scholarly journals IMPULSE CONTROL OF THE MANIPULATION ROBOT

2019 ◽  
Vol 5 (2) ◽  
pp. 13 ◽  
Author(s):  
Yurii F. Dolgii ◽  
Alexander N. Sesekin ◽  
Ilya G. Chupin
Keyword(s):  
Computer Simulation ◽  
Kinetic Energy ◽  
Impulse Control ◽  
First Integrals ◽  
Lagrangian Mechanics ◽  
Solvability Conditions ◽  
Control Goal ◽  
Analytical Formulas ◽  
Impulse Controls ◽  
Manipulation Robot

A nonlinear control problem for a manipulation robot is considered. The solvability conditions for the problem are obtained in the class of special impulse controls. To achieve the control goal, the kinetic energy of the manipulation robot is used. When finding analytical formulas for controls, the classical first integrals of Lagrangian mechanics were used. The effectiveness of the proposed algorithm is illustrated by computer simulation.

scholarly journals Impulse control of a two-link manipulation robot

2021 ◽  
Vol 57 ◽  
pp. 77-90
Author(s):  
Yu.F. Dolgii ◽  
I.A. Chupin
Keyword(s):  
Computer Simulation ◽  
Configuration Space ◽  
Impulse Control ◽  
Nonlinear Differential Equations ◽  
Classical Mechanics ◽  
First Integrals ◽  
Initial Moment ◽  
Analytical Integration ◽  
Impulse Controls ◽  
Manipulation Robot

A nonlinear problem of controlling the movements of a two-link manipulation robot is considered. The free mechanical system has two first integrals in involution. Methods of classical mechanics are used for analytical integration of the system of nonlinear differential equations. A trajectory connecting the initial and final positions of the two-link manipulation robot in the configuration space is found. Impulse controls at the initial moment of time impart the necessary energy to the robot to enter this trajectory. Impulse controls are also used to damp the speeds of the robot at the end position. In a computer simulation of the proposed procedure for moving the robot, generalized impulse controls are approximated by rectangular impulses.

Poisson Brackets & Angular Momentum

2018 ◽  
Author(s):  
Peter Mann
Keyword(s):  
Generating Functions ◽  
First Integrals ◽  
Lagrangian Mechanics ◽  
Poisson Brackets ◽  
Coordinate Transformations ◽  
Canonical Transformations ◽  
Gauge Transformations ◽  
The Third ◽  
Point Transformations ◽  
Canonical Coordinate

This chapter discusses canonical transformations and gauge transformations and is divided into three sections. In the first section, canonical coordinate transformations are introduced to the reader through generating functions as the extension of point transformations used in Lagrangian mechanics, with the harmonic oscillator being used as an example of a canonical transformation. In the second section, gauge theory is discussed in the canonical framework and compared to the Lagrangian case. Action-angle variables, direct conditions, symplectomorphisms, holomorphic variables, integrable systems and first integrals are examined. The third section looks at infinitesimal canonical transformations resulting from functions on phase space. Ostrogradsky equations in the canonical setting are also detailed.

scholarly journals Oscillation of a pendulum subject to a horizontal trajectory with different kinds of motion

2019 ◽  
pp. 17-29
Author(s):  
Rodolfo Espindola-Heredia ◽  
Gabriela Del Valle ◽  
Damián Muciño-Cruz ◽  
Guadalupe Hernandez-Morales
Keyword(s):  
Horizontal Plane ◽  
Wireless Sensors ◽  
Equations Of Motion ◽  
First Integrals ◽  
Experimental Results ◽  
Lagrangian Mechanics ◽  
Experimental Prototype ◽  
Oscillatory Movement ◽  
Spatial Coordinates ◽  
Rigid Rod

