Simulation Study of a Spherical Inverted Pendulum on an Omnidirectional Cart With Holonomic Constraints

2018 ◽  
Author(s):  
Sayani Maity ◽  
Greg R. Luecke
Keyword(s):  
Experimental Data ◽  
Horizontal Plane ◽  
Inverted Pendulum ◽  
Vertical Axis ◽  
Dynamic Equations ◽  
Spherical Pendulum ◽  
Holonomic Constraints ◽  
One Dimensional ◽  
Lqr Controller ◽  
Simulation Results

In this paper we develop the control and stabilization of a spherical jointed inverted pendulum balanced on an omnidirectional cart. The system consists of an omnidirectional cart with mecanum wheels equipped with a spherical inverted pendulum attached at the center of the platform. The inverted pendulum is free to fall in any direction perpendicular to the horizontal plane. The omnidirectional cart has the special ability to move in any direction without changing orientation. It can also rotate around its vertical axis. This balancing platform provides a base with holonomic motion to support and balance the pendulum. In this work, the system has been decoupled into two separate subsystems in the x-z and y-z plane. We develop the system dynamic equations in both vertical planes and design a LQR controller to stabilize the system. Using one-dimensional pendulum experimental data, we validate our controller and extend the approach to stabilize the spherical pendulum in both vertical directions. Simulation results are presented to show the effectiveness of the decoupled system LQR controller in stabilizing the spherical pendulum.

scholarly journals Design and simulate of LQR-Fuzzy controller for unicycle robot with double flywheels

2018 ◽  
Vol 192 ◽  
pp. 02001 ◽  
Author(s):  
Surachat Chantarachit
Keyword(s):  
Angular Momentum ◽  
Inverted Pendulum ◽  
Fuzzy Controller ◽  
Taylor Series Expansion ◽  
Lagrange Equations ◽  
Main Structure ◽  
Structure Control ◽  
Controller Gain ◽  
Lqr Controller ◽  
Simulation Results

This research is focus on design and simulate unicycle robot with double flywheels model with LQR-Fuzzy controller. Roll balancing torque is generated by gyroscopic effect. Pitch balancing torque is applied by inverted pendulum concept. To control the heading of the robot, the angular momentum from both flywheel is applied to control this. The robot model is based on Euler-Lagrange equations. The non-linear model is linearization by Taylor series expansion. The simulation results conducted by MATLAB/Simulink. LQR-Fuzzy is combination algorithm between LQR and Fuzzy controller. The main structure control is the LQR controller and use the Fuzzy controller to adjust the close loop controller gain. The simulation results is simulated and compared with conventional LQR.

General Equations of a Helical Spring With a Cup Damper and Static Verification

1997 ◽  
Vol 119 (2) ◽  
pp. 319-326 ◽  
Author(s):  
Ming Hsun Wu ◽  
Jing Yuan Ho ◽  
Wensyang Hsu
Keyword(s):  
Experimental Data ◽  
Pitch Angle ◽  
Equations Of Motion ◽  
Maximum Error ◽  
Dynamic Equations ◽  
Helical Spring ◽  
Static Force ◽  
Static Verification ◽  
Simulation Results ◽  
Force Displacement

In this study, we derive the general equations of motion for the helical spring with a cup damper by considering the damper’s dilation and varying pitch angle of the helical spring. These dynamic equations are simplified to correlate with previous models. The static force-displacement relation is also derived. The extra stiffness due to the damper’s dilation considered in the force-displacement relation is the first such modeling in this area. In addition, a method is presented to predict the compressing spring’s coil close length and is then verified by experimental data. Moreover, the simulation results of the static force-displacement relation are found to correspond to the experimental data. The maximum error is around 0.6 percent.

Conception and Dynamic Modeling of an Assisted Passive Snake-Like Robot Using Gibbs-Appell Method

2005 ◽  
Author(s):  
Golamreza Vossoughi ◽  
Hodjat Pendar ◽  
Zoya Heidari ◽  
Saman Mohammadi
Keyword(s):  
Limit Cycle ◽  
Dynamic Modeling ◽  
Initial Conditions ◽  
Kinematic Model ◽  
Dynamic Equations ◽  
Joint Angles ◽  
Holonomic Constraints ◽  
Time Simulation ◽  
Simulation Results ◽  
Simulation Time

In this paper we present a novel planar structure of a snake-like robot. This structure enables passive locomotion in snake-like robots through an auxiliary link in joint and a torsional spring. Dynamic equations are derived, using Gibbs-Appell method. Kinematic model of the robot include numerous non-holonomic constraints, which can be omitted at the beginning by choosing proper coordinates to describe the model in Gibbs-Appell framework. In such a case, dynamic equations will be significantly simplified, resulting in significant reduction of simulation time. Simulation results show that, by proper selecting initial conditions, joint angles operate in a limit cycle and robot can locomote steadily on a passive trajectory. It can be seen that the passive trajectory is approximately a Serpenoid curve.

