On the passivity of mechanical integrators in haptic rendering

We propose a novel haptic rendering scheme based on passive midpoint integrator (PMI), which is an extension of our prior non-iterative passive mechanical integrator (NPMI) to maximal coordinates for simulation of complex articulated rigid bodies and to multi-point intermittent contact with the linear complementarity problem (LCP) formulation incorporated. The proposed PMI-based haptic rendering then can stably simulate mechanical systems with wide-range of parameters/updaterates (in contrast to semi-implicit Euler integrator), while maintaining losslessness of simple harmonic oscillation (in contrast to implicit Euler integrator), as compared in this paper. Application of this PMI-based haptic rendering is also presented for multi-user virtual co-manipulation of shared rigid object in SE(3) using hand/fingers with multi-point contact over the Internet.