Control Of Inverted Pendulum Research Articles

On the Implementation of Fuzzy Inference Engines on Quantum Computers

Quantum computers can be a revolutionary tool to implement inference engines for fuzzy rule-based systems. In fact, the use of quantum mechanical principles can enable parallel execution of fuzzy rules and allow them to be used efficiently in complex contexts such as distributed and big data environments. This paper introduces the very first quantum-based fuzzy inference engine that is capable of providing exponential acceleration in fuzzy rule execution compared to its classical counterpart, and allows a quantum computer to be programmed by fuzzy linguistic rules. The proposed inference engine was implemented using a quantum algorithm design scheme based on the oracle notion. This scheme allows the modeling of a fuzzy rule-based system as a Boolean function, the oracle, which is able to reconstruct the relationships between the antecedent and consequent parts of fuzzy rules, and can be efficiently computed on a quantum computer. The suitability of the proposed quantum algorithm for use as a fuzzy inference engine was tested in a typical benchmark scenario, such as that provided by inverted pendulum control.

Optimization of the model predictive control meta-parameters through reinforcement learning

Model predictive control (MPC) is increasingly being considered for control of fast systems and embedded applications. However, MPC has some significant challenges for such systems, such as its high computational complexity. Further, the MPC parameters must be tuned, which is largely a trial-and-error process that affects the control performance, the robustness, and the computational complexity of the controller to a high degree. This paper presents a multivariate optimization method based on reinforcement learning (RL) that automatically tunes the control algorithm’s parameters from data to achieve optimal closed-loop performance. The main contribution of our method is the inclusion of state-dependent optimization of the meta-parameters of MPC, i.e. parameters that are non-differentiable wrt. the MPC solution. Our control algorithm is based on an event-triggered MPC, where we learn when the MPC should be re-computed, and a dual-mode MPC and linear state feedback control law applied in between MPC computations. We formulate a novel mixture-distribution RL policy determining the meta-parameters of our control algorithm and show that with joint optimization we achieve improvements that do not present themselves with univariate optimization of the same parameters. We demonstrate our framework on the inverted pendulum control task, reducing the total computation time of the control system by 36% while also improving the control performance by 18.4%.

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.

Optimization Reinforced PID-Sliding Mode Controller for Rotary Inverted Pendulum

The control of a rotary inverted pendulum (RIP) is challenging because it is an underactuated, highly sensitive, and unsteady system. Sliding mode control (SMC) is a nonlinear control method with high-frequency switching control. Designing a proportional integral derivative (PID) controller for a RIP is challenging due to its nonlinearity and instability in open-loop characteristics. The primacy of the SMC over the PID is the stability of the closed-loop. Hybrid control of a PID-SMC controller can provide better performance because this technique demonstrates less chatter, higher precision, no oscillation, and adequate gain tuning. To achieve gain tuning, the PID and SMC parameters must be optimized. Thus, this paper proposed a congruently tuned control strategy (CTCS) to fine-tune the controller parameters. The proposed strategy uses an improved whale optimization algorithm (WOA), i.e., the modified Manhattan distance updated WOA (MMD-WOA) to identify effective coefficient values for the sliding surface to reduce tracking errors while reaching the desired position. The proposed CTCS for a RIP with the MMD-WOA was implemented, and the results are very promising.

Metaheuristic Optimization Algorithm for Optimal Design of Type-2 Fuzzy Controller

The utilization of Le`vy flight to create new candidate solutions is one of the most powerful elements of CS. Candidate solutions are modified using this method by making a lot of minor modifications and a few big jumps. As a result, CS will be able to significantly increase the link between exploration and exploitation while also improving its search capabilities. The cuckoo search optimization (CSO) algorithm is applied to interval type-2 fuzzy logic controller (IT2FLC) in this research to determine the optimal parameters of membership functions (MFs) of interval type-2 fuzzy logic systems (IT2FLSs). The study takes into account two forms of MFs: triangular and trapezoidal. When perturbations are applied during the execution of each control issue, the CSO algorithm's performance and efficiency improve significantly. The proposed approach is tested using two benchmark control problems: water tank controller and inverted pendulum controller.

