Inverse Pendulum Research Articles

Improving Walking Path Generation Through Biped Constraint in Indoor Navigation System for Visually Impaired Individuals.

This paper introduces a walking path generation method specifically developed for the Smart Cane, which is a RNA (Robotic Navigation Assistance Device) aimed at enhancing indoor navigation for visually impaired individuals. The proposed approach combines the utilization of a LIPM (Linear Inverse Pendulum Model) and LFPC (Linear Foot Placement Controller) motion primitives to generate walking paths specifically designed for visually impaired individuals. The primary objective is to generate paths that conform to human motion constraints, thereby guaranteeing an efficient and natural navigation experience. Integrating autonomous navigation framework, the Smart Cane facilitates safe and effective guidance for visually impaired participants in the indoor environments. Furthermore, comparative experiments have been conducted to validate the effectiveness of the proposed method, providing evidence of its capability to generate walking paths that conform to human motion constraints. The experiment results indicate that the proposed walking path generation method is a promising solution to enhance the navigation experience of visually impaired individuals.

Speed-and-pressure combined control for the CPHPTO of an inverse pendulum wave energy converter

Constant pressure hydraulic power take-off (CPHPTO) utilizes a high-pressure accumulator to weaken its oil pressure fluctuations. However, CPHPTO operating point still changes violently under the circumstance of the changeable irregular waves as well as the limited volume of the high-pressure accumulator. This causes CPHPTO to work away from the designed operating point and even to run in the inefficient and unstable region. This paper proposes a speed-and-pressure combined control (SPCC) strategy, which keeps system speed/pressure around the designed value via the vector control of a PMSG or the displacement tuning of a hydraulic motor, for the efficient and stable operation of a CPHPTO. A SPCC strategy for the CPHPTO embedded in a novel inverse pendulum wave energy converter (NIPWEC) is designed in detail. Furthermore, the overall wave-to-wire dynamic model is simulated in irregular waves to research the effect of SPCC. Results show that both the SPCC with an oil pressure open-loop regulator (OPOLR) and the SPCC with an oil pressure closed-loop regulator (OPCLR) can effectively stabilize the system speed/pressure. Besides, SPCC, especially the SPCC with OPCLR, can effectively improve both the efficiency and stability of CPHPTO. Moreover, system-speed control is more significant than system-pressure control in terms of improving CPHPTO efficiency.

Identification of Optimal Movement Patterns for Energy Pumping

Energy pumping is a way to gain kinetic energy based on an active vertical center of mass movement in rollers in sports like skateboarding, skicross, snowboard cross and BMX. While the principle of the energy transfer from the vertical movement to the horizontal movement is well understood, the question of how to achieve the optimal energy transfer is still unresolved. In this paper, we introduce an inverse pendulum model to describe the movement of the center of mass of an athlete performing energy pumping. On this basis, the problem of identifying the optimal movement pattern is formulated as an optimal control problem. We solve the discretized optimal control problem with the help of a SQP-algorithm. We uncover that the optimal movement pattern consists of a jumping, flying, and landing phase, which has to be timed precisely. We investigate how the maximal horizontal speed depends on parameters like rollers height and maximal normal force of the athlete. Additionally, we present a qualitative comparison of our results with measured results from BMX-racing. For athletes and coaches, we advice on the basis of our results that athlete's performance is optimized by using maximal force and adopt an exact and proper timing of the movement pattern.

On the Output Regulation for an Underactuated Inverse Pendulum When the Exosystem Is a High-Gain Observer

This paper is devoted to solving the output regulation problem on the basis of the new Francis equations for arbitrary reference/disturbance signals, whose model are obtained by High-Gain observers, providing in this way, the regulation of unmodeled but measurable reference signals. The design is given by fixing a steady state globally attractive by means of LMIs which allows controlling the decay rate by considering input bounds; while the regulation problem is solved by computing the steady-state input based on a modified set of the regulation equations, when the exosystem is constructed upon High-Gain observers, extending in this way, the classical output regulation theory for unmodeled reference/disturbance signal. The Furuta pendulum is used to illustrate the viability of the proposed approach.

МОДЕЛИРОВАНИЕ ПОЛУАВТОМАТИЧЕСКОГО РЕЖИМА УПРАВЛЕНИЯ ДВИЖЕНИЕМ ДВУНОГИХ ШАГАЮЩИХ РОБОТОВ В СИСТЕМАХ ВИРТУАЛЬНОГО ОКРУЖЕНИЯ

The paper considers methods and approaches for semi-automatic motion control of bipedal walking robots in virtual environment systems. The proposed solutions include generating a walking pattern, calculating inverse kinematics, and synthesis of PD-controllers with feedback based on the angle sensor readings. To ensure the static and dynamic stability of the walking robot, generating its movement trajectories is implemented using the criterion of zero mo-ment point (ZMP) and the inverse pendulum model with virtual height. In this case, the walking pattern is generated by solving the problem of inverse kinematics using the Leven-berg-Marquardt method to calculate the rotation angles in the robot joints. To implement semi-automatic motion control of a walking robot in a virtual environment, an approach based on the technology of functional diagrams and virtual control panels is used. Testing the proposed methods and approaches is carried out in the VirSim virtual environment software package and shows their adequacy and efficiency for modelling a walking robot movement while maintaining its balance.

