运用非线性规划对小型机械臂逆运动学的优化求解

摘要

应用Denavit-Hartenberg法建立起简化的小型机械臂的正运动学方程,并以机械臂由起始点到目标点各关节角度变化最小为优化目标,运用非线性规划针对运动方程的求解非进行优化,相应地运用Matlab构建出在非线性约束下的多变量最优化问题的fmincon函数.运用多组数据,以Robot-ics Toolbox作为对照对象,对机械臂正逆运动学进行仿真,从而验证所构建机械臂运动方程的正确性及非线性规划的合理性,为简单小型机械臂的末端定位问题提供了一种高效准确的逆向求解方法.%The kinematics equations of a small simplified mechanical arm were established in Denavit -Hartenberg method, and optimized the goal of the minimum overall changes of each joint angle from the starting point to the target point, thus using linear programming for solving the non-optimized motion equa-tion to construct multi-variable-optimization problem under nonlinear constraints with the function fmincon in Matlab. By using multiple sets of data, compared with Robotics Toolbox, the forward kinematics and in-verse kinematics of the manipulator were simulated, which verifies the correctness of the kinematic equation of the manipulator and the rationality of the nonlinear programming. It provides an efficient and accurate method for solving the problem of the terminal location of small simplified mechanical arms.