3단 도립진자의 구조 제안 및 LW-RCP02를 이용한 Swing-up Control의 구현

In this paper, we propose a new structure for a triple inverted pendulum with easy construction properties. We also implement a swing-up control for the proposed triple inverted pendulum using a lab-built rapid control prototyping environment known as light-weight rapid control prototyping 02 (LW-RCP02). The swing-up control of a triple inverted pendulum has a two-degree-of-freedom structure and requires a very accurate mathematical model. The proposed triple inverted pendulum adopts the same method that was developed for a double inverted pendulum by the authors’ laboratory to achieve excellent matching properties with the model. For free rotation of three pendulums, a hollow shaft revolute joint that can be used with a slip ring is newly proposed. Swing-up control of a triple inverted pendulum is implemented using Simulink and LW-RCP02. Moreover, a two-degree-of-freedom control structure combining feedforward and feedback is adopted for swing-up control of a triple inverted pendulum. We implement the parameter estimation method for the triple inverted pendulum and calculate the trajectory for feedforward control using estimated parameters and the direct transcription method. The uncertainty of feedforward control is compensated by adding a time-varying LQ feedback controller. As the sampling frequency of the implemented controller is 1KHz, real-time control is achievable using a standard PC.

모델기반 swing-up 제어를 위한 2단 도립진자의 구조 설계 및 계수 추정에 대한 연구

Mathematical models and parameters with high accuracy are required for the swing-up control of a double inverted pendulum. This study proposes a mechanical structure of a double inverted pendulum having excellent matching characteristics with a mathematical model. The implementation of a parameter estimation method based on nonlinear optimization, which is essential for swing-up control, is also proposed. The proposed structure of a double inverted pendulum eliminates backlash using the direct drive of a BLDC motor, minimizes the unmodeled frictional force through bearing cleaning and oiling, minimizes unnecessary load torque using the double support of a timing pulley shaft and power transmission through a coupling, and constrains the pendulum rotation to one degree-of-freedom by adopting a dual-bearing joint. In addition, both 3D printing and CNC milling are appropriately used to satisfy the requirements for each mechanical part. The swing motion of the manufactured double inverted pendulum is measured using the lab-built light-weight rapid control prototyping 02 (LW-RCP02). The proposed parameter estimation method based on nonlinear optimization is implemented to match the response trajectory of the actual double inverted pendulum with that of a Simulink model implemented as an S-function. Finally, the effectiveness of the proposed double inverted pendulum design and parameter estimation method is confirmed by showing that the mathematical model that, based on the parameters estimated using the proposed method, accurately describes the response characteristics of the double inverted pendulum.

SECURITY APPLICATION OF NEURAL NETWORKS UNDER THE INSPECTION OF NONLINEAR DYNAMIC SYSTEMS

Based on the improved BP neural network, this paper establishes an adaptive online controlling model and adopts the model to optimize the controlling accuracies in discrete nonlinear dynamic systems and inverted pendulum systems. To avoid the local minimum problem of the BP neural network’s objective function in the training process, this paper proposes a neural network training method based on the quasi-Newton method (BFGS) optimization algorithm. Compared with other control methods, the neural network-based inverted pendulum control method proposed in this paper has higher control accuracy. Through the control simulation of its power system uses a discrete control method and the control of the inverted pendulum model system, this paper verifies the validity and good control has significantly improved the control method.

State-space segmentation for faster training reinforcement learning

Nonlinear control problems have been the main subjects in control engineering from theoretical and applicational aspects. Reinforcement learning shows promising results for solving highly nonlinear control problems. Among many variants of reinforcement learning, Deep Deterministic Policy Gradient (DDPG) considers continuous control signals, which makes it an ideal candidate for solving nonlinear control problems. The training requires frequently, however, a large number of computations. To improve the convergence of DDPG, we present a state-space segmentation method dividing the state-space to expand the target space defined by the best reward. An inverted pendulum control example demonstrates the performance of the proposed segmentation method.

