面向节点化运动学模型的几何逆运动学

Geometric Inverse Kinematics for Node-based Kinematics Model

针对在度量空间中利用距离表征机器人运动学模型时的逆运动学求解问题,提出了一种基于普氏分析和列文伯格-马夸尔特法的几何逆运动学模型及求解算法。通过节点化机器人,针对机器人构型构建其三维形状,将机器人的几何逆运动学问题转化为当前形状与目标形状差异最小化的优化问题。具体地,首先对当前形状和目标形状进行普氏分析,以普氏距离作为度量损失,根据构型相似度优先或实时性优先需求决定普氏重叠策略;然后基于列文伯格-马夸尔特优化框架求解所构建的优化问题;最后通过350组求解算例与主流算法进行定性与定量对比、分析。实验结果表明,在选择不同策略时,所提方法在绝对精度、构型相似度、计算耗时三方面均优于主流逆运动学求解方法。

To address the inverse kinematics problem of using distance to represent the kinematic model of robots in metric spaces,a geometric inverse kinematics algorithm based on Procrustes analysis and Levenberg-Marquardt algorithm is proposed.After abstracting the robot with nodes,a three-dimensional shape is constructed for the robot configuration,and the geometric inverse kinematics problem is transformed into an optimization problem that minimizes the difference between the current shape and the target shape.Specifically,Procrustes analysis is performed on the current shape and the target shape,and the Procrustes distance is used as the metric loss.The Procrustes superimposition strategy is determined according to the configuration similarity priority or real-time priority requirement.Then,based on the Levenberg-Marquardt optimization framework,the constructed optimization problem is solved.Finally,qualitative and quantitative comparisons are made with mainstream algorithms through 350 groups of examples.The experimental results show that,when choosing different strategies,the proposed method achieves the best results in terms of absolute accuracy,configuration similarity,computational time compared with mainstream methods.