A Numerical Approximation Approach for Deriving Computational Efficient Inverse Dynamics of 6-DOF Parallel Robots Based on Principle of Virtual Work

The inverse dynamics of the six degree-of-freedom (6-DOF) parallel robot (PR) presents an inherent complexity due to the closed-loop kinematic chains. To derive computational efficient inverse dynamics for real-time control, this study presents a numerical approximation (NA) approach based on the principle of virtual work. The analytical integration of the inertial wrenches is conducted for more concise formulas and then the numerical differentiation of these formulas is presented for more computational efficient inertial wrenches. The principle of virtual work is applied to derive the inverse dynamics by using the numerical inertial wrenches together with the analytical Jacobian matrices. The NA approach can reduce the computational cost of the inverse dynamics by up to 27% with a considerable computational accuracy. The real-time experimental results demonstrate that the NA approach has shortened the time interval of driving force compensation and significantly reduced the trajectory tracking error from 2.59 mm to 0.51 mm.