Two-wheeled Inverted Pendulum Research Articles

Design and Implementation of a Two-Wheeled Inverted Pendulum Robot With a Sliding Mechanism for Off-Road Transportation

This paper proposes a multi-degrees-of-freedom two-wheeled inverted pendulum robot (mD-TWIPR) for off-road transportation. A two-wheeled inverted pendulum robot (TWIPR), popularly known as a segway, has high mobility owing to its simple structure without steering or suspension. The proposed robot has a car-like structure with a low and elongated body that provides advantages for transporting long objects, such as pipes, or transferring patients on off-road terrain. However, a car-like TWIPR structure faces several challenges, including limited acceleration, difficulty traversing slopes, asymmetric payload, and lower ability to climb steps. To address these issues, we implemented a sliding mechanism in the mD-TWIPR. The proposed mD-TWIPR is designed to move without tilting while carrying movable mass, and tilt the torso according to the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$20^{\circ }$</tex-math></inline-formula> slope. It can also maintain stationary on a slope with only a small wheel torque by positioning the center of mass on the fulcrum, which is advantageous for transportation operations. Furthermore, it can climb a step using a combination of the wheel and sliding mechanism. The paper discusses the modeling and design specifications and presents a prototype and experiments to verify the proposed performance of mD-TWIPR.

Modelling and Control of a Two-Wheel Inverted Pendulum Using Fuzzy-PID-Modified State Feedback

Control of mechanical systems by electronic systems controlled by computer programs is one of the most active research areas in mechatronic systems engineering. These programs carry out control laws, which are algorithms. This study focuses on Segway control (a two-wheeled inverted pendulum which is a highly nonlinear and unstable open-loop system). Our research entails creating a control law to stabilize this system. We proposed using a state feedback controller, which provided us with a stable system and a lower error margin; however, to correct this error, we used a combination of the state feedback controller and the fuzzy-PID controller. The effectiveness of the proposed method is demonstrated using simulation results.

Balancing-Prioritized Anti-Slip Control of a Two-Wheeled Inverted Pendulum Robot Vehicle on Low-Frictional Surfaces with an Acceleration Slip Indicator

When a two-wheeled inverted pendulum (TWIP) robot vehicle travels on slippery roads, the occurrence of wheel slip extremely threatens its postural stability owing to the loss of wheel traction. If a severe wheel slip happens between the driving wheels and contact surfaces, no control techniques can guarantee the driving performance and stability of the TWIP robots in the absence of an extra wheel slip control strategy. In this paper, a TWIP-compatible countermeasure against the wheel slip phenomena is investigated for enhancing the reliability of the vehicle and the robustness of the motion control performance on low-frictional surfaces. To this end, we propose a balancing-prioritized anti-slip control method based on the maximum transmissible torque estimation, which is activated only when a wheel slip is detected by the acceleration slip indicator utilizing accessible data from the IMU and wheel encoders. It is proved that the TWIP vehicles applying the proposed method can successfully cope with low frictional surfaces while maintaining postural stability. Finally, comparative simulations and experiments demonstrate the effectiveness and feasibility of the proposed scheme.

Observer-Based Integral Sliding Mode Controller for a Two-Wheeled Inverted Pendulum

The modeling and control of a two-wheeled inverted pendulum (TWIP) is gaining much interest due to the various advancements in hardware and computing technologies. A TWIP system has many advantages and applications. However, it still faces many challenges such as positioning, disturbance rejection, parameter uncertainties, etc. In this paper, a control scheme based on modern control techniques is presented to overcome these issues. Furthermore, an observer-based robust integral sliding mode controller (ISMC) is proposed for the nonlinear TWIP system. Firstly, a robust integral sliding mode controller is designed to tackle short-term and long-term constant and time-varying disturbances as well as issues relating to parameter variation. Secondly, the reduced-order observer is designed to estimate immeasurable states, enabling simplified implementation. It is then applied to the nonlinear model of the TWIP system, and performance is observed under different transient conditions. A comparison with prevalent controllers in the literature is carried out. This comparison relates to graphical results, time domain specifications, and error performance indices, calculated for states. From this, a significant qualitative improvement can be observed with the proposed controller for all types of transients. In quantitative terms, zero steady-state error with disturbances and a five-fold improvement in settling time with parameter variations are observed. This paper also discusses the software Simulink realization for modeling and control of the TWIP system, which can be valuable for novices working in this area.

