基于数值变分计算的Acrobot机器臂能量最优控制

Energy optimal control for Acrobot with anipulators based on numerical calculus of variations

针对最小能量控制中初始参数难以确定的问题,利用欧拉-拉格朗日乘子处理系统约束而获得积分形式的变分方程,通过离散化变分方程,得到系统最优控制的必要条件,并选定合适的积分方法,求解非线性方程而得到系统最优控制解。仿真实验表明,该方法求解变分方程是可行的。

Aiming at the problem that the initial parameters are difficult to determine in the minimum energy control,the Euler Lagrange multiplier is used to deal with the system constraints to obtain the integral form of the variational equation.By discretizing the variational equation,the necessary conditions for the optimal control of the system are obtained,and the appropriate integration method is selected to solve the nonlinear equation to obtain the optimal control solution of the system.The simulation results show that the method is feasible.