Reproducing physical dynamics with hardware-in-the-loop simulators: A passive and explicit discrete integrator

In this paper we present a passive and reliable explicit discrete integrator, which allows to preserve the energy and dynamic properties of a physical body rendered on a hardware-in-the-loop simulator. Starting from the standard Euler integrator, we identify the energy generation that results from the integration process. This energy makes the time discrete dynamics deviate from the ideal one, resulting in position drifts or stability issues. By exploiting the time domain passivity approach, the simulated dynamics is reshaped in order to preserve its physical energy properties. The proposed integration method allows precise simulation of virtual bodies on industrial robot facilities. The method has been validated in simulation and experimentally tested on the DLR OOS-SIM facility.