Double Inverted Pendulum Research Articles

Research of DD2UD with Human Simulating Intelligent Control for a Double Inverted Pendulum

A double pendulum has four equilibrium points (Down-Down, Down-Up, Up-Down, Up-Up). With those equilibrium points, many transfer actions from one equilibrium point to another can be formed. Using the Human Simulated Intelligent Control (HSIC) method based on Sensor-Motor Intelligent Schema, an intelligent control system for the double inverted pendulum which has the structure of multi controller and multi control mode is designed. With this controller, the transfer action of Down-Down to Up-Down (DD2UD) is achieved. The design process of HSIC controller is discussed. The real-time experiment result testified the validation of proposed method.

Hybrid NN predictive-based LQR controller for rotary double inverted pendulum systems: an analytical study

This paper introduces a rotary double inverted pendulum (RDIP) systems. The model is derived by using Euler–Lagrange. Linear quadratic regulator (LQR) controller is applied as the main controller to stabilise the rotary double. However, LQR alone cannot control RDIP efficiently because the plant derived in linear model is not exact model of the real plant. Practically, controller design aiming to guarantee robustness has to consider these uncertainties. In this paper, neural network predictive control is proposed to improve control performance of the conventional LQR controller. Results on control techniques from computer simulation are evaluated and compared.

Vibration Suppression of Two-Wheel Mobile Manipulator Using Resonance-Ratio-Control-Based Null-Space Control

A two-wheel mobile manipulator has the potential to become a multiskilled robot in the field of robotics, and it is already implemented by using inverted pendulum control. The center of gravity (COG) position is controlled to achieve the balancing of the robot. Since the vibrations of manipulator arms affect the COG positions of the inverted pendulum, balancing of the robot deteriorates. Therefore, the vibration control of manipulator arms of the two-wheel mobile manipulator is proposed in this paper. The virtual double-inverted pendulum is modeled using a “4-DOF” manipulator, and it is controlled in work space and null space. Resonance ratio control is utilized for vibration-suppression control. The resonance ratio of a system can be determined arbitrarily by the feedback of reaction torque, and reaction torque observers are implemented for each and every manipulator motor. The feedback signal for vibration suppression is introduced to the null space of the manipulator. Simulations and experiments were carried out to check the validity of the proposed method, and results prove the effectiveness of the proposed vibration controller.

Reinforcement learning using swarm intelligence-trained neural networks

This article proposes a new reinforcement learning method using the swarm intelligence-trained neural network (SWINN) to generate solutions to various real-world problems efficiently. The swarm intelligence algorithm, particle swarm optimisation (PSO), is combined with a training resource allocator (TRA) in SWINN for specific problems. TRA, as a heuristic global search method, controls the allocation of training resources to different candidate topologies of artificial neural networks (ANNs) to expedite the system convergence, while PSO is applied as a local search algorithm to adjust the ANNs connection weights. To evaluate the performance of the SWINN algorithm, two reinforcement learning case studies: the double pole balance (a.k.a. double inverted pendulum) problem and a mobile robot localisation problem are conducted. Extensive simulation results successfully demonstrate that SWINN offers performance that is competitive with modern neuroevolutionary techniques, and is viable for real-world problems.

Watching quiet human stance to shake off its straitjacket

The single-inverted pendulum (SIP) model is still the paradigm describing dynamics and control of quiet human stance in the sagittal plane. We used two methods to verify this paradigm. First, in an experimental approach we acquired kinematic data of both legs of ten subjects at high spatial resolution while quietly standing on two force platforms. We calculated all leg joint angles, the belonging joint torques using inverse dynamics and estimates of joint stiffnesses. Some linear correlations and regressions of both local (joint) and global (COM, COP: centre of mass respectively pressure) variables predicted by the SIP model were investigated. All three verification criteria applied to mean values extracted from experimental data revealed that the SIP is not a valid model for quiet human stance. As a second method, we used computer synthesis to demonstrate that a double-inverted pendulum (DIP) model enters a stable attractor when just the “hip” joint torque is regulated, whereas no torque is applied to the “ankle” joint. Here, angle and torque fluctuations are necessary because such a DIP strategy is of inevitable dynamic character. The two predicted eigenfrequencies of this regulated DIP model approximate the upper and lower limits of the main part of measured power spectra of quiet human stance. We suggest this dynamic necessity to be representative of the biological constraints under which a mechanically unstable inverted multi-segment chain must be stabilised.

