Exploring Energy in the Direct Correction Method for Correcting Geometric Constraint Violations

Abstract

The direct correction method is widely used for eliminating geometric constraint violations. This method involves iteratively adjusting the generalized coordinates, which are assumed to be consistent and remain so during the velocity-level corrections. However, the corrected generalized coordinates cause a significant effect on the velocity constraint violations. In this paper, simultaneously correcting both the generalized coordinates and velocities is proposed. A semi-analytic approach to solve the Jacobian matrix, which is used to correct the generalized coordinates and velocities, was employed. Further, the position level, velocity level, and energy constraint equations were corrected simultaneously to ensure that the corrected generalized coordinates and velocities complied with the dynamic equations. The corresponding semi-analytic Jacobian matrix was derived to solve the constraint equations. The methods were demonstrated to be effective using examples, with the simultaneous correction of position-level and velocity-level constraints showing the best results when combined with the energy correction.