Adaptive integration for controlling speed vs. accuracy in multi-rigid body simulation

Most current approaches for simulating robots in 3D with rigid body dynamics and contact operate by taking fixed, first order integration steps. In this paper, we investigate the viability of various integration approaches (semi implicit and fully explicit first-order, fourth order Runge Kutta, and variable step first order) for maximizing computational efficiency (accuracy and stability vs. running time) on typical robotics manipulation and locomotion applications. After arguing that first-order accuracy to the dynamics models is sufficient for most manipulator and locomotion robotics applications, we focus our investigation on methods for efficient, stable dynamic simulations. We describe a novel algorithm that attempts to provide smooth convergence to the true dynamics solution, which allows us to estimate the error in kinetic energy around an integration step size (as a proxy for the simulation stability). We use this algorithm to evaluate multiple hypotheses using simulation-based experiments with two virtual robot models toward developing methods for faster dynamic simulations.