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An efficient real-time vehicle simulation method using a chassis-based kinematic formulation

The purpose of this research is to develop an efficient kinematic formulation for an implicit integration method so that relatively low-cost computers can be used for the real-time simulation of multi-body vehicle dynamics models without sacrificing modelling details. The most time-consuming processes associated with the implicit method are the generation and LU decomposition of the system Jacobian matrix of the augmented equations of motion and the constraints at every time step. In order to save the computation time in these processes, a new kinematic formulation is developed to make the system Jacobian remain nearly constant. This allows us to employ a Newton chord method for implicit integration without the need to update the Jacobian. The formulation is motivated by the idea that relative motions between the chassis and other bodies (e.g. suspension components) are limited. Thus, the equations of motion, as well as the joint constraint equations and the generalized force equations, are formulated with respect to the chassis-body reference frame instead of the inertial reference frame. Consequently, the initial Jacobian can be used for long-term vehicle simulation. A comparison of the proposed approach with the conventional approach shows that the proposed approach drastically improved the computational efficiency; i.e. the computational cost of the proposed method was only 35% of the cost of the conventional method. The proposed algorithm yielded almost exact solutions for a prototype multi-body vehicle model run in real time on a 3.5 GHz personal computer.