Double Pendulum Research Articles

GOPS: A general optimal control problem solver for autonomous driving and industrial control applications

Solving optimal control problems serves as the basic demand of industrial control tasks. Existing methods like model predictive control often suffer from heavy online computational burdens. Reinforcement learning has shown promise in computer and board games but has yet to be widely adopted in industrial applications due to a lack of accessible, high-accuracy solvers. Current Reinforcement learning (RL) solvers are often developed for academic research and require a significant amount of theoretical knowledge and programming skills. Besides, many of them only support Python-based environments and limit to model-free algorithms. To address this gap, this paper develops General Optimal control Problems Solver (GOPS), an easy-to-use RL solver package that aims to build real-time and high-performance controllers in industrial fields. GOPS is built with a highly modular structure that retains a flexible framework for secondary development. Considering the diversity of industrial control tasks, GOPS also includes a conversion tool that allows for the use of Matlab/Simulink to support environment construction, controller design, and performance validation. To handle large-scale problems, GOPS can automatically create various serial and parallel trainers by flexibly combining embedded buffers and samplers. It offers a variety of common approximate functions for policy and value functions, including polynomial, multilayer perceptron, convolutional neural network, etc. Additionally, constrained and robust algorithms for special industrial control systems with state constraints and model uncertainties are also integrated into GOPS. Several examples, including linear quadratic control, inverted double pendulum, vehicle tracking, humanoid robot, obstacle avoidance, and active suspension control, are tested to verify the performances of GOPS.

Input-limited optimal control for overhead cranes with payload hoisting/lowering and double pendulum effects

Input-limited optimal control for overhead cranes with payload hoisting/lowering and double pendulum effects

Seismic isolation effect of a new type of friction pendulum bearing in high-speed railway girder bridge

Residual displacement exists in the traditional friction pendulum bearings (FPB) under the action of earthquakes, which makes them fail to self-reset. In view of this, a new type of FPB called double concave friction pendulum with spring (DCFPS) is proposed. Firstly, the restoring force model and hysteresis characteristics of the theoretical DCFPS are derived. Then, the seismic isolation effect of the high-speed railway simply supported girder bridges (HRSB) equipped with the DCFPS is evaluated. Finally, the optimal spring parameters of the DCFPS are determined in terms of the efficiency coefficient and the optimal order method. The results show that the DCFPS has superior self-reset performance, and the hysteresis curve is “S” shaped. The stiffness of the DCFPS gradually increases with the swing displacement, which heightens the overall stiffness of the structure equipped with DCFPS. After HRSB is installed DCFPS, the displacement of the girder and the residual displacement of the DCFPS itself are reduced. The optimal stiffness and the initial tension of spring for the bridges exemplified in the paper are suggested as 3000 kN/m and 9 kN, respectively, through the efficiency coefficient method and the optimal order method. This research proposes a feasible solution for reducing the maximum displacement and residual displacement of bearings under an earthquake.

Closed Form Constraint Equations Used to Express Frictionless Slip of Multibody Systems Attached to Finite Elements—Application to a Contact between a Double Pendulum and a Beam

This paper focuses on the numerical modeling of the dynamics of mechanical systems. Robots that can inspect high-voltage lines inspired this research. Their control systems must anticipate potential grab positions appropriately. We intend to formulate equations dedicated to the numerical description of the robot/cable contact. The investigated problem is not straightforward, since parts of the modeled systems are numerically inhomogeneous. They consist of multibody and finite element components. These components interact with each other only through frictionless point contact. We limit the present investigation to the mathematical modeling of these frictionless point connections. According to the model-adopted assumption, the location of the contact point is invariant in the multibody structure, but it is variable in the finite elements part. Unlike the classically used models (i.e., spring/damper models of elastic contacts), we focus on constraint equations. We present and discuss their details in this paper. Following the presence of the constraint equations, their associated Lagrange multipliers appear in the dynamics equations of the two sub-models. The main feature/result of the presently proposed method is the closed form of the coordinate-portioning formulae, proposed in this paper, employed to eliminate the dependent coordinates and the constraint-associated Lagrange multipliers. To verify the applicability of the proposed elimination methodology, we test its use in a dedicated numerical example. During the test, we limit the investigation to a frictionless connection between a double pendulum and a beam. The results confirm that the proposed methodology allows us to model the investigated frictionless contact. We shall underline a vital property, that the proposed elimination method is universal, and thus one can easily extend/modify the above methodology to operate with other multibody/finite element contacts.

