Two-wheeledself-balancingrobot 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.
effort, stability control of a two- wheeled mobile manipulator is analyzed on the ramps . To proof the aim of this paper, the Lagrange approach is utilized. Then, Lyapunov method is used to determine stability margins. Position and velocity control process based on the optimal controller is done to satisfy stability margins. As the other effort related to the locomotion on ramp, a dynamical simulation is done in [25, 26]. Extracted equations are used to simulate locomotion on even surfaces or ramps. According to optimalcontrol based on the optimal gains, stability of mobile manipulator is investigated. Juang and Lum  considered the dynamic simulation of two-wheeled robots by means of using various PID based controllers. On an uneven surface, climbing can improve ability of locomotion. Mobile robots that can climb obstacles, or stairs have been investigated in order to generalize their missions. As a solution, the wheel of mobile manipulator can be transformed to be in , the body is knitted to two parts to elevate easier . In other more complex solution, wheels are armed by active linkages . The hybrid locomotion done by complex leg (linkage and wheel) can improve ability of climbing besides legged locomotion. Some of climbers are armed by passive linkages [31, 32]. In other efforts, 1-DOF link is deformed to the half circle shape [33, 34]. Rhex is a novel platform improved to running and climbing . Some other mobile platforms are specially designed for climbing like Msrox [36, 37]. Msrox is a four-wheeled rover armed by hybrid wheels to climb stairs. The hybrid wheel composition is obtained from installing three wheels on a triangular part. Triangular part is located on each wheel connection point on the main body. In other effort, a four-wheeledrobot armed by parallel mechanism is proposed to climb stair . In this research, using of linkage is considered to obtain climber mechanism. As a powerful climber mechanism, a rail mobile manipulator is proposed in a hybrid structure. This mechanism is designed based on compounded duty of mobile part and manipulator part in climbing and locomotion missions , . The research reported in ,  is the first inspiration for new idea of current development to improve new mechanism proposed at the previous part of introduction. Hybrid locomotion using arm beside mobile parts is a good solution to climbing.
Twowheeledself-balancing vehicle based on the concept of an inverted pendulum is built by researchers at the industrial electronics laboratory. SEGWAY PT is such a one machine developed by Dean Kamen, now commercially obtainable as a battery-powered electric vehicle in the market. Researchers and engineers are working to develop techniques to make a dynamically stable system and to guarantee desired performance and robust solution. Many methods are applied and tested on this system platform. Dual-PID and LQR control techniques are designed and tested in Simulink and analysed for vertical balance and position control . There are many past studies about the stabilization and optimization of two-wheeled inverted pendulum robots. They are state feedback control with pole placement method , Proportional-Integral- Derivative (PID) and Proportional-Derivative(PD) controllers, LQR ,  , Model Predictive Control (MPC) . Kalman filtering and PID algorithm is used for a twowheeled car . PI control is not satisfactory for a twowheeledself-balancingrobot to act in a real time application. Different new research works has found on inverted pendulum techniques in the implementation of bipedal locomotion , . This paper presents LQGand H-infinity mixed sensitivity design for a twowheeledself-balancingrobot. Section two presents system modeling. Section three presents the control techniques. The simulation results are discussed in section four. Conclusions of the work are drawn in section five.
(COTS) sensors and microprocessor boards. While JOEfeatured a digital signal processor board, controller boards based on microprocessor such as the 68HC11, ARM and the ATmega series of the Atmel architecture have become the staple in recent years. Arduino is an open prototyping platform based on ATmega processors and a C language-like software development environment, and can be connected with a variety of COTS sensors  . It is fast becoming popular platform for both education  and product development, with applications ranging from robotics , to process control ,  and networked control  .In this paper, we report a student project on the design, construction and control of a two-wheel self-balancingrobot. The robot is driven by two DC motors, and is equipped with an Arduino Uno board which is based on the ATmega328 processor, 3-axis MEMS (Micro Electrical Mechanical Systems) accelerometer and 3-axis MEMS gyroscope. Twocontrol designs based on the linearized equations of motion is adopted for this project: a proportional-integral-differential (PID) control. The approach is found to be robust to modelling errors which can be incurred during experimental determination of such electrical and kinematic parameters as moments of inertia and motor gains. Simulation and experimental results are presented, which show that stability of the upright position is achieved with PI- PD control within small tilt angles.
inverted pendulum concept. In this concept an inverted pendulum is positioned on a cart and the cart is allowed to move on the horizontal axis and the pendulum is required to stand upright . This type of case is that of an unstable system. The angle measurement is done with the help of a sensor fusion of gyroscope and accelerometer i.e using an IMU, requiring filtering mechanism as both provide erroneous angle results. One such filter is the Kalman Filter, but the design and implementation of that filter is lengthy, tiresome and difficult to implement on smaller 8-bit micro controllers. This paper intends to design and implement a Selfbalancingrobot with the help of a Complementary filter using PID algorithm as the control strategy. The robot is powered with a Hi-watt 9 volts battery to power the Arduino and sensor and AC to DC adapter to power the motor.
