Two-wheeled self-balancing robot is a popular model in control system experiments which is more widely known as inverted pendulum and cart model. This is a multi-input and multi-output system which is theoretical and has been applied in many systems in daily use. Anyway, most research just focus on balancing this model through try-on experiments or by using simple form of mathematical model. There were still few researches that focus on complete mathematic modeling and designing a mathematical model based controller for such system. This paper analyzed mathematical model of the system. Then, the authors successfully applied a Linear Quadratic Regulator (LQR) controller for this system. This controller was tested with different case of system condition. Controlling results was proved to work well and tested on different case of system condition through simulation on matlab/Simulink program.
Balancing a Segway robot using LQR controller based on genetic and bacteria f...TELKOMNIKA JOURNAL
A two-wheeled single seat Segway robot is a special kind of wheeled mobile robot, using it as a human transporter system needs applying a robust control system to overcome its inherent unstable problem. The mathematical model of the system dynamics is derived and then state space formulation for the system is presented to enable design state feedback controller scheme. In this research, an optimal control system based on linear quadratic regulator (LQR) technique is proposed to stabilize the mobile robot. The LQR controller is designed to control the position and yaw rotation of the two-wheeled vehicle. The proposed balancing robot system is validated by simulating the LQR using Matlab software. Two tuning methods, genetic algorithm (GA) and bacteria foraging optimization algorithm (BFOA) are used to obtain optimal values for controller parameters. A comparison between the performance of both controllers GA-LQR and BFO-LQR is achieved based on the standard control criteria which includes rise time, maximum overshoot, settling time and control input of the system. Simulation results suggest that the BFOA-LQR controller can be adopted to balance the Segway robot with minimal overshoot and oscillation frequency.
Autonomous Balancing of 2-wheeled segway robotJash Shah
This document describes a project to design an optimal controller for a Segway robot using linear quadratic regulator (LQR) and soft computing optimization techniques like genetic algorithm (GA) and bacteria foraging algorithm (BFOA). The project aims to derive the Segway robot's mathematical model and use LQR with GA and BFOA to tune controller parameters to stabilize the robot. Simulation results show that GA-LQR provides better performance than BFOA-LQR, achieving the robot's stabilization with less computational power. While the paper concludes BFOA is better, the values it provides do not match simulation results. The document also discusses modeling approach, methodology, observations, and opportunities for future work.
This document describes a line-following robotic car created by a team of students for a course project. The robotic car uses an Arduino microcontroller along with sensors, motors, and other components to follow a black line on the ground. It uses articulated steering controlled by a servo motor. The team designed and 3D printed a chassis for the components. They implemented proportional-integral-derivative (PID) control using the Arduino to process sensor readings and steer the car along the line. The car successfully navigated intermediate test tracks but struggled with tighter turns on an advanced course due to mechanical limitations of its design.
Nhận viết luận văn đại học, thạc sĩ trọn gói, chất lượng, LH ZALO=>0909232620
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Download đề tài nghiên cứu khoa học: Thiết kế mô hình cân bằng con lắc ngược, cho các bạn làm luận văn tham khảo
This document describes an eye-controlled wheelchair that allows quadriplegic users to move independently. A webcam detects eye movements using MATLAB software and sends signals to a microcontroller. The microcontroller then drives motors to move the wheelchair left, right or straight. Key aspects include using eye detection algorithms to determine direction, an ATMega32A microcontroller to control motors based on eye signals, and safety features like speed control and blink detection to halt movement. The system aims to improve mobility for quadriplegic individuals but requires further refinement for commercial use, such as improving movement detection during casual eye movements.
Nhận viết luận văn đại học, thạc sĩ trọn gói, chất lượng, LH ZALO=>0909232620
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Download luận văn đồ án tốt nghiệp với đề tài: Thiết kế, chế tạo và điều khiển cánh tay robot 3 bậc tự do, cho các bạn làm luận văn tham khảo
Balancing a Segway robot using LQR controller based on genetic and bacteria f...TELKOMNIKA JOURNAL
A two-wheeled single seat Segway robot is a special kind of wheeled mobile robot, using it as a human transporter system needs applying a robust control system to overcome its inherent unstable problem. The mathematical model of the system dynamics is derived and then state space formulation for the system is presented to enable design state feedback controller scheme. In this research, an optimal control system based on linear quadratic regulator (LQR) technique is proposed to stabilize the mobile robot. The LQR controller is designed to control the position and yaw rotation of the two-wheeled vehicle. The proposed balancing robot system is validated by simulating the LQR using Matlab software. Two tuning methods, genetic algorithm (GA) and bacteria foraging optimization algorithm (BFOA) are used to obtain optimal values for controller parameters. A comparison between the performance of both controllers GA-LQR and BFO-LQR is achieved based on the standard control criteria which includes rise time, maximum overshoot, settling time and control input of the system. Simulation results suggest that the BFOA-LQR controller can be adopted to balance the Segway robot with minimal overshoot and oscillation frequency.
Autonomous Balancing of 2-wheeled segway robotJash Shah
This document describes a project to design an optimal controller for a Segway robot using linear quadratic regulator (LQR) and soft computing optimization techniques like genetic algorithm (GA) and bacteria foraging algorithm (BFOA). The project aims to derive the Segway robot's mathematical model and use LQR with GA and BFOA to tune controller parameters to stabilize the robot. Simulation results show that GA-LQR provides better performance than BFOA-LQR, achieving the robot's stabilization with less computational power. While the paper concludes BFOA is better, the values it provides do not match simulation results. The document also discusses modeling approach, methodology, observations, and opportunities for future work.
This document describes a line-following robotic car created by a team of students for a course project. The robotic car uses an Arduino microcontroller along with sensors, motors, and other components to follow a black line on the ground. It uses articulated steering controlled by a servo motor. The team designed and 3D printed a chassis for the components. They implemented proportional-integral-derivative (PID) control using the Arduino to process sensor readings and steer the car along the line. The car successfully navigated intermediate test tracks but struggled with tighter turns on an advanced course due to mechanical limitations of its design.
