Mobile Inverted Pendulum Research Articles

Dynamic Output Feedback of Second-Order Systems: An Observer-Based Controller with Linear Matrix Inequality Design

This paper presents an observer-based dynamic output-feedback controller design procedure using linear matrix inequality (LMI) optimization for second-order systems with uncertainty and persistent perturbation in the states. Using linear-quadratic criteria, cost functions are minimized in a two-stage procedure to compute optimal state-feedback gains, and observer gains are coupled into a dynamic output-feedback optimal controller. The LMI set used in the two stages is matrix inversion free, a key issue for polytope formulation when uncertainty is present. The approach is tested in a mobile inverted pendulum robotic platform, and the effectiveness is verified in this underactuated and undesensed case.

Machine Learning Based Self-Balancing and Motion Control of the Underactuated Mobile Inverted Pendulum With Variable Load

In this paper, a novel Machine Learning (ML) based Adaptive Fuzzy Logic-Proportional Integral (AFL-PI) controller was developed for the self-balancing and precision motion control of a two wheeled Underactuated-Mobile Inverted Pendulum (U-MIP) under variable payloads. One of the external disturbances in balance and movement control of the U-MIP is the amount of payload it carries on. To investigate the effectiveness of the proposed controller, a load bar was mounted on top of the U-MIP. The weights of 55gr each can be attached to this bar for variable payloads. The weights on the bar were labeled as three different classes: Low Load (LL), Normal Load (NL) and Heavy Load (HL). Artificial Neural Network (ANN), Linear Discriminant Analysis (LDA), Support Vector Machine (SVM) and k-Nearest Neighbors (k-NN) models were tested to obtain the highest load class estimation. The highest load classification accuracy was achieved with ANN. Therefore, the ANN model was applied on the U-MIP. The balance performance of the U-MIP was compared by applying the classical FL-PI and ANN based AFL-PI controller on the robot. In order to compare the body tilt angle performance of the U-MIP, the optimal FL-PI parameter in LL was applied for NL and HL conditions without changing. Then, the proposed ANN-based AFL-PI controller was implemented on U-MIP. With the proposed controller, the body tilt angle variation of the U-MIP was improved by %29.42 for NL and %55.62 for HL compared to the classical FL-PI controller. The validity of the proposed controller was proved by real experiments.

Linear Quadratic Gaussian Regulator for the Nonlinear Observer-Based Control of a Dynamic Base Inverted Pendulum

The inverted pendulum is a non-linear control problem permanently tending towards instability. The main aim of this study is to design a controller capable enough to work within the given conditions while also keeping the pendulum erect given the impulsive movement of the cart to which it is joint via a hinge. The first half of the paper presents the mathematical modelling of the dynamic system, together with the design of a linear quadratic regulator (LQR). This paper also discusses a novel adaptive control mechanism employing a Kalman filter for the mobile inverted pendulum system (MIPS). In the second half of the paper, a Gaussian Quadratic Linear Controller (LQG) is adapted to improve on previous deficiencies. The simulation is done through Simulink and results show that both controllers are capable of managing the multiple output model. However, data from simulations clearly showed that an LQG controller is a better choice.

A memristor-based hybrid analog-digital computing platform for mobile robotics.

Algorithms for mobile robotic systems are generally implemented on purely digital computing platforms. Developing alternative computational platforms may lead to more energy-efficient and responsive mobile robotics. Here, we report a hybrid analog-digital computing platform enabled by memristors on a mobile inverted pendulum robot. Our mobile robotic system can tune the conductance states of memristors adaptively using a model-free optimization method to achieve optimal control performance. We implement sensor fusion and the motion control algorithms on our hybrid analog-digital computing platform and demonstrate more than one order of magnitude enhancement of speed and energy efficiency over traditional digital platforms.

Adjustable and Adaptive Control for an Unstable Mobile Robot Using Imitation Learning with Trajectory Optimization

In this contribution, we develop a feedback controller in the form of a parametric function for a mobile inverted pendulum. The control both stabilizes the system and drives it to target positions with target orientations. A design of the controller based only on a cost function is difficult for this task, which is why we choose to train the controller using imitation learning on optimized trajectories. In contrast to popular approaches like policy gradient methods, this approach allows us to shape the behavior of the system by including equality constraints. When transferring the parametric controller from simulation to the real mobile inverted pendulum, the control performance is degraded due to the reality gap. A robust control design can reduce the degradation. However, for the framework of imitation learning on optimized trajectories, methods that explicitly consider robustness do not yet exist to the knowledge of the authors. We tackle this research gap by presenting a method to design a robust controller in the form of a recurrent neural network, to improve the transferability of the trained controller to the real system. As a last step, we make the behavior of the parametric controller adjustable to allow for the fine tuning of the behavior of the real system. We design the controller for our system and show in the application that the recurrent neural network has increased performance compared to a static neural network without robustness considerations.