Experimental Build of a Two-Wheeled Inverted Pendulum Mobile Robot

This undergraduate research project describes the construction, autonomous control, and exploration of potential uses of a Two-Wheeled Inverted Pendulum (TWIP) in uncontrolled environments [1]. Initially, the non-functioning physical design is two repurposed wheelchair wheels and motors mounted to a chassis that holds two batteries to power the robot. The goal was to continue with the legacy design, augment the build to the point where the robot is programmable, and potentially add sensors for further applications. Another goal was to learn how to design a safe circuit to power the robot and its controllers. Another objective was to learn about the fundamentals of programming an autonomous robot. This paper describes the experimental research progress and findings. The robot is currently programmable with an Arduino Mega 2560, which controls the wheels with two separate motor controllers. It has a limited footprint and has the potential to carry substantial payloads, which promises to be beneficial in uncontrolled workspaces. The initial research has the robot capable of being programmed to go in a straight line and currently has an MPU 6050 accelerometer and gyro attached to the Arduino, delivers state data used to make accurate turns and sense whether the robot has accelerated too quickly and may be in danger of becoming unbalanced.

Robust Stabilization of Underactuated Two-Wheeled Balancing Vehicles on Uncertain Terrains with Nonlinear-Model-Based Disturbance Compensation

Two-wheeled inverted pendulum (TWIP) vehicles are prone to lose their mobility and postural stability owing to their inherently unstable and underactuated dynamic characteristics, specifically when they encounter abruptly changed slopes or ground friction. Overcoming such environmental disturbances is essential to realize an agile TWIP-based mobile platform. In this paper, we suggest a disturbance compensation method that is compatible with unmanned TWIP systems in terms of the nonlinear-model-based disturbance observer, where the underactuated dynamic model is transformed to a fully actuated form by regarding the gravitational moment of the inverted pendulum as a supplementary pseudo-actuator to counteract the pitch-directional disturbances. Consequently, it enables us to intuitively determine the disturbance compensation input of the two wheels and the pitch reference input accommodating to uncertain terrains in real time. Through simulation and experimental results, the effectiveness of the proposed method is validated.

A Novel LiDAR-IMU-Odometer Coupling Framework for Two-Wheeled Inverted Pendulum (TWIP) Robot Localization and Mapping with Nonholonomic Constraint Factors.

This paper proposes a method to solve the problem of localization and mapping of a two-wheeled inverted pendulum (TWIP) robot on approximately flat ground using a Lidar–IMU–Odometer system. When TWIP is in motion, it is constrained by the ground and suffers from motion disturbances caused by rough terrain or motion shaking. Combining the motion characteristics of TWIP, this paper proposes a framework for localization consisting of a Lidar-IMU-Odometer system. This system formulates a factor graph with five types of factors, thereby coupling relative and absolute measurements from different sensors (including ground constraints) into the system. Moreover, we analyze the constraint dimension of each factor according to the motion characteristics of TWIP and propose a new nonholonomic constraint factor for the odometry pre-integration constraint and ground constraint factor in order to add them naturally to the factor graph with the robot state node on SE(3). Meanwhile, we calculate the uncertainty of each constraint. Utilizing such a nonholonomic constraint factor, a complete lidar–IMU–odometry-based motion estimation system for TWIP is developed via smoothing and mapping. Indoor and outdoor experiments show that our method has better accuracy for two-wheeled inverted pendulum robots.