Robust transient oscillation reduction for rest-to-rest motion of underactuated multibody systems

Conventional model-based design methods are often limited in their effectiveness by model-plant discrepancy. A solution to this problem is proposed in this work to enhance the robustness of motion planning solution for systems affected by parametric uncertainty. The method exploits a variational formulation in the form of a two-point boundary value problem (TPBVP) in which the robustness is achieved as a constraint enforced at the two boundaries. The formulation, which is specifically targeted at underactuated systems, aims at reducing both the transient and residual vibrations, as well as at mitigating the actuation effort. The development of the method is supported by its application to two numerical test-cases in the form of a double pendulum on a cart and a translating flexible beam.

Comparison as a Social Practice in the Analysis of Chaotic Phenomena: the Case of the Double Pendulum

Comparison as a Social Practice in the Analysis of Chaotic Phenomena: the Case of the Double Pendulum

Experimental Investigation of Wear Effects on the Friction Coefficient of a Curved Surface Slider: Comparison of Small- and Full-Scale Tests

ABSTRACT The current practice to determine friction properties of sliding isolation systems is to perform displacement-controlled dynamic tests where the effects of several loading conditions with different amplitudes, loading velocities, and vertical forces are of concern. The number of cycles in these tests is generally three for most of the loading conditions assumed to be representative of seismic conditions. On the other hand, the isolator may undergo small-amplitude but large-cycles of service motions due to thermal deformations and accidental loads. In that case, the methodology requires to perform cyclic tests on small-scale samples of the slider material (not the isolator) considering very large accumulated sliding distances such as 1000 m for use in buildings, and 10,000 m for use in bridges. However, two unsettled issues are regarded: (i) the suitability of small-scale slider tests to estimate the characteristics of full-scale sliding isolation systems and (ii) the change in seismic performance of a sliding isolation system after it is subjected to a large amount of accumulated sliding distance. In the present study, both a full-scale double concave friction pendulum (DCFP) and small-scale sample composed of the slider of the DCFP are subjected to a total accumulated sliding distance of 1000 m. The corresponding variations in friction properties are comparatively presented, demonstrating that small-scale test results provide reasonable estimates for the friction properties of the tested full-scale DCFP. Moreover, the seismic response of the investigated DCFP remains almost the same regardless of the considered sliding distance.

Shaking table tests of base-isolated reinforced concrete frame by double friction pendulum bearings

The effectiveness of seismic isolation by friction pendulum bearings (FPBs) in protecting structural and non-structural components from damage was evaluated by shaking table tests. A base-isolated reinforced concrete frame model by double friction pendulum bearings (DFPBs) with 1/5 scale was considered in the experimental program. A non-isolated model was also tested for comparison. The models were subjected to ground motions with incremental earthquake intensities. This paper presents a comprehensive overview of the test results in terms of peak inter-story drifts, peak floor accelerations, floor acceleration response spectra, hysteretic behaviors, seismic responses of the DFPBs and damage mechanisms of the structures. The results demonstrated that the base-isolated system can effectively protect both structural and non-structural components even under earthquakes larger than maximum considered intensities. The residual displacements of DFPBs remained small after multiple inputs and showed no direct correlation with the maximum sliding displacement and earthquake intensities. The effects of vertical earthquake shaking on the displacement responses of DFPBs were negligible for the test model.

Research Development of Centroid Deviation Type Spherical Robot

Background: With the continuous development of science and technology, more and more human work has been replaced by robots because robots can do many jobs that human beings are not competent for. At present, researchers pay more and more attention to a new type of robot, the spherical robot. The most widely used spherical robot is the centroid deviation spherical robot. This paper mainly introduces the driving mode and structure of the spherical robot with centroid deviation. Objective: This paper explores the classification, development, advantages, and disadvantages of the driving modes of the spherical robot with centroid deviation. Methods: This paper reviews various products and patents related to centroid deviation spherical robot. This paper also introduces the structural characteristics, differences, and applications of the existing spherical robots with centroid deviation. Results: This paper compares and analyzes various spherical robots with centroid deviation, and their typical characteristics are summarized. This paper analyzes the main problems existing in various structures of the spherical robot, looks forward to the development trend of spherical robot, and discusses the research status and future of products and patents of the spherical robot. Conclusion: According to different driving modes, the spherical robot with centroid deviation can be divided into single pendulum drive, double pendulum drive, trolley drive, rolling body drive, and multi mass block drive. Among them, single pendulum drive, trolley drive, and rolling element drive are the most studied. At present, the structures of products and patents are similar, and the research direction has shifted from innovation to optimization.