Euler–Lagrange as Pseudo-metric of the RRT algorithm for optimal-time trajectory of flight simulation model in high-density obstacle environment

Robotica ◽  
2015 ◽  
Vol 35 (5) ◽  
pp. 1138-1156 ◽  
Author(s):  
Mohammad Altaher ◽  
Omaima Nomir
Keyword(s):  
Equations Of Motion ◽  
Flight Simulation ◽  
Dynamic Equations ◽  
Optimal Time ◽  
Holonomic Constraints ◽  
Lagrange Formula ◽  
Path Constraints ◽  
Optimized Model ◽  
Simulation Results ◽  
Path Constraint

SUMMARYThis paper introduces a solution to the problem of steering an aerodynamical system, with non-holonomic constraints superimposed on dynamic equations of motion. The proposed approach is a dimensionality reduction of the Optimal Control Problem (OCP) with heavy path constraints to be solved by Rapidly-Exploring Random Tree (RRT) algorithm. In this research, we formulated and solved the OCP with Euler–Lagrange formula in order to find the optimal-time trajectory. The RRT constructs a non-collision path in static, high-dense obstacle environment (i.e. heavy path constraint). Based on a real-world aircraft model, our simulation results found the collision-free path and gave improvements of time and fuel consumption of the optimized Hamiltonian-based model over the original non-optimized model.

Design of LQR Controller for the Inverted Pendulum

2014 ◽  
Vol 1037 ◽  
pp. 221-224
Author(s):  
Li Li Wan ◽  
Juan Lei ◽  
Hong Xia Wu
Keyword(s):  
Optimal Control ◽  
Basic Principle ◽  
Control Algorithm ◽  
Inverted Pendulum ◽  
Stability Control ◽  
Good Effect ◽  
Lqr Controller ◽  
Simulation Results

For the instability of the inverted pendulum, a LQR controller is designed based on optimal control algorithm in this paper, which can control the pendulum angle and the cart position at the same time. The basic principle of LQR optimal control is analyzed and the LQR controller is designed and simulated in this paper. The simulation results show that the designed controller is effective. It has a good effect of equilibrium and stability control, and the system's anti-interference ability is improved.

scholarly journals Simulation of Hall field elements based on nanoscale silicon-on-insulator heterostructures

2020 ◽  
Vol 23 (2) ◽  
pp. 109-115
Author(s):  
V. N. Mordkovich ◽  
K. K. Abgaryan ◽  
D. L. Reviznikov ◽  
A. V. Leonov
Keyword(s):  
Experimental Data ◽  
Numerical Simulation ◽  
Multivariate Analysis ◽  
Silicon On Insulator ◽  
One Dimensional ◽  
Poisson Equations ◽  
Simulation Results ◽  
Current Characteristics ◽  
Hall Sensors ◽  
Good Agreement

The article is devoted to the issues of numerical simulation of field Hall sensors based on the "silicon on insulator" structure with two control gates. To solve the problem, a two-level local-one-dimensional computational model is used. At the first level, a series of one-dimensional Schrödinger—Poisson equations are solved, which describe the distribution of the electron density across the heterostructure in different sections. The obtained information is transmitted to the second level, where the current characteristics of the element are calculated. The numerical simulation results are compared with the experimental data obtained for field Hall sensors. Comparative analysis shows good agreement between calculated and experimental data. The developed computer model makes it possible to carry out a multivariate analysis of various heterostructures, which creates the basis for optimizing devices of the class under consideration.

BEHAVIORAL MODEL OF A LINEAR VOLTAGE STABILIZER IN THE SPICE LANGUAGE

2019 ◽  
Author(s):  
Aleksey Malahanov
Keyword(s):  
Experimental Data ◽  
Behavioral Model ◽  
Voltage Stabilizer ◽  
Static Mode ◽  
Technical Description ◽  
Simulation Results ◽  
Chip Manufacturer ◽  
Linear Voltage

A variant of the implementation of the behavioral model of a linear voltage stabilizer in the Spice language is presented. The results of modeling in static mode are presented. The simulation results are compared with experimental data and technical description of the chip manufacturer.

scholarly journals Realization of a fractional-order RLC circuit via constant phase element

2021 ◽  
Author(s):  
Riccardo Caponetto ◽  
Salvatore Graziani ◽  
Emanuele Murgano
Keyword(s):  
Experimental Data ◽  
Carbon Black ◽  
Fractional Order ◽  
Constant Phase Element ◽  
Polymeric Matrix ◽  
Fractional Order Systems ◽  
New Device ◽  
Rlc Circuit ◽  
Simulation Results

AbstractIn the paper, a fractional-order RLC circuit is presented. The circuit is realized by using a fractional-order capacitor. This is realized by using carbon black dispersed in a polymeric matrix. Simulation results are compared with the experimental data, confirming the suitability of applying this new device in the circuital implementation of fractional-order systems.

scholarly journals Investigation of the Thickness Differential on the Formability of Aluminum Tailor Welded Blanks

Metals ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 875
Author(s):  
Jie Wu ◽  
Yuri Hovanski ◽  
Michael Miles
Keyword(s):  
Experimental Data ◽  
Finite Element ◽  
Numerical Model ◽  
Plastic Strain ◽  
Finite Element Model ◽  
Equivalent Plastic Strain ◽  
Element Model ◽  
Dome Height ◽  
Tailor Welded Blanks ◽  
Simulation Results

A finite element model is proposed to investigate the effect of thickness differential on Limiting Dome Height (LDH) testing of aluminum tailor-welded blanks. The numerical model is validated via comparison of the equivalent plastic strain and displacement distribution between the simulation results and the experimental data. The normalized equivalent plastic strain and normalized LDH values are proposed as a means of quantifying the influence of thickness differential for a variety of different ratios. Increasing thickness differential was found to decrease the normalized equivalent plastic strain and normalized LDH values, this providing an evaluation of blank formability.

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