Integrated inverted pendulum and whole-body control design for bipedal robot with foot slip

Low-friction ground surfaces present a particular challenge for control of bipedal walking robots. The onset of foot slip changes the robot dynamics and the commonly designed walking controllers assuming non-slip conditions cannot maintain balance and prevent the walker from falling. We present a two-level robot controller for bipedal walker under foot slip. The high-level control is built on a two-mass linear inverted pendulum (TMLIP) model to generate the appropriate step location such that the robot walker maintains dynamic balance through multiple planned steps. The specified stepping tasks are fed to the low-level control that is based on a whole-body operational space (WBOS) framework. The WBOS controller uses the dynamic model of the multi-link bipedal walker and generates joint torques to maintain balance and follow the given stepping task in the presence of foot slip. Performance of the integrated TMLIP-WBOS control algorithm is demonstrated through extensive simulation studies of a 5-link robotic walker.

Evolution of adaptive learning for nonlinear dynamic systems: a systematic survey

The extreme nonlinearity of robotic systems renders the control design step harder. The consideration of adaptive control in robotic manipulation started in the 1970s. However, in the presence of bounded disturbances, the limitations of adaptive control rise considerably, which led researchers to exploit some “algorithm modifications”. Unfortunately, these modifications often require a priori knowledge of bounds on the parameters and the perturbations and noise. In the 1990s, the field of Artificial Neural Networks was hugely investigated in general, and for control of dynamical systems in particular. Several types of Neural Networks (NNs) appear to be promising candidates for control system applications. In robotics, it all boils down to making the actuator perform the desired action. While purely control-based robots use the system model to define their input-output relations, Artificial Intelligence (AI)-based robots may or may not use the system model and rather manipulate the robot based on the experience they have with the system while training or possibly enhance it in real-time as well. In this paper, after discussing the drawbacks of adaptive control with bounded disturbances and the proposed modifications to overcome these limitations, we focus on presenting the work that implemented AI in nonlinear dynamical systems and particularly in robotics. We cite some work that targeted the inverted pendulum control problem using NNs. Finally, we emphasize the previous research concerning RL and Deep RL-based control problems and their implementation in robotics manipulation, while highlighting some of their major drawbacks in the field.

Comparing system identification techniques for identifying human-like walking controllers.

While human walking has been well studied, the exact controller is unknown. This paper used human experimental walking data and system identification techniques to infer a human-like controller for a spring-loaded inverted pendulum (SLIP) model. Because the best system identification technique is unknown, three methods were used and compared. First, a linear system was found using ordinary least squares. A second linear system was found that both encoded the linearized SLIP model and matched the first linear system as closely as possible. A third nonlinear system used sparse identification of nonlinear dynamics (SINDY). When directly mapping states from the start to the end of a step, all three methods were accurate, with errors below 10% of the mean experimental values in most cases. When using the controllers in simulation, the errors were significantly higher but remained below 10% for all but one state. Thus, all three system identification methods generated accurate system models. Somewhat surprisingly, the linearized system was the most accurate, followed closely by SINDY. This suggests that nonlinear system identification techniques are not needed when finding a discrete human gait controller, at least for unperturbed walking. It may also suggest that human control of normal, unperturbed walking is approximately linear.

Swing up and stabilization control of rotary inverted pendulum based on energy balance, fuzzy logic, and LQR controllers

Rotary Inverted Pendulum (RIP) mimics the behavior of many practical control systems like crane mechanism, segway, unicycle robot, traction control in vehicles, rocket stabilization, and launching. RIP is a fourth-order nonlinear open-loop unstable dynamical system and is widely used for testing the effectiveness of the newly developed control algorithms. In this paper, a Hybrid Control Scheme (HCS) based on energy balance and fuzzy logic controllers is proposed to implement the swing up and stabilization control of RIP. In the proposed control scheme, the fuzzy logic-based state feedback gains are dynamically tuned in real-time by minimizing the absolute error between the desired and actual states to get robust control performance. The proposed HCS is also compared with the conventional Linear Quadratic Controller (LQR) for this application. The comparative results show that the proposed fuzzy logic-based hybrid control scheme gives the optimal control performance in terms of achieving satisfactory transient, steady-state, and robust responses from a given RIP system, as compared to the conventional LQR based control scheme. The proposed control scheme is also relatively less complex with a low computational cost and provides desired response characteristics as compared to the existing ones in the literature.

