Search Results (11)

This study presents a sim2real reinforcement learning-based controller for transition control in a double-inverted pendulum system, addressing the limitations of traditional control methods that rely on precomputed trajectories and lack adaptability to strong external disturbances. By introducing the novel concept of ‘transition control’, this research expands the scope of inverted pendulum studies to tackle the challenging task of navigating between multiple equilibrium points. To overcome the reality gap—a persistent challenge in sim2real transfer—a hardware-centered approach was employed, aligning the physical system’s mechanical design with high-fidelity dynamic equations derived from the Euler–Lagrange equation. This design eliminates the need for software-based corrections, ensuring consistent and robust system performance across simulated and real-world environments. Experimental validation demonstrates the controller’s ability to reliably execute all 12 transition scenarios within the double-inverted pendulum system. Additionally, it exhibits recovery characteristics, enabling the system to stabilize and return to equilibrium point even under severe disturbances. Full article

This paper proposes a distributed passivity-based control scheme for the consensus and vibration suppression of multiple space manipulators holding flexible beams. A space manipulator holding a flexible beam is essentially a rigid–flexible underactuated system. The bending deformation of the flexible beam is discretized by employing the assumed modes method. Based on Lagrange’s equations of the second kind, the dynamics model of each manipulator holding a flexible beam is established. By connecting such underactuated systems with the auxiliary Euler–Lagrange systems, a distributed passivity-based controller is designed under undirected communication graphs. To suppress flexible vibration effectively, a distributed controller with the feedback of the velocity of deflection at the free end of the flexible beam is proposed to achieve the manipulator synchronization and vibration suppression simultaneously. The stability of the proposed controller is analyzed with LaSalle’s invariance principle. Numerical simulations and experiments are conducted to show the effectiveness of the designed controllers. Full article

In this paper, we considered the Neumann elliptic equation $\left({\mathcal{P}}_{\epsilon }\right)$: $-\Delta u+K\left(x\right)u=u^{(n+2)/(n-2)-\epsilon }$, $u>0$ in $\Omega$, $\partial u/\partial \nu =0$ on $\partial \Omega$, where $\Omega$ is a smooth bounded domain in ${\mathbb{R}}^n$, $n\ge 6$, $\epsilon$ is a small positive real and K is a smooth positive function on $\overline{\Omega }$. Using refined asymptotic estimates of the gradient of the associated Euler–Lagrange functional, we constructed simple and non-simple interior bubbling solutions of $\left({\mathcal{P}}_{\epsilon }\right)$ which allowed us to prove multiplicity results for $\left({\mathcal{P}}_{\epsilon }\right)$ provided that $\epsilon$ is small. The existence of non-simple interior bubbling solutions is a new phenomenon for the positive solutions of subcritical problems. Full article

In the fields of control engineering and robotics, either the Lagrange or Newton–Euler method is generally used to analyze and design systems using equations of motion. Although the Lagrange method can obtain analytical solutions, it is difficult to handle in multi-degree-of-freedom systems because the computational complexity increases explosively as the number of degrees of freedom increases. Conversely, the Newton–Euler method requires less computation even for multi-degree-of-freedom systems, but it cannot obtain an analytical solution. Therefore, we propose a partial Lagrange method that can handle the Lagrange equation efficiently even for multi-degree-of-freedom systems by using a divide-and-conquer approach. The proposed method can easily handle system extensions and system reconstructions, such as changes to intermediate links, for multi-degree-of-freedom serial link manipulators. In addition, the proposed method facilitates the derivation of the equations of motion-by-hand calculations, and when combined with an analysis algorithm using automatic differentiation, it can easily realize motion analysis and control the simulation of multi-degree-of-freedom models. Using multiple pendulums as examples, we confirm the effectiveness of system expansion and system reconstruction with the partial Lagrangians. The derivation of their equations of motion and the results of motion analysis by simulation and motion control experiments are presented. The system extensions and reconstructions proposed herein can be used simultaneously with conventional analytical methods, allowing manual derivations of equations of motion and numerical computer simulations to be performed more efficiently. Full article

Hard-magnetic soft materials belong to a class of the highly deformable magneto-active elastomer family of smart materials and provide a promising technology for flexible electronics, soft robots, and functional metamaterials. When hard-magnetic soft actuators are driven by a multiple-step input signal (Heaviside magnetic field signal), the residual oscillations exhibited by the actuator about equilibrium positions may limit their performance and accuracy in practical applications. This work aims at developing a command-shaping scheme for alleviating residual vibrations in a magnetically driven planar hard-magnetic soft actuator. The control scheme is based on the balance of magnetic and elastic forces at a critical point in an oscillation cycle. The equation governing the dynamics of the actuator is devised using the Euler–Lagrange equation. The constitutive behaviour of the hard-magnetic soft material is modeled using the Gent model of hyperelasticity, which accounts for the strain-stiffening effects. The dynamic response of the actuator under a step input signal is obtained by numerically solving the devised dynamic governing equation using MATLAB ODE solver. To demonstrate the applicability of the developed command-shaping scheme, a thorough investigation showing the effect of various parameters such as material damping, the sequence of desired equilibrium positions, and polymer chain extensibility on the performance of the proposed scheme is performed. The designed control scheme is found to be effective in controlling the motion of the hard-magnetic soft actuator at any desired equilibrium position. The present study can find its potential application in the design and development of an open-loop controller for hard-magnetic soft actuators. Full article

