효율적인 실시간 차량 시뮬레이션을 위한 자코비안 갱신이 불필요한 뉴턴 적분방법

Abstract

While implicit integration methods such as Newtons method have excellent stability for the analysis of stiff and constrained mechanical systems, they have the drawback that the evaluation and LU-factorization of the system Jacobian matrix required at every time step are time-consuming. This paper proposes a Jacobian update-free Newtons method in order to overcome these defects. Because the motions of all bodies in a vehicle model are limited with respect to the chassis body, the equations are formulated with respect to the moving chassis-body reference frame instead of the fixed inertial reference frame. This makes the system Jacobian remain nearly constant, and thus allows the Newtons method to be free from the Jacobian update. Consequently, the proposed method significantly decreases the computational cost of the vehicle dynamic simulation. This paper provides detailed generalized formulation procedures for the equations of motion, constraint equations, and generalized forces of the proposed method.