Wheeled Inverted Pendulum System Research Articles

Robust compound control for wheeled inverted pendulum in an uncertain and disturbed environment

This paper proposes a robust control for wheeled inverted pendulum (WIP) taking into account the wheel position and pendulum angle in the presence of uncertain disturbances. The proposed control algorithm is a combination of time-varying sliding mode control (TVSMC), exponential reaching law (ERL), and nonlinear feedback control (NFC) to eliminate the chattering phenomenon and arrive at better stability and tracking performance. For consistency, the nonlinear dynamic model of WIP is derived using Lagrangian and Newtonian approaches. The convergence and stability of the proposed control scheme are proved using Lyapunov theorem. The study also presents a comparative analysis of linear and nonlinear control strategies based on investigation of time response, tracking error, and control energy. The WIP system has been subjected to various rigorous initial conditions and disturbances to characterize the stability and tracking performance of the implemented controllers. The simulation results demonstrate the promising performance of the proposed control scheme in eliminating the chattering phenomenon, suppressing the uncertain disturbances effect, and improving the stability and tracking performance.

Adaptive Reinforcement Learning Strategy with Sliding Mode Control for Unknown and Disturbed Wheeled Inverted Pendulum

This paper develops a novel adaptive integral sliding-mode control (SMC) technique to improve the tracking performance of a wheeled inverted pendulum (WIP) system, which belongs to a class of continuous time systems with input disturbance and/or unknown parameters. The proposed algorithm is established based on an integrating between the advantage of online adaptive reinforcement learning control and the high robustness of integral sliding-mode control (SMC) law. The main objective is to find a general structure of integral sliding mode control law that can guarantee the system state reaching a sliding surface in finite time. An adaptive/approximate optimal control based on the approximate/adaptive dynamic programming (ADP) is responsible for the asymptotic stability of the closed loop system. Furthermore, the convergence possibility of proposed output feedback optimal control was determined without the convergence of additional state observer. Finally, the theoretical analysis and simulation results validate the performance of the proposed control structure.

Structure-Preserving Constrained Optimal Trajectory Planning of a Wheeled Inverted Pendulum

The wheeled inverted pendulum (WIP) is an underactuated, nonholonomic mechatronic system, and has been popularized commercially as the Segway . Designing a control law for motion planning, that incorporates the state and control constraints, while respecting the configuration manifold, is a challenging problem. In this article, we derive a discrete-time model of the WIP system using discrete mechanics and generate optimal trajectories for the WIP system by solving a discrete-time constrained optimal control problem. Furthermore, we describe a nonlinear continuous-time model with parameters for designing a closed-loop linear–quadratic regulator (LQR). A dual control architecture is implemented in which the designed optimal trajectory is, then, provided as a reference to the robot with the optimal control trajectory as a feedforward control action, and an LQR in the feedback mode is employed to mitigate noise and disturbances for ensuing stable motion of the WIP system. While performing experiments on the WIP system involving aggressive maneuvers with fairly sharp turns, we found a high degree of congruence in the designed optimal trajectories and the path traced by the robot while tracking these trajectories. This corroborates the validity of the nonlinear model and the control scheme. Finally, these experiments demonstrate the highly nonlinear nature of the WIP system and robustness of the control scheme.

High-Order Disturbance-Observer-Based Sliding Mode Control for Mobile Wheeled Inverted Pendulum Systems

In this paper, a novel high-order disturbance observer (HODO) for the mobile wheeled inverted pendulum (MWIP) system is first proposed. Based on a choice method of optimal gain matrices, the estimation accuracy of the HODO can be improved. Combining the proposed HODO and sliding mode control (SMC), a new control strategy is designed for the balance and speed control of the MWIP system. The boundness of the estimation error of HODO is proved and the stability of the closed-loop control system is achieved through the appropriate selection of sliding surface coefficients. The effectiveness of all proposed methods is verified by experiments on a real MWIP system.

Full State Feedback 𝐇𝟐 and H-infinity Controllers Design for a Two Wheeled Inverted Pendulum System

In this work, two robust controllers, which are full state feedback, 𝐻2 and full state feedback 𝐻∞ controllers are proposed for the two wheeled inverted pendulum system. The nonlinear equations for the two wheeled inverted pendulum system are developed using Euler – Lagrange equation. The system parameters changes are considered to show the effectiveness of the proposed robust controllers. These controllers are proposed not only to stabilize the pendulum in upright position but also to drive the position to track a given reference input. The results show that more desirable robustness and time response specifications can be achieved using the proposed controllers. The effectiveness of the proposed controllers is verified experimentally using real two wheeled inverted pendulum system.