Limited works were succeeded in balancing the two- wheeled EV3 Lego Robot by using the PID controller. There are a few linear controllers that have been used by previous researchers as their control strategy for two-wheeled inverted pendulums (TWIP). Most of these researchers aimed to find and analyse the designated controller according to its ability to stabilise the overall performance of controller on the TWIP. A.M Almeshal et. al. used PD-PID controllers for their simulation and found that this controller able to stabilise the TWIP successfully, but further studies have to make to
Self-balancing robots have existed for years. Most notably the Segway has been prominent in media over the last two decades. The principle is simple: a robot is equipped with one or more wheels allowing it drive forward and backward to compensate as the robot begins to fall. While practical implementations are limited, balance bots are pertinent in the field of control theory, because they are naturally unstable systems. In other words, without a closed-loop feedback controller the balance bot is bound to fall over if given even a slight perturbation from equilibrium. Only through proper controller design can a stable system be achieved. The same theory used in the development of a balance bot can be applied to any system that is naturally unstable, such as a rocket or a spacecraft.
A two-wheel mobile robot is one of the applications for the inverted pendulum system. Inverted pendulum is a classical model of under-actuated, non-linear and unstable system. Hence, control of a two-wheel mobile robot is very challenging as it is non-linear, unstable and uncontrollable system. Research and study on the controlling self-balancingtwo-wheel robot has contributed to the practical interest which is the applications on the vehicle field and autonomous robotics. Many practical systems have been implemented based on the two-wheel self-balancingrobot models . Among these applications, Segway PT has been a popular personal transporter since invented in 2001.
This project concerns the development of a mobile robot with a platform, which can be levelled using PID controller. The main objective is to control the flatness of the platform efficiently with a low cost hardware without limiting the strength and performance of the whole system. There are various stages that have been used to stabilize the platform such as modelling the system, obtaining the data from sensors and determining how the control algorithms will be implemented. V.J. Van Doren (2009) suggested a twowheeledrobot to perform the balancing and control of mobile robots. In this project the Proportional, Integral, Derivative (PID) has been implemented to control the flatness of a mobile robot platform. PID has proven to be popular among the control engineering community. As stated by the author of article Vance J. Van Doren (2009), “For more than 60 years after the introduction of Proportional-Integral-Derivative controllers, remain the workhorse of industrial process control”
Twowheeledbalancing robots are an area of research that may well provide the future locomotion for everyday robots. The unique stability control that is required to keep the robot upright differentiates it from traditional forms of robotics. The inverted pendulum principle provides the mathematical modelling of the naturally unstable system. This is then utilized to develop and implement a suitable stability control system that is responsive, timely and successful in achieving this objective. Completing the design and development phase of the robot requires careful consideration of all aspects including operating conditions, materials, hardware, sensors and software. This process provides the ongoing opportunity of implementing continued improvements to its perceived operation whilst also ensuring that obvious problems and potential faults are removed before construction
As a class of under-driven robots, the primary task of the spherical self-balancingrobot is to maintain its posture balance. In this paper, three nonlinear PD controllers are set up respectively in the pitch direction, roll direction and yaw direction. In the balance control of the robot, the reason for selecting PD control instead of PID control is that the noise signals are unavoidable in the gesture detection. Those noise signals are accumulated over time through the integral link, which can cause the integrator lose the adjustment function of the net offset and produce the control error. Compared with PD control, the nonlinear PD control has the advantages of large control margin and high robustness, and it is not easy to produce self-oscillation near the equilibrium point. The control algorithm is as follows.
11 enough for robot’s balance. When the appropriate Kp and Ki gain values are chosen for PI controller, it has been observed that the robot can balance itself for a short time and try to maintain its balance by swinging. In addition, when PID controller is applied, the two-wheel robot can stand in upright position longer compare to the previous two cases. This can be happen if only appropriate value of Kp, Ki, and Kd gain are chosen. Meanwhile, Nasir  states that PID controller capable to control the nonlinear inverted pendulum system angular and linear position in Matlab Simulink. However, PID controller should be improved so that the maximum overshoot for the linear and angular positions do not have high range as required by the design. W.An  claim that Matlab can be used to compare the performance of PID Controller and Linear- quadratic regulator (LQR) in controlling two-wheeledself-balancingrobot. It is concluded that LQR has a better performance than PID in self-balancingcontrol in term of the time to achieve the steady state of robot.
The conclusion from this research is that Modified PSO proposed is capable enough to optimize multivariable function (verified by Benchmark Function test). For simulation on balancingrobot, the MPSO – PID be able to control 3 DOF movement of the robot (balancing, distance, and heading) with less oscillation and faster responses (verified by simulations) than PSO – PID. By using the Integral Square Error (ISE) for evaluating the error, the results are better than using the Integral Absolute Error (IAE).
