Velocity Control of a Cylindrical Rolling Robot by Surface-Morphing

2015 ◽  
Author(s):  
Michael Puopolo ◽  
J. D. Jacob
Keyword(s):  
Mathematical Model ◽  
Angular Velocity ◽  
Velocity Profile ◽  
Average Velocity ◽  
Equations Of Motion ◽  
Angular Position ◽  
Velocity Control ◽  
Control Scheme ◽  
Rolling Robot ◽  
Angular Velocity Profile

A mathematical model is developed for a rolling robot with a cylindrically-shaped, elliptical outer surface that has the ability to alter its shape as it rolls, resulting in a torque imbalance that accelerates or decelerates the robot. A control scheme is implemented, whereby angular position and angular velocity are used as feedback to trigger and define morphing actuation. The goal of the control is to direct the robot to follow a given angular velocity profile. Equations of motion for the rolling robot are formulated and solved numerically. Results show that by automatically morphing its shape in a periodic fashion, the rolling robot is able to start from rest, achieve constant average velocity and slow itself in order to follow a desired velocity profile with significant accuracy.

scholarly journals Locomotion of a Cylindrical Rolling Robot with a Shape Changing Outer Surface

Robotics ◽  
2018 ◽  
Vol 7 (3) ◽  
pp. 52 ◽  
Author(s):  
Michael Puopolo ◽  
Jamey Jacob ◽  
Emilio Gabino
Keyword(s):  
Mathematical Model ◽  
Angular Velocity ◽  
Outer Surface ◽  
Shape Change ◽  
Angular Position ◽  
Low Energy ◽  
Roll Torque ◽  
Low Energy Consumption ◽  
Rolling Robot ◽  
Angular Velocity Profile

A cylindrical rolling robot is developed that generates roll torque by changing the shape of its flexible, elliptical outer surface whenever one of four elliptical axes rotates past an inclination called trigger angle. The robot is equipped with a sensing/control system by which it measures angular position and angular velocity, and computes error with respect to a desired step angular velocity profile. When shape change is triggered, the newly assumed shape of the outer surface is determined according to the computed error. A series of trial rolls is conducted using various trigger angles, and energy consumed by the actuation motor per unit roll distance is measured. Results show that, for each of three desired velocity profiles investigated, there exists a range of trigger angles that results in relatively low energy consumption per unit roll distance, and when the robot operates within this optimal trigger angle range, it undergoes minimal actuation burdening and inadvertent braking, both of which are inherent to the mechanics of rolling robots that use shape change to generate roll torque. A mathematical model of motion is developed and applied in a simulation program that can be used to predict and further understand behavior of the robot.

Tracking Control of a Software Cam Machining System

1999 ◽  
Vol 121 (4) ◽  
pp. 729-735 ◽  
Author(s):  
Mi-Ching Tsai ◽  
Yaw-Hwei Lee
Keyword(s):  
Control System ◽  
Angular Velocity ◽  
Velocity Profile ◽  
Tracking Control ◽  
Contact Point ◽  
Tangential Velocity ◽  
Position Tracking ◽  
Servo Motor ◽  
Cam Profile ◽  
Angular Velocity Profile

This paper presents a software cam manufacturing system. It includes a position tracking control system, a programmable cam profile, and a programmable variable angular velocity profile. The position tracking system consists of a rotary direct drive (DD) servo motor and a linear servo-motor. The rotary DD servo-motor is controlled to track the variable angular velocity profile, while the linear servo-motor is controlled to synchronously track the desired cam profile. Such a tracking control system is proposed to achieve a constant removal rate for fine machining (i.e., the relative tangential velocity at the contact point should be constant). A numerical method for off-line derivation of the variable angular velocity profile with respect to the desired cam profile is developed to achieve constant relative tangential velocity at the contact point. An experimental tracking control system with two servo controllers is developed to study the feasibility of this approach.

