【摘要】 为了更好地利用柔性关节机械臂的固有柔顺性,使机械臂具有更佳的运动性能,将障碍函数法同迭代线性二次型调节(ILQR)算法相结合,提出了改进型ILQR算法,来处理受物理约束限制的柔性关节机械臂的最优控制问题,并通过KKT条件系统地证明了改进型ILQR算法的收敛性;采用PD方法对电机端进行控制,使电机端动力学模型转化为二阶临界阻尼系统,将电机端运动轨迹约束转化为控制量上下界约束,并通过模型参数嵌入到电机端动力学模型当中,从而减少了最优控制系统中软约束的数量,建立了易于改进型ILQR算法求解的数学模型;对不同类型的柔性关节机械臂最优控制问题进行求解,仿真结果表明:所提出的改进型ILQR算法可实现受物理约束限制的柔性关节机械臂的最优控制,并可利用其固有柔顺性提高机械臂的运动性能。更多还原

【Abstract】 In order to utilize the inherent flexibility which has a better motion performance of flexible joint manipulators, the penalty function was introduced into the iterative linear quadratic regulator(ILQR), and an improved ILQR algorithm was proposed to deal with the optimal control of flexible joint manipulators with arbitrary inequality constraints. Besides, the convergence of the improved ILQR algorithm was proved by KKT condition. The motor-side dynamic model of flexible joint manipulator was transformed into a second-order critical damping system by PD control. The motor-side trajectory constraints were transformed into the upper and lower bound constraints of the control quantity, and were embedded into the motor-side dynamic model with the model parameter. The soft constraints’ quantity of optimal control system for flexible joint manipulators was reduced and the mathematical model which is easy to be solved by improved ILQR algorithm was established. The optimal control problem of different types of flexible joint manipulators was solved. The simulation results show that the improved ILQR algorithm can realize optimal control for flexible joint manipulators with physical constraints and improve the motion performance of the manipulators by its inherent flexibility.更多还原