Control descentralizado basado en eventos para el consenso de múltiples robots tipo péndulo invertido en el esquema líder-seguidor

<p>El trabajo presenta el diseno de una estrategia de control distribuido con comunicación activada por eventos, que resuelve el problema de consenso líder-seguidor, de un conjunto de robots móviles tipo péndulo invertido (RMPI). La linealización de las ecuaciones de movimiento de los RMPI, alrededor del punto de equilibrio, permiten explotar las propiedades de planitud diferencial, dando lugar a una reparametrizacion del sistema mediante la salida plana. Asumiendo que los vehículos se comunican mediante una red, cuya topología es representada por un grafo no dirigido y fuertemente conectado, se disena una ley de control distribuido y una funcion de evento que indica el instante en el que el i-ésimo vehículo debe transmitir informacion (su estado) a sus vecinos. El resultado es un intercambio asíncrono de informacion entre vehículos y donde el tiempo entre eventos no es equidistante. El analisis de estabilidad se lleva a cabo en el sentido de Lyapunov y en el sentido entrada-estado ISS (Input-to-State Stability). Los resultados en simulacion numérica muestran el buen desempeño del consenso de la red de vehículos en dos escenarios representativos: regulacion y seguimiento de trayectoria.</p>

Inquiry-based learning: Development of an introductory manufacturing processes course based on a mobile inverted pendulum robot

This paper describes the development of an innovative introductory manufacturing processes course designed to expose students to a broad overview of fundamental concepts, methods, procedures, tools, and equipment used in the manufacturing industry. Based on an educational mobile inverted pendulum robot, students are introduced to product design and prototyping by identifying an existing problem with a component in the robot, redesigning the component using computer aided design software, and then building a prototype using additive manufacturing methods. Subsequently, a set of hypothetical design requirement changes is imposed, and various design methods and manufacturing processes that can be used to make components to satisfy these new requirements are discussed. Topics covered include integrated product design, additive manufacturing prototyping based on different technologies, plastic injection molding, sand casting, and fundamentals of both computer aided manufacturing and computer numerical control machining. Tools, fixtures, and accessories required in these processes, as well as associated challenges, are also discussed. This course adapts the inquiry-based learning active learning pedagogical approach and focuses on the development of students’ ability to conduct analytical analysis and to apply a knowledge of mathematics, science, engineering, and technology to solve practical engineering technology problems. As an introductory course designed to be offered to freshman level students, this course engages students in engineering technology related topics and stimulates their interest in manufacturing related subjects. It helps with improving the engineering student retention rate and serves as a pathway connecting students to more advanced specialized manufacturing courses such as computer numerical control machining technology. This paper presents course materials developed and student feedback as well as their evaluation of the course effectiveness based on a summative questionnaire-style survey from the first cohort of students.

H2 Sliding Mode Controller Design for Mobile Inverted Pendulum System

The design of an H2 sliding mode controller for a mobile inverted pendulum system is proposed in this paper. This controller is conducted to stabilize the mobile inverted pendulum in the upright position and drive the system to a desired position. Lagrangian approach is used to develop the mathematical model of the system. The H2 controller is combined with the sliding mode control to give a better performance compared to the case of using each of the above controllers alone. The results show that the proposed controller can stabilize the system and drive the output to a given desired input. Furthermore, variations in system parameters and disturbance are considered to illustrate the robustness of the proposed controller.

Self Balancing Scooter

The self balancing scooter is a project that has become very popular in the field of engineering. This project draws on the theoretical principles of the equally popular experiment of the inverted pendulum. The inverted pendulum system, unlike many other control systems is naturally unstable. This unique behavior of the inverted pendulum has drawn interest from many researchers. Due to this unstable condition, a controller has to be designed so that the system reaches stability in the unstable state. The idea of a mobile inverted pendulum robot has surfaced in recent years and has attracted interest from control system researchers worldwide. A two wheel mobile robot in the inverted pendulum model is built. As the robot is mechanically unstable, it becomes necessary to explore the possibilities of implementing a control system to keep the system in equilibrium. This project is divided into three main groups which are the hardware implementation, software implementation, and the control algorithm. The discussion of the developments of each stage is covered in this report.

