基于倍四元数的机器人运动灵活性评价

Kinematic dexterity measures for robot manipulators based on double quaternion

针对机器人的雅可比矩阵量纲不统一而不能对其进行灵活性评价这一问题，提出了一种新的雅可比矩阵量纲统一及评价方法。首先基于倍四元数，将三维空间的旋转和平移统一为四维空间的纯转动，推导了基于倍四元数的连杆坐标系变换通式。然后利用该方法对机器人进行了运动学建模，得到了具有统一量纲的雅可比矩阵，并根据该矩阵定义了新的评价指标。该方法解决了混合关节机器人建模时所产生的雅可比矩阵量纲不统一的问题。最后，对空间3R机器人和空间RPR机器人的灵活性进行了数值仿真分析，结果表明该评价方法不仅适用于相同类型关节的机器人，同时适用于混合关节类型的机器人。

In view of the fact that the dexterity evaluation on robots cannot be made due to the dimensional inhomogeneity of Jaeobian, a new approach to formulation of the dimensional homogeneous Jacobian and kinematic dexterity measure for the robot with mixed joints is proposed. According to the double quaternion, the rotation and translation in three-dimensional Euclidean spaces are converted to the pure rotation in four-dimensional Euclidean spaces. The universal transformational expression of the link coordinate system is derived based on double quaternion. Then the kinematics model of robot is developed and more, a new performance index is proposed. an which occurs for robots with mixed joints. the non-dimensional Jacobian is The new approach can solve the obtained by this approach. Furtherdimensional inhomogeneity of JacobivFinally, the kinematic dexterity of spatial 3R and the spatial RPR robot is analyzed by numerical simulation. The results show that this approach is not only applicable to the robot with same joints, but also to the robot with mixed joints.