Nhận viết luận văn đại học, thạc sĩ trọn gói, chất lượng, LH ZALO=>0909232620
Tham khảo dịch vụ, bảng giá tại: https://vietbaitotnghiep.com/dich-vu-viet-thue-luan-van
Download đề tài nghiên cứu khoa học: Thiết kế mô hình cân bằng con lắc ngược, cho các bạn làm luận văn tham khảo
This document describes an eye-controlled wheelchair that allows quadriplegic users to move independently. A webcam detects eye movements using MATLAB software and sends signals to a microcontroller. The microcontroller then drives motors to move the wheelchair left, right or straight. Key aspects include using eye detection algorithms to determine direction, an ATMega32A microcontroller to control motors based on eye signals, and safety features like speed control and blink detection to halt movement. The system aims to improve mobility for quadriplegic individuals but requires further refinement for commercial use, such as improving movement detection during casual eye movements.
Nhận viết luận văn đại học, thạc sĩ trọn gói, chất lượng, LH ZALO=>0909232620
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Download luận văn đồ án tốt nghiệp với đề tài: Thiết kế, chế tạo và điều khiển cánh tay robot 3 bậc tự do, cho các bạn làm luận văn tham khảo
This technical seminar report summarizes information about quadcopters. It begins with an introduction that defines unmanned aerial vehicles and notes that quadcopters use four rotors for lift and propulsion. The document then discusses the basic materials needed for a quadcopter, including brushless DC motors, electronic speed controllers, propellers, and sensor boards. It explains the working principles of quadcopters, how the rotation of the four motors allows for different movements. Applications mentioned include military surveillance, commercial drone delivery services, and agricultural monitoring. The conclusion states that quadcopter control and functions continue to improve with additional research.
Nhận viết luận văn đại học, thạc sĩ trọn gói, chất lượng, LH ZALO=>0909232620
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Download luận văn tóm tắt ngành kĩ thuật điều khiển với đề tài: Điều khiển bám cho robot di động sử dụng bộ điều khiển mờ - nơron, cho các bạn làm luận văn tham khảo
Nguyễn Đình Thông - Thiết kế bộ điều khiển vận tốc và vị trí cho quadcopter s...Thong Nguyen Dinh
Luận văn tốt nghiệp Trường Đại học Bách Khoa - Đại học Quốc gia Thành phố hồ Chí Minh.
Full source code trên Github: https://github.com/dinhthong/quadrotor_bk
This document summarizes the implementation of a quadcopter with live video monitoring. It discusses the structure of the quadcopter, including its mechanical and electronic components. It also describes the SolidWorks design, MATLAB simulation, control theory using PID controllers, and sensor fusion techniques. The goal is to develop a stable quadcopter that can be flown wirelessly from a distance while transmitting live video footage. Future work may focus on more complex autonomous flight routines and swarm coordination.
IR BASED HOME AUTOMATION USING ARDUINO UNOMln Phaneendra
In this work, a remote controlled device is used to control 1 - 6 different single phase loads like Fans, Tube Lights and etc.,
This Automation can be operated up to a 30 feet of distance . Our work is based on Infra-Red(IR) technology and a simple Arduino Board(AB) using Printed Circuit Board(PCB).
The new designed circuit is more advantageous as it is portable, easy to carry and use.
This document is a report submitted by Michael Bseliss in partial fulfillment of the requirements for a Bachelor of Technology degree in Aerospace Engineering from Amity University, Dubai. The report evaluates a practical training on the construction of a quadcopter. It includes sections on the introduction, literature review, components, flight control, applications and advantages/disadvantages of quadcopters. Key components discussed include the frame, propellers, motors, flight controller, batteries and other optional additions like cameras. Applications highlighted are in areas like agriculture, delivery services, and photography.
Nhận viết luận văn đại học, thạc sĩ trọn gói, chất lượng, LH ZALO=>0909232620
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Download luận án tiến sĩ ngành kĩ thuật điều khiển với đề tài: Nghiên cứu các bài toán thiết kế các luật điều khiển cho rô bốt di động kiểu bánh xe, cho các bạn làm luận án tham khảo
A line follower robot detects and follows a line on the floor using sensors. It uses a microcontroller like the AT89S52 to process sensor input and control motors to stay on the line. The hardware includes a power supply, sensors, motors, and other components. An embedded system combines both hardware and software to perform tasks. Line follower robots are used in manufacturing for transporting items between processes.
This document provides an overview of humanoid robots, including their purpose, design considerations, and development process. Some key points:
- Humanoid robots are designed to resemble the human form and allow for interacting with human tools and environments. Their design often aims to study bipedal locomotion or close cooperation with humans.
- Developing a humanoid robot requires integrating mechanical, electronic, and software components while considering factors like safety, efficiency and dynamic behavior.
- The document outlines a process for efficiently designing humanoid robot modules through subdivision, requirements analysis, component selection, and an iterative development sequence.
- An example is given for developing a shoulder joint module according to this process, considering joint kinematics
These slides have been made by the members of roboVITics club - The Official Robotics Club of VIT. It deals with the basic concepts related to making a Line Follower Robot.
For details, visit http://maxEmbedded.com/
http://robovitics.in/
A Design Of Omni-Directional Mobile Robot Based On Mecanum WheelsIJRESJOURNAL
ABSTRACT:As one of the important branch of mobile robotics, wheel mobile robot has long been paid atten tion to by the research people at home and abroad for its high load ability, positioning accuracy, high efficiency, simple control, etc. Mobile robot has close relation to many technologies suc-h as control theory, computer tech nology, sensor technology, etc. Therefore, research on the mobile robot has important significance
This document summarizes a research paper that presents a non-linear control law to track a reference trajectory for a mobile robot with caster wheels. The control law integrates kinematic and dynamic controllers to minimize position/orientation errors and differences between actual and reference velocities. The stability of the control law is proven using Lyapunov theory. Numerical simulations and experiments on a differential-drive mobile robot show the integrated control provides faster convergence and eliminates overshoot compared to just kinematic control.
