Mobile Robots Characterized by Kinematic and Dynamic Equations: Motion Planning, Trajectory Tracking, and Group Control

2008 ◽  
Author(s):  
Amit Ailon
Keyword(s):  
Mathematical Model ◽  
Motion Planning ◽  
Mobile Robots ◽  
Dynamic Equations ◽  
Kinematics And Dynamics ◽  
Control Problems ◽  
Reference Trajectory ◽  
Numerical Examples ◽  
Group Control ◽  
The Mathematical Model

The paper solves some control problems of mobile robots as both kinematics and dynamics are intertwined in the mathematical model. The problems of driving the vehicle to a desired configuration in a specified time and tracking a reference trajectory are considered. The control problems associated with motion in convoy and rigid formations of a group of vehicles are studied and some results are demonstrated by numerical examples.

Dynamic Analysis on a Cable-Driven Interventional Active Catheter Using Kane's Method Combined with Screw Theory

2014 ◽  
Vol 527 ◽  
pp. 140-145
Author(s):  
Da Xu Zhao ◽  
Bai Chen ◽  
Guo Zhong Shou ◽  
Yu Qi Gu
Keyword(s):  
Mathematical Model ◽  
Dynamic Analysis ◽  
Motion Control ◽  
Screw Theory ◽  
Driving Forces ◽  
Structure Design ◽  
Kinematics And Dynamics ◽  
Existing Problems ◽  
Blind Area ◽  
The Mathematical Model

In view of the existing problems of traditional interventional catheters, particularly poor activity, operation difficulty and mass blind area, a novel interventional catheter with a cable-driven active head-end is proposed, and a prototype was built to verify the performance. This paper deals with the kinematics and dynamics of the cable-driven prototype, a dynamic model based on Kanes method combined with screw theory was presented in this paper. According the mathematical model and the prototypes structure, the analysis of kinematics and dynamics of active head-end-end is done in the environment of Mathematica. The needed driving forces of every joint when the system moving along planned trajectory are calculated. The results can provide a basis for the structure design and motion control of the interventional active catheter.

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.

Modeling and Analyses of the N-Link Bent-Arm PenduBot

2010 ◽  
Vol 171-172 ◽  
pp. 644-647
Author(s):  
Shao Qiang Yuan ◽  
Xin Xin Li
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Nonlinear Model ◽  
Condition Number ◽  
Kinematics And Dynamics ◽  
Controllability Matrix ◽  
Human Arm ◽  
The World ◽  
The Mathematical Model ◽  
Natural Characteristics

Bent-arm PenduBot is more similar to human arm, which attaches more and more robot experts’ attention around the world. As the foundation of the multi-link PenduBot control, the mathematical model should be established first. Based on the method of kinematics and dynamics, the N-link bent-arm PenduBot mathematical models are established in this paper, including the nonlinear model and the linear model. The natural characteristics of different pendulum are analyzed. By using the condition number of the controllability matrix, the control difficulty for higher order systems is compared.

A Study of the Effects of Baffles on Rotating Compressible Flows

1989 ◽  
Vol 56 (3) ◽  
pp. 710-712
Author(s):  
Max D. Gunzburger ◽  
Houston G. Wood ◽  
Rosser L. Wayland
Keyword(s):  
Fluid Dynamics ◽  
Mathematical Model ◽  
Compressible Flows ◽  
Numerical Examples ◽  
Thermal Boundary Conditions ◽  
Gas Centrifuge ◽  
Mass Injection ◽  
Flow Domain ◽  
The Mathematical Model ◽  
Element Algorithm

Onsager’s pancake equation for the fluid dynamics of a gas centrifuge is modified for the case of centrifuges with baffles which render the flow domain doubly connected. A finite element algorithm is used for solving the mathematical model and to compute numerical examples for flow fields induced by thermal boundary conditions and by mass injection and extraction.

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.

Dynamics of a Rolling Wheelset

1993 ◽  
Vol 46 (7) ◽  
pp. 438-444 ◽  
Author(s):  
Hans True
Keyword(s):  
Mathematical Model ◽  
Equilibrium Point ◽  
Chaotic Motion ◽  
Dynamical Behavior ◽  
Railway Track ◽  
Kinematics And Dynamics ◽  
Bifurcation Diagrams ◽  
Speed Range ◽  
Set Up ◽  
The Mathematical Model

We discuss the kinematics and dynamics of a wheelset rolling on a railway track. The mathematical model of a suspended wheelset rolling with constant speed on a straight track is set up and its dynamics is investigated numerically. The results are presented mainly on bifurcation diagrams. Several kinds of dynamical behavior is identified within the investigated speed range. We find a stationary equilibrium point at low speeds and at higher speeds symmetric and asymmetric oscillations are found and ranges with chaotic motion are identified. The bifurcations are described.

