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This work introduces a model-free reinforcement learning framework that enables various modes of motion (quadruped, tripod, or biped) and diverse tasks for legged robot locomotion. We employ a motion-style reward based on a relaxed logarithmic barrier function as a soft constraint, to bias the learning process toward the desired motion style, such as gait, foot clearance, joint position, or body height. The predefined gait cycle is encoded in a flexible manner, facilitating gait adjustments throughout the learning process. Extensive experiments demonstrate that KAIST HOUND, a 45 kg robotic system, can achieve biped, tripod, and quadruped locomotion using the proposed framework; quadrupedal capabilities include traversing uneven terrain, galloping at 4.67 m/s, and overcoming obstacles up to 58 cm (67 cm for HOUND2); bipedal capabilities include running at 3.6 m/s, carrying a 7.5 kg object, and ascending stairs-all performed without exteroceptive input., Comment: 7 pages, 5 figures, Videos at https://youtu.be/JV2_HfTlOKI

Floating offshore wind turbine (FOWT) systems involve several coupled physical analysis disciplines, including aeroelasticity, multi-body structural dynamics, hydrodynamics, and controls. Conventionally, physical structure (plant) and control design decisions are treated as two separate problems, and generally, control design is performed after the plant design is complete. However, this sequential design approach cannot fully capitalize upon the synergy between plant and control design decisions. These conventional design practices produce suboptimal designs, especially in cases with strong coupling between plant and control design decisions. Control co-design (CCD) is a holistic design approach that accounts fully for plant-control design coupling by optimizing these decisions simultaneously. CCD is especially advantageous for system design problems with complex interactions between physics disciplines, which is the case for FOWT systems. This paper presents and demonstrates a nested CCD approach using open-loop optimal control (OLOC) for a simplified reduced-order model that simulates FOWT dynamic behavior. This simplified model is helpful for optimization studies due to its computational efficiency, but is still sufficiently rich enough to capture important multidisciplinary physics couplings and plant-control design coupling associated with a horizontal-axis FOWT system with a spar buoy floating platform. The CCD result shows an improvement in the objective function, annual energy production (AEP), compared to the baseline design by more than eleven percent. Optimization studies at this fidelity level can provide system design engineers with insights into design directions that leverage design coupling to improve performance. These studies also provide a template for future more detailed turbine CCD optimization studies that utilize higher fidelity models and design representations., Comment: 21 pages, 15 figures, 5 tables

This paper discusses a framework to design elements of the plant and control systems for floating offshore wind turbines in an integrated manner using linear parameter-varying models. Multiple linearized models derived from aeroelastic simulation software in different operating regions characterized by the incoming wind speed are combined to construct an approximate low-fidelity model of the system. The combined model is then used to generate open-loop, optimal control trajectories as part of a nested control co-design strategy that explores the system's power production and stability using the platform pitch tilt as a proxy in the context of crucial plant and control design decisions. The radial distance between the central and outer columns and the diameter of the outer columns of the semisubmersible platform are the plant design variables. The platform stability and power production are studied for different plant design decisions. The effect of plant decisions on subsequent power production and stability response of the floating wind turbine is quantified in terms of the levelized cost of energy. The results show that the inner-loop constraints and the plant design decisions affect the turbine's power and, subsequently, the cost of the system., Comment: 16 pages 47 figures

In this paper, we study the existence of positive solutions for nonlinear fractional differential equations with a singular weight. We derive Green's function and corresponding integral operator and then examine the compactness of the operator. As an application, we prove an existence-result for positive solutions when a nonlinear term satisfies either superlinear or sublinear conditions. The proof was mainly employed by Krasnoselski's classical fixed point theorem., Comment: arXiv admin note: substantial text overlap with arXiv:2202.09015

In this work, we study the regularity of positive solutions for nonlinear fractional differential equation with a singular weight. We define the new Banach space and use this space to show the regularity. We also give an example with a singular weight which may not be in $L^1.$

By providing an effective way to leverage nonlinear phenomena in chip-scale, high-Q optical resonators have induced the recent advances of on-chip photonics represented by micro-combs and ultra-narrow linewidth lasers. These achievements mainly relying on Si, SiO$_{2}$, and Si$_{3}$N$_{4}$ are expected to be further improved by introducing new materials having higher nonlinearity. However, establishing fabrication processes to shape a new material into the resonator geometries having extremely smooth surfaces on a chip has been a challenging task. Here we describe a universal method to implement high-Q resonators with any materials which can be deposited in high vacuum. This approach, by which light-guiding cores having surface roughness in molecular-scale is automatically defined along the prepatterned platform structures during the deposition, is verified with As$_{2}$S$_{3}$, a typical chalcogenide glass of high-nonlinearity. The Q-factor of the developed resonator is 14.4 million approaching the loss of chalcogenide fibers, which is measured in newly proposed tunable waveguide-to-resonator coupling scheme with high ideality. Lasing by stimulated Brillouin process is demonstrated with threshold power of 0.53 mW which is 100 times lower than the previous record based on chalcogenide glasses. This approach paves the way for bringing various materials of distinguished virtues to the on-chip domain while keeping the loss performance comparable to that of bulk form., Comment: 9 pages, 4 figures