This technical seminar report summarizes information about quadcopters. It begins with an introduction that defines unmanned aerial vehicles and notes that quadcopters use four rotors for lift and propulsion. The document then discusses the basic materials needed for a quadcopter, including brushless DC motors, electronic speed controllers, propellers, and sensor boards. It explains the working principles of quadcopters, how the rotation of the four motors allows for different movements. Applications mentioned include military surveillance, commercial drone delivery services, and agricultural monitoring. The conclusion states that quadcopter control and functions continue to improve with additional research.
Nhận viết luận văn đại học, thạc sĩ trọn gói, chất lượng, LH ZALO=>0909232620
Tham khảo dịch vụ, bảng giá tại: https://baocaothuctap.net
Download luận văn tóm tắt ngành kĩ thuật điều khiển với đề tài: Điều khiển bám cho robot di động sử dụng bộ điều khiển mờ - nơron, cho các bạn làm luận văn tham khảo
Nguyễn Đình Thông - Thiết kế bộ điều khiển vận tốc và vị trí cho quadcopter s...Thong Nguyen Dinh
Luận văn tốt nghiệp Trường Đại học Bách Khoa - Đại học Quốc gia Thành phố hồ Chí Minh.
Full source code trên Github: https://github.com/dinhthong/quadrotor_bk
This document summarizes the implementation of a quadcopter with live video monitoring. It discusses the structure of the quadcopter, including its mechanical and electronic components. It also describes the SolidWorks design, MATLAB simulation, control theory using PID controllers, and sensor fusion techniques. The goal is to develop a stable quadcopter that can be flown wirelessly from a distance while transmitting live video footage. Future work may focus on more complex autonomous flight routines and swarm coordination.
IR BASED HOME AUTOMATION USING ARDUINO UNOMln Phaneendra
In this work, a remote controlled device is used to control 1 - 6 different single phase loads like Fans, Tube Lights and etc.,
This Automation can be operated up to a 30 feet of distance . Our work is based on Infra-Red(IR) technology and a simple Arduino Board(AB) using Printed Circuit Board(PCB).
The new designed circuit is more advantageous as it is portable, easy to carry and use.
This document is a report submitted by Michael Bseliss in partial fulfillment of the requirements for a Bachelor of Technology degree in Aerospace Engineering from Amity University, Dubai. The report evaluates a practical training on the construction of a quadcopter. It includes sections on the introduction, literature review, components, flight control, applications and advantages/disadvantages of quadcopters. Key components discussed include the frame, propellers, motors, flight controller, batteries and other optional additions like cameras. Applications highlighted are in areas like agriculture, delivery services, and photography.
Nhận viết luận văn đại học, thạc sĩ trọn gói, chất lượng, LH ZALO=>0909232620
Tham khảo dịch vụ, bảng giá tại: https://vietbaitotnghiep.com/dich-vu-viet-thue-luan-van
Download luận án tiến sĩ ngành kĩ thuật điều khiển với đề tài: Nghiên cứu các bài toán thiết kế các luật điều khiển cho rô bốt di động kiểu bánh xe, cho các bạn làm luận án tham khảo
A line follower robot detects and follows a line on the floor using sensors. It uses a microcontroller like the AT89S52 to process sensor input and control motors to stay on the line. The hardware includes a power supply, sensors, motors, and other components. An embedded system combines both hardware and software to perform tasks. Line follower robots are used in manufacturing for transporting items between processes.
This document provides an overview of humanoid robots, including their purpose, design considerations, and development process. Some key points:
- Humanoid robots are designed to resemble the human form and allow for interacting with human tools and environments. Their design often aims to study bipedal locomotion or close cooperation with humans.
- Developing a humanoid robot requires integrating mechanical, electronic, and software components while considering factors like safety, efficiency and dynamic behavior.
- The document outlines a process for efficiently designing humanoid robot modules through subdivision, requirements analysis, component selection, and an iterative development sequence.
- An example is given for developing a shoulder joint module according to this process, considering joint kinematics
These slides have been made by the members of roboVITics club - The Official Robotics Club of VIT. It deals with the basic concepts related to making a Line Follower Robot.
For details, visit http://maxEmbedded.com/
http://robovitics.in/
A Design Of Omni-Directional Mobile Robot Based On Mecanum WheelsIJRESJOURNAL
ABSTRACT:As one of the important branch of mobile robotics, wheel mobile robot has long been paid atten tion to by the research people at home and abroad for its high load ability, positioning accuracy, high efficiency, simple control, etc. Mobile robot has close relation to many technologies suc-h as control theory, computer tech nology, sensor technology, etc. Therefore, research on the mobile robot has important significance
This document summarizes a research paper that presents a non-linear control law to track a reference trajectory for a mobile robot with caster wheels. The control law integrates kinematic and dynamic controllers to minimize position/orientation errors and differences between actual and reference velocities. The stability of the control law is proven using Lyapunov theory. Numerical simulations and experiments on a differential-drive mobile robot show the integrated control provides faster convergence and eliminates overshoot compared to just kinematic control.
An introduction to robotics classification, kinematics and hardwareNikhil Shrivas
Introduction to robots, classification of robots, Kinematics of robot manipulator, Introduction to a mobile robot, kinematics of mobile robot, sensors used in robots, microcontrollers for robots
Kinematics Analysis of Parallel Mechanism Based on Force Feedback DeviceIJRES Journal
Kinematic analysis of mechanism is the fundamental work of force feedback device research.The
composition of Delta mechanism based on Omega.7 force feedback device was illustrated in this paper.The
kinematic loop equations of Delta mechanism was established according to its geometric relationship,also the
inverse kinematics solution of Delta mechanism were obtained. And the numerical forward kinematics were
calculated by Newton iteration algorithm.Finally,The analysis of velocity and acceleration was carried out
through matrix operations.Kinematic analysis of Delta mechanism provides a theoretical basis for following
study.