Formation Control and Trajectory Tracking of Nonholonomic Mobile Robots

In this brief, we design Lyapunov-based control laws to achieve two multi-objective tasks for a network of open-loop unstable, nonholonomic mobile inverted pendulum (MIP) robots, using a connected undirected graph for inter-agent communication. Using the first protocol, translationally invariant formations are achieved along with the synchronization of attitudes and heading velocities to desired values. Using the second protocol, the robots move into a formation and asymptotically track a trajectory. The control laws are based on the kinematic model of the mobile robot, and control torques for the MIPs are extracted using a two-loop control architecture. Both the protocols guarantee boundedness of the linear heading velocity, which is necessary for the stability of the two-loop control architecture. The proposed control laws are experimentally validated on indigenously built MIP robots.

Intelligent decoupled controller for mobile inverted pendulum real-time implementation

Intelligent decoupled controller for mobile inverted pendulum real-time implementation

LMI-based LSVF control of a class of nonlinear systems with parametric uncertainty: an application to an inverted pendulum system

ABSTRACTThis work centres around the stabilisation of a nonlinear system containing parametric uncertainty using a new Control Lyapunov Function (using Lie derivatives) which comes up with a linear matrix inequality-based design. The paper has three major contributions. The first one is an extension of a theorem proposed to find the convex-concave bounds of nonlinear function towards robustness. With some restrictions in the structure of the uncertainty, the theory developed here may be applied to find out the bounds of any nonlinear function with uncertainty. The next one is the main contribution of this paper in which the form of the control law obtained is linear and has several advantages from a practical point of view over almost all other nonlinear control techniques. The third one is the expansion of the proposed control scheme towards underactuated systems. To show the effectiveness of the proposed theory the controller design is attempted for both the traditional cart inverted pendulum and the more complex mobile wheeled inverted pendulum model.

Trajectory following control of mobile inverted pendulum robot with pre-determined tilt angle

S-curved trajectory following control of a mobile inverted pendulum robot (MIR) was implemented in this research based on the MIR dynamics. The tilt angle of the inverted pendulum was determined from the MIR dynamics for a given acceleration to keep the inverted pendulum stable. The driving algorithm for a four-wheeled mobile platform was designed using state feedback to keep the inverted pendulum upright while maintaining the desired velocity trajectory along the entire path. To overcome the disturbances produced by the mobile robot motion, the ground’s slant angle was detected by a tilt sensor and used to adjust the pendulum’s operating point. This allowed the MIR to be driven to the desired position while maintaining the desired velocity profile and keeping the inverted pendulum upright. The proposed algorithm was verified using real experiments with straight line and S-curved paths.

Dynamics-Based Nonlinear Acceleration Control With Energy Shaping for a Mobile Inverted Pendulum With a Slider Mechanism

A nonlinear controller to accelerate a mobile inverted pendulum (MIP) with a slider mechanism is proposed. The concept of this paper is to control translational acceleration and deceleration of the MIP in a dynamically reasonable manner. The body angle and slider displacement are controlled to maintain reference states where the MIP is statically unstable but dynamically stable, which leads to a constant translational acceleration due to instability of the vehicle. The accelerating motion is like a sprinter moving from the crouch start, and it fully exploits the dynamics of the MIP. To achieve it, the total energy of the system is shaped to have the minimum at the given reference states and the system is controlled to converge to them. The controller can achieve various properties through the energy-shaping procedure. In particular, an energy function that will lead to safe operation of the MIP is proposed. The function ensures that motion of the MIP is restricted within predefined regions. The controller also returns the system back to the reference states with state-dependent gains that become large if the system comes close to falling over. The effectiveness of the controller is verified in simulations. Finally, a new physical MIP was constructed, and experiments were carried out with an additional friction compensation method. The results show that the proposed controller works well in the presence of uncertainty, such as noise and modeling errors.

