冗余铺放机器人的自运动流形及逆解优化研究

Self-motion manifolds and inverse kinematic optimization of redundant fiber placement robot

针对用于复合材料铺放成型的八自由度冗余机器人系统的逆运动学问题,提出了一种求解其自运动流形及逆解优化的算法。首先,基于位姿分离思想定义了位置子流形和姿态子流形,采用几何求解法得到了基于自运动变量的参数化方程形式的位置子流形和姿态子流形;然后,根据机器人的关节约束和实际铺放工艺过程,对给定的铺放位姿进行了位置子流形和姿态子流形配对的仿真,并用流形中若干组逆解通过正向运动学得到了末端位姿矩阵(其结果均与给定位姿相符,从而验证了自运动流形求解过程的正确性);最后,在完成自运动流形求解的基础上,从机械臂运动的平滑性和关节运动变化量两个方面出发,提出了一种基于自运动变量参数化方程的全局优化目标函数;以飞机尾椎模型为实验研究对象,对其中一条铺放路径进行了逆解全局优化仿真,得到了自运动变量和机器人各关节角在铺放路径上的优化曲线,将仿真结果与一种多目标优化算法进行了比较。研究结果表明:针对相同的铺放路径,采用上述优化算法后关节角变化总量降低了11.25%;该算法能够有效地求解八自由度冗余铺放机器人系统的自运动流形,基于全局优化目标函数,其能够在自运动流形中寻找出自运动变量和机器人各关节的最优解。该算法同样也适用于其他位姿解耦的冗余机器人系统逆解问题的求解。

Aiming at the inverse kinematic problem of 8-DOF redundant robotic manipulator system which was used for automatic fiber placement,a kind of algorithm was proposed for obtaining its self-motion manifolds and optimizing inverse kinematics.Firstly,position sub-manifolds and orientation sub-manifolds were defined based on the idea that position and orientation of end-effector could be decoupled,and position and orientation sub-manifolds in the form of parameterized formulations were both obtained by geometric methods.Then,according to the joint constraints and actual laying process,position sub-manifolds and orientation sub-manifolds were simulated for given end-effector posture,several inverse kinematic solutions from the manifolds were used to obtain the end-effector posture matrix by positive kinematics,which was consistent with the given posture matrix,so the correctness of self-motion manifolds calculation process was proved.Finally,based on the calculation of self-motion manifolds,a global inverse kinematic optimal objective function was proposed based on the parameterized self-motion formulation considering two aspects of manipulator moving smoothness and total joints motion variation.The aircraft tail was taken as the object of study and one of the laying paths was simulated to get the optimal inverse kinematic curves of self-motion variables and robotic manipulator joint angles.The simulation results were compared with a multi-objective optimization algorithm.The results indicate that the total variation of joints motion is decreased by 11.25%for the same laying path.The algorithm is valid for obtaining the self-motion manifolds and searching optimal solutions for each joint and self-motion variable based on the global optimal objective function,the proposed algorithm is also fit for the inverse kinematic problem of other redundant robotic systems in which position and orientation are decoupled.