Robust Control of a Spherical Mobile RobotIRJET Journal
This document summarizes a research paper about controlling a spherical mobile robot using sliding mode control. It begins with an abstract that describes the challenges of controlling spherical robots due to their underactuated systems. It then provides background on previous control methods for spherical robots. The document presents the kinematic model of a 2-DOF spherical robot and describes how sliding mode control can be used to provide robust control and path following for the robot. It provides the equations for the sliding mode controller design. Finally, it presents simulation results showing the robot following a desired trajectory with minimal tracking error using the sliding mode controller.
simuliton of biped walkinng robot using kinematicsReza Fazaeli
This document describes simulation and control of a biped walking robot using kinematic and dynamic modeling. It presents the dynamic equations of motion for a 2D model of the robot with 5 degrees of freedom. It then describes how impacts are modeled when the swing foot makes contact with the ground. A linear control method is developed using selected outputs to control the robot's motion along a straight line. Simulation results are shown for both 2D and 3D dynamic models of the robot, with angles, velocities, accelerations, and torques calculated. The robot is able to walk stably along a straight line by maintaining balance during single support phases, demonstrating the effectiveness of the control approach.
A New Type Reconfigurable Mobile Manufacturing RobotIJRESJOURNAL
This document presents a new type of reconfigurable mobile manufacturing robot for welding applications. It proposes using a cooperative welding system consisting of a 6 degree of freedom serial robot and a 2 degree of freedom position changing machine. It describes the coordinate systems of the system and presents the kinematic modeling and parameter solving process. Constraint equations are developed to ensure the positioner and robot kinematic chains are coupled for coordinated motion during welding. Both forward and inverse kinematic models of the position changing machine are developed. The results confirm the proposed method provides a foundation for automatic welding production line research.
A New Method For Solving Kinematics Model Of An RA-02IJERA Editor
The kinematics miniature are established for a 4 DOF robotic arm. Denavit-Hartenberg (DH) convention and the
product of exponential formula are used for solving kinematic problem based on screw theory. For acquiring
simple matrix for inverse kinematics a new simple method is derived by solving problems like robot base
movement, actuator restoration. Simulations are done by using MATlab programming for the kinematics
exemplary.
Insect inspired hexapod robot for terrain navigationeSAT Journals
Abstract The aim of this paper is to build a sixlegged walking robot that is capable of basicmobility tasks such as walking forward, backward, rotating in place and raising orlowering the body height. The legs will be of a modular design and will have threedegrees of freedom each. This robot will serve as a platform onto which additionalsensory components could be added, or which could be programmed to performincreasingly complex motions. This report discusses the components that make up ourfinal design.In this paper we have selected ahexapod robot; we are focusing &developingmainly on efficient navigation method indifferent terrain using opposite gait of locomotion, which will make it faster and at sametime energy efficient to navigate and negotiate difficult terrain.This paper discuss the Features, development, and implementation of the Hexapod robot Index Terms:Biologically inspired, Gait Generation,Legged hexapod, Navigation.
Kinematics Analysis Of 8-UPS Parallel Robot Walking ModeIJRESJOURNAL
ABSTRACT: Achieving stable machining is a difficult problem in large workspace robot field, this paper
proposes a new 8-UPS parallel robot with 6 DOF as well as walking and machining ability. In machining mode,
it equals to a traditional parallel robot, in walking mode it is a 4 legs walking robot. It mainly from kinematics
and inverse solution, workspace, mobile platform trajectory planning, singularity analysis, performance analysis
to do kinematics analysis in machining mode; when the robot works in walking mode, the reseach mainly from
configuration design, gait planning and kinematics analysis aspects. The inverse kinematic model of 8-UPS
Parallel robot under machining mode was established, and the rod length function was obtained. Based on the
machining mode workspace, a robot design method was proposed, and the full performance indicator was used
to help design the main parameters of the robot. Based on MATLAB, Simulink model was established to
complete inverse kinematics simulation and get the rod length as well as drive speed variation of the 8-UPS
parallel robot. Based on SolidWorks, 8-UPS model was established, with using Motion part according to the
specified trajectory, kinematics simulation curve was obtained to help analyse the performance of the robot. At
the end, interference checking process was proposed to help to check the interface between hinge and rods
A Simple Integrative Solution For Simultaneous Localization And MappingWaqas Tariq
Simultaneous Localization and Mapping is a method used to find the location of a mobile robot while at the same time build a constructive map of its surrounding environment. This paper gives a brief description about a simple integrative SLAM technique using a Laser Range Finder (LRF) and Odometry data, primarily for indoor environments. In this project, a solution for the SLAM problem was implemented on a differential drive mobile robot equipped with a SICK laser scanner.
Dynamics and control of a robotic arm having four linksAmin A. Mohammed
This document presents the dynamics modeling and control of a 4 degree-of-freedom robotic arm. It first derives the dynamic model of the robotic arm using the Euler-Lagrange approach. It then describes implementing two control approaches for position control of the arm joints: PID control and feedback linearization control. Simulation results show that PID control coupled with a differential evolution algorithm and feedback linearization control improve the robotic arm's performance. Increasing the arm link masses is found to not affect PID position control performance but require higher control torques.
1) The document discusses robot dynamics and defines equations for velocity and kinetic energy.
2) It presents equations to calculate the velocity of points on robot links using transformation matrices and derivatives with respect to joint variables.
3) Equations are provided to calculate the kinetic energy of elements of mass on robot links as a function of linear and angular velocities, allowing the total kinetic energy to be determined by summing over all links.
Determination of the Operational Parameters of a Planar Robot with Three JointsWaqas Tariq
Robots are currently made in numerous types and are used in diverse roles such as production lines, daily living activities and some security fields. These types of robots are well designed and successfully applied in many areas requiring high sensitivity and stability. The aim of this study was to determine the optimum values of several operational parameters for a planar robot with respect to robot design and construction. With this aim, a small planar robot with a three-jointed arm activated by hydraulic cylinders in each segment was evaluated using a technical design drawing. The arm motions of the planar robot are rotary and parallel within a vertical plane. The resulting optimal operational parameters of the planar robot were determined as starting and target positions of 31.5 cm and 55 cm, respectively, on the x-axis and 17.18 cm and 118.44 cm on the y–axis. Time-position and time-velocity graphs were constructed corresponding to the orbit-planning parameters, resulting in Cartesian velocities for the terminal processor of 13.98 m/sec on the x-axis and 20.16 m/sec on the y-axis at 1.5 seconds after initiation. The maximum power consumption of the robot was determined as 1 kW according to the outer load and arm weights.