Development of a structural health monitoring system with IoT smart nodes based on mathematical model of inverted pendulums equipped with accelerometers

For centuries, the Italian historical and cultural heritage has been subject to seismic events that have damaged its integrity. The only way to preserve historic centres is to monitor their health through the integration of the traditional structural health monitoring (SHM) system. The aim of the work is to extend the monitoring of historical masonry buildings using an innovative approach based on the simultaneous use of mathematical and finite element models to detect a reduced number of points to be monitored and establish the maximum stress that they can withstand before considering the whole structure in danger. The paper proposes an IoT-based SHM, for the online assessment of the displacement of the control points of a historic structure subject to an earthquake, which minimises the computational burden and reduces construction costs. This will be done by implementing a mathematical model with an inverse pendulum and using it to derive the parameters of interest.

Whole-body kinematic and dynamic modeling for quadruped robot under different gaits and mechanism topologies.

Dynamic locomotion plays a crucial role for legged robots to fulfill tasks in unstructured environments. This paper proposes whole-body kinematic and dynamic modeling method s based on screw theory for a quadruped robot using different gaits and mechanism topologies. Unlike simplified models such as centroid or inverse pendulum models, the methods proposed here can handle 10-dimensional mass and inertia for each part. The only simplification is that foot contact models are treated as spherical joints. Models of three different mechanism topologies are formulated: (1) Standing phase: a system consisting of one end-effector, the body, and four limbs, the legs; (2) Walking phase: a system consisting of one or two lifting legs (depending on the chosen gait), two or three supporting legs; (3) Floating phase: a system in which all legs detach from the ground. Control strategies based on our models are also introduced, which includes walk and trot gait plans. In our control system, two additional types of information are provided: (1) contacting forces are given by force sensors installed under feet; (2) body poses are determined by an inertial measurement unit (IMU). Combined with the sensor data and calibrated mass, inertia, and friction, the joint torque can be estimated accurately in simulation and experiment. Our prototype, the “XiLing” robot, is built to verify the methods proposed in this paper, and the results show that the models can be solved quickly and leads to steady locomotions.

Spiking PID Control Applied in the Van de Vusse Reaction

Artificial neural networks (ANN) can approximate signals and give interesting results in pattern recognition; some works use neural networks for control applications. However, biological neurons do not generate similar signals to the obtained by ANN. The spiking neurons are an interesting topic since they simulate the real behavior depicted by biological neurons. This paper employed a spiking neuron to compute a PID control, which is further applied to the Van de Vusse reaction. This reaction, as the inverse pendulum, is a benchmark used to work with systems that has inverse response producing the output to undershoot. One problem is how to code information that the neuron can interpret and decode the peak generated by the neuron to interpret the neuron's behavior. In this work, a spiking neuron is used to compute a PID control by coding in time the peaks generated by the neuron. The neuron has as synaptic weights the PID gains, and the peak observed in the axon is the coded control signal. The neuron adaptation tries to obtain the necessary weights to generate the peak instant necessary to control the chemical reaction. The simulation results show the possibility of using this kind of neuron for control issues and the possibility of using a spiking neural network to overcome the undershoot obtained due to the inverse response of the chemical reaction.

Analysis of Postural Instability in the Upright Position on Narrow Platforms and the Interactions with Postural Constraints.

Background: Loss of balance is a considerable risk factor for workers while using ladders, because they are required to maintain static postural balance on platforms of a restricted size. This study observed center of mass (CoM) and center of pressure (CoP) behaviors and evaluated the effects of the platform depth (anterior–posterior length) and working postures. Methods: Eleven male participants stood on four platforms with depths ranging from 6 to 15 cm and maintained their positions for 60 s while performing or not performing other tasks (object holding, upward viewing, or both simultaneously). The kinematics were analyzed on the sagittal plane based on the inverse pendulum model. Results: The absolute moving range for the CoP–CoM linearly increased with the decreasing platform depth, and the working postures affected the slopes of the linear fits. The relative range of CoP–CoM displacement on narrow platforms was highly correlated with the subjective sense of instability. Conclusions: Monitoring the CoP is effective for a better understanding and evaluation of static postural balance. This study’s findings contribute to improving the design of work equipment through the use of wider platforms that are robust against the effects of working postures.