A novel motor learning method is present based on the cooperation of the cerebellum and basal ganglia for the behavior learning of agent. The motor learning method derives from the principle of CNS and operant learning mechanism and it depends on the interactions between the basal ganglia and cerebellum. The whole learning system is composed of evaluation mechanism, action selection mechanism, tropism mechanism. The learning signals come from not only the Inferior Olive but also the Substantia Nigra in the beginning. The speed of learning is increased as well as the failure time is reduced with the cerebellum as a supervisor. Convergence can be guaranteed in the sense of entropy. With the proposed motor learning method, a motor learning system for the self-balancingtwo-wheeledrobot has been built using the RBF neural networks as the actor and evaluation function approximator. The simulation experiments showed that the proposed motor learning system achieved a better learning effect, so the motor learning based on the coordination of cere- bellum and basal ganglia is effective.
Thirdly, it will be verified whether the total controlled system satisfies controller requirement 5). Analogous to the design of a LQR controller, controller requirement 5) is verified by considering the three scenarios, described in Sec. 4.3.4. Again, to predict which scenario will be most probable for the BBR, two different situations will be simulated. They are also described in Sec. 4.3.4, but for sake of clarity, they will be repeated here. In the first simulation, the closed loop system is simulated with the nonlinear model in Simulink for 5 seconds with a sinusoidal disturbance d for the roll angle, with a frequency of 0.5 Hz and an amplitude of 5 ◦ , which is for now assumed to be a natural disturbance signal for the BBR. The references are set to zero for all states, which means that the BBR is balancing and station keeping at the position (x S ,
There are several control schemes of the self-balancingtwo-wheeled vehicle at home and abroad. A reference scheme of three PID controllers which are linear combined is given by Freescale Smart Car Competition Com- mittee . The two-wheeledrobot JOE developed by the Swiss federal university of technology is designed based on optimalcontrol and state-feedback control . The artificial neural network has been used to construct the adaptive controller for the self-balancingtwo-wheeledrobot . On the basis of the first scheme, this article presents a new method of double cascade PID control. The structure of the control system itself greatly reduces the mutual coupling among balance control, speed control and direction control, so that the parameters of the system are easy to be adjusted, What’s more, compared with state-feedback control and advanced intelligent control, it do not require very precise system model, and the complexity of the control method is reduced.
The paper has developed, modeled a two-wheeledself-balancing bicycle model and designed a robust controller to control the balance of two-wheeled bicyle. The paper also introduces the stochastic balanced truncation algorithm based on Schur analysis and applies this algorithm to reduce the high order robust controller using to control the balance of two-wheeled bicyle. In particularly, the reduced 4 th and 5 th order controller can replace the original controller (30 th -order) while the performance of the control system is ensured. Using the reduced controller simplify the program, so the computational time is reduced. Therefore, the system respose is improved, and the requirements in real-time application are met. The simulation results show the correctness of the model reduction algorithm and the robust control algorithm of two-wheeledself-balancingtwo-wheeled bicycle.
The system architecture comprises a pair of DC motor and an Arduino microcontroller board; a single-axis gyroscope and a 2-axis accelerometer are employed for attitude determination. In addition, a complementary filter is implemented to compensate for gyro drifts. Electrical and kinematic parameters are determined experimentally; PID and LQR-based PI- PD control designs, respectively, are performed on the linearized equations of motion.The types of control is categorized as linear and non-linear control. In some instances, the linear control is sufficient to control a system. One of the most widely used is the Proportional Derivative Integral controller or better known as the PID controller .
A two-wheeled mobile robot is defined as the combination of wheeled mobile robot and inverted pendulum system. An inverted pendulum is a pendulum whose centroid is above its pivot point and a system that equipped with inverted pendulum will become unstable. The inverted pendulum system of a two-wheeled mobile robot is not self-actuated, on the contrary, it is actuated by the movement of the robot. For example, when the two- wheeled mobile robot is moving forward, the inverted pendulum system will lean to backward and the robot have to do something to prevent itself from toppling. Therefore, in order to help the robot to regain its stability, it is always mounted with sensors like gyroscopes and accelerometers whose task is to sense detect the inclination off the vertical axis. After that, the degree of inclination will be sent as feedback to the controller. Based on the received feedback, the controller will sent torque signal to each motor to prevent the system from losing its balance and eventually fall down to the ground. Thus, the two- wheeled mobile robot will have a to and fro movement to overcome its unstable nature (An & Li, 2013).
Proportional control deals with present error. Proportional factor is the product of gain and measured error. Hence, larger proportional gain has faster response time and smaller steady state error but causes overshoots over the desired set point. Setting the proportional gain too high causes a system to oscillate around the set point without settling. For a controller with proportional control action. The relationship between the output of the controller u(t) and the actuating error signal e(t) is