Iterative Refinement of Accelerations in Real-Time Vehicle Dynamics

A number of strategies can be followed for the real-time simulation of multibody systems. The main contributing factor to computational efficiency is usually the algorithm itself (the number of equations and their structure, the number of coordinates, the time integration scheme, etc.). Additional (but equally important) aspects have to do with implementation (linear solvers, sparse matrices, parallel computing, etc.). In this paper, an iterative refinement technique is introduced into a semirecursive multibody formulation. First, the formulation is summarized and its basic features are highlighted. Then, the basic goal is to iteratively solve the fundamental system of equations to obtain the accelerations. The iterative process is applied to compute corrections of the solution in an economic way, terminating as soon as a given precision is reached. We show that, upon implementation of this method, the computation time can be reduced at a very low implementation and accuracy costs. Two vehicles are simulated to prove the numerical benefits, namely a 16-degrees-of-freedom (DOF) sedan vehicle and a 40-degrees-of-freedom semitrailer truck. In short, a simple method to iteratively solve for the accelerations of vehicle systems in an efficient way is presented.