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针对机械臂运动需满足快速性、低能耗和低冲击的问题,建立五次非均匀有理B样条(NURBS)曲线数学模型,构造端点运动参数均可指定的高阶连续的关节轨迹,采用带精英策略的非支配排序遗传算法(NSGA-II)以运行时间、能量消耗和轨迹平滑性为目标对机械臂运动轨迹进行优化,获得Pareto最优解集。对六自由度机器人的仿真结果表明,高次NURBS曲线可以很好的构造平滑轨迹,NSGA-II算法可对五次NURBS曲线轨迹实现有效的多目标优化,得到理想的Pareto分布。通过构造归一化权重目标函数,选择期望解,获得高阶连续的优化轨迹。
Aiming at the problems of rapidity, low energy consumption and low impact, the mathematical model of non-uniform NURBS curves is established to construct the high-order continuous joint trajectories of end-point motion parameters. The elitist non-dominated ranking genetic algorithm (NSGA-II) optimizes the trajectory of the robot with the objective of running time, energy consumption and trajectory smoothness, and obtains the Pareto optimal solution set. The simulation results of a six-degree-of-freedom robot show that the high-order NURBS curve can construct the smooth trajectory well, and the NSGA-II algorithm can achieve effective multi-objective optimization of the fifth-order NURBS curve trajectory and obtain the ideal Pareto distribution. By constructing the normalized weighted objective function, the expected solution is selected and the high-order continuous optimization trajectory is obtained.