斜坡行走：基于遗传算法优化轨迹的稳定双足步态

中文摘要 AI 辅助

本文介绍了在平坦和倾斜地形上行走的8自由度（DOF）双足机器人的运动学和动力学建模、轨迹生成及稳定性分析。利用Denavit-Hartenberg（DH）参数和齐次变换推导了正运动学，而闭式逆运动学则将期望的髋部和摆动脚笛卡尔轨迹（由三次样条生成）映射到关节角度。关节力矩使用Newton-Euler迭代算法计算，动态稳定性通过零力矩点（ZMP）准则评估。遗传算法（GA）通过最小化关节做功并施加ZMP可行性惩罚，优化了髋部高度、最大摆动脚抬升高度和额状面倾斜角。MATLAB仿真结果表明，在给定足部几何形状下，标称8自由度模型在步态完成时间低至0.5秒、坡度倾斜高达22.5度时仍保持ZMP稳定。超出这些限制时，ZMP会离开支撑多边形，必须修改足部尺寸或轨迹参数。结果还表明，ZMP稳定性由各连杆间的质量分布决定，而非机器人的总质量。

英文摘要

This paper presents the kinematic and dynamic modeling, trajectory generation, and stability analysis of an 8-degree-of-freedom (DOF) biped robot walking on flat and inclined terrain. Denavit-Hartenberg (DH) parameters and homogeneous transformations are used to derive the forward kinematics, while closed-form inverse kinematics maps the desired hip and swing-foot Cartesian trajectories, generated with cubic splines, to joint angles. Joint torques are computed using the Newton-Euler iterative algorithm, and dynamic stability is evaluated using the zero moment point (ZMP) criterion. A genetic algorithm (GA) optimizes the hip height, maximum swing-foot lift, and frontal-plane tilt angle by minimizing the work done by the joints subject to a ZMP feasibility penalty. Simulation results in MATLAB show that the nominal 8-DOF model remains ZMP-stable for step completion times down to 0.5 s and for slope inclinations up to 22.5 degrees with the given foot geometry. Beyond these limits, the ZMP leaves the support polygon, and either the foot dimensions or the trajectory parameters must be modified. The results also show that ZMP stability is governed by the mass distribution among the links rather than the total mass of the robot.

发表机构

• Indian Institute of Technology Kanpur（印度理工学院坎普尔分校）

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