Modeling, Simulation, and Optimal Control for Two-Wheeled Self-Balancing Robot

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

Synchronizing of Stabilizing Platform Mounted on a Two-Wheeled Robot

This paper represents the designing, building, and testing of a self-stabilizing platform mounted on a self-balancing robot. For the self-stabilizing platform, a servo motor is used and for the self-balancing robot, two dc motors are used with an encoder, inertial measurement unit, motor driver, an Arduino UNO microcontroller board. A PID controller is used to control the balancing of the system. The PID controller gains (Kp, Ki, and Kd) were evaluated experimentally. The value of the tilted angle from IMU was fed to the PID controller to control the actuated motors for balancing the system. For the self-stabilizing control part, whenever the robot tilted, it maintained the horizontal position by rotating that much in the opposite direction

ROS-based Controller for a Two-Wheeled Self-Balancing Robot

In this article, a controller based on a Robot Operating System (ROS) for a two-wheeled self-balancing robot is designed. The proposed ROS architecture is open, allowing the integration of different sensors, actuators, and processing units. The low-cost robot was designed for educational purposes. It used an ESP32 microcontroller as the central unit, an MPU6050 Inertial Measurement Unit sensor, DC motors with encoders, and an L298N integrated circuit as a power stage. The mathematical model is analyzed through Newton-Euler and linearized around an equilibrium point. The control objective is to self-balance the robot to the vertical axis in the presence of disturbances. The proposed control is based on a bounded saturation, which is lightweight and easy to implement in embedded systems with low computational resources. Experimental results are performed in real-time under regulation, conditions far from the equilibrium point, and rejection of external disturbances. The results show a good performance, thus validating the mechanical design, the embedded system, and the control scheme. The proposed ROS architecture allows the incorporation of different modules, such as mapping, autonomous navigation, and manipulation, which contribute to studying robotics, control, and embedded systems

A Fuzzy LQR PID Control for a Two-Legged Wheel Robot with Uncertainties and Variant Height

This paper proposes a fuzzy LQR PID control for a two-legged wheeled balancing robot for keeping stability against uncertainties and variant heights. The proposed control includes the fuzzy supervisor, LQR, PID, and two calibrations. The fuzzy LQR is conducted to control the stability and motion of the robot while its posture changes with respect to time. The fuzzy supervisor is used to adjust the LQR control according to the robotic height. It consists of one input and one output. The input and output have three membership functions, respectively, to three postures of the robot. The PID control is used to control the posture of the robot. The first calibration is used to compensate for the bias value of the tilting angle when the robot changes its posture. The second calibration is applied to compute the robotic height according to the hip angle. In order to verify the effectiveness of the proposed control, a practical robot with the variant height is constructed, and the proposed control is embedded in the control board. Finally, two experiments are also conducted to verify the balancing and moving ability of the robot with the variant posture

Balancing a Segway robot using LQR controller based on genetic and bacteria foraging optimization algorithms

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

Fish Swarmed Kalman Filter for State Observer Feedback of Two-Wheeled Mobile Robot Stabilization

Over the past few decades, there have been significant technological advancements in the field of robots, particularly in the area of mobile robots. The performance standards of speed, accuracy, and stability have become key indicators of progress in robotic technology. Self-balancing robots are designed to maintain an upright position without toppling over. By continuously adjusting their center of mass, they can maintain stability even when disturbed by external forces. This research aims to achieving and maintaining balance is a complex task. Self-balancing robots must accurately sense their orientation, calculate corrective actions, and execute precise movements to stay upright. Eliminating disturbances and measurement noise in self-balancing robot can enhance the accuracy of their output. One common technique for achieving this is by using Kalman filters, which are effective in addressing non-stationary linear plants with unknown input signal strengths that can be optimized through filter poles and process covariances. Additionally, advanced Kalman filter methods have been developed to account for white measurement noise. In this research, state estimation was conducted using the Fish Swarm Optimization Algorithm (FSOA) to provide feedback to the controller to overcome the effects of disturbances and noise in the measurements through the designed filter. FSOA mimics the social interactions and coordinated movements observed in fish groups to solve optimization problems. FSOA is primarily used for optimization tasks where finding the global optimal solution is desired. The results show that the use of an optimized Kalman filter with FSOA on a two-wheeled mobile robot to handle system stability reduces noise values by 38.37%, and the system reaches a steady state value of 3.8 s with a steady error of 0.2%. In addition, by using the proposed method, filtering disturbances and measurement noise in self-balancing robot can help improve the accuracy of the self balancing robot’s output. System response becomes faster towards stability compared to other methods which are also applied to two-wheeled mobile robots

Comparison of Control Methods PD, PI, and PID on Two Wheeled Self Balancing Robot

A robot must employ a suitable control method to obtain a good stability. The Two-Wheeled Self Balancing Robot in this paper is designed using a MPU-6050 IMU sensor module and ATmega128 microcontroller as its controller board. This IMU sensor module is employed to measure any change in the robot's tilt angle based on gyroscope and accelerometer readings contained in the module. The tilt angle readings are then utilized as the setpoint on the control methods, namely PD (Proportional Derivative), PI (Proportional Integral), or PID (Proportional Integral Derivative). Based on the conducted testing results, the PID controller is the best control strategy when compared to the PD and PI control. With parameters of Kp = 14, Ki = 0005 and Kd = 0.1, the robot is able to adjust the speed and direction of DC motor rotation to maintain upright positions on flat surfaces