Solving the Time-Varying Inverse Kinematics Problem for the Da Vinci Surgical Robot

摘要

A dialytic-elimination and Newton-iteration based quasi-analytic inverse kinematics approach is proposed for the 6 degree of freedom (DOF) active slave manipulator in the Da Vinci surgical robot and other similar systems. First, the transformation matrix-based inverse kinematics model is derived; then, its high-dimensional nonlinear equations are transformed to a high-order nonlinear equation with only one unknown variable by using the dialytic elimination with a unitary matrix. Finally, the quasi-analytic solution is eventually obtained by the Newton iteration method. Simulations are conducted, and the result show that the proposed quasi-analytic approach has advantages in terms of accuracy (error < 0.00004 degree (or mm)), solution speed (<20 ms) and is barely affected by the singularity during intermediate calculations, which proves that the approach meets the real-time and high-accuracy requirements of master–slave mapping control for the Da Vinci surgical robots and other similar systems. In addition, the proposed approach can also serve as a design reference for other types of robotic arms that do not satisfy the Pieper principle.