A Robust Control of Two-Wheeled Mobile Manipulator with Underactuated Joint by Nonlinear Backstepping Method

In this paper, a robust control of two-wheeled mobile manipulator with underactuated joint is considered. Two-wheeled mobile manipulators are dynamically balanced two-wheeled driven systems that do not have any caster or extra wheels to stabilize their body. Two-wheeled mobile manipulators mainly have an important feature that makes them more flexible and agile than the statically stable mobile manipulators. However, two-wheeled mobile manipulator is an underactuated system due to its two-wheeled structure. Therefore, it is required to stabilize the underactuated passive body and, at the same time, control the position of the center of gravity (CoG) of the manipulator in this system. To realize this, nonlinear backstepping based control method with virtual double inverted pendulum model is proposed in this paper. Backstepping is used with sliding mode to increase the robustness of the system against modeling errors and other perturbations. Then robust acceleration control is also achieved by utilizing disturbance observer. Performance of the proposed method is evaluated by several experiments.

A simple new device to examine human stance: the totter-slab

This article describes a new measuring device to investigate balancing strategies of human stance: the totter-slab, i.e., a standing plate suspended with steel cables to hooks on a steel frame. First, we analysed the physical properties of the device by recording free oscillations under different conditions [varying amplitude, mass and centre of mass (COM) height]. This allowed us to determine the eigenfrequency f and the damping coefficient D<1 Ns/m for each trial. The trials showed that the measured damped eigenfrequency of f is approximately 0.63 Hz is barely dependent on the mass loaded. The ratio D/M is approximately 0.015 1/s is a constant almost independent of the different conditions. Furthermore, we determined the stiffnesses of the suspending cables and their suspension points to check for potential energy storage capacity of the totter-slab. We found that the totter-slab is a useful, well-defined, reliable and developable measuring device for different non-rigid-ground stance conditions. In a second part of the investigation, we compared the frequency spectra of six subjects balancing on the totter-slab with their spectra while standing quietly on a force plate fixed to the ground. The totter-slab spectra showed two distinct, dominant peak regions at approximately 0.3 and 1.1 Hz. This finding enforces the double inverted pendulum to be an adequate model particularly for balancing on the totter-slab. Compared with the firm ground condition, these two peak regions were more pronounced when balancing on the totter-slab. However, there is a variety of frequencies in the region 0.2...1.5 Hz specific for an individual subject in both balancing conditions.

適応制御器を用いた回転型二重倒立振子の二段階による制御系

Inverted pendulums are very often used to verify many control theories, because they are typical unstable systems and also are interesting objects. However, few innovative methods with respect to the adaptive control of inverted pendulum (IP) are reported. This paper presents a stabilization method by using the adaptive control for a serial rotary-type double inverted pendulum (SRDIP) whose whole basic parameters are unknown. The control system of a SRDIP is achieved by separating the control mode to two stages. The first stage is an adaptive control mode of the single IP placing the second IP in downward directions and another stage is a LQ control mode of the SRDIP. The control system prepares two kinds of adaptive controllers, which are a variable structure system (VSS) robust adaptive control and a self-tuning control (STC). The rotational angle of the first IP is stabilized by the VSS adaptive control, and the stability of the rotary arm is also achieved by constructing the STC that guarantees the boundary reference angle of the first IP. It is then difficult to construct the STC by only adjustable parameters of the VSS adaptive control system. Whole basic parameters of a SRDIP are estimated by adopting the recursive least squares (RLS) estimation method in order to accomplish both of the STC system and the LQ design of a SRDIP. The RLS algorithm is performed by superposing an available perturbation signal to the adaptive manipulated variable on a limited short interval. The STC system updates a LQ controller based on the QR methods devised for the real time operation. Before completing the first stage, a LQ controller for the SRDIP is obtained through a state space description from the estimated basic parameters. The control law is changed to a LQ control for the SRDIP from an adaptive control mode in the second stage. Finally, it is verified by simulation studies and practical experiments that the proposed system is useful as a control strategy of the SRDIP with an unknown parameter.

폴리토픽 모델을 갖는 대규모 시스템을 위한 비집중화 슬라이딩 모드 제어기 설계

Based on the sliding mode control theory, a decentralized controller design method is developed for a large scale system with a poly topic model. In terms of LMIs, we derive sufficient conditions for the existence of the decentralized controller guaranteeing a stable sliding motion. We also give an LMI-based control design algorithm. Finally, the proposed method is applied to decentralized stabilization of double-inverted pendulums. Simulation results show that our method gives not only the robust stability but perfect rejection of norm-bounded uncertainties.

