Two implementations of IRK integrators for real-time multibody dynamics

Recently, several authors have proposed the use of implicit Runge–Kutta (IRK) integrators for the dynamics of multibody systems. On the other hand, Newmark-type or structural integrators have shown to be appropriate when real-time performance is demanded in that field. Therefore, the following question arises: might the IRK integrators be suitable for real-time purposes? And, provided the answer is positive: might they be preferable to the Newmark-type family? This paper reports an investigation which has been conducted by the authors in order to get insight into the two questions formulated above. Since, based on previous experiences, it can be suspected that the performance of the integrators may be dependent on the type of dynamic formulation applied, the following three formulations have been considered for the study: a global penalty formulation in dependent natural co-ordinates (many constraints), a topological semi-recursive penalty formulation in dependent relative co-ordinates (few constraints), and a topological semi-recursive formulation in independent relative co-ordinates (no constraints). As representative of the IRK family, a two-stage SDIRK integrator has been selected due to its low associated computational burden, while, on the side of the structural integrators, the trapezoidal rule has been chosen. Two alternative implementations have been proposed to combine the dynamic formulations and the SDIRK integrator. A very demanding maneuver of the whole model of a vehicle has been simulated through all the possible combinations dynamic-formulation/integrator, for different time-steps. Conclusions have been drawn based on the obtained results, which provide some practical criteria for those interested in achieving real-time performance for large and complex multibody systems