Optimization of Oscillation Damping Modes of a Spatial Double Pendulum: 2. Solution of the Problem and Analysis of the Results

Optimization of Oscillation Damping Modes of a Spatial Double Pendulum: 2. Solution of the Problem and Analysis of the Results

INVESTIGATION OF THE IMPLEMENTATION OF LEADER-FOLLOWER FORMATION CONTROL TO BIPEDAL LOCOMOTION

Robot that uses bipedal locomotion such as humanoid robot has a unique appeal in which the robot can perform many duties/works that cannot be done by wheeled robots due to spatial and environmental constraints. Related literature were about biped robots and robot arm that uses the concept of central pattern generator (CPG). Biped robots that use CPG (technically a neural oscillators) do not need any mathematical model of the robot itself. The controller “exploits” the dynamics of the robot to achieve an efficient way to drive the robot’s joints. The driving frequency from this type of controller is thus heavily influenced by the dynamics of the robot it controls. One disadvantage of this method is that we cannot adjust the walking/movement parameter easily. Inspired by the idea of central pattern generator where one central “brain” controls the movement of the joints of the robot and the fact that the system uses neural oscillators reach some kind of “consensus”, we are interested to study the feasibility of the implementation of leader – follower formation control based on consensus algorithm to bipedal locomotion system. The method studied in this report is to force the dynamic model of the double pendulum to match the kinematic model of the double integrator agent that uses consensus algorithm in forming formation. The walking/movement parameters of the robot using the proposed method are defined by one central “brain”, and then the joints are working in consensus way to achieve the target joints’ trajectories specified by the “brain”. The study also concludes the notion of stability of the system driven by this controller which strongly related to the consensus ability in the context of Multi – Agent System.

A Study of Chaos in Nonlinear Electronic Circuits and Applications in Game Theory

Chaos is a ubiquitous part of daily life. The weather, fractal landscapes, and the double pendulum all embody the notion of chaos. The general concepts and the key characteristics of chaos are explored and manifested in a nonlinear electronic circuit known as the Chua’s circuit. The Chua’s Circuit was built and characterized to illustrate chaos behavior in the form of Lorenz attractors. The circuit chaotic behavior was further demonstrated in a numerical model built in MATLAB. More practical chaos applications in secure communication and game theory are discussed. A case study is presented at the end to apply the chaos concept into the model of the strength of poker hands, which displays properties of a chaotic system and resembles Elementary Cellular Automata (ECA) in the chaos application.

Vibration analysis and experimental study of the effects of mechanised grape picking on the fruit–stem system

The problem of breakage and shedding in the mechanical harvesting of edible grapes has not been fully studied. Particularly, the responsiveness and shedding of berries caused by excited vibrations when the stem is sheared. This work combines modal analysis and swept frequency analysis to study the oscillation response and critical shedding characteristics of excited grape systems. First, a dynamic grape main stem-split stem-berry plane double pendulum model is established based on shedding theory, and the theoretical angular velocity of berry swing is deduced. Then, the berry separation and shedding processes are accurately simulated by a simplified multi-berry model that eliminates interference and penetration effects. The modal analysis shows that the berries exhibited multidirectional and multistate disordered swings and rotations at different frequencies. Finally, the critical shedding parameters, including the acceleration, velocity, displacement, stress and shedding frequency of the dynamic responses of the berries in the simulations and picking experiments are compared. The results show that the dynamic response trends of the simulation and picking experiments are consistent, and the berries fall off when the amplitude is 49.88 mm and the frequency is approximately 4 Hz. Therefore, this study provides theoretical parameters for optimising the picking mechanism.

Adaptive swing reduction control of double-pendulum tower crane time-varying system based on real-time update mutation factor

As representative underactuated and nonlinear systems, tower crane involves the multi-direction movement of the payload and even shows a more complex double pendulum in many actual situations, which makes the control problem more complicated. Most anti-swing controllers are mainly based on the linear design of tower crane dynamics at present and are insensitive to the position far from the equilibrium point. The time-varying cable length and double-pendulum effect are not taken into account simultaneously. Aiming at the problem of anti-swing control, a dynamic model of time-varying cable length tower crane with double-pendulum effect is established and an adaptive control method is proposed, which used the adaptive mutation strategy to update the mutation factor in real-time, and the parameters of the controller are tuned by an improved differential evolutionary algorithm. The simulations and experiments are carried out to verify the better optimization ability and faster convergence speed of the improved evolutionary algorithm in the process of parameter tuning and the effectiveness and superiority of the proposed control method are verified by comparing it with PID (proportion integration differentiation) and LQR (linear quadratic regulator) controllers.