PID-Like Neural Network Nonlinear Adaptive Control for Uncertain Multivariable Motion Control Systems

A mix locally recurrent neural network was used to create a proportional-integral-derivative (PID)-like neural network nonlinear adaptive controller for uncertain multivariable single-input/multi-output system. It is composed of a neural network with no more than three neural nodes in hidden layer, and there are included an activation feedback and an output feedback, respectively, in a hidden layer. Such a special structure makes the exterior feature of the neural network controller able to become a P, PI, PD, or PID controller as needed. The closed-loop error between directly measured output and expected value of the system is chosen to be the input of the controller. Only a group of initial weights values, which can run the controlled closed-loop system stably, are required to be determined. The proposed controller can update weights of the neural network online according to errors caused by uncertain factors of system such as modeling error and external disturbance, based on stable learning rate. The resilient back-propagation algorithm with sign instead of the gradient is used to update the network weights. The basic ideas, techniques, and system stability proof were presented in detail. Finally, actual experiments both of single and double inverted pendulums were implemented, and the comparison of effectiveness between the proposed controller and the linear optimal regulator were given.

Mechatronic System Design Applied to Double Inverted Pendulum with Flywheel Actuator

In this paper we study the stabilization problem of double inverted pendulum via wlywheel actuator. The main issue of the paper is whether such system can be stabilized in real conditions or not. It is shown that the answer strongly depends on the structural (geometric and physical) parameters of the system. The paper gives the procedure for optimizing these parameters under specified conditions to obtain the most robust closed loop system.

Non-linear control of under-actuated mechanical systems

In this paper, non-linear controls of three kinds of under-actuated mechanical systems are summarised. The systems are: inverted pendulum systems, Acrobot system and helicopter experimental system. In particular, concerning the inverted pendulum system, a parallel cart-type double inverted pendulum and a serial cart-type double inverted pendulum are introduced. For the systems, different controller design schemes are considered. Experimental results on the systems are also shown.

Instance-based Policy Learning by Real-coded Genetic Algorithms and Its Application to Control of Nonholonomic Systems

The stabilization control of nonholonomic systems have been extensively studied because it is essential for nonholonomic robot control problems. The difficulty in this problem is that the theoretical derivation of control policy is not necessarily guaranteed achievable. In this paper, we present a reinforcement learning (RL) method with instance-based policy (IBP) representation, in which control policies for this class are optimized with respect to user-defined cost functions. Direct policy search (DPS) is an approach for RL; the policy is represented by parametric models and the model parameters are directly searched by optimization techniques including genetic algorithms (GAs). In IBP representation an instance consists of a state and an action pair; a policy consists of a set of instances. Several DPSs with IBP have been previously proposed. In these methods, sometimes fail to obtain optimal control policies when state-action variables are continuous. In this paper, we present a real-coded GA for DPSs with IBP. Our method is specifically designed for continuous domains. Optimization of IBP has three difficulties; high-dimensionality, epistasis, and multi-modality. Our solution is designed for overcoming these difficulties. The policy search with IBP representation appears to be high-dimensional optimization; however, instances which can improve the fitness are often limited to active instances (instances used for the evaluation). In fact, the number of active instances is small. Therefore, we treat the search problem as a low dimensional problem by restricting search variables only to active instances. It has been commonly known that functions with epistasis can be efficiently optimized with crossovers which satisfy the inheritance of statistics. For efficient search of IBP, we propose extended crossover-like mutation (extended XLM) which generates a new instance around an instance with satisfying the inheritance of statistics. For overcoming multi-modality, we propose extended CCM for selection. Extended CCM always chooses the child for next generation among children and a parent which generates the children. By doing so, the diversity of the population is expected to be well maintained. Our proposals, FLIP (Functionally sophisticated Learner for IBP), consist of extended XLM and extended CCM. The effectiveness of FLIP is shown by experiments with nonholonomic control problems, a space robot, a car-like robot, and a parallel-type double inverted pendulum.

Global stabilization of a double inverted pendulum with control at the hinge between the links

We study the plane motion of a double pendulum with fixed suspension point. The pendulum is controlled by a single moment applied to the internal hinge between the links. The moment is assumed to be bounded in absolute value. We construct a feedback control law bringing the pendulum from the position in which both links hang vertically downwards into the unstable upper position in which both links are inverted. The same feedback ensures the asymptotic stability of the pendulum in the upper equilibrium position. Since the pendulum can be brought to the lower equilibrium position from any initial states, it follows that the constructed control law ensures the global stability of the inverted pendulum.