Design and Simulation of Different Controllers for Stabilizing Inverted Pendu...IJERA Editor
The Inverted Pendulum system has been identified for implementing controllers as it is an inherently unstable system having nonlinear dynamics. The system has fewer control inputs than degrees of freedom which makes it fall under the class of under-actuated systems. It makes the control task more challenging making the inverted pendulum system a classical benchmark for the design, testing, evaluating and comparing. The inverted pendulum to be discussed in this paper is an inverted pendulum mounted on a motor driven cart. The aim is to stabilize the system such that the position of the cart on the track is controlled quickly and accurately so that the pendulum is always erected in its vertical position. In this paper the linearized model was obtained by Jacobian matrix method. The Matlab-Simulink models have been developed for simulation for optimal control design of nonlinear inverted pendulum-cart dynamic system using different control methods. The methods discussed in this paper are a double Proportional-Integral-Derivative (PID) control method, a modern Linear Quadratic Regulator (LQR) control method and a combination of PID and Linear Quadratic Regulator (LQR) control methods. The dynamic and steady state performance are investigated and compared for the above controllers.
Wheeled robots are often utilized for various remote sensing and telerobotic applications because of their ability to navigate through dynamic environments, mostly under the partial control of a human operator. To make these robots capable to traverse through terrains of rough and uneven topography, their driving mechanisms and controllers must be very efficient at producing and controlling large mechanical power with great precision in real-time, however small the robot may be. This paper discusses an approach for designing a quad-wheeled robot, which is wirelessly controlled with a personal computer (PC) by medium-range radio frequency (RF) transceiver, to navigate through unpaved paths with little or no difficulty. An efficient servo-controlled Ackerman steering mechanism and a high-torque driving power-train were developed. The robot’s controller is programmed to receive and respond to RF control signals from the PC to perform the desired motions. The dynamics of the robot’s drivetrain is modeled and analyzed on MATLAB to predict its performances. The robot was tested on various topographies to determine its physical capabilities. Results show that the robot is capable of non-holonomically constrained motions on rough and uneven terrains.
Stairs Detection Algorithm for Tri-Star Wheeled Robot and Experimental Valida...Premier Publishers
This paper presents two contributions in the development of stair detection algorithm for climbing robot. First, a new tri-star wheeled mechanism was developed to smoothly overcome the stairs. Second, the sensor-based algorithm was proposed for detection of stairs and switching states autonomously. Two motor driven ultrasonic sensors feed the posture information of the robot back to the controller to recognize the climbing environment. The validity of the proposed algorithm was demonstrated through experiments in realizing climbing environment. The experiments prove that the proposed algorithm can do rolling, ascending and descending on the staircase.
This work presents the kinematics model of an RA-
02 (a 4 DOF) robotic arm. The direct kinematic problem is
addressed using both the Denavit-Hartenberg (DH) convention
and the product of exponential formula, which is based on the
screw theory. By comparing the results of both approaches, it
turns out that they provide identical solutions for the
manipulator kinematics. Furthermore, an algebraic solution of
the inverse kinematics problem based on trigonometric
formulas is also provided. Finally, simulation results for the
kinematics model using the Matlab program based on the DH
convention are presented. Since the two approaches are
identical, the product of exponential formula is supposed to
produce same simulation results on the robotic arm studied.
Keywords-Robotics; DH convention; product of exponentials;
kinematics; simulations
This document presents a mathematical model and control schemes for a hexacopter unmanned aerial vehicle. It first develops the nonlinear dynamic model of the hexacopter using Newton-Euler equations, including rotor dynamics. It then proposes two control schemes - PID and backstepping controllers - to control the hexacopter's attitude and altitude. Simulation experiments in Simulink are used to evaluate and compare the performance and stability of the two control techniques under possible disturbances.
Similar to Modeling, Simulation, and Optimal Control for Two-Wheeled Self-Balancing Robot (20)
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2. IJECE ISSN: 2088-8708
Modeling, Simulation, and Optimal Control for Two-Wheeled Self-Balancing …. (Modestus Oliver Asali)
2009
been presented while the heading angle of the robot was also studied in the dynamic equation that was
derived using Lagrangian method.
This paper concerns the two-wheeled self-balancing robot system as the research object, which uses
the Newtonian mechanics equation method to derive the dynamic equation. The linear state-space model that
approximates the nonlinear system in the region of operation than obtained by assuming the system operates
only around an operating point and the signals involved are small signal. Based from the mathematical model
of the system, LQR Controller is designed to control the system tilt angle and heading angle so that the
system can be controlled to move to a desired position. Performance of control strategy with respect to the
output tilt angle ( ) and heading angle ( ) are examined and presented by using matlab / Simulink program.
2. RESEARCH METHOD
2.1. Mathematical Modeling of the Robot
The robot consists of 3 major parts, namely the wheels, platform, and the pendulum as the mass.
The robot with its three degrees of freedom is able to linearly move which is characterized by position x, able
to rotate around the z-axis (yaw) with associated angle ( ), and able to rotate around the y-axis (pitch) where
the movement is described by angle ( ) as shown in Figure 1. The inputs of the system are the torques and
which both are applied to the two wheels which located on the left side and right side of the robot. List of
parameters for the two-wheeled self-balancing robot are shown in Table 1. These parameters are based on the
project conducted by Li as stated by [12]. The objectives of the control schemes are to control the system’s
model shown in Figure 1 to move to a desired position while keeping the robot’s tilt angle in the upright
position. The controller must be able to stabilize the system with acceptable overshoot and settling time.