Nonlinear control of mobile inverted pendulum

The mobile inverted pendulum (MIP) is a robotic system with nonholonomic constraint due to no-slip condition imposed on the wheel. In particular, it has four configuration variables to be controlled using only two control inputs. In this paper, we propose a nonlinear control strategy to move the MIP from one point to another point in the configuration space while stabilizing the pendulum. The proposed single level controller is designed using a nonlinear co-ordinate transformation which leads to a simple three step navigation design procedure. The proposed controller stabilizes all four configuration variables without switching between the controllers. Simulation results are presented to validate the proposed technique.

Position Stabilization and Waypoint Tracking Control of Mobile Inverted Pendulum Robot

The mobile inverted pendulum (MIP) is a mechanical system that presents multiple control challenges. In particular, two objectives, namely desired position control and stabilization of the unstable pendulum-like central body, need to be simultaneously met. In this brief, we propose a novel smooth time-invariant controller to achieve the twin objectives. A feature of the controller design is that it readily extends to achieve waypoint tracking, another interesting task for mobile platforms. To validate the theory developed, an MIP has been indigenously designed and fabricated. Extensive experiments on the MIP have been performed. It has been observed that the system accomplishes position stabilization as well as waypoint tracking with negligible error.

Control of a two-wheel robotic vehicle for personal transportation

SUMMARYRecently, small-sized compact electric vehicles have been in demand for short-distance travel in urban areas, although battery charging in electric vehicles present in the market is still problematic. Borrowing from the concept of a mobile inverted pendulum system, in this paper, a two-wheel robotic vehicle system is implemented and controlled as the future personal transportation device called the TransBOT. The TransBOT has two driving modes: a regular vehicle mode, where stable contact on the ground is maintained by two wheels and two casters, and the balancing mode, which maintains the stable posture with two wheels on the ground. The two-wheel balancing mechanism can be used as a transportation vehicle in narrow and busy urban areas. Gain scheduling control methods based on linear controllers are used for different drivers. In addition, desired balancing angles are specified for the different sizes of drivers in order to have a stable balancing control performance. These desired balancing angle values have been found by empirical studies. Experimental studies with drivers of different weights, as well as indoor and outdoor driving tasks, were conducted to ensure the feasibility of TransBOT.

자율주행 모바일 역진자의 비주얼서보잉에 대한 연구

This paper proposes an optimal three-dimensional coordinate implementation of the vision sensor using two CCD cameras. The PBVS (Position based visual servoing) is implemented using the positional information obtained from images. Stereo vision by PBVS method that has enhanced every frame using calibration parameters is effective in the distance calculation. The IBVS (Image based visual servoing) is also implemented using the difference between reference and obtained images. Stereo vision by IBVS method calculates the distance using rotation angle of motors that correspond eyes and neck without enhanced images. The PBVS method is compared with the IBVS method in terms of advantages, disadvantages, computing time, and performances. Finally, the IBVS method is applied for the dual arm manipulator on the mobile inverted pendulum. The autonomous mobile inverted pendulum is successfully demonstrated using the center of the manipulator's mass.

Velocity control of mobile wheeled inverted pendulum

The mobile wheeled inverted pendulum (MWIP) is widely used in many robotic applications and also paid attention by theorists due to its essentially unstable dynamics. The equilibrium control and velocity control of a mobile wheeled inverted pendulum are discussed in this paper. Based on the three-dimensional (3D) dynamic model of this underactuated system running on the flat ground derived by Lagrange’s motion equation, a terminal sliding mode control (TSMC) is proposed to ensure the underactuated system can be self-balanced and variables converge to desired states. The proposed controller can guarantee the system both stays at the equilibrium and tracks a given yaw angle while LQR controller can only stay the MWIP system at equilibrium. Numerical simulations are provided to verify and illustrate the effectiveness of the proposed model and controllers.

A new device laboratory: Experimental validation

A device laboratory was designed to create a commanded disturbance to the Furuta inverted pendulum. This pendulum was modified by adding a second inverted pendulum coupled to the main one by means of a semi-rigid spring. The induced motion on the second inverted pendulum causes displacement of the center of mass of the system, producing a kind of perturbation similar to that presented on mobile inverted pendulum transportation units. A linear matrix inequality (LMI) controller is designed from the unperturbed model (based on the main pendulum without the second inverted one) and implemented to our system. Then, experimentally, the behaviour of the whole closed-loop system and the controller performance was analysed. According to the laboratory test, the LMI controller is robust enough in front of perturbation induced on the second pendulum.