A novel Stereo-IMU system based on accurate pose parameterization of two-wheeled inverted pendulum (TWIP) robot in localization and mapping

PurposeThis paper aims to propose a method to solve the problem of localization and mapping of a two-wheeled inverted pendulum (TWIP) robot on the ground using the Stereo–inertial measurement unit (IMU) system. This method reparametrizes the pose according to the motion characteristics of TWIP and considers the impact of uneven ground on vision and IMU, which is more adaptable to the real environment.Design/methodology/approachWhen TWIP moves, it is constrained by the ground and swings back and forth to maintain balance. Therefore, the authors parameterize the robot pose as SE(2) pose plus pitch according to the motion characteristics of TWIP. However, the authors do not omit disturbances in other directions but perform error modeling, which is integrated into the visual constraints and IMU pre-integration constraints as an error term. Finally, the authors analyze the influence of the error term on the vision and IMU constraints during the optimization process. Compared to traditional algorithms, the algorithm is simpler and better adapt to the real environment.FindingsThe results of indoor and outdoor experiments show that, for the TWIP robot, the method has better positioning accuracy and robustness compared with the state-of-the-art.Originality/valueThe algorithm in this paper is proposed for the localization and mapping of a TWIP robot. Different from the traditional positioning method on SE(3), this paper parameterizes the robot pose as SE(2) pose plus pitch according to the motion of TWIP and the motion disturbances in other directions are integrated into visual constraints and IMU pre-integration constraints as error terms, which simplifies the optimization parameters, better adapts to the real environment and improves the accuracy of positioning.

Decoupled Multi-Loop Robust Control for a Walk-Assistance Robot Employing a Two-Wheeled Inverted Pendulum

This paper develops a decoupled multi-loop control for a two-wheeled inverted pendulum (TWIP) robot that can assist user’s with walking. The TWIP robot is equipped with two wheels driven by electrical motors. We derive the system’s transfer function and design a robust loop-shaping controller to balance the system. The simulation and experimental results show that the TWIP system can be balanced but might experience velocity drifts because its balancing point is affected by model variations and disturbances. Therefore, we propose a multi-loop control layout consisting of a velocity loop and a position loop for the TWIP robot. The velocity loop can adjust the balancing point in real-time and regulate the forward velocity, while the position loop can achieve position tracking. For walking assistance, we design a decoupled control structure that transfers the linear and rotational motions of the robot to the commands of two parallel motors. We implement the designed controllers for simulation and experiments and show that the TWIP system employing the proposed decoupled multi-loop control can provide satisfactory responses when assisting with walking.

Design and Real-Time Implementation of a nonlinear regulation controller for the RMP-100 Segway TWIP

The RMP-100 is an underactuated robot known in the literature as two wheeled inverted pendulum (TWIP). This mechanism has two independent wheels that allow to perform two tasks simultaneously: keep the inverted pendulum in its upright position (balancing) and move the robot to a specific location on the workspace terrain. This paper proposes (as an extension of the work of Gutiérrez Frías, 2013) a nonlinear Lyapunov-based controller with the purpose to stabilize the pose (position and orientation) of the robot while balancing the pendulum. Moreover, asymptotic stability is proven using LaSalle’s invariance principle. Furthermore, the development of a new software for implementing real-time controllers on the RMP-100 is briefly explained; and finally, in order to validate the performance of the proposed controller, experimental results are included.

Udwadia-Kalaba Equation Based Adaptive Robust Control for Two-wheeled Inverted Pendulum System: Underactuation and Uncertainty

A new adaptive robust control method based on Udwadia-Kalaba(U-K) approach which can be applied to the underactuated system is designed and used to two-wheeled inverted pendulum system in this paper. We separate this typical underactuated system into two subsystems(forward subsystem and yaw subsystem), which are fully underactuated and actuated. For these different subsystems, we use different control methods. We apply an adaptive robust control method which has been proved many times to the fully actuated subsystem. Based on this adaptive robust method, a new control strategy can be redesigned and applied to the underactuated subsystem by modifying the adaptive law and other things. This adaptive robust control with a leakage-type adaptive law could guarantee the uniform boundedness and uniform ultimate boundedness of the system. Finally, the simulation is executed to demonstrate the advantage and simplicity of the proposed method.