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.

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.

MODELING, SIMULATION AND NEURAL CONTROL OF WHEELED INVERTED PENDULUM

By Muhammad Yasir Amir Khan, Vali Uddin Abbas. Proposed modeling and control of wheeled inverted pendulum (WIP), an underactuated and highly unstable system, as a hybrid automation based on torque equations rather than Lagrangian method.

Time-Optimal Point Stabilization Control for WIP Vehicles Using Quasi-Convex Optimization and B-Spline Adaptive Interpolation Techniques

This paper addresses a time-optimal point stabilization control for inherent unstable wheeled inverted pendulum (WIP) vehicles using quasi-convex optimization and B-spline adaptive interpolation techniques. First, to handle the difficulty caused by the inherent unstable characteristic, a state feedback control law is introduced to the state-space model deduced with the kinematic coupling relationship between the longitudinal motion and tilt angle of vehicle body. Then, by system discretization, a standard quasi-convex optimization problem is formulated to plan a time-optimal trajectory with various constraints being taken into account, and the optimization problem can be solved by a bisection method combined with solving a series of convex feasibility problems. Next, to obtain the analytic expression of the discrete optimal trajectory, a B-spline interpolation algorithm with adaptive curve refinement is presented based on feature points recognition. Furthermore, as the time-optimal trajectories with analytic expressions, including displacement, velocity, and acceleration trajectories, have been obtained, a proportional-integral-derivative (PID) tracking controller is applied to control the vehicle to track the optimal trajectories and, thus, the time-optimal point stabilization control for the WIP vehicle can be realized. Finally, simulation results of a numerical example is presented to validate the feasibility and effectiveness of the proposed method.

Difference-Based Mutation Operation for Neuroevolution of Augmented Topologies

In this paper, a novel search operation is proposed for the neuroevolution of augmented topologies, namely the difference-based mutation. This operator uses the differences between individuals in the population to perform more efficient search for optimal weights and structure of the model. The difference is determined according to the innovation numbers assigned to each node and connection, allowing tracking the changes. The implemented neuroevolution algorithm allows backward connections and loops in the topology, and uses a set of mutation operators, including connections merging and deletion. The algorithm is tested on a set of classification problems and the rotary inverted pendulum control problem. The comparison is performed between the basic approach and modified versions. The sensitivity to parameter values is examined. The experimental results prove that the newly developed operator delivers significant improvements to the classification quality in several cases, and allow finding better control algorithms.

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.

An Efficient Chicken Search Optimization Algorithm for the Optimal Design of Fuzzy Controllers

A proposed architecture to design the optimal parameters of Membership Functions (MFs) of Type-1 Fuzzy Logic Systems (T1FLSs) using the Chicken Search Optimization (CSO) is applied to three Fuzzy Logic Controllers (FLCs) in this paper. Two types of MFs are considered in the study: triangular and trapezoidal ones. The performance and efficiency of the CSO algorithm are particularly good when perturbations are added during the execution in each control problem. Two benchmark control problems: Water Tank Controller and Inverted Pendulum Controller are considered for testing the proposed approach. Also, the optimal design of a fuzzy controller for trajectory tracking of an Autonomous Mobile Robot (AMR) is considered to test the CSO. The main goal is to highlight the efficiency of CSO algorithm in finding optimal fuzzy controllers of non-linear plants. Two types of perturbations are considered in each control problem. Results show that the CSO algorithm presents excellent results in the field of Fuzzy Logic Controllers. Two types of Fuzzy Inference Systems: Takagi-Sugeno and Mamdani FLSs, are implemented in this paper. The most important metrics usually applied in control are used in this paper, such as: Integral Time Absolute Error (ITAE), Integral Time Squared Error (ITSE), Integral Absolute Error (IAE), Integral Square Error (ISE), Mean Square Error (MSE), and Root Mean Square Error (RMSE).