Simulation Issues in Haptics

In this paper, two problems related to the simulation of virtual environments for haptic systems are considered. The first problem is how to simulate, in discrete time and with low computational effort, dynamic systems in order to preserve their passivity properties. As a matter of fact, simulation of complex systems in real time may lead to undesired effects, like unstable behaviours of the haptic interface, if proper care is not given to the definition of the simulation algorithm. An algorithm is presented here able to maintain the passivity properties of the physical (simulated) system with a reduced computational complexity. The second problem discussed in this paper is the interconnection of algorithms running at different frequencies, i.e., the control algorithm of the haptic interface (running typically at high frequency) and the algorithm simulating the virtual environment (running at lower frequency). A proper software interface, able to connect these two algorithms in an energetic-consistent manner, is presented and discussed. The general framework of both these techniques is the passivity theory and the so-called port-Hamiltonian formalism.