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依据完整约束下的拉格朗日方程,推导了同轴两轮移动机器人做平面直线运动时的动力学模型,并在此基础上设计了基于极点配置的状态反馈控制模型和系统数字仿真模型。结合控制模型进行了数字仿真实验研究和物理实验研究,并给出了实验分析结果。研究表明,采用基于极点配置的状态反馈控制方案,能够实现机器人动态平衡控制;机器人在初始偏角绝对值小于0.25 rad时,能够在2 s内恢复平衡,当外部干扰使机器人偏离平衡位置后,机器人能够在3 s内恢复平衡;机器人模型推导合理、有效,数字仿真和物理实验一致性好。
Based on the Lagrange equation with complete constraint, the dynamic model of coaxial two-wheeled mobile robot in plane linear motion is deduced. Based on this, a state feedback control model and system digital simulation model based on pole configuration are designed. Combined with the control model, the numerical simulation experiment and the physical experiment are carried out, and the experimental analysis results are given. The research shows that the state feedback control scheme based on the pole placement can realize the robot dynamic balance control. When the initial absolute value of the declination angle is less than 0.25 rad, the robot can recover the balance within 2 s. When the external disturbance causes the robot to deviate from the equilibrium position, The robot can recover the balance within 3 s. The robot model is reasonable and effective, and the numerical simulation and physical experiment are in good agreement.