An analysis of higher-order kinematics formalisms for an innovative surgical parallel robot

• The higher-order kinematics are derived using multiple formalisms. • The comparison of the kinematic algorithms shows statistical difference. • Multidual methods proved to be efficient in deriving kinematic models. The paper presents a novel modular parallel robot for pancreatic surgery and its higher-order kinematics derived based on various formalisms. The classical vector, homogeneous transformation matrices and dual quaternion approaches are studied for the kinematic functions using both classical differentiation and multidual algebra. The algorithms for inverse kinematics for all three studied formalisms are presented for both differentiation and multidual algebra approaches. Furthermore, these algorithms are compared based on numerical stability, execution times and number and type of mathematical functions and operators contained in each algorithm. A statistical analysis shows that there is significant improvement in execution time for the algorithms implemented using multidual algebra, while the numerical stability is appropriate for all algorithms derived based on differentiation and multidual algebra. While the implementation of the kinematic algorithms using multidual algebra shows positive results when benchmarked on a standard PC, further work is required to evaluate the multidual algorithms on hardware/software used for the modular parallel robot command and control.