时变二次规划的高精度数值算法

Numerical Algorithm With High Computational Precision for Time-Varying Quadratic Program

提出一种用于求解时变二次规划问题的高精度数值算法.首先,给出求解时变二次规划问题的连续模型;然后,采用新型泰勒差分公式将连续模型离散,得到具有高计算精度的数值算法;最后,通过理论分析和仿真实验表明该数值算法的优越性和有效性,并将所提出的数值算法应用于一个五连杆机械臂的运动控制中.研究结果表明:所提算法的计算稳态误差与采样间隔τ具有O(τ~4)的关系,该数值算法既可以有效地求解时变二次规划问题,又能有效地应用于机械臂的运动控制.

A high precision numerical algorithm is proposed to solve the problem of time-varying quadratic program. Firstly, the continuous-time model for time-varying quadratic program is given. Secondly, the numerical algorithm with a high computational precision is then derived by employing a new Taylor difference formula to discretize the above continuous-time model. Finally, the theoretical analysis and simulational experiments further indicate the superiority and effectiveness of the proposed numerical algorithm, and the proposed algorithm is applied to the motion control of a five-link robot manipulator. The results show that the calculated steady-state error of the proposed algorithm has a relationship of O(τ~4) with the sampling interval τ, this numerical algorithm can both effectively solve the time-varying quadratic programming problem and apply to the motion control of the manipulator.