scholarly journals Modeling the Dynamics of Two Cooperating Robots

2021 ◽  
Vol 11 (13) ◽  
pp. 6019
Author(s):  
Andrzej Burghardt ◽  
Wincenty Skwarek
Keyword(s):  
Mathematical Model ◽  
Control System ◽  
Mobile Robots ◽  
Structural Properties ◽  
Lagrange Multipliers ◽  
Dry Friction ◽  
Lagrange Equations ◽  
Friction Forces ◽  
Contact Points ◽  
Cooperating Robots

The paper presents a description of the dynamics of two mobile robots cooperating in the transport of a bulky load in the form of a beam. The purpose of modeling such a system was to obtain a mathematical model in an appropriate form. Lagrange equations of the second type were used to describe the dynamics, followed by the projection method, which allowed for the elimination of Lagrange multipliers. Thanks to this approach, the unknown dry friction forces at the contact points of the robots’ wheels with the ground were eliminated from the description, and the dynamics in the controllable coordinates were obtained. The resulting model has structural properties that enable its use in the synthesis of a control system based on a mathematical model.

Mobile Worm-Like Robots for Pipe Inspection

2015 ◽  
pp. 168-218 ◽  
Author(s):  
Sergey Fedorovich Jatsun ◽  
Andrei Vasilevich Malchikov
Keyword(s):  
Mathematical Model ◽  
Control System ◽  
Mobile Robots ◽  
Experimental Studies ◽  
Design Parameters ◽  
Robot Motion ◽  
Robot Dynamics ◽  
Confined Space ◽  
Pipe Inspection ◽  
The Mathematical Model

This chapter describes various designs of multilink mobile robots intended to move inside the confined space of pipelines. The mathematical model that describes robot dynamics and controlled motion, which allows simulating different regimes of robot motion and determining design parameters of the device and its control system, is presented. The chapter contains the results of numerical simulations for different types of worm-like mobile robots. The experimental studies of the in-pipe robots prototypes and their analyses are presented in this chapter.

scholarly journals Modelling of Dynamics of a Wheeled Mobile Robot with Mecanum Wheels with the use of Lagrange Equations of the Second Kind

2017 ◽  
Vol 22 (1) ◽  
pp. 81-99 ◽  
Author(s):  
Z. Hendzel ◽  
Ł. Rykała
Keyword(s):  
Mathematical Model ◽  
Kinetic Energy ◽  
Mobile Robot ◽  
Mobile Robots ◽  
Equations Of Motion ◽  
Wheeled Mobile Robot ◽  
Dynamic Equations ◽  
Lagrange Equations ◽  
Wheeled Mobile Robots ◽  
New Type

Abstract The work presents the dynamic equations of motion of a wheeled mobile robot with mecanum wheels derived with the use of Lagrange equations of the second kind. Mecanum wheels are a new type of wheels used in wheeled mobile robots and they consist of freely rotating rollers attached to the circumference of the wheels. In order to derive dynamic equations of motion of a wheeled mobile robot, the kinetic energy of the system is determined, as well as the generalised forces affecting the system. The resulting mathematical model of a wheeled mobile robot was generated with the use of Maple V software. The results of a solution of inverse and forward problems of dynamics of the discussed object are also published.

Ultrasonic sensor system for the uses in intelligent motion control system of a mobile robots group

2010 ◽  
Vol 7 ◽  
pp. 109-117
Author(s):  
O.V. Darintsev ◽  
A.B. Migranov ◽  
B.S. Yudintsev
Keyword(s):  
Control System ◽  
Mobile Robot ◽  
Mobile Robots ◽  
Motion Control ◽  
High Speed ◽  
Ultrasonic Sensor ◽  
Sensor System ◽  
Motion Control System ◽  
Speed Sensor ◽  
Working Space

The article deals with the development of a high-speed sensor system for a mobile robot, used in conjunction with an intelligent method of planning trajectories in conditions of high dynamism of the working space.

scholarly journals Slipping–rolling transitions of a body with two contact points

2021 ◽  
Author(s):  
Mate Antali ◽  
Gabor Stepan
Keyword(s):  
Rigid Body ◽  
Contact Point ◽  
Static Friction ◽  
Rigid Body Dynamics ◽  
Contact Forces ◽  
Friction Forces ◽  
Contact Points ◽  
Body Dynamics ◽  
Coulomb Model ◽  
Rigid Surfaces

AbstractIn this paper, the general kinematics and dynamics of a rigid body is analysed, which is in contact with two rigid surfaces in the presence of dry friction. Due to the rolling or slipping state at each contact point, four kinematic scenarios occur. In the two-point rolling case, the contact forces are undetermined; consequently, the condition of the static friction forces cannot be checked from the Coulomb model to decide whether two-point rolling is possible. However, this issue can be resolved within the scope of rigid body dynamics by analysing the nonsmooth vector field of the system at the possible transitions between slipping and rolling. Based on the concept of limit directions of codimension-2 discontinuities, a method is presented to determine the conditions when the two-point rolling is realizable without slipping.