Figure 1. A model of two-wheeled self-balancing robot
Table 1. List of parameters of two-wheeled self-balancing robot
Symbol Parameter Unit
Fl , Fr Interacting forces between the left and right wheels and the platform N
Hl , Hr Friction forces acting on the left and right wheels N
Torques provided by wheel actuators acting on the left and right wheels N/m
Rotational angles of the left and the right wheels rad
xl, xr Displacements of the left and right wheels along the x-axis m
Tilt angle of the robot rad
Heading angle of the robot with respect to the z-axis rad
MW Mass of the each wheel Kg
IW Moment of inertia of the wheel about the y-axis Kg.m2
r Radius of the wheel m
m Mass of the pendulum Kg
g Gravity acceleration m/s2
Distance from the platform to the center of mass of the pendulum along the z-axis m
d Distance between the left and right wheels along the y-axis m
M Mass of the platform Kg
IM Moment of inertia of the platform about the y-axis Kg.m2
IP Moment of inertia of the platform and pendulum about the z-axis Kg.m2
FP Interacting forces between the pendulum and the platform on the x-axis N
MP Interacting moment between the pendulum and the platform about the y-axis N/m
V The forward velocity of the robot m/s
The rotation velocity of the robot rad / s
3. ISSN: 2088-8708
IJECE Vol. 7, No. 4, August 2017 : 2008 – 2017
2010
With assumption that there is no slip between the wheels and the ground, by applying Newton’s law
for the linear and rotational motion based [13] and [14], balancing forces and moment acting on the left
wheel results in the following equations of motion:
∑ ̈ ( ) (1)
∑ ̈ (2)
Similiarly, for the right wheel we have:
∑ ̈ ( ) (3)
∑ ̈ (4)
Balancing forces acting on the pendulum on the x-axis direction and moments between the
pendulum and the platform about the y-axis results in:
̈ ̈ ̇ (5)
̈ (6)
̈ ̈ (7)
̈ (8)
Balancing the moments acting on the platform and pendulum about the z-axis gives:
̈ ( ) (9)
The relationship between the displacements of the wheel along the x-axis and the rotational angle of
the wheel about the y-axis is:
(10)
On the other hand, the relationship between the heading angle ( ) of the robot about the z-axis and the
displacement of the wheel along the x-axis is:
(11)
By subtracting (1) and (2) from (3) and (4) respectively then substituting it to (11) result in:
( ̈ ̈ ) ( ) (12)
( ̈ ̈ ) ( ) (13)
( ) ̈ ( ) ( ) (14)
̈
( ( ) )
( ) (15)
By adding (1) and (2) with (3) and (4) respectively then substituting it to (10), we have:
̈ ( ) (16)
̈ ( ) (17)
4. IJECE ISSN: 2088-8708
Modeling, Simulation, and Optimal Control for Two-Wheeled Self-Balancing …. (Modestus Oliver Asali)
2011
Adding (16) and (17) we have:
( ) ̈ ( ) (18)
By substituting (18) to (5) and (6) we obtain:
̈ ( ( )) ̈ ̇ (19)
By substituting (7) to (8) result in:
( ) ̈ ̈ (20)
From the above derivation, we can obtain the dynamics equation of motion of the two-wheeled self-
balancing robot as (15), (19), and (20). Assuming that the robot only around a small operating point, the
dynamic model of the robot is then linearized around the point ̇ . Equation
(19), and (20) then became:
̈ ( ( )) ̈ (21)
( ) ̈ ̈ (22)
By defining the following 5-dimensional vector of state variable:
[ ] [
̇
̇]
(23)
Using (15), (21), and (22) the linearized two-wheeled self-balancing robot model can be expressed
in the following state-space form:
[
̇
̈
̇
̇
̈] [ ] [
̇
̇] [ ]
* + (24)
where:
( ( ))
(( ( )) ( ))
(25)
(( ( )) ( ))
(26)
( (( ( )) ( )))
(27)
( (( ( )) ( )))
(28)
( (( ( )) ( )))
(29)
5. ISSN: 2088-8708
IJECE Vol. 7, No. 4, August 2017 : 2008 – 2017
2012
( (( ( )) ( )))
(30)
( ( ))
(31)
( ( ))
(32)
From the state-space model described above, there are a number of dynamic parameters in the
system which will result in variation of the state matrices. In order to simplify the problem and give a clear
physical meaning to the state matrix and input matrix to design a controller, the value of parameters of the
system was shown in Table 2.
Table 2. Specifications of the two-wheeled self-balancing robot
Symbol Value Unit
MW 1 Kg
IW 0.0313 Kg.m2
r 0.25 m
m 70 Kg
g 9.8 m/s2
1 m
d 0.5 m
M 5 Kg
IM 0.0385 Kg.m2
IP 1.8569 Kg.m2
Based on the value in Table 2, it is easy to have a linear state-space equation as:
[
̇
̈
̇
̇
̈] [ ] [
̇
̇] [ ]
* + (33)
2.2. LQR Controller Design and Simulation
LQR is a method in modern control theory that uses state-space approach to analyze such a system.
Using state-space methods, it is relatively simple to work with a multi-input multi-output system. Assuming
all state variables are available for feedback, the system described in previous section can be stabilized using
full state feedback [15]. The schematic of this type of control system for a two-wheeled self balancing robot
is shown in Figure 2.
Referring to [16] For the Linear Time Invariant (LTI) system, the LQR control theory involves
choosing a control law:
( ) ( ) (34)
which stabilizes the origin while minimizing the quadratic cost function which can be presented:
∫ ( ( ) ( ) ( ) ( )) (35)
where is a symmetric positive definite or positive semi-definite matrix, R is a symmetric positive definite
matrix and is unconstrained. The final control law can be derived as:
( ) ( ) (36)
6. IJECE ISSN: 2088-8708
Modeling, Simulation, and Optimal Control for Two-Wheeled Self-Balancing …. (Modestus Oliver Asali)
2013
Figure 2. The LQR control scheme for two-wheeled self-balancing robot
where a symmetric positive definite matrix is a solution to the following equation:
(37)
In designing LQR controller, LQR function in matlab m-file can be used to determine the value of
the vector K which determines the feedback control law. This is done by choosing two parameter values,
matrix and . The objective of controlling the two-wheeled self-balancing robot system is to minimize
robot’s pitch angle ( ) while control the heading angle ( ) toward the reference angle, so designate and
as two main control variables and and is given larger weights. After tuning the value of matrix
and matrix using the trial and error method, we found the following state weighting matrix and input
weighting matrix to be appropriate:
[ ]
* + (38)
Using (38) and (37), the control gains in (36) are found to be:
[ ]
(39)
3. RESULTS AND ANALYSIS
In this section, the simulation results of the proposed controller, which is performed on the model of
a two-wheeled self-balancing robot are presented. In order to design and stimulate the LQR Controller for
system, matlab/simulink simulation tool is used. Performance characteristics of the controller are also
discussed in details in this section.
