System components usually attain marginal lifetimes with stochastic dependence in the context of load-sharing reliability structures. This study deals with the load-sharing parallel systems of two components. We prove that two marginal lifetimes are positively quadrant dependent when component lifetimes have continuous probability distributions, and such a stochastic dependence is upgraded to the total positive of order 2 in the setting of component lifetimes having an exponential distribution. In addition, we discuss how these findings shed light on related results for the load-sharing Ross model, the conditional residual lifetime, and the conditional inactivity time.

Legged robots have demonstrated remarkable potential for dynamic locomotion and terrain adaptability, making them a prominent focus of research. However, achieving robust and agile bipedal running remains challenging due to the complex dynamics of legged locomotion. In this paper, we propose a reinforcement learning framework for robust bipedal running, incorporating a simple reference trajectory generator and an asymmetric actor-critic architecture. The reference generator, based on kinematics, provides diverse trajectory references while preserving key gait characteristics, facilitating efficient policy exploration. To mitigate the simulation-to-reality gap, we extract latent variables encoding environmental and motion information from dual historical observations. Our method simplifies the trajectory generation process while maintaining effective guidance for learning. Extensive simulation and physical experiments demonstrate that, compared to model-based and learning-based baselines, our approach achieves higher agility, more accurate velocity tracking, and stronger disturbance rejection while preserving gait stability. The resulting controller exhibits spring–mass running dynamics that remain robust on both flat and uneven terrains.

In this paper, we study the joint distribution of the forward and backward recurrence times in a delayed renewal process, as well as their marginal distributions. We obtain several exact results and bounds for these quantities. Some of these bounds are “general,” in the sense that the bounds are valid for any arbitrary distributions of the inter-arrival times, and some are based on aging properties of the distributions of the interarrival times of the renewals. Finally, several numerical examples are presented to illustrate the results.

Constant-force mechanisms (CFMs) are attractive for mechanical energy storage owing to their distinctive force–displacement characteristics, particularly under conditions with limited external load capacity and restricted space. However, conventional CFMs often suffer from short constant-force strokes and inefficient space utilization, which hinder their broader application. To address these limitations, this study exploits the buckling of compliant beams and increases the structural degrees of freedom by adopting a less constrained configuration, which extends the constant-force stroke and space utilization while reducing the required external load, thus improving energy storage efficiency for the same stored elastic energy. A novel catapult was developed through NSGA-II multi-objective optimization, achieving a high energy-to-cost ratio and an extended constant-force stroke. This work presents an effective design approach for motion mechanisms that demand high energy-storage efficiency and high-power output.

In this research, a hierarchical dynamic and kinematic modeling framework is proposed for a wheeled-legged manipulator (WLM), explicitly incorporating wheel slip and skid effects through the Gibbs–Appell formulation. Unlike traditional Lagrangian methods that depend on constraint multipliers, the proposed approach unifies the platform and manipulator dynamics while substantially reducing computational complexity. This integration enables efficient handling of nonholonomic constraints without compromising physical fidelity and offers a clear separation between subsystems, allowing the effects of wheel-ground interactions to be analyzed independently from manipulator motions. The proposed formulation is validated through a combination of MATLAB/Webots simulations and laboratory experiments conducted under both dry and wet (soapy ceramic) surface conditions. Experimental results indicate end-effector position deviations of 8–10.5% primarily due to wheel slip and initial joint torque discrepancies of 6.5–20% that progressively diminish as steady-state motion is reached. Comparative evaluation against a conventional Lagrangian model highlights the computational advantage of the Gibbs–Appell formulation, demonstrating reduced assembly time and fewer symbolic differentiation operations. Furthermore, a sensitivity analysis on friction coefficients and slip ratios confirms the robustness of the model to variations in surface conditions. Beyond accurate dynamic prediction, the hierarchical structure enables modular real-time implementation, supporting controller design, trajectory planning, and fault detection. Overall, the results demonstrate that the Gibbs–Appell-based hierarchical modeling framework combines analytical rigor with computational efficiency, providing a robust foundation for control and optimization in advanced wheeled-legged robotic manipulators.

We evaluate the effect of reciprocal trust within pairs of individuals—gauged by total potential earnings in a trust experiment—on the probability of relationship formation, in comparison with well-known determinants of social ties, such as time of exposure and homophily along demographic traits. We measured trust and trustworthiness for every individual in an incoming cohort of undergraduate students before they began interacting. Using relationship data sourced from surveys and campus entry/exit times between one month and two years after the trust experiment, we find that reciprocal trust is neither a statistically nor an economically significant factor in determining the students’ social networks. Instead, time of exposure, prior acquaintance, and other demographic characteristics play important and persistent roles in relationship formation.

Efficient global localization of mobile robots in symmetrical indoor environments remains a formidable challenge, given the inherent complexities arising from uniform structures and a dearth of distinctive features. This review paper conducts an in-depth investigation into the nuances of global localization strategies, focusing on symmetrical environments, such as extended corridors, symmetrical rooms, tunnels, and industrial warehouses. The study comprehensively reviews and categorizes key techniques employed in this context, encompassing probabilistic-based approaches, learning-based approaches, Simultaneous Localization and Mapping (SLAM)-based approaches, and optimization-based approaches. The primary goal is to provide a contemporary and thorough literature review, offering insights into existing global localization solutions, followed by extant methods tailored for symmetrical indoor spaces. Also, the paper addresses practical challenges associated with implementing various global localization techniques, contributing to a holistic understanding of their real-world applicability. Comparative experimental results demonstrate that hybrid approaches achieve superior localization accuracy in symmetrical environments compared to any single method alone. These experiments, conducted in indoor settings with different symmetry levels, highlight the hybrid approach’s robustness and precision in resolving symmetry-induced ambiguities. This work signifies a significant step forward in mobile robot global localization, which addresses symmetrical environments’ complexities by leveraging the strengths of hybrid methodologies.