The Determination of Maximum Range for an Unpowered Atmospheric Vehicle

1964 ◽  
Vol 68 (638) ◽  
pp. 111-116 ◽  
Author(s):  
D. J. Bell
Keyword(s):  
Calculus Of Variations ◽  
Lagrange Multipliers ◽  
Digital Computer ◽  
Necessary Conditions ◽  
Lagrange Equations ◽  
Initial Portion ◽  
End Conditions ◽  
Maximum Range ◽  
Isothermal Atmosphere

SummaryThe problem of maximising the range of a given unpowered, air-launched vehicle is formed as one of Mayer type in the calculus of variations. Eulers’ necessary conditions for the existence of an extremal are stated together with the natural end conditions. The problem reduces to finding the incidence programme which will give the greatest range.The vehicle is assumed to be an air-to-ground, winged unpowered vehicle flying in an isothermal atmosphere above a flat earth. It is also assumed to be a point mass acted upon by the forces of lift, drag and weight. The acceleration due to gravity is assumed constant.The fundamental constraints of the problem and the Euler-Lagrange equations are programmed for an automatic digital computer. By considering the Lagrange multipliers involved in the problem a method of search is devised based on finding flight paths with maximum range for specified final velocities. It is shown that this method leads to trajectories which are sufficiently close to the “best” trajectory for most practical purposes.It is concluded that such a method is practical and is particularly useful in obtaining the optimum incidence programme during the initial portion of the flight path.

A Model Improvement of a Supercritical Unit Coordination Control System

2013 ◽  
Vol 680 ◽  
pp. 488-494
Author(s):  
Hai Ming Niu ◽  
Zhong Xu Han ◽  
Huan Pao Huang ◽  
Hong Min Zhang
Keyword(s):  
Mathematical Model ◽  
Control System ◽  
Coordinated Control ◽  
Coordination Control ◽  
Model Improvement ◽  
Unit Coordination ◽  
The Mathematical Model ◽  
Controlled Object

Base on the mathematical model of a common coordinated control system in field of thermal, by analyzing characteristics of the controlled object supercritical once-through boiler coordinated control system, the article puts forward suggestions for improvement, and verifies the results of the analysis by test.

The Control of Vibration Transmissibility Using an Electrodynamic Actuator –Close-Loop Solution

2013 ◽  
Vol 436 ◽  
pp. 166-173
Author(s):  
A. Mihaela Mîţiu ◽  
Daniel Constantin Comeagă ◽  
Octavian G. Donţu
Keyword(s):  
Mathematical Model ◽  
Control System ◽  
Mechanical System ◽  
Closed Loop ◽  
Mechanical Systems ◽  
Vibration Transmissibility ◽  
Technical Solutions ◽  
The Mathematical Model

In this paper are presented some aspects of transmissibility control of mechanical systems with 1 DOF so that the effects of vibration on their action to be minimized. Some technical solutions that can be used for this purpose is analyzed. Starting from the mathematical model of an electro-mechanical system with 1 DOF, are identified the parameters which influence the effectiveness of the transmissibility control system using an electrodynamic actuator who work in "closed loop".

An Experimental Study of Tendon Vibration Control System for Flexible Space Structures

1991 ◽  
Author(s):  
Yoshisada Murotsu ◽  
Hiroshi Okubo ◽  
Kei Senda
Keyword(s):  
Mathematical Model ◽  
Control System ◽  
Vibration Control ◽  
Transfer Functions ◽  
Mimo Systems ◽  
Experimental System ◽  
Space Structures ◽  
Flexible Beam ◽  
Tendon Vibration ◽  
Large Space

Abstract The idea of a tendon vibration control system for a beam-like flexible space structure has been proposed. To verify the feasibility of the concept, an experimental tendon control system has been constructed for the vibration control of a flexible beam simulating Large Space Structures (LSS). This paper discusses modeling, identification, actuator disposition, and controller design for the experimental system. First, a mathematical model of the whole system of the beam and tendon actuator is developed through a finite element method (FEM). Second, to obtain an accurate mathematical model for designing a controller, unknown characteristic parameters are estimated by using an output error method. The validity of the proposed identification scheme is demonstrated by good agreement between the transfer functions of the experimental system and an identified model. Then, disposition of actuators is discussed by using the modal cost analysis. Finally, controllers are designed for SISO and MIMO systems. The feasibility of the proposed controller is verified through numerical simulation and hardware experiments.

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