Discrete-Time Control of Linear Time-Periodic Systems

A discrete-time control design approach for periodically time-varying systems is introduced. The method employs a period-to-period (point-mapping) formulation of the system’s dynamics and a parametrization of the control input to obtain an equivalent time-invariant discrete-time representation of the system. The representation is generalized to include sampling within the period and varying sampling rates in different feedback loops. The proposed formulation allows for the design of feedback control laws using established discrete-time control methodologies. In this paper, dead-beat and optimal control laws with state- or output-feedback control are presented. An example of a multivariable control design for double inverted pendulum with periodic forcing is used to illustrate the proposed approach.

Stabilization of linear undamped systems via position and delayed position feedbacks

This paper presents a systematic approach to stabilizing a kind of linear undamped systems of multiple degrees of freedom by using both position and delayed position feedbacks, namely, PDP feedbacks for short. For the fully actuated system, the approach enables one to complete the design of controller directly through the use of modal decoupling and a stability chart. For the under-actuated system, the approach includes two steps. The first step is to move all the eigenvalues of the system on the imaginary axis of the complex plane by using a position feedback, and the second step is to drag all the eigenvalues of the system to the left half open complex plane through the use of a delayed position feedback, which can be determined on the basis of sensitivity analysis of eigenvalues. Two examples, i.e., a fully actuated robotic manipulator and an under-actuated double inverted pendulum, are discussed in the paper to demonstrate the design of controllers for the two different types of systems and to support the efficacy of the proposed approach.

Novel active fault-tolerant control scheme and its application to a double inverted pendulum system

On the basis of the gain-scheduled H ∞ design strategy, a novel active fault-tolerant control scheme is proposed. Under the assumption that the effects of faults on the state-space matrices of systems can be of affine parameter dependence, a reconfigurable robust H ∞ linear parameter varying controller is developed. The designed controller is a function of the fault effect factors that can be derived online by using a well-trained neural network. To demonstrate the effectiveness of the proposed method, a double inverted pendulum system, with a fault in the motor tachometer loop, is considered.

Analysis and experiment on simultaneous swing‐up of a parallel cart‐type double inverted pendulum

AbstractThis paper considers experimental study and analysis on simultaneous swing‐up control of a parallel cart‐type double inverted pendulum. The proposed controller includes both a swing‐up controller based on weighted energy related function and a cart travel controller designed by a pole assignment control scheme. The cart travel controller can restrict cart travel during the swing‐up. When the two pendulums are swung up, the controller will be switched to a stabilizing controller, and the controller can take the cart to the initial position. Control simulation and experiment were successfully conducted. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Stability Improvement of Two Wheel Driven Mobile Manipulator Using Nonlinear PD Controller

This paper proposes the stability improvement of two wheeled mobile manipulator using nonlinear Proportional Derivative (PD) controller. Nonlinear PD controller is a controller which automatically adjusts its gains according to the stability conditions on running. Lyapunov function based on kinetic energy of the system and position error are used to re-schedule the gains of the nonlinear PD controller. This method will expand the stability margin of the two wheeled mobile manipulator. Further advantages of this method are reducing the parameter uncertainty and difficulty of adjusting gains due to nonlinear nature of system. In the proposed approach, virtual double inverted pendulum is introduced for the control of the two wheeled mobile manipulator. The model based on the double inverted pendulum, makes it easy to design the controller. Here, wheel control and manipulator control are designed separately and unified by using two nonlinear PD controllers. Two nonlinear PD controllers are implemented for better stability. The method proposed in this paper has used nonlinear PD controller in work space of the manipulator controller together with null space control. Here the null space control increases the control stability of manipulator configuration. The effectiveness of the proposed method was confirmed by the experiment of two wheel mobile manipulator.

LMI based output-feedback controllers: γ-optimal versus linear quadratic

Solution to the linear quadratic control problem is given in the class of linear dynamic output-feedback full order controllers. Necessary and sufficient conditions for existence of such an optimal controller are stated in terms of linear matrix inequalities provided that initial conditions for controller states to be zero. It is shown that parameters of the optimal controller depend on an initial plant state. As an alternative we introduce γ-optimal controller which minimizes the maximal ratio of the performance index and square of the norm of the initial plant state. Numerical comparison for two kinds of these controllers is presented for inverted and double inverted pendulums.