Two wheeled self balancing robot system with LQR controller method produced two output
responses, robot’s pitch angle ( ) and the heading angle ( ). In this research, the initial value of pitch angle
( ) of the balancing robot was set to – 1 rad to simulate the performance of the controller. It means that the
initial condition of the robot is very unstable. On the other hand, the initial state of the heading angle ( ) was
set to 0 rad and given a unit step as the reference signal.
Figure 3 shows the response of two-wheeled self-balancing robot pitch angle ( ) in normal
condition while Figure 4 shows the responses of two-wheeled self-balancing robot heading angle ( ) in
normal condition. In the Figure, the response for the pitch angle ( ) and heading angle ( ) is represented by
straight line or red color line and the reference for the system response is represented by dotted line or blue
Errorr
x1
x2
x3
x5
x4
left torque
right torque
x' = Ax+Bu
y = Cx+Du
Two-wheeled self balancing robot
Error
U1
U2
K4
x1
x2
x3
x5
U1
U2
K
x1
x2
x3
x4
x5
yfcn
C
1
x4 reference
7. ISSN: 2088-8708
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2014
color line. From the figure, it can be seen that the LQR controller are capable to control the pitch angle and
heading angle of the robot to the desired value. The settling time for the pitch angle to reach balance state in
2.23 sec while the steady-state error is 0.0086 rad. Meanwhile, the settling time for the heading angle to
reach the steady-state value is 2.76 sec while the steady-state error is 0 rad. The control effort of the system’s
response is as shown in Figure 5. The torques applied to the left and the right wheel show a slight difference.
This is due to the desired value of the system’s heading angle = 1 rad and the system try to follow the
reference signal.
Figure 3. Two-wheeled self-balancing robot pitch
angle response in normal condition
Figure 4. Two-wheeled self-balancing robot
heading angle response in normal condition
Figure 6 shows the response of two-wheeled self-balancing robot pitch angle ( ) with the
pendulum’s mass being decreased to 40 Kg. From the figure it can be seen that the LQR controller are
capable to control and balance the pitch angle despite the change in the pendulum’s mass. It show that the
result has got similar pattern and not much different from the normal condition system. Almost no significant
differences were apparent from controller’s performance in normal condition with decreased mass condition
as shown by Figures 3 and Figure 6.
Figure 5. Control effort of two-wheeled self-
balancing robot in normal condition
Figure 6. Two-wheeled self-balancing robot pitch
angle response with decreased mass of the
pendulum = 40 Kg
Meanwhile, Figure 7. shows the response of two-wheeled self-balancing robot pitch angle ( ) with
the pendulum’s mass being increased to 110 Kg. From the figure it can be seen that the system’s response
became a little bit quicker while changes in the steady-state error is relatively small and can be ignored.
When the pendulum’s mass were being increased, there is a significance increase in system’s maximum
0 1 2 3 4 5 6 7 8 9 10
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
time (sec)
pitchangle(rad)
Two-wheeled self-balancing robot pitch angle response
pitch angle response
reference
0 1 2 3 4 5 6 7 8 9 10
-0.5
0
0.5
1
1.5
Two-wheeled self-balancing robot heading angle response
Headingagle(rad)
time (sec)
0 1 2 3 4 5 6 7 8 9 10
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
time (sec)
pitchangle(rad)
Two-wheeled self-balancing robot pitch angle response
pitch angle response
reference
0 1 2 3 4 5 6 7 8 9 10
-0.5
0
0.5
1
1.5
time (sec)
Headingangle(rad)
Two-wheeled self-balancing robot heading angle response
heading angle response
reference
0 1 2 3 4 5 6 7 8 9 10
-160
-140
-120
-100
-80
-60
-40
-20
0
20
time (sec)
Torque(N/m)
Control effort of two-wheeled self-balancing robot
Left Torque (u1)
Right Torque (u2)
0 1 2 3 4 5 6 7 8 9 10
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
time (sec)
pitchangle(rad)
Two-wheeled self-balancing robot pitch angle response
pitch angle response
reference
0 1
-0.5
0
0.5
1
1.5
Headingangle(rad)
Two
8. IJECE ISSN: 2088-8708
Modeling, Simulation, and Optimal Control for Two-Wheeled Self-Balancing …. (Modestus Oliver Asali)
2015
overshoot and steady-state error but overall, the performance of the controller was still acceptable because it
can still maintain it’s upright position. The performance of the controller in Figure 7 gives the conclusion that
the performance of LQR controllers is limited to a certain range of pendulum’s mass from the normal
conditions. If the pendulum mass is increased to a certain point, it is possible that the controller will fail to
control the system so that the robot will fall. Therefore, when designing LQR controllers it should also take
into account the range of pendulum’s mass in which the system will operate most.
The disturbance rejection performance of the controller is shown in Figure 8. An impulse
disturbance is applied at around 5 sec to the robot while it is stabilizing. It can be observed that the robot is
able to reject this disturbance and regains its balance position in a short amount of time. A greater control
effort is used by the robot to overcome the disturbance force as shown in Figure 9.
Figure 7. Two-wheeled self-balancing robot pitch
angle response with increased mass of the
pendulum = 110 Kg
Figure 8. Two-wheeled self-balancing robot pitch
angle response with disturbance applied to the
body pitch angle
Figure 9. Control effort of two-wheeled self-balancing robot during disturbance rejection
Table 3 shows the summary of the performance characteristics of the two-wheeled self-balancing
robot in various conditions. Based on the data tabulated in Table 3, it can be seen that the responses of the
self-balancing robot pitch angle and heading angle have acceptable overshoot and undershoot.