scholarly journals Simulated Sensor Based Strategies for Obstacle Avoidance Using Velocity Profiling for Autonomous Vehicle FURBOT

Electronics ◽  
2020 ◽  
Vol 9 (6) ◽  
pp. 883 ◽  
Author(s):  
Khayyam Masood ◽  
Rezia Molfino ◽  
Matteo Zoppi
Keyword(s):  
Mathematical Model ◽  
Velocity Profile ◽  
Obstacle Avoidance ◽  
Autonomous Vehicle ◽  
Velocity Control ◽  
Steering Control ◽  
Traffic Lights ◽  
Simulated Environment ◽  
Last Mile ◽  
Robotic Vehicle

Freight Urban Robotic Vehicle (FURBOT) is an autonomous vehicle designed to transport last mile freight to designated urban stations. It is a slow vehicle designed to tackle urban environment with complete autonomy. A slow vehicle may have slightly different strategies for avoiding obstacles. Unlike on a highway, it has to deal with pedestrians, traffic lights and slower vehicles while maintaining smoothness in its drive. To tackle obstacle avoidance for this vehicle, sensor feedback based strategies have been formulated for smooth drive and obstacle avoidance. A full mathematical model for the vehicle is formulated and simulated in MATLAB environment. The mathematical model uses velocity control for obstacle avoidance without steering control. The obstacle avoidance is attained through velocity control and strategies are formulated with velocity profiling. Innovative techniques are formulated in creating the simulated sensory feed-backs of the environment. Using these feed-backs, correct velocity profiling is autonomously created for giving velocity profile input to the velocity controller. Proximity measurements are assumed to be available for the vehicle in its given range of drive. Novelty is attained by manipulating velocity profile without prior knowledge of the environment. Four different type of obstacles are modeled for simulated environment of the vehicle. These obstacles are randomly placed in the path of the vehicle and autonomous velocity profiling is verified in simulated environment. The simulated results obtained show satisfactory velocity profiling for controller input. The current technique helps to tune the existing controller and in designing of a better velocity controller for the autonomous vehicle and bridges the gap between sensor feed-back and controller input. Moreover, accurate input profiling creates less strain on the system and brings smoothness in drive for an overall safer environment.

Effect of gravity and angular velocity on an automatic ball balancer

2005 ◽  
Vol 219 (1) ◽  
pp. 43-51 ◽  
Author(s):  
J Chung
Keyword(s):  
Angular Velocity ◽  
Velocity Profile ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Angular Acceleration ◽  
Polar Coordinates ◽  
Lagrange’S Equation ◽  
Jeffcott Rotor ◽  
Analysis Of Results ◽  
Linear Equations Of Motion

The effects of gravity and an angular velocity profile on the performance of an automatic ball balancer (ABB) are studied in this paper. In order to investigate these effects, a physical model of a Jeffcott rotor with an ABB is adopted in this study, in which gravity as well as the angular acceleration is considered. With the polar coordinates, the non-linear equations of motion are derived by using Lagrange's equation. These equations include gravity, the angular acceleration, and the angular jerk. Based on the equations derived, time responses are computed by using the generalized α method. The effects of gravity on the balancing performance are analysed. For various angular velocity profiles, the ABB performance is also evaluated. The analysis of results shows that the balancing of the rotor with an ABB can be achieved regardless of gravity. It is also shown that a smooth velocity profile results in less vibration compared with a non-smooth velocity profile.

