Novel Trajectory Planning Method Based on Double Quaternion and Tau Theory

The double quaternion represents the double rotation in four-dimensional space. It has the advantage of fast computing, robustness, and no singularity, hence the double quaternion can be used in the trajectory planning of the robotic manipulator. To make the position and orientation of the end-effector change continuously and smoothly in the trajectory, another compliant trajectory planning algorithm is needed. Algorithms based on Tau theory are an ideal solution since they use the inner mechanism of humans and animals plan trajectories and the planned trajectories are compliant. The effectiveness of the proposed method is verified on both virtual and real robotic manipulator.