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.

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.

Optimal Stabling of Attitude Maneuver for a Special Satellite With Reaction Wheel Actuators

2010 ◽  
Author(s):  
Seyed Hasan Miri Roknabadi ◽  
Mohamad Fakhari Mehrjardi ◽  
Mehran Mirshams
Keyword(s):  
Attitude Control ◽  
Equations Of Motion ◽  
Low Energy ◽  
Dynamic Equations ◽  
Satellite Motion ◽  
Reaction Wheel ◽  
State Equations ◽  
Time Consumption ◽  
Attitude Maneuver ◽  
Simulation Results

This paper presents an optimal attitude maneuver by Reaction Wheels to achieve desired attitude for a Satellite. At first, Dynamic Equations of motion for a satellite with just three Reaction Wheels of its active actuators are educed, and then State Equations of this system are obtained. An optimal attitude control with the LQR method has exerted for a distinct satellite by its Reaction Wheels. As a result simulation has presented an optimal effort by calculated Gain matrix to achieve desired attitude for chosen Satellite. It shows that satellite becomes stable in desired attitude with a low energy and time consumption. Furthermore equations derivation, coupling of electrical Reaction Wheel equations with dynamic equations of satellite motion, linearizes them and Reaction wheel saturation avoidance approaches are innovative. Simulation results, accuracy of achieving desired attitude and satellite stability support this statement.

Optimal Control of an Assisted Passive Snake-Like Robot Using Feedback Linearization

2007 ◽  
Author(s):  
Saman Mohammadi ◽  
Zoya Heidari ◽  
Hojjat Pendar ◽  
Aria Alasty ◽  
Gholamreza Vossoughi
Keyword(s):  
Optimal Control ◽  
Nonlinear System ◽  
Nonlinear Control ◽  
Feedback Linearization ◽  
Equations Of Motion ◽  
Dynamic Equations ◽  
Unmodeled Dynamics ◽  
Pd Controller ◽  
Simulation Results ◽  
Distinct Line

In this paper we follow two approaches in optimal nonlinear control of a snake-like robot. After deriving the dynamic equations of motion using Gibbs-Appell method, reducing these equations, and some assumptions, feedbacklinearization method was used to linearize the nonlinear system. The obtained controller is used in simulations to control robot to track a desired line, with minimum required torques. Two goals are desired. First the robot’s head is expected to track a distinct line with a given speed. And next, tracking the serpenoid curve is desired. The simulation results prove the controller efficiency. The robustness of the designed controller is shown by comparing the torques with the required torques using a PD controller. Additionally, although we had model mismatches and unmodeled dynamics in controller part, we achieved the desired goals.

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.

Cooperative parameter estimation of a nonuniform payload by multiple quadrotors

Robotica ◽  
2021 ◽  
pp. 1-20
Author(s):  
Farhad Arab ◽  
Farzad A. Shirazi ◽  
Mohammad Reza Hairi Yazdi
Keyword(s):  
Attitude Control ◽  
Equations Of Motion ◽  
Estimation Algorithm ◽  
Adaptive Controller ◽  
Dynamic Equations ◽  
Physical Parameters ◽  
Constraint Forces ◽  
Outer Loop ◽  
Simulation Results

Abstract Thispaper addresses the problem of carrying an unknown nonuniform payload by multiple quadrotor agents. The load is modeled as a rigid body with unknown weight and position of Center of Gravity (CG) for the agents, and is included in their dynamic equations of motion. The agents and the load are assumed to be connected to each other by taut ropes. The Udwadia–Kalaba equation is used to calculate the constraint forces on the ropes acting on each quadrotor. Inner-loop and outer-loop controllers for quadrotors position and attitude control are presented. For the outer loop, an estimation algorithm based on the invariance and immersion adaptive control is utilized to estimate the unknown physical parameters of the payload including mass and CG position without using multi-axes force/torque sensors. The inner-loop controller employs an adaptive controller. Simulation results, for two and four agents carrying a nonuniform rod and cubic payload, show the effectiveness of the proposed algorithm. A case study is also performed to investigate the effect of quadrotors positioning on flight endurance of the cooperative aerial team carrying a nonuniform payload.