ANN-Based Control of a Wheeled Inverted Pendulum System Using an Extended DBD Learning Algorithm

This paper presents a dynamic model for a self-balancing vehicle using the Euler-Lagrange approach. The design and deployment of an artificial neuronal network (ANN) in a closed-loop control is described. The ANN is characterized by integration of the extended delta-bar-delta algorithm (DBD), which accelerates the adjustment of synaptic weights. The results of the control strategy in the dynamic model of the robot are also presented.

Nonlinear Disturbance Observer-Based Dynamic Surface Control of Mobile Wheeled Inverted Pendulum

In this brief, a dynamic model of a mobile wheeled inverted pendulum (MWIP) system is improved considering friction forces, and a nonlinear disturbance observer (NDO)-based dynamic surface controller is investigated to control the MWIP system. Using a coordinate transformation, this non-Class-I type underactuated system is presented as a semistrict feedback form, which is convenient for dynamic surface controller design. A dynamic surface controller together with an NDO is designed to stabilize the underactuated plant. The proposed approach can compensate the external disturbances and the model uncertainties to improve the system performance significantly. The stability of the closed-loop MWIP system is proved by Lyapunov theorem. Experiment results are presented to illustrate the feasibility and efficiency of the proposed method.

Dynamic Motion Planning and Adaptive Tracking Control for a Class of Two-Wheeled Autonomous Vehicle With an Underactuated Pendular Suspension

This paper investigates a dynamic motion planning approach and an adaptive tracking control scheme for a class of two-wheeled autonomous vehicle with an underactuated pendular suspension subject to nonholonomic constraint. Compared with the wheeled inverted pendulum system, this kind of two-wheeled pendular suspension (WPS) vehicle is more suitable for autonomous exploration in the complex unstructured environment. By Lagrange principle, a four-independent-coordinate dynamic model, which can describe the multivariate, nonlinear, and underactuated characteristics of the system, is first proposed. Besides, a reduced order dynamic is developed in the following so as to tackle the nonholonomic problem, and then the three-independent-coordinate reduced order dynamic is divided into an actuated part constituted by the rotational subsystem, and an underactuated part combined by the longitudinal and the swing angle subsystems. The sliding mode control (SMC) technique is utilized to construct the controller; especially, a composite sliding mode surface is proposed which can realize the velocity tracking and oscillation suppression for pendular suspension simultaneously. Furthermore, the adaptive mechanism is employed to update the true values of the inaccessible physical parameters which can enhance the adaptability of the WPS vehicle in unstructured environment. In addition, a dynamic motion planning method is presented, by aid of which the vehicle can track an arbitrary trajectory in Cartesian coordinate. The simulation results show the effectiveness and merits of the proposed control approaches.

Sliding-Mode Control for Transformation to an Inverted Pendulum Mode of a Mobile Robot With Wheel-Arms

This paper proposes a control method for locomotion mode transformation of a mobile robot with wheel-arms. The proposed method aims at transformation from a four-wheeled mode for high-speed mobility to an inverted pendulum mode, which has advantages of high viewing position and small turning radius. Since the initial state of the system is far away from the target equilibrium point of the wheeled inverted pendulum system, we use a nonlinear controller based on sliding-mode control. While the previous transformation methods cannot control the robot velocity until the robot body is lifted up, the proposed method can take into account the robot velocity from the beginning of the transformation, which enables us to complete the transformation in a smaller space. To analyze the asymptotic stability of the control system on the sliding surface, we derive an invariant set in which the system state converges to the origin without going out. Furthermore, the effectiveness of the proposed method is demonstrated in both simulations and real robot experiments.

Motion Controller Design of Wheeled Inverted Pendulum with an Input Delay Via Optimal Control Theory

This paper investigates the control of Back-and-Forth motion to fetch object and Lower-Raise-Head motion to avoid obstacle of the wheeled inverted pendulum system with an input delay. In controlling the Back-and-Forth motion, the linear optimal control theory is used because the tilt angle of the pendulum is forced to be small enough by minimizing a quadratic performance criterion with large weight of tilt angle error, and the controller is represented by using predictor-based feedback. In controlling the Lower-Raise-Head motion, linearized models do not work due to the strong nonlinearity caused by big tilt angle for avoiding obstacle. Without considering yaw movement, the wheeled inverted pendulum system is decoupled, the subsystem governing the state of the tilt angle is transformed into a simple linear system by using feedback linearization. With a properly chosen trajectory tracking target, the control of Lower-Raise-Head motion is solved on the basis of optimal trajectory tracking control for linear subsystems with an input delay. Numerical simulations illustrate the effectiveness of the proposed approaches.