Kinematics and Dynamics Analysis of a Micro-Robotic Platform Driven by Inertial-Force Propulsion

2015 ◽  
Vol 733 ◽  
pp. 531-534
Author(s):  
Qing Ming Wang ◽  
Wu Ming Zhang ◽  
Jia Chen Ju
Keyword(s):  
Mathematical Model ◽  
Angular Velocity ◽  
Inertial Force ◽  
Displacement Velocity ◽  
Kinematics And Dynamics ◽  
Dynamics Analysis ◽  
Robotic Platform ◽  
The Mathematical Model

In this paper, we make the kinematics and dynamics analysis of a micro-robotic platform [3] driven by inertial force generated by eccentric masses. We establish the mathematical model and get the displacement, velocity and acceleration relationships of the platform. According to movement and stability requirements of the micro-robotic platform, we get a conclusion that the minimum angular velocity of the motor when the platform moves and the maximum angular velocity of the motor when the platform jumps.

Verification of the Mathematical Model for an Underwater Crawler Robot

2016 ◽  
Vol 817 ◽  
pp. 223-233
Author(s):  
Krzysztof Kurc ◽  
Dariusz Szybicki
Keyword(s):  
Mathematical Model ◽  
Water Supply ◽  
Cross Sections ◽  
Structural Model ◽  
Virtual Prototyping ◽  
Real Object ◽  
Design Stage ◽  
Kinematics And Dynamics ◽  
The Mathematical Model

This paper presents the mathematical and structural model as well as the verificationof a designed and built underwater crawler robot. The underwater crawler robot is designed to inspect elements of the water supply infrastructure, including pools, reservoirs and pipelines with round or square cross-sections. 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. The mathematical model was used for a number of simulations and subjected to verification on a real object in two test environments.

Compliant Five Bar Mechanism Control to Achieve a Desired Trajectory

2017 ◽  
Author(s):  
Ayse Tekes
Keyword(s):  
Mathematical Model ◽  
High Precision ◽  
Degrees Of Freedom ◽  
Controller Design ◽  
Path Tracking ◽  
Reference Trajectory ◽  
Compliant Joints ◽  
Torsional Spring ◽  
Short Beam ◽  
The Mathematical Model

In this study, two degrees of freedom planar compliant five-bar mechanism design is explored and synthesized to achieve a desired trajectory and to perform various defined tasks. The mechanism consists of five rigid links (including the ground) connected by the compliant large deflecting short beam joints and it is excited by the applied torques at the base links. The compliant five bar mechanism has not been explored in the literature for either a path tracking task or a function generation problem. The novelty of the compliant five bar mechanism presented in this paper is its large deflecting/rotating pivots joining the mechanism links. The mathematical model of the compliant five-bar mechanism is derived by using vector loop closures and dynamic inertia equations of the mechanism links. The dynamic response of the mechanism is investigated under the applied torques to the corresponding base links, using numerical 4th order Runge-Kutta methods. Compliant joints are represented by their equivalent torsional spring parameters so that the nonlinear large deflection equations of short beam joints are eliminated from the kinematic equations of the system using its equivalent Pseudo Rigid Body Model (PRBM). The torsional spring constants can be obtained, either by using nonlinear exact mathematical equations or by using geometrically nonlinear Finite Element Method software. The scope of this research is to derive a mathematical model of the system and to analyze the compliant five bar mechanism including the controller design for arbitrary predefined tasks to achieve the desired path for the end effector. The compliant five-bar mechanisms are superior to traditional rigid five-bar mechanisms in high precision tasks since compliant joints and links have no backlash and friction. This study explores path generation of compliant five bar mechanism resulting in high precision path tracking. The presented mechanism might be manufactured as a single piece using an injection molding technique or 3D printing by polypropylene and it is also suitable for a fully compliant Micro Electro Mechanical System fabrication. The mathematical model of the mechanism is validated by utilizing inverse-forward dynamic model. The tip point of the mechanism successfully follows the reference trajectory by employing model based PID controller.

scholarly journals Coordinating a three level supply chain with multiple retailers

2021 ◽  
Author(s):  
Shahzad Naqvi
Keyword(s):  
Mathematical Model ◽  
Supply Chain ◽  
Supply Chain Coordination ◽  
Research Work ◽  
The Other ◽  
Total Cost ◽  
Numerical Examples ◽  
Conflicting Interests ◽  
Order Quantities ◽  
The Mathematical Model

The objective of this research is to highlight the factors that can optimize the total cost of a centralized supply chain through coordination of order quantities amongst the players in a supply chain. Survey of earlier research reveals that players in a supply chain usually have conflicting interests, such as reducing inventories and increasing profitability. Thus, to make coordination feasible, it is essential to provide proper incentives to individual players. Munson and Rosenblatt (2001) were the first to discuss coordination in a three level supply chain with a single player at each level. On the other hand, Viswanathan and Piplani (2001) are believed to be the first to consider cooordination in a two level supply chain with a single vendor and multiple retailers. This research extends upon these works by investigating coordination in a three level supply chain with multiple retailers. This is done by incorporating the model of Viswanathan and Piplani (2001) into that of Munson and Rosenblatt (2001). A new mathematical model is developed, with numerical examples presented and results discussed. When players in a supply chain agree to coordinate, it is possible to have some of the players benefiting more than others in the chain, if not losing. The mathematical model developed in this research work guarantees that the local costs for the players either remain the same as before coordination, or decrease as a result of coordination. Furthermore, this research work assumes that savings generated from coordination should be distributed among the players of the chain. This led to developing a scheme to fairly distribute savings amongst the players of the supply chain. Results indicate that even though players may have conflicting interests in the supply chain, coordination is recommended and should be pursued.

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