Contributions to topological formulations for the dynamic simulation of vehicles

Résumé

There exist a wide variety of topological formulations that deal with the dynamic simulation of medium-large multibody systems. In recent decades, with the strong demand of real-time simulation, a great deal of interest has emerged around efficient topological formulations. This Thesis investigates the computational efficiency of different numerical approaches applied to a number of realistic vehicle models, and introduces a number of novel techniques into a state-of-the-art topological formulation. First, three state-of-the-art topological formulations (generalized semi-recursive, double-step semi-recursive and subsystem synthesis) have been investigated in terms of underlying principles, numerical efficiency and accuracy. They have been numerically implemented and applied to a 28-degree-of-freedom, open-loop rover and a 16-degree-of-freedom, closed-loop sedan vehicle. Second, an original improvement to the rod-removal technique, based on the approximation of second-derivative-based inertia forces, has been introduced into the double-step semi-recursive formulation. This reduces the complexity of the system inertia matrix and improves computational efficiency. Three extrapolation methods are used to approximate the accelerations: constant, linear and quadratic Lagrange. Further, a novel method for the matrix partitioning of the rod inertia has been introduced to preserve accuracy. Third, an iterative refinement technique for the speedup of the 4th-order Runge-Kutta integrator has been presented, whereby the generalized mass matrix factorization and its calculation are avoided. A 16-degree-of-freedom sedan vehicle model and a 40-degree-of-freedom semi-trailer truck model have been simulated in detail to evaluate the computational efficiency and accuracy. In summary, a number of improvements to both the form of the equations of motion and the time integration scheme have been implemented within a topological formulation. The improvements are backed by a comparison with alternative state-of-the-art methods and the simulation of realistic vehicles.