Dynamic Surface Control of Mobile Wheeled Inverted Pendulum Systems with Nonlinear Disturbance Observer

In this study, a dynamic surface controller based on a nonlinear disturbance observer is investigated to control mobile wheeled inverted pendulum system. By using a coordinate transformation, the underactuated system is presented as a semi-strict feedback form which is convenient for controller design. A dynamic surface controller together with a nonlinear disturbance observer is designed to stabilize the underactuated plant. The proposed dynamic surface controller with a nonlinear disturbance observer can compensate the external disturbances and the model uncertainties to improve the system performance significantly. The stability of the closed-loop mobile wheeled inverted pendulum system is proved by Lyapunov theorem. Simulation results show that the dynamic surface controller with a nonlinear disturbance observer can suppress the effects of external disturbances and model uncertainties effectively.

Terminal Sliding Mode Control of Mobile Wheeled Inverted Pendulum System with Nonlinear Disturbance Observer

A terminal sliding mode controller with nonlinear disturbance observer is investigated to control mobile wheeled inverted pendulum system. In order to eliminate the main drawback of the sliding mode control, “chattering” phenomenon, and for compensation of the model uncertainties and external disturbance, we designed a nonlinear disturbance observer of the mobile wheeled inverted pendulum system. Based on the nonlinear disturbance observer, a terminal sliding mode controller is also proposed. The stability of the closed-loop mobile wheeled inverted pendulum system is proved by Lyapunov theorem. Simulation results show that the terminal sliding mode controller with nonlinear disturbance observer can eliminate the “chattering” phenomenon, improve the control precision, and suppress the effects of external disturbance and model uncertainties effectively.

Design and implementation of a new sliding mode controller on an underactuated wheeled inverted pendulum

In this paper, a sliding mode controller (SMC) is proposed for control of a wheeled inverted pendulum (WIP) system, which consists of a pendulum and two wheels in parallel. The control objective is to use only one actuator to perform setpoint control of the wheels while balance the pendulum around the upright position, which is an unstable equilibrium. When designing the SMC for the WIP system, various uncertainties are taken into consideration, including matched uncertainties such as the joint friction, and unmatched uncertainties such as the ground friction, payload variation, or road slope. The SMC proposed is capable of handling system uncertainties and applicable to general underactuated systems with or without input coupling. For switching surface design, the selection of the switching surface coefficients is in general a sophisticated design issue because those coefficients are nonaffine in the sliding manifold. In this work, the switching surface design is transformed into a linear controller design, which is simple and systematic. By virtue of the systematic design, various linear control techniques, such as linear quadratic regulator (LQR) or linear matrix inequality (LMI), can be incorporated in the switching surface design to achieve optimality or robustness for the sliding manifold. To further improve the WIP responses, the design of reference signals is addressed. The reference position for the pendulum is adjusted according to the actual equilibrium of the pendulum, which depends on the size of the friction and slope angle of the traveling surface. A smooth reference trajectory for the setpoint of the wheel is applied to avoid abrupt jumps in the system responses, meanwhile the reaching time of the switching surface can be reduced. The effectiveness of the SMC is validated using intensive simulations and experiment testings.

Neural-Adaptive Output Feedback Control of a Class of Transportation Vehicles Based on Wheeled Inverted Pendulum Models

The wheeled inverted pendulum (WIP) models have been widely applied in the transportation vehicles formed by a mobile wheeled inverted pendulum system with an operator (demonstrated in Fig. 1 ). In this paper, we focus on the study of nonlinear control design for the WIP model-based vehicles, for which accurate dynamics could not be obtained beforehand due to the presence of uncertainties caused by the human operator as well as the vehicle. We develop an output feedback adaptive neural network (NN) control incorporating a linear dynamic compensator to achieve stable dynamic balance and tracking of the desired given trajectories. Comparison simulation studies demonstrate guaranteed tracking performance and stable dynamics balance in the presence of uncertainties and thus verify the efficiency of the developed nonlinear controller.

Balancing control of a single-wheel inverted pendulum system using air blowers: Evolution of Mechatronics capstone design

Inverted pendulum systems are one of typical control systems suitable for cross-disciplinary education. This article delivers the historical evolution of inverted pendulum systems as Mechatronics capstone design projects for undergraduate students. A wheeled inverted pendulum system is quite a challenging and interesting system to appeal students as a design project. Several design examples from two-wheel to one-wheel inverted pendulum system are elaborated. As a current design, a one-wheel inverted pendulum system which is our main contribution, is presented to deliver novel ideas of using air power to balance the system. The roll angle is regulated by air pressure generated from ducted fans while the pitch angle is controlled by a dc motor. Air pressure is controlled by linear control methods to keep the balancing in the roll direction. Experimental studies demonstrate the successful balancing performance.