Motion control of a two-wheeled inverted pendulum with uncertain rolling resistance and angle constraint based on slow-fast dynamics

Rolling resistance and angle constraint are important factors affecting the control performance and dynamics of Two-Wheeled Inverted Pendulums (TWIPs, for short), but they are usually neglected in previous studies. Taking both factors into account, this paper presents new control designs for the angle control of the pendulum, for the velocity control and the position control of the TWIP system. Firstly, based on dimensionality reduction and the nonlinear dynamics of the inverted pendulum, a controller with simple structure is designed for controlling the pendulum angle when the rolling resistance is precisely known. Then an improved robust controller against the unknown rolling resistance is designed for the pendulum angle. Secondly, by using the dynamics theory of slow-fast systems, velocity and position controllers for the wheels of the TWIP system are proposed with known and unknown rolling resistance. In the position control, the overshoots can be adjusted close enough to zero. Numerical examples are given to verify and demonstrate the theoretical results.

Regular form-based sliding mode control design on a two-wheeled inverted pendulum

Regular form-based sliding mode control design on a two-wheeled inverted pendulum

Regular form-based sliding mode control design on a two-wheeled inverted pendulum

Regular form-based sliding mode control design on a two-wheeled inverted pendulum

Control of the two-wheeled inverted pendulum (TWIP) robot in presence of model uncertainty and motion restriction

Purpose The purpose of this paper is to improve control performance and safety of a real two-wheeled inverted pendulum (TWIP) robot by dealing with model uncertainty and motion restriction simultaneously, which can be extended to other TWIP robotic systems. Design/methodology/approach The inequality of lumped model uncertainty boundary is derived from original TWIP dynamics. Several motion restriction conditions are derived considering zero dynamics, centripedal force, ground friction condition, posture stability, control torque limitation and so on. Sliding-mode control (SMC) and model predictive control (MPC) are separately adopted to design controllers for longitudinal and rotational motion, while taking model uncertainty into account. The reference value of the moving velocity and acceleration, delivered to the designed controller, should be restricted in a specified range, limited by motion restrictions, to keep safe. Findings The cancelation of model uncertainty commonly existing in real system can improve control performance. The motion commands play an important role in maintaining safety and reliability of TWIP, which can be ensured by the proposed motion restriction to avoid potential movement failure, such as slipping, lateral tipping over because of turning and large fluctuation of body. Originality/value An inequation of lumped model uncertainty boundary incorporating comprehensive errors and uncertainties of system is derived and elaborately calculated to determine the switching coefficients of SMC. The motion restrictions for TWIP robot moving in 3D are derived and used to impose constraints on reference trajectory to avoid possible instability or failure of movement.

Optimal PID Controller Autotuning Design for MIMO Nonlinear Systems Based on the Adaptive SLP Algorithm

In this paper, an adaptive swarm learning process (SLP) algorithm for designing the optimal proportional integral and derivative (PID) parameter for a multiple-input multiple-output (MIMO) control system is proposed. The SLP algorithm is proposed to improve the performance and convergence of PID parameter autotuning by applying the swarm algorithm and the learning process. The adaptive SLP algorithm improves the stability, performance and robustness of the traditional SLP algorithm to apply it to a MIMO control system. It can update the online weights of the SLP algorithm caused by the errors in the settling time, rise time and overshoot of the system based on a stable learning rate. The gradient descent is applied to update the weights. The stable learning rate is verified based on the Lyapunov stability theorem. Additionally, simulations are performed to verify the superiority of the algorithm in terms of performance and robustness. Results that compare the adaptive SLP algorithm with the traditional SLP, a neural network (NN), the genetic algorithm (GA), the particle swarm and optimization (PSO) algorithm and the kidney-inspired algorithm (KIA) based on a two-wheel inverted pendulum system are presented. With respect to performance and robustness, the adaptive SLP algorithm provides a better response than the traditional SLP, NN, GA, PSO and KIA.