Digital control of structurally unstable power facilities using a polynomial approach

The problem of improving the quality of control of structurally unstable power facilities is viewed based on a polynomial controller with a dynamic change in settings using the inverse pendulum on a carriage as an example. The mathematical model of the control object was built; a polynomial controller was synthesized using the method of symbolic computation of systems of differential equations with an additional input for specifying the geometric mean root from the outside. Reverse pendulum model on a carriage and a model of regulators were created using the MATLAB Simulink visual modeling environment to analyze the quality and parameters of the created control system. As a result of modeling, direct dependence of the position setting time of pendulum on the value of the geometric mean root was obtained which confirmed the possibility of external control of the speed of the control system. The possibility to control the control actions level to prevent saturation of executive devices was investigated and confirmed. In fact, a system of external parametric control of the processes dynamics was created and the described regulator does not require adaptation and training.

Control of a flexible inverse pendulum based on the singular perturbation method

In this article, a partial differential equation model for a flexible inverted pendulum system is derived by using the Hamilton principle. Specifically, problems of stabilization and the optimization of such a system are considered. In addition, the singular perturbation method has been used to divide the partial differential equation model for a fast and a slow subsystem. For a fast subsystem stabilization, the control algorithm proposed a boundary force applied at the free end of the beam which proved that the closed-loop subsystem is appropriate and exponentially stable. To stabilize the slow subsystem, a sliding mode control method was used to design the controller, while the method of linear matrix inequality was used in designing the sliding surface. In conclusion, it was shown that the slow subsystem is exponentially stable.

Çift Ters Sarkaç Sisteminin Kontrolü için PID ve LQR Kontrolcü Tasarımlarının Modellenmesi

Nowadays, stability of the inverted pendulum system is an up-to-date topic in which researchers working on control systems compare control theories and methods. The inverse pendulum systems are unstable and nonlinear systems in terms of controllability. Due to the complexity of the structure and the difficulty of the control process, many advanced control theories can be applied on these systems to improving the performance of the controllers. In this study, PID and LQR controller methods were applied on a double inverted pendulum modeled in MATLAB environment and their controller performances were compared. The results via experimental studies were evaluated on the applicability of PID and LQR control methods.

New structural seismic protection for high-rise building structures

Presented Structural Seismic Isolation Method (SSIM) aims to provide high safety for Highly Reliable Structures (HRS) against strong earthquakes including near-fault and long-period ground motions. The examined structure is converted to Structural Seismic Isolation System (SSIS) by the SSIM method which exhibited inverse pendulum behaviour. For this purpose, structure foot base and foundation contact surfaces have been designed as any curved surfaces (spherical, elliptical, etc.) depending on the earthquake-soil-superstructure parameters and this contact surfaces have been separated by elastomeric (lead core rubber or laminated rubber bearings) seismic isolation devices. It would allow the structure foot base to turn around gyration centre through rubber bearing contact and maintains similar behaviour to the super-structure. SSIS system provides the possibility of keeping the natural-period of the structure in a larger interval, which is greater than the predominant-period of the majority of possible earthquakes (including near-fault pulse) using currently existing conventional elastomeric isolators with up to 4 second period. Thus, the structure can sustain its serviceability after strong and long-period earthquakes. In this study SSIS system’s performance is presented for high-rise building structures, for this aim, the finite element model of the building (Bg) structure with SSIS system (SSIS-Bg) has been prepared and the nonlinear dynamic analysis of the model has been conducted using strong and long-period ground motions. Results indicate that the base and top accelerations, base shear and base moment responses of the SSIS-Bg structure is 23.21 %, 75.47 % and 85.74 % in average lower than the Conventional Application Method of Seismic Base Isolation Devices for Building (CAMSBID-Bg) structures respectively and it is not prone to resonant vibrations under long-period earthquakes related with the excessive deformation in the isolation layers in case of using CAMSBID-Bg structures. It should be noted that in this study with the presented SSIM method and SSIS system, it is aimed to protect only the Highly Reliable Structures(HRS) from the effects of strong and long-period ground motions and these structures (HRS) are classified as follows: 1) Nuclear Containment Structures; 2) High-rise buildings that contain information, operating systems, sensitive instruments, communication systems, routing systems, bank operating systems, databases, management systems and other similar facilities that are linked to the security and economy of a country; 3) High-rise hospitals etc.