A compound double pendulum with friction

We study a version of the two-degree-of-freedom double pendulum in which the two point masses are replaced by rigid bodies of irregular shape and nonconservative forces are permitted. We derive the equations of motion by analysing the forces involved in the framework of screw theory. This distinguishes the work from similar studies in the literature, which typically consider a double pendulum composed with rods and assume equations of motion without derivation. The equations of motion are solved numerically using the fourth-order Runge-Kutta method to show that decreasing the friction of the axles can cause the trajectory of one of the pendulums to become aperiodic. The stability of steady state solutions is also analysed.

Rotational modes of a double conical pendulum

Theoretical and experimental results are presented for a double conical pendulum rotated at the top end in a circular path of radius r 0. The rotation modes are different from those with r 0 = 0 and depend on whether the two pendulum masses rotate in or out of phase with the upper end and with each other. The results extend those already described in the physics teaching literature for a single conical pendulum, would be suitable as a lecture demonstration or an undergraduate laboratory experiment, and are closely analogous to those for a chain that is rotated at its upper end.

Saddle transport and chaos in the double pendulum

Pendulums are simple mechanical systems that have been studied for centuries and exhibit many aspects of modern dynamical systems theory. In particular, the double pendulum is a prototypical chaotic system that is frequently used to illustrate a variety of phenomena in nonlinear dynamics. In this work, we explore the existence and implications of codimension-1 invariant manifolds in the double pendulum, which originate from unstable periodic orbits around saddle equilibria and act as separatrices that mediate the global phase space transport. Motivated in part by similar studies on the three-body problem, we are able to draw a direct comparison between the dynamics of the double pendulum and transport in the solar system, which exist on vastly different scales. Thus, the double pendulum may be viewed as a table-top benchmark for chaotic, saddle-mediated transport, with direct relevance to energy-efficient space mission design. The analytical results of this work provide an existence result, concerning arbitrarily long itineraries in phase space, that is applicable to a wide class of two degree of freedom Hamiltonian systems, including the three-body problem and the double pendulum. This manuscript details a variety of periodic orbits corresponding to acrobatic motions of the double pendulum that can be identified and controlled in a laboratory setting.

Linear Control Schemes for Rotary Double Inverted Pendulum

In this article, the rotary double parallel inverted pendulum (RDPIP) is researched and presented. Additionally, some linear controllers, such as PID, PID, PID-LQR cascade, are proposed, developed to control RDPIP, and the impact of those controllers on the rotary double inverted pendulum was examined. The research and simulation results are implemented in the Matlab/Simulink toolbox to prove the ability of these types of controller in balancing this model.

Vibration control of double pendulum type crane system with uncertainty in parameters by elimination of the natural frequency component

Overhead cranes are widely used to transport heavy loads, and their efficient operation requires fast and accurate positioning. However, residual vibration which prevents positioning accuracy generally tends to be induced by fast transportation. In previous paper, we proposed a control method which is based on the characteristic that the residual vibration is completely suppressed in a linear undamped system when excited by an external force which does not contain the natural frequency component of the system. To apply this characteristic to nonlinear damped systems, we defined the apparent external force which includes the influence of system nonlinearity and damping. It was confirmed that the residual vibration of a double pendulum type system model of crane can be suppressed by eliminating two natural frequency components from each the apparent external forces. In this paper, in addition, to improve the robustness for a double pendulum type system against the estimation error, new conditions are added to reduce the component around the natural frequencies from each of the two apparent external forces. The effectiveness of these conditions for robustness is verified through numerical simulations. Furthermore, changes in the robustness are examined when the position of the mass point near the support point of the double pendulum is changed. The results showed that the robustness can be improved in many cases except when the control time is short and the mass point is close to the support point.

Optimization of oscillation damping modes of spatial double pendulum. II. Solving the problem and analyzing the results

This paper is a continuation of the article «Optimization of oscillation damping modes of spatial double pendulum. I. Formulation of the problem», in which the problem formulation of the optimal oscillations damping of double pendulum with joint axes not collinear to each other was given. Passive damping (viscous friction) is considered separately, and the possibility of additional accounting of active impacts (collinear control) is also discussed. Two optimization criteria are adopted that characterize the efficiency of the damping processes of system movements: first, the degree of stability is maximized, and then the integral energy-time criterion is minimized. The optimal values of the parameters of the considered damping options are determined according to both criteria in the course of the exact solution of the problem within the framework of a linear model. The obtained results are presented in the form of visual graphic illustrations which allow to establish their main qualitative and quantitative features. The conclusions can be useful in studying the movements of manipulators and various robotic structures.