Application of Repetitive Control to a Peristaltic Pump

1994 ◽  
Vol 116 (4) ◽  
pp. 786-789 ◽  
Author(s):  
Gunnar Hillerstro¨m ◽  
Jan Sternby
Keyword(s):  
Angular Velocity ◽  
Sampling Rate ◽  
Repetitive Control ◽  
Peristaltic Pump ◽  
Time Varying ◽  
Velocity Control ◽  
Reduced Order ◽  
Control Scheme ◽  
Model Independent ◽  
Disturbance Model

The aim of this paper is to study angular velocity control of a rotating axis, a peristaltic pump where the disturbance is associated with certain angular positions. The use of constant sampling rate then implies varying disturbance period. A discrete repetitive control scheme based on a reduced order disturbance model tuned to the setpoint of the angular velocity is shown to reject the modeled disturbance with asymptotically zero error. With axis angle synchronization of sampling, the plant model is time-varying but it gives a static discrete disturbance model independent of the angular velocity. If the deviation from the nominal working point is not too large this is to prefer while it gives faster convergence.

scholarly journals Super-Twisting Algorithm Applied to Velocity Control of DC Motor without Mechanical Sensors Dependence

Energies ◽  
2020 ◽  
Vol 13 (22) ◽  
pp. 6041
Author(s):  
Fredy A. Valenzuela ◽  
Reymundo Ramírez ◽  
Fermín Martínez ◽  
Onofre A. Morfín ◽  
Carlos E. Castañeda
Keyword(s):  
Controller Design ◽  
Sliding Mode ◽  
Dc Motor ◽  
Experimental Results ◽  
Resistive Load ◽  
Velocity Control ◽  
Velocity Sensor ◽  
Control Scheme ◽  
Mechanical Sensors ◽  
Twisting Algorithm

A DC motor velocity control in feedback systems usually requires a velocity sensor, which increases the controller cost. Additionally, the velocity sensor used in industrial applications presents several disadvantages such as maintenance requirements and signal conditioning. In this work, we propose a robust velocity control scheme applied to a DC motor based on estimation strategies using a sliding-mode observer. This means that measurements with mechanical sensors are not required in the controller design. The proposed observer estimates the rotational velocity and load torque of the motor. The controller design applies the exact-linearization technique combined with the super-twisting algorithm to achieve robust performance in the closed-loop system. The controller validation was carried out by experimental tests using a workbench, which is composed of a control and data acquisition Digital Signal Proccessor board, a DC-DC electronic converter, an interface board for signals conditioning, and a DC electric generator connected to an adjustable resistive load. The simulation and experimental results show a significant performance of the proposed control scheme. During tests, the accuracy, robustness, and speed response on the controller were evaluated and the experimental results were compared with a classic proportional-integral controller, which uses a conventional encoder.

Numerical modelling of swirling momentumless turbulent wake dynamics

2018 ◽  
pp. 37-48
Author(s):  
Андрей Геннадьевич Деменков ◽  
Геннадий Георгиевич Черных
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Mathematical Models ◽  
Equations Of Motion ◽  
Turbulent Wake ◽  
The Body ◽  
Jet Flows ◽  
Reynolds Stresses ◽  
Bodies Of Revolution ◽  
Averaged Equations

С применением математической модели, включающей осредненные уравнения движения и дифференциальные уравнения переноса нормальных рейнольдсовых напряжений и скорости диссипации, выполнено численное моделирование эволюции безымпульсного закрученного турбулентного следа с ненулевым моментом количества движения за телом вращения. Получено, что начиная с расстояний порядка 1000 диаметров от тела течение становится автомодельным. На основе анализа результатов численных экспериментов построены упрощенные математические модели дальнего следа. Swirling turbulent jet flows are of interest in connection with the design and development of various energy and chemical-technological devices as well as both study of flow around bodies and solving problems of environmental hydrodynamics, etc. An interesting example of such a flow is a swirling turbulent wake behind bodies of revolution. Analysis of the known works on the numerical simulation of swirling turbulent wakes behind bodies of revolution indicates lack of knowledge on the dynamics of the momentumless swirling turbulent wake. A special case of the motion of a body with a propulsor whose thrust compensates the swirl is studied, but there is a nonzero integral swirl in the flow. In previous works with the participation of the authors, a numerical simulation of the initial stage of the evolution of a swirling momentumless turbulent wake based on a hierarchy of second-order mathematical models was performed. It is shown that a satisfactory agreement of the results of calculations with the available experimental data is possible only with the use of a mathematical model that includes the averaged equations of motion and differential equations for the transfer of normal Reynolds stresses along the rate of dissipation. In the present work, based on the above mentioned mathematical model, a numerical simulation of the evolution of a far momentumless swirling turbulent wake with a nonzero angular momentum behind the body of revolution is performed. It is shown that starting from distances of the order of 1000 diameters from the body the flow becomes self-similar. Based on the analysis of the results of numerical experiments, simplified mathematical models of the far wake are constructed. The authors dedicate this work to the blessed memory of Vladimir Alekseevich Kostomakha.

