cient dynamic simulation of robotic systems with hierarchy

In this paper multirate numerical integration techniques are introduced as a tool for simulating robotic systems. In contrast with traditional simulation techniques where a single global time step is used, multirate methods seek a gain in e ciency by using larger step sizes for the slow varying components and smaller step sizes for components with rapidly changing solutions. We argue that many robotic systems inherently posses di erent time scales, and therefore can bene t from multirate techniques. We have developed a multirate version of the popular Adams Predictor Corrector methods, which has a variety of modern features. We present results on the accuracy, stability and e ciency of the algorithm along with simulation results.