双足欠驱动机器人能量成型控制

Energy Shaping Control of Under-actuated Biped Robot

研究欠驱动双足机器人在3D空间稳定行走控制器。建立双足机器人的3D动力学模型,通过构建概循环拉格朗日函数,把欠驱动双足机器人的3D动态系统解耦成前向和侧向部分。针对前向2D欠驱动部分设计势能成型和动能成型控制器,为了求解能量成型控制器,将匹配方程分解成分别与角度和角速度相关的两个子条件,再将非线性偏微分方程变为线性偏微分方程,求解出能量成型控制器对前向行走进行控制,使前向行走获得稳定且具有仿生特点。对侧向部分采用零动态控制,在保证侧向稳定同时,还满足系统的动态解耦条件。对不同步长行走进行仿真试验,仿真结果表明,动态步行收敛于稳定的极限环,步态符合仿生规律,验证了所提出理论的可行性和有效性。

The walking stability controller is designed for researching the biped robots in 3D （three-dimensional） space. The 3D dynamics model of biped robot is established. By constructing the almost-cyclic Lagrange function, the biped robot dynamic system is decoupled into sagittal and lateral portions. The potential energy shaping and kinetic energy shaping controller is designed for the sagittal portion of under-actuated robot in 2D space. In order to solve the energy shaping controller, the matching condition is be separated into two sub-conditions which relate to angle and angular velocity respectively. The nonlinear partial differential equation is changed into linear partial differential equation, and the energy controller is solved to regulate sagittal locomotion, so that the stable walking gait and bionic characteristic gait can be obtained. The output zero dynamic controller is applied to control the lateral portion, which satisfies the dynamic decoupling conditions of the system. The simulation experiments are carried out on different step length. The simulation results show that the dynamic walking converges to a stable limit cycle and the gait accord with biomimetic law, the feasibility and effectiveness of the theory is verified.