This paper comprehensively reviews the nonlinear dynamics given by some classes of constrained control problems which involve second-order partial derivatives. Specifically, necessary optimality conditions are formulated and proved for the considered variational control problems governed by integral functionals. In addition, the well-posedness and the associated variational inequalities are considered in the present review paper. Full article

Various factors and challenges are involved in efficiently delivering drugs using nasal sprays to the olfactory region to treat central nervous system diseases. In this study, computational fluid dynamics was used to simulate nasal drug delivery to (1) examine effects on drug deposition when various external magnetic fields are applied to charged particles, (2) comprehensively study effects of multiple parameters (i.e., particle aerodynamic diameter; injection velocity magnitude, angle, and position; magnetic force strength and direction), and (3) determine how to achieve the optimal delivery efficiency to the olfactory epithelium. The Reynolds-averaged Navier–Stokes equations governed airflow, with a realistic inhalation waveform implemented at the nostrils. Particle trajectories were modeled using the one-way coupled Euler–Lagrange model. A current-carrying wire generated a magnetic field to apply force on charged particles and direct them to the olfactory region. Once drug particles reached the olfactory region, their diffusion through mucus to the epithelium was calculated analytically. Particle aerodynamic diameter, injection position, and magnetic field strength were found to be interconnected in their effects on delivery efficiency. Specific combinations of these parameters achieved over 65-fold higher drug delivery efficiency compared with uniform injections with no magnetic fields. The insight gained suggests how to integrate these factors to achieve the optimal efficiency. Full article

The calculus of variations is a field of mathematical analysis born in 1687 with Newton’s problem of minimal resistance, which is concerned with the maxima or minima of integral functionals. Finding the solution of such problems leads to solving the associated Euler–Lagrange equations. The subject has found many applications over the centuries, e.g., in physics, economics, engineering and biology. Up to this moment, however, the theory of the calculus of variations has been confined to Newton’s approach to calculus. As in many applications negative values of admissible functions are not physically plausible, we propose here to develop an alternative calculus of variations based on the non-Newtonian approach first introduced by Grossman and Katz in the period between 1967 and 1970, which provides a calculus defined, from the very beginning, for positive real numbers only, and it is based on a (non-Newtonian) derivative that permits one to compare relative changes between a dependent positive variable and an independent variable that is also positive. In this way, the non-Newtonian calculus of variations we introduce here provides a natural framework for problems involving functions with positive images. Our main result is a first-order optimality condition of Euler–Lagrange type. The new calculus of variations complements the standard one in a nontrivial/multiplicative way, guaranteeing that the solution remains in the physically admissible positive range. An illustrative example is given. Full article

The present paper deals with a class of second-order PDE constrained controlled optimization problems with application in Lagrange–Hamilton dynamics. Concretely, we formulate and prove necessary conditions of optimality for the considered class of control problems driven by multiple integral cost functionals involving second-order partial derivatives. Moreover, an illustrative example is provided to highlight the effectiveness of the results derived in the paper. In the final part of the paper, we present an algorithm to summarize the steps for solving a control problem such as the one investigated here. Full article

This paper presents an upright piezoelectric energy harvester (UPEH) with cylinder extension along its longitudinal direction. The UPEH can generate energy from low-speed wind by bending deformation produced by vortex-induced vibrations (VIVs). The UPEH has the advantages of less working space and ease of setting up an array over conventional vortex-induced vibration harvesters. The nonlinear distributed modeling method is established based on Euler–Bernoulli beam theory and aerodynamic vortex-induced force of the cylinder is obtained by the van der Pol wake oscillator theory. The fluid–solid–electricity governing coupled equations are derived using Lagrange’s equation and solved through Galerkin discretization. The effect of cylinder gravity on the dynamic characteristics of the UPEH is also considered using the energy method. The influences of substrate dimension, piezoelectric dimension, the mass of cylinder extension, and electrical load resistance on the output performance of harvester are studied using the theoretical model. Experiments were carried out and the results were in good agreement with the numerical results. The results showed that a UPEH configuration achieves the maximum power of 635.04 μW at optimum resistance of 250 kΩ when tested at a wind speed of 4.20 m/s. The theoretical results show that the UPEH can get better energy harvesting output performance with a lighter tip mass of cylinder, and thicker and shorter substrate in its synchronization working region. This work will provide the theoretical guidance for studying the array of multiple upright energy harvesters. Full article