In the children's movie The Incredibles there is a scene where Mr Incredible faces Bomb Voyage, while Incredi Boy wants to help Mr Incredible, Incredi Boy flies with Mr Incredible, who holds on to the hero's cloak, affecting Incredi Boy’s flight plan. To understand how an oscillatory movement affects non-oscillatory movement, an experimental prototype was constructed with a particle of mass m, attached to a rigid rod and without mass of length l, to a swivel of negligible mass, which was subject to a mass M. The swivel always remained on a horizontal plane, allowing the oscillatory movement of mass m. Experimental results were obtained by means of wireless sensors which recorded the spatial coordinates of the mass m. Using Lagrangian mechanics we obtained the equations of motion and expressed the possible first integrals of movement, when the movement of the mass M was: linear uniform (ULM), uniformly accelerated, (UAM), uniform circular (UCM), accelerated circular (ACM) and forced circular (FCM). The dynamics were analyzed, the equations of movement obtained, they were solved numerically, and the experimental results were compared to theoretical and numerical results.

scholarly journals Mining excavator working equipment load forecasting according to a fuzzy-logistic model

2020 ◽  
Vol 241 ◽  
pp. 29
Author(s):  
V. Velikanov
Keyword(s):  
Computer Simulation ◽  
Fuzzy Logic ◽  
Statistical Analysis ◽  
Logistic Model ◽  
Load Forecasting ◽  
Experimental Studies ◽  
Multiple Stress ◽  
Accurate Forecast ◽  
Analytical Formulas ◽  
Qualitative Nature

Due to the fact that the loads occurring in the working equipment of mining excavators are determined by a large number of random factors that are difficult to represent by analytical formulas, for estimating and predicting loads the models must be introduced using non-standard approaches. In this study, we used the methodology of the theory of fuzzy logic and fuzzy pluralities, which allows to overcome the difficulties associated with the incompleteness and vagueness of the data in assessing and predicting the  forces encountered in the working equipment of mining excavators, as well as with the qualitative nature of these data.As a result of computer simulation in the fuzzyTECH environment, data comparable with experimental studies were obtained to determine the level of loading of the main elements of the working equipment of mining excavators. Based on a representative sample, a statistical analysis of the data was performed, as a result of which the equation of linear multiple stress regression in the handle of mining excavators was obtained, which allows to make an accurate forecast of the loading of the working equipment of the excavator.

Lagrangian Mechanics

2017 ◽  
Author(s):  
Jennifer Coopersmith
Keyword(s):  
Kinetic Energy ◽  
Quadratic Form ◽  
Lagrangian Mechanics ◽  
Conservation Of Energy ◽  
Curved Space ◽  
Generalized Coordinates ◽  
Least Action ◽  
Principle Of Least Action ◽  
External Conditions ◽  
Definition Of

It is demonstrated how d’Alembert’s Principle can be used as the basis for a more general mechanics – Lagrangian Mechanics. How this leads to Hamilton’s Principle (the Principle of Least Action) is shown mathematically and in words. It is further explained why Lagrangian Mechanics is so general, why forces of constraint may be ignored, and how external conditions lead to “curved space.” Also, it is explained why the Lagrangian, L, has the form L = T − V (where T is the kinetic energy and V is the potential energy), and why T is in “quadratic form” (T = 1/2mv2). It is shown how Noether’s Theorem leads to a more fundamental definition of energy and links the conservation of energy to the homogeneity of time. The ingenious Lagrange multipliers are explained, and also generalized forces and generalized coordinates.

A generalization of the Liouville–Arnol'd theorem

1995 ◽  
Vol 117 (2) ◽  
pp. 353-370 ◽  
Author(s):  
G. E. Prince ◽  
G. B. Byrnes ◽  
J. Sherring ◽  
S. E. Godfrey
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Hamiltonian Systems ◽  
First Integrals ◽  
Second Order ◽  
Lagrangian Mechanics ◽  
Original Theorem

AbstractWe show that the Liouville-Arnol'd theorem concerning knowledge of involutory first integrals for Hamiltonian systems is available for any system of second order ordinary differential equations. In establishing this result we also provide a new proof of the standard theorem in the setting of non-autonomous, regular Lagrangian mechanics on the evolution space ℝ × TM of a manifold M. Both the original theorem and its generalization rely on a certain bijection between symmetries of the system and its first integrals. We give two examples of the use of the theorem for systems on ℝ2 which are not Euler-Lagrange.

