The definition of design load with walking crowd excitation on these slender structures is a significant problem to human-induced vibration. To capture the characteristics of walking crowd loads, this article researches both the ground reaction force and ground reaction moment for 36 healthy adults. Firstly, a oscillate system modeling walking leg is used to build a governing equation, which further transformed into the discrete state space. Then the Kalman method is applied to filter the noises for the measured ground reaction force, which can well remove the noises hiding in the measured signals. In addition, the Fourier series are used to model the ground reaction force and ground reaction moment, and the first six corresponding coefficients are obtained and analyzed. This work comprehensively explores the excitation force and moment from walking pedestrian feet. The result of this study provides the reference of load design for these slender structures such as footbridges, grandstands, or stations under crowd excitation.

This research delves into the dynamic interaction between bipedal pedestrians and truss structures, utilizing the Lagrangian equation theory to formulate the governing equations of the pedestrian-truss system. This advanced theoretical approach effectively accounts for the dynamic properties of the human body and their consequential effects on the structural dynamics. A comprehensive numerical analysis was conducted on a 22.4-m truss structure, revealing that the proposed methodology produces results that are consistent with those obtained from finite element analysis. The findings demonstrate that consistent numerical solutions were achieved, the significant influence of pedestrian movement on the structure’s dominant natural frequencies and damping characteristics, and how human body model parameters alter under specific gait conditions. The versatility of this theory is highlighted by its potential application not only to horizontal truss bridges but also to cantilever and arch truss configurations, thereby underscoring its substantial relevance and transformative potential for real-world engineering projects.

Trajectory planning for the center of mass (CoM) constitutes a fundamental challenge in bipedal locomotion. Conventional approaches, which predominantly rely on experimental measurements or simplified analytical models, are often constrained by discretization errors, parameter uncertainty, and prohibitive experimental costs. To address these limitations, this paper proposes a numerical framework for generating CoM trajectories directly from ground reaction force (GRF) dynamics. The methodology first determines key gait event positions and formulates a coupled system of governing equations that integrate force and motion. The method then establishes a unified spatio-temporal-GRF coordinate system and incorporates boundary conditions, along with load-sharing mechanisms between the trailing and leading legs, to derive the force and geometric constraint equations. The resulting reference trajectory is represented using Fourier coefficients, which are determined via an Adam-based constrained residual minimization solver. This Fourier-based representation offers notable advantages, including a compact parameter set, high computational efficiency, and the capacity to capture the essential kinematic features of bipedal walking. To validate the proposed reference trajectory, a sliding mode control (SMC) framework is employed for bipedal walking control, in which the walker successfully tracks the reference trajectory with stable gait execution. The results confirm that the generated trajectory faithfully reproduces the characteristic CoM response of bipedal walking, thereby providing a high-fidelity reference for robust motion control. Furthermore, a systematic analysis of the control parameters is conducted to evaluate their influence on walking stability. This work offers a new paradigm that synergistically combines physical interpretability with computational efficiency, holding significant promise for applications in humanoid robot motion control and biomechanical analysis.