﻿ 基于LQR的4关节欠驱动体操机器人平衡控制

# 基于LQR的4关节欠驱动体操机器人平衡控制Balance Control of a 4-DOF Underactuated Gymnastic Robot Based on LQR

4关节欠驱动体操机器人是一个多变量、非线性、强耦合的复杂控制系统。本文针对该类机器人系统，首先利用拉格朗日法建立了其刚体动力学方程，然后探讨了非线性机器人数学模型在垂直倒立平衡点附近的线性化方法，接着采用了线性二次型调节器(LQR)对体操机器人进行了倒立平衡最优控制器的设计，最后通过仿真实验验证了提出方法的有效性。

Abstract: The 4-DOF underactuated gymnastic robot is a complex control system which is multivariable, nonlinear and strong coupling. In this paper, according to the system of this kind of robot, the dynamic equation of rigid body is established firstly by using Lagrange method. Secondly, a linearization method for nonlinear robot mathematical model in the vicinity of vertical inverted equilibrium point is discussed. Then, a Linear Quadratic Regulator (LQR) is used to design the optimal controller of the handstand balance. Finally, some simulation results show the effectiveness of the proposed method.

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