Design and Experimental Validation of a LQG Control System for the Stabilization of a 2DOF Commercial Gimbal Using Physical Modelling Techniques

2020 ◽  
Author(s):  
Julián Andres Gómez Gómez ◽  
Camilo E. Moncada Guayazán ◽  
Sebastián Roa Prada ◽  
Hernando Gonzalez Acevedo
Keyword(s):  
Mathematical Model ◽  
Control System ◽  
State Space ◽  
Transient Response ◽  
Space Form ◽  
Angular Position ◽  
Physical Modelling ◽  
Motor Shaft ◽  
Brushless Dc ◽  
The Mathematical Model

Abstract Gimbals are mechatronic systems well known for their use in the stabilization of cameras which are under the effect of sudden movements. Gimbals help keeping cameras at previously defined fixed orientations, so that the captured images have the highest quality. This paper focuses on the design of a Linear Quadratic Gaussian, LQG, controller, based on the physical modeling of a commercial Gimbal with two degrees of freedom (2DOF), which is used for first-person applications in unmanned aerial vehicle (UAV). This approach is proposed to make a more realistic representation of the system under study, since it guarantees high accuracy in the simulation of the dynamic response, as compared to the prediction of the mathematical model of the same system. The development of the model starts by sectioning the Gimbal into a series of interconnected links. Subsequently, a fixed reference system is assigned to each link body and the corresponding homogeneous transformation matrices are established, which will allow the calculation of the orientation of each link and the displacement of their centers of mass. Once the total kinetic and potential energy of the mechanical components are obtained, Lagrange’s method is utilized to establish the mathematical model of the mechanical structure of the Gimbal. The equations of motion of the system are then expressed in state space form, with two inputs, two outputs and four states, where the inputs are the torques produced by each one of the motors, the outputs are the orientation of the first two links, and the states are the aforementioned orientations along with their time derivatives. The state space model was implemented in MATLAB’s Simulink environment to compare its prediction of the transient response with the prediction obtained with the representation of the same system using MATLAB’s SimMechanics physical modelling interface. The mathematical model of each one of the three-phase Brushless DC motors is also expressed in state space form, where the three inputs of each motor model are the voltages of the corresponding motor phases, its two outputs are the angular position and angular velocity, and its four states are the currents in two of the phases, the orientation of the motor shaft and its rate of change. This model is experimentally validated by performing a switching sequence in both the simulation model and the physical system and observing that the transient response of the angular position of the motor shaft is in accordance with the theoretical model. The control system design process starts with the interconnection of the models of the mechanical components and the models of the Brushless DC Motor, using their corresponding state space representations. The resulting model features six inputs, two outputs and eight states. The inputs are the voltages in each phase of the two motors in the Gimbal, the outputs are the angular positions of the first two links, and the states are the currents in two of the phases for each motor and the orientations of the first two links, along with their corresponding time derivatives. An optimal LQG control system is designed using MATLAB’s dlqr and Kalman functions, which calculate the gains for the control system and the gains for the states estimated by the observer. The external excitation in each of the phases is carried out by pulse width modulation. Finally, the transient response of the overall system is evaluated for different reference points. The simulation results show very good agreement with the experimental measurements.

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