Verified Interval Enclosure Techniques for Robust Gain Scheduling Controllers

In real-life applications, dynamic systems are often subject to uncertainty due to model simplifications, measurement inaccuracy or approximation errors which can be mapped to specific parameters. Uncertainty in dynamic systems can come either in stochastic forms or as interval representations, when they are considered as bounded as it will be done in this paper. The main idea, here, is to find a joint approach for an interval-based gain scheduling controller while simultaneously reducing overestimation by enclosing state intervals with the least amount of conservativity. The robust and/ or optimal control design is realized using linear matrix inequalities (LMIs) to find an efficient solution and aims at a guaranteed stabilization of the system dynamics over a predefined time horizon. Since the resulting system is assumed to be asymptotically stable, a temporal reduction of the widths of intervals representing worst-case bounds of the system states at a specific point of time should occur. However, for commonly used approaches in the computation of interval enclosures those interval widths seemingly blow up due to the wrapping effect in many cases. To avoid this, we provide two interval enclosure techniques --- an exploitation of cooperativity and an exponential approach --- and discuss their applicability taking into account two real-life applications, a high-bay rack feeder and an inverse pendulum.

New Structural Seismic Isolation for Nuclear Containment Structures

The new Structural Seismic Isolation System (SSIS) intends to provide high safety for important structures such as nuclear power plants, offshore oil platforms, and high-rise buildings against near-fault and long-period earthquakes. The presented SSIS structure foot base and foundation contact surfaces have been designed as any curved surfaces (spherical, elliptical, etc.) depending on the earthquake-soil-superstructure parameters, and these contact surfaces have been separated by using elastomeric (lead core rubber or laminated rubber bearings with up to 4-second period) seismic isolation devices. It would allow providing inverse pendulum behavior to the structure. As a result of this behavior, the natural period of the structure will possess greater intervals which are larger than the predominant period of the majority of the possible earthquakes including near-fault zones. Consequently, the structure can maintain its serviceability after the occurrence of strong and long-period earthquakes. This study has investigated the performance of the SSIS for the nuclear containment (SSIS-NC) structure. The finite element model of SISS-NC structure has been developed, and nonlinear dynamic analysis of the model has been conducted under the strong and long-period ground motions. The results have been presented in comparison with the conventional application method of the seismic base isolation devices for nuclear containment (CAMSBID-NC) and fixed base nuclear containment (FB-NC) structures. The base and top accelerations, effective stress, and critical shear stress responses of the SSIS-NC structure are 48.67%, 36.70%, and 32.60% on average lower than those of CAMSBID-NC structure, respectively. The result also confirms that the SSIS-NC structure did not cause resonant vibrations under long-period earthquakes. On the other hand, there is excessive deformation in the isolation layers of CAMSBID-NC structure.

Development and Control of Rotary Inverse Pendulum by LQR with Integral Action

This research a basic well-known hardware, is introduced. The inverse pendulum is the focused in this research. In order to prove the control algorithm LQR with integral action. The dynamic model is obtained by Euler-Lagrange equation. Motor actuator is included in the model in order to get the correct model. The model is linearize by Taylor series expansion. The model parameters are identified by software simulation. The inversed pendulum prototype is manufactured and assembled. The Linear Quadratic Regulator with Integral (LQR+I) controller is presented and applied to control the inverse pendulum. The control simulation and experiment results are present in the performance of this controller

Stabilization of Furuta Pendulum Using Nonlinear MPC

Abstract This paper is devoted to design of a non-linear model predictive controller (NMPC), which will swing-up and stabilize an inverse rotary pendulum known as the Furuta Pendulum. This paper presents a simulation validation of the NMPC strategy using a full-fidelity non-linear mathematical model of the Furuta pendulum obtained from the Euler-Lagrange motion equations. The NMPC strategy was implemented in MATLAB using the MATMPC toolbox.

Tactile Identification of a Surface by Fuzzy Control

A hybrid control system has been developed for an anthropomorphic gripping device capable of grasping an object whose physicomechanical and geometric characteristics are unknown. The surface is identified on the basis of a multiply connected inverse pendulum, simulating the hand of a gripping device. A fuzzy control algorithm is synthesized for a two-level hybrid automatic control system.

Proposal of Half Drone Inverse Pendulum Transportation Robot

Proposal of Half Drone Inverse Pendulum Transportation Robot

Determination of the Glass-Transition Temperature of GRPS and CFRPS Using a Torsion Pendulum in Regimes of Freely Damped Vibrations and Quasi-Stastic Torsion of Specimens

A method to measure the glass-transition temperature of polymers and polymeric matrices of composite materials with the help of an inverse torsion pendulum over a wide range of temperatures is considered combining the method of free torsional vibrations and a quasi-static torsion of specimens. The glass-transition temperature Tg of a KMKS-1-80. T10 fiberglass, on increasing the frequency of freely damped torsional vibrations from 0.7 to 9.6 Hz, was found to increase from 132 to 140°С. The value of Tg of these specimens, determined by measuring the work of their torsion through a small fixed angle was 128.6°C ± 0.8°C. It is shown that the use of a torsion pendulum allows one to determine the glass-transition temperature of polymeric or polymer matrices of PCMs in dynamic and quasi-static deformation regimes of specimens.