机构柔性引起的四足机器人行走过程中的多维振动，是降低其运动稳定性的基本因素。目前相关研究集中在柔性机械臂的振动控制上。随着对机构更为复杂的四足机器人运动稳定性要求的提高，其行走振动问题亟待解决。本课题从步态规划角度研究四足机器人行走过程中多维振动的主动控制方法。首先，以ZMP点（零力矩点）的振动表征机器人水平方向的振动，以各支撑腿足端竖直方向的综合振动表征机器人竖直方向的振动，建立四足机器人行走过程中多维振动的系统模型；其次，以ZMP参考路径前馈和状态反馈的方式，设计以抑制机器人振动为目标的最优控制器（步态生成器）；最后，基于生成函数求解带输入约束的离散时间最优控制问题，生成最优步态，能实时有效地抑制四足机器人行走过程中的多维振动，实现稳定行走。本课题为四足机器人运动控制提供基础，可促进四足机器人运动稳定性研究的发展，也可促进最优控制数值方法研究的发展。

The multi-dimensional vibration of the quadruped robot caused by mechanism compliance during walking is the basic factor that reduces the stability of the quadrupedal locomotion. At present, the related research only focuses on the vibration control of the flexible manipulator. With the increasing stability requirement of the more complex quadrupedal locomotion, its walking vibration problem needs to be solved urgently. This research studies the active control of the quadruped robot’s multi-dimensional vibration during walking by gait planning. Firstly, characterize the horizontal vibration of the robot by the vibration of the ZMP (Zero Moment Point), and characterize the vertical vibration of the robot by the vector sum of the vertical vibration of the supporting leg’s foot end, model the multi-dimensional vibration of the quadruped robot during walking. Secondly, design the optimal controller (gait generator) with the objective of vibration suppression by the reference ZMP feedforward and the state feedback. Finally, solve the discrete-time input-constrained optimal control problem by the generating function to generate the optimal gait, which can real-time suppress the walking vibration of the quadruped robot effectively, and achieve the stable walking. This study provides the basis for the locomotion control of the quadruped robot, can promote the research of the stability of quadrupedal locomotion and the numerical method of optimal control.