Optimal Adaptive Robust Control Based on Cooperative Game Theory for a Class of Fuzzy Underactuated Mechanical Systems.

While designing control for a class of underactuated mechanical systems (UMSs), the uncertainty and the prescribed nonholonomic tracking trajectories should be taken into consideration. Uncertainty considered in this article is time varying and bounded, and the bound of uncertainty is described using the fuzzy set theory, namely, fuzzy UMSs. An analytical dynamics-based view is taken in which the prescribed tracking trajectories are viewed as servo constraints which can be linear, nonlinear, holonomic, and nonholonomic. Using this view, a novel closed form solution of adaptive robust control is found with leakage type adaptive law to guarantee deterministic system performance, including uniform boundedness and uniform ultimate boundedness. In order to find the optimal dual gain parameters of the designed control, a two-player cooperative game is proposed for which the Pareto optimality can always be guaranteed. The effectiveness of the proposed control is shown through numerical simulation of a two-wheeled inverted pendulum vehicle.

Real-time Mamdani-like fuzzy and fusion-based fuzzy controllers for balancing two-wheeled inverted pendulum

Two wheeled inverted pendulum (TWIP) resembles many industrial as well as real life applications. TWIP is underactuated, nonlinear and unstable system. Therefore, it is widely used as benchmark for illustrating control concepts, theories, and algorithms that deal with these challenges. The main motivations of this paper are designing controllers that deal with lack of information that accompanying an inexpensive cheap TWIP and verified its stability, proper speed, robustness and smooth tracking. Consequently, intelligent technique instead of conventional ones that depends on mathematical models should be used. In this article hybrid controllers, consisting of fuzzy controllers and three mode controllers’ (PID), are developed. Two major techniques are used, Mamdani-Like Fuzzy and Fusion-Based function, to design five controllers. Moreover, dynamic indices and steady state indices are implemented to choose the most proper controllers among various designed ones. A new criterion is defined to measure steady state performance of oscillation. All controllers were tested in real-time to control the angle of the TWIP for stability and disturbance rejection. The experimental results showed that both strategies of Mamdani-Like Fuzzy and Fusion-Based fuzzy can control and balance adequately the TWIP, but the PD-Like fuzzy yielded more better performance.

CONTROL OF TWO-WHEELED INVERTED PENDULUM ROBOT USING ROBUST PI AND LQR CONTROLLERS

In this paper, a robust PI controller in combination with a linear quadratic regulator (LQR) is proposed to control a two-wheeled inverted pendulum robot (TWIPR) such that it is kept balanced while moving. The proposed TWIPR control system consists of two control loops. The inner loop has two PI controllers for two DC motors’ currents, which are separately designed based on a robust PI controller structure. The outer loop contains a LQR controller for the tilt angle, heading angle and position of the TWIPR. The proposed PI controller is compared to the existing method such as the magnitude optimum (MO) and genetic algorithm (GA) methods. The proposed control scheme is verified through simulations and practical tests, and it is also compared to the MO-LQR and GA-LQR strategies.

CONVENTIONAL FUZZY LOGIC CONTROLLER FOR BALANCING TWO-WHEEL INVERTED PENDULUM

This paper presents the design and the Real-Time implementation of self-balancing Two-Wheeled Inverted Pendulum (TWIP) using state-feedback controller and a conventional fuzzy logic controller (CFLC) on Real-Time. The state-feedback controller consists of two parts PD controller and PI controller. The state-feedback controller was designed first for the nonlinear model then it was updated for the Real-Time implementation. The CFLC was designed first based on the state-feedback controller to reach the point of using pure fuzzy controller for the TWIP. The CFLC was designed with Mamdani fuzzy inference architecture if-then rules. The TWIP is balanced with CFLC with a base of 7 rules only. Different controller’s types were tested on real-Time to perform a good balance for the TWIP. Fuzzy PI, Fuzzy PD, and combination of two independent CFLC were used to achieve the balancing of the TWIP on Real-Time.