Elastic-Plastic Dynamic Response of the Tube with Free Boundary Condition Subjected to Impact

2007 ◽  
Vol 340-341 ◽  
pp. 263-268
Author(s):  
Guo Yun Lu ◽  
Shan Yuan Zhang
Keyword(s):  
Computer Simulation ◽  
Kinetic Energy ◽  
Dynamic Response ◽  
Internal Energy ◽  
Tube Wall ◽  
Plastic Behavior ◽  
Finite Element Program ◽  
Elastic Plastic ◽  
The Impact ◽  
Circular Shell

Some experimental results of the free-free tubes laterally impacted by the missile were given and the finite element program LS-DYNA was used to simulate this dynamic response process. The instantaneous deformation of the circular shell given by experiments and computer simulation were compared and discussed. It can be seen that when the impact occur the local dents firstly appear at the beginning of impact. With time increase, the depth of the dents increase, the scope of the deformation of the tube wall is enlarged; the total stiffness of the cross-section of the tube is weaken and decreases at the impact point, the beam-like bending deformation take place and the rigid-body translations occur. Through the computer simulation the exchanged energy between the missile and the tube were acquired. The impact energy of the missile is transferred to internal energy and kinetic energy of the tube. The ratio of the internal energy with the kinetic energy of the tube is great for the weakness rigidity of the tube wall, which is opposite to that of a free-free beam. This research made us deeply understand the character of the response when studying the elastic-plastic behavior of the free circular shell under intense dynamic loading.

Development of a Non-Gating Guardrail Terminal

2021 ◽  
pp. 036119812110148
Author(s):  
Kevin D. Schrum ◽  
Kenneth Walls ◽  
Joseph Schwertz ◽  
Blake Feltman ◽  
Dakotah Sicking ◽  
...  
Keyword(s):  
Computer Simulation ◽  
Kinetic Energy ◽  
Internal Structure ◽  
Longitudinal Force ◽  
Test Results ◽  
Test Vehicle ◽  
Section Modulus ◽  
Lateral Forces ◽  
Crash Tests

Guardrail terminals have evolved to the point where they absorb energy while utilizing tension in the rail to countermand the compression. However, non-gating terminals have yet to be developed. In the present study, the possibility of a non-gating guardrail terminal was investigated. Specifically, the combination of lateral and longitudinal forces that produce non-gating performance were determined from computer simulation. Next, a prototype terminal was crash tested at the research team’s laboratory. A terminal head was designed to deform the guardrail, and its internal structure was adjustable to control the longitudinal force. Posts were designed to control lateral forces by modifying their section modulus. This controlled the force at which the posts buckled in response to a collision. A prototype was subjected to two 15° crash tests using an SUV and a small car. In both tests, the kinetic energy of the test vehicle was fully absorbed and the Manual for Assessing Safety Hardware (MASH) criteria would have been met. Neither vehicle passed beyond the terminal head, making these test results the first of their kind.

scholarly journals Some control problems with random intervention times

2001 ◽  
Vol 33 (2) ◽  
pp. 404-422 ◽  
Author(s):  
Hui Wang
Keyword(s):  
Poisson Process ◽  
Impulse Control ◽  
Value Functions ◽  
Control Cost ◽  
Signal Process ◽  
Arrival Times ◽  
Quadratic Deviation ◽  
Ergodic Problem ◽  
Impulse Controls ◽  
Admissible Controls

We consider the problem of optimally tracking a Brownian motion by a sequence of impulse controls, in such a way as to minimize the total expected cost that consists of a quadratic deviation cost and a proportional control cost. The main feature of our model is that the control can only be exerted at the arrival times of an exogenous uncontrolled Poisson process (signal). In other words, the set of possible intervention times are discrete, random and determined by the signal process (not by the decision maker). We discuss both the discounted problem and the ergodic problem, where explicit solutions can be found. We also derive the asymptotic behavior of the optimal control policies and the value functions as the intensity of the Poisson process goes to infinity, or roughly speaking, as the set of admissible controls goes from the discrete-time impulse control to the continuous-time bounded variation control.

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