the trajectory and behavior of the biomechanical system at specified reference points of the phase structure of the simulated motion. The article deals with one of the methods of biomechanical synthesis of movements: synthesis of control of the final state of biomechanical systems, based on the reduction of finite control to a given program control after attenuation of the transient component of acceleration. The mathematical description of the object motion is based on the known law of finite control with feedback. Integration of the mathematical model constructed in the form of the differential equation of the second order was carried out by one of the numerical methods of integration: Runge–Kutta method of the fourth order of accuracy. Consideration of the method is based on a mathematical apparatus describing the motion of a material point, which can be represented by a common center of mass of a biomechanical system, a joint, a center of mass of a segment, etc. Results. The mathematical model of the motion of a material point with the given kinematic parameters of motion at the initial and final moments is implemented in a computer program in the Visual Basic 2010 language environment based on the integrated development environment Visual Studio Express 2013. The output provides numerical and visual support for simulation results. Conclusion. It is shown that the developed computer model of the method always implements the goal of motion: to transfer an object from a given initial state by speed to a given final state for a fixed time of movement.

scholarly journals MODELING OF THE SPINE COMPENSATORY RESPONSE TO DEFORMITY

2018 ◽  
Vol 15 (3) ◽  
pp. 85-91
Author(s):  
A. V. Krutko ◽  
A. V. Gladkov ◽  
V. V. Komissarov ◽  
N. V. Komissarova
Keyword(s):  
Mathematical Model ◽  
Center Of Mass ◽  
Kinematic Model ◽  
Sagittal Imbalance ◽  
Spine Deformity ◽  
Compensatory Mechanism ◽  
Spinal Deformities ◽  
Compensatory Response ◽  
The Mathematical Model ◽  
Pathological Situation

Objective. To analyze mathematical model of the efficiency of the compensatory mechanism of the deformed spine. Material and Methods. The developed basic kinematic model of the spine was used. The restoration of the position of the projection of the general center of mass (GCM) was mathematically modeled, and mechanogenesis of the spinal deformity and possibility of its compensation were evaluated. To assess the reliability of the mathematical model, spinal skiagrams taken from patients with clinically confirmed pathology and sagittal imbalance were used. Results. On the basis of quantitative characteristics of the primary spine deformity of a certain clinical case and using the developed algorithm, it is possible to create a model of both a primary deformity and a compensatory response from intact segments of the spine taking into account the influencing factors. This makes it possible to use the proposed kinematic model in scientific research on predicting the course of various types of spinal deformities. Conclusion. The proposed algorithms simulating the development of spinal deformities based on the restoration of the position of the GCM projection reflect their mechanogenesis and can be used to model various pathological conditions of the spine. A complete correction of the deformity does not mean a complete cure, since the required spinal fusion creates a new, prognostically less significant, but pathological situation.

scholarly journals Analysis of Platform Leveling Systems for Tracked Feller-Buncher Machines

Inventions ◽  
2021 ◽  
Vol 6 (4) ◽  
pp. 96
Author(s):  
Andronov Alexandr ◽  
Bacherikov Ivan ◽  
Zverev Igor
Keyword(s):  
Mathematical Model ◽  
Center Of Mass ◽  
Slope Angle ◽  
Hydraulic Cylinder ◽  
Second Stage ◽  
Modeling Methods ◽  
The Third ◽  
Support Reaction ◽  
Third Stage ◽  
The Stability