From this research it can be seen that LQR controllers can be implemented to control the two-
wheeled self-balancing robot system and provide quite good results. In this research, we also tested the
controller on various state of the system which has not been shown so clearly in previous research. From the
simulation, it can be seen that although the controller is capable of controlling the system despite being
subjected to a change in mass or disturbance to the body pitch angle, there is a tolerable limit of mass change
0 1 2 3 4 5 6 7 8 9 10
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
time (sec)
pitchangle(rad)
Two-wheeled self-balancing robot pitch angle response
pitch angle response
reference
0 1 2 3 4 5 6 7 8 9 10
-0.5
0
0.5
1
1.5
time (sec)
Headingangle(rad)
Two-wheeled self-balancing robot heading angle response
heading angle response
reference
0 1 2 3 4 5 6 7 8 9 10
-3
-2
-1
0
1
2
3
time (sec)
pitchangle(rad)
Two-wheeled self-balancing robot pitch angle response
pitch angle response
reference
0 1
-0.5
0
0.5
1
1.5
Headingangle(rad)
Tw
0 1 2 3 4 5 6 7 8 9 10
-160
-140
-120
-100
-80
-60
-40
-20
0
20
40
time (sec)
Torque(N/m)
Control effort of two-wheeled self-balancing robot
Left Torque (u1)
Right Torque (u2)
9. ISSN: 2088-8708
IJECE Vol. 7, No. 4, August 2017 : 2008 – 2017
2016
or pitch angle change. Therefore, when designing the controller, the values of the system parameters should
be considered sothat the controller can work well under ideal or non ideal conditions.
Table 3. Specifications of the two-wheeled self-balancing robot
System’s condition
Pitch angle ( ) Heading angle ( )
(s) (rad) (s) (rad)
Normal condition 2.23 0.0086 2.76 0
Increased pendulum’s
mass
7.04 0.0144 - -
Decreased pendulum’s
mass
0.52 0.0057 - -
4. CONCLUSION
In this paper, the design and implementation of LQR controller for stabilizing a two-wheeled self-
balancing robot is presented. The performance of LQR is simulated and analyzed with matlab/simulink
program. Based on the results and the analysis, a conclusion has been made that the LQR controller are
capable of controlling the two-wheeled self-balancing robot’s pitch angle and heading angle and yields
acceptable and good results without falling. In normal condition the system can be engaged to balance itself
and give transient response characteristics settling time = 2.23 sec and steady-state error = 0.0086 rad for tilt
angle response and settling time = 2.76 sec and steady-state error = 0 rad for heading angle response. When
the pendulum’s mass is being increased by 30 Kg, the system give transient response characteristics settling
time = 7.04 sec and steady-state error = 0.0144 rad for tilt angle and when the pendulum’s mass is being
decreased by 30 Kg the system give transient response characteristics settling time = 0.52 sec and steady-
state error = 0.0057 rad for tilt angle. However, more experiment needs to be performed to evaluate the
robustness of the system. Nonlinear controller is fully recommended for balancing the two-wheeled self-
balancing robot as it will upgrade the robustness of the system.
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[2] H. Liu, J. Xu, Y. Sun, “Adaptive Fuzzy Sliding Mode Stabilization Controller for Inverted Pendulums”, in
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December 2013.
[3] T.Y. Chuan, L. Feng, Q. Qian, Y. Yang, “Stabilizing Planar Inverted Pendulum Systems Based on Fuzzy Nine-
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422-432, January 2014.
[4] T.O.S Hanafy, M.K. Metwally, “Simplifications the Rule Base for Stabilization of Inverted Pendulum System”, in
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2014.
[5] M. ul Hasan, K.M. Hasam, et al., “Design and Experimental Evaluation of a State Feedback Controller for Two
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Modeling, Simulation, and Optimal Control for Two-Wheeled Self-Balancing …. (Modestus Oliver Asali)
2017
[12] Zhijun Li, Chenguang Yang, Liping Fan, “Advanced Control of Wheeled Inverted Pendulum Systems”, London:
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BIOGRAPHIES OF AUTHORS
Modestus Oliver Asali was born in Pontianak, Indonesia, in 1994. He received his Bachelor’s degree
with a concentration in control engineering from Department of Electrical, Tanjungpura University,
Pontianak in 2017. He is interested in modern control engineering, and control of nonlinear dynamical
system. He now lived in Pontianak and may be reached at modestus_oliver@yahoo.com
Ferry Hadary is an Assistant Professor of Robotics, Control and Computation at Tanjungpura
University (UNTAN), Pontianak, Indonesia. He earned his B.Eng. degree from Tanjungpura
University, M. Eng. from Tokyo Institute of Technology, Japan, and Dr. Eng. from Kyushu Institute of
Technology, Japan. He is currently teaching at Department of Electrical Engineering, Tanjungpura
University. In his career as a researcher he received several research grants prestige of the Ministry of
Research Technology and Higher Education of the Republic of Indonesia, Grants International
Cooperation and the National Strategic (highest research grants in Indonesia). He is also a recipient of
the National Work Featured Technology of the Ministry of Research and Technology of Indonesia in
2014. His interests are in control systems, robotics, new and renewable energy. He may be reached at
ferry.hadary@invent.untan.ac.id
Bomo Wibowo Sanjaya was born in Pontianak, Indonesia, in 1974. He received his Bachelor’s degree
in control engineering from Department of Electrical, Tanjungpura University, Pontianak in 2008, his
Master’s Degree in control engineering from Department of Electrical, Bandung Institute of
Technology in 2013, and his Doctor’s Degree in control engineering from School of Electrical
Engineering and Informatics, Bandung Institute of Technology in 2014. Now, he is a lecturer at
Department of Electrical, Tanjungpura University. He current research interests are in fuzzy logic,
neural networks, control of nonlinear dynamical systems. He may be reached at
bomo.wibowo@ee.untan.ac.id