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.

Application of the Maggi Equations to Mathematical Modeling of a Robotic Underwater Vehicle as an Object with Superimposed Non-Holonomic Constraints Treated as Control Laws

2011 ◽  
Vol 180 ◽  
pp. 152-159 ◽  
Author(s):  
Edyta Ladyżyńska-Kozdraś
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Equations Of Motion ◽  
Underwater Vehicle ◽  
Dynamic Equations ◽  
Control Laws ◽  
Holonomic Constraints ◽  
Coupling Dynamics ◽  
Controlled Object

Based on torpedoes, a universal mathematical model of a robotic underwater vehicle comprising coupling dynamics of a controlled object with superimposed guidance has been built. Using control laws as kinematic correlation of deviation from pre-defined parameters of ideal control, the control laws have been tied to the dynamic equations of motion.

scholarly journals Simulation and Nonlinearity Optimization of a High-Pressure Sensor

Sensors ◽  
2020 ◽  
Vol 20 (16) ◽  
pp. 4419
Author(s):  
Ting Li ◽  
Haiping Shang ◽  
Weibing Wang
Keyword(s):  
High Pressure ◽  
Pressure Sensor ◽  
Pressure Sensors ◽  
Original Model ◽  
Ansys Software ◽  
Nonlinear Error ◽  
Sensor Model ◽  
Optimized Model ◽  
Simulation Results ◽  
Better Than

A pressure sensor in the range of 0–120 MPa with a square diaphragm was designed and fabricated, which was isolated by the oil-filled package. The nonlinearity of the device without circuit compensation is better than 0.4%, and the accuracy is 0.43%. This sensor model was simulated by ANSYS software. Based on this model, we simulated the output voltage and nonlinearity when piezoresistors locations change. The simulation results showed that as the stress of the longitudinal resistor (RL) was increased compared to the transverse resistor (RT), the nonlinear error of the pressure sensor would first decrease to about 0 and then increase. The theoretical calculation and mathematical fitting were given to this phenomenon. Based on this discovery, a method for optimizing the nonlinearity of high-pressure sensors while ensuring the maximum sensitivity was proposed. In the simulation, the output of the optimized model had a significant improvement over the original model, and the nonlinear error significantly decreased from 0.106% to 0.0000713%.

Dynamics Simulation and Analysis of Transition Stage of Tilt-Rotor Aircraft

2016 ◽  
Vol 842 ◽  
pp. 251-258 ◽  
Author(s):  
Muhammad Rafi Hadytama ◽  
Rianto A. Sasongko
Keyword(s):  
Dynamic Response ◽  
Equations Of Motion ◽  
Flight Dynamics ◽  
Dynamics Simulation ◽  
Tilt Rotor ◽  
Vertical Takeoff And Landing ◽  
Improved Stability ◽  
Simulation Results ◽  
Vtol Aircraft ◽  
Vertical Takeoff

This paper presents the flight dynamics simulation and analysis of a tilt-rotor vertical takeoff and landing (VTOL) aircraft on transition phase, that is conversion from vertical or hover to horizontal or level flight and vice versa. The model of the aircraft is derived from simplified equations of motion comprising the forces and moments working on the aircraft in the airplane's longitudinal plane of motion. This study focuses on the problem of the airplane's dynamic response during conversion phase, which gives an understanding about the flight characteristics of the vehicle. The understanding about the flight dynamics characteristics is important for the control system design phase. Some simulation results are given to provide better visualization about the behaviour of the tilt-rotor. The simulation results show that both transition phases are quite stable, although an improved stability can give better manoeuver and attitude handling. Improvement on the simulation model is also required to provide more accurate and realistic dynamic response of the vehicle.

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