The study was devoted to the analysis of feller buncher platform leveling systems. The widespread use of these systems in the design of modern feller-buncher machines makes the study relevant to assess operational efficiency. The analysis was conducted in five stages using analytical and stochastic mathematical modeling methods. In the first stage, the existing layouts of alignment systems were analyzed from the position of force on the hydraulic cylinder rods of the platform tilt drive. The three-cylinder layout scheme, where the force on the hydraulic cylinder rod was 50…60% less than that on the two-cylinder layout, appeared to be the most expedient. In the second stage, a mathematical model for determining changes in the position of the center of mass of the feller-buncher depending on the inclination angle of the platform was derived. In the third stage, a mathematical model was derived for determining the limiting angle of slope of the terrain when the feller buncher moved up the slope. For this purpose, two calculation schemes were considered when the machine moved up the slope without and with a tilted platform. Zero support reaction on the front roller was taken as the stability criterion. In the fourth stage, a mathematical model for determining the limiting angle of slope of the terrain during the roll of the feller-buncher machine was obtained. In the fifth stage, the efficiency of the application of leveling systems was evaluated. A graph of the dependence of changes in the terrain slope angle on the platform slope angle was plotted, and a regression dependence for an approximate estimate was obtained. A regression analysis was also carried out, and dependencies were obtained to determine the weight of a feller-buncher with a leveling system and the added pressure on the ground caused by the increase in the weight of the base machine. The analysis of platform leveling systems showed the effectiveness of their application in the designs of feller-buncher machines, as it allows the machines to work on slopes with an inclination of 50…60% more than without them.

Extended validation of a ground-based three-axis spacecraft simulator model

2020 ◽  
pp. 095441002093896
Author(s):  
H Sh Ousaloo ◽  
Gh Sharifi ◽  
B Akbarinia
Keyword(s):  
Mathematical Model ◽  
Attitude Control ◽  
Aerodynamic Drag ◽  
Center Of Mass ◽  
Model Development ◽  
Optimization Method ◽  
Experimental Results ◽  
Spacecraft Dynamics ◽  
Detailed Model ◽  
Mass Properties

The ground-based spacecraft dynamics simulator plays an important role in the implementation and validation of attitude control scenarios before a mission. The development of a comprehensive mathematical model of the platform is one of the indispensable and challenging steps during the control design process. A precise mathematical model should include mass properties, disturbances forces, mathematical models of actuators and uncertainties. This paper presents an approach for synthesizing a set of trajectories scenarios to estimate the platform inertia tensor, center of mass and aerodynamic drag coefficients. Reaction wheel drag torque is also estimated for having better performance. In order to verify the estimation techniques, a dynamics model of the satellite simulator using MATLAB software was developed, and the problem reduces to a parameter estimation problem to match the experimental results obtained from the simulator using a classical Lenevnberg-Marquardt optimization method. The process of parameter identification and mathematical model development has implemented on a three-axis spherical satellite simulator using air bearing, and several experiments are performed to validate the results. For validation of the simulator model, the model and experimental results must be carefully matched. The experimental results demonstrate that step-by-step implementation of this scenario leads to a detailed model of the platform which can be employed to design and develop control algorithms.

scholarly journals Modeling and Optimal Controller Based on Disturbance Detector for the Stabilization of a Three-link Inverted Pendulum Mobile Robot

Electronics ◽  
2020 ◽  
Vol 9 (11) ◽  
pp. 1821
Author(s):  
Luis Alfonso Jordán-Martínez ◽  
Maricela Guadalupe Figueroa-García ◽  
José Humberto Pérez-Cruz
Keyword(s):  
Mathematical Model ◽  
Mobile Robot ◽  
Nonlinear Model ◽  
Direct Current ◽  
Inverted Pendulum ◽  
Experimental Tests ◽  
Optimal Controller ◽  
Stabilization Problem ◽  
Lagrange Equations ◽  
Direct Measurements

This work presents the realization of a complicated stabilization problem for a three inverted pendulum links-based mobile robot. The actuators of the mobile robot are direct current motors that have tachometer couplings to measure both the position and speed of the wheels and links. Using direct measurements under load and analyzing the deceleration curve, the motor parameters are determined experimentally. A mathematical model of the robot is obtained via the Euler–Lagrange equations. Next, the nonlinear model is linearized and discretized. Based on this discrete LTI model, an optimal controller is designed. The states and disturbances are estimated using a robust detector. Both the controller and detector are implemented in the robot processor. Numerical simulations and experimental tests show a good performance of the controller despite the presence of disturbances.

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