Uniformly Interpolated Elements of SE(3) and their Application to Manipulator Design

This paper presents a computational method to generate a sequence of uniformly interpolated elements between an arbitrary pair of elements in the special Euclidean group, SE(3). The significance of the proposed method is that the uniformity of the distribution of sequential frames on SE(3) is guaranteed through a metric defined for rigid body motion. The necessity of this computation can be often found in robotics applications. The computational method will be adapted to a kinematic synthesis problem for a class of robotic manipulators as an example application. A "discretely actuated robotic manipulator (D-ARM)", is any member of a class of robotic manipulators powered by actuators such as solenoids that have only discrete stable positional states. One of the most significant kinematic phenomena of D-ARMs is the discreteness of both input range and end-effector frames. The conducted simulations demonstrate the feasibility of the synthesis procedure with the proposed frame interpolation method