Dual Quaternion based modal kinematics for multisection continuum arms

This paper presents general modal dual Quaternion (DQ) kinematics for multisection continuum arms. DQ's produce higher accuracy than homogeneous transformation matrices (HTM) when transformed to modal shape functions (MSF) of similar order and are numerically stable. Thus, the model is compact, more accurate and computationally efficient than the modal kinematics proposed by the author based on HTM's. Also, DQ kinematics does not suffer from singularity related limitations of Euler angle based inverse orientation kinematics. Recursive schemes for deriving DQ's and DQ Jacobians are also presented and can be extended arbitrarily. Both modal HTM and modal DQ kinematics are then applied to solve illustrative spatial inverse position and orientation tracking problems. Based on the results, this paper quantitatively compares both methods and highlights the advantages of modal DQ kinematics. The proposed DQ kinematics are easily extensible to variable length multisection continuum arm with general actuator configurations.