When digitally realized, virtual environments (VEs) do not perfectly match the physical environments they are supposed to emulate. This paper deals with energy aspects of such a mismatch, i.e., artificial energy leaks. A methodology is developed that employs smooth correction (SC) and leak dissipation (LD) to achieve a stable interconnection of the VE with the haptic device. The SC-LD naturally blends with the original laws for rendering the VE and gives rise to modified force feedback laws. These laws can be regarded as energy-consistent discretizations of their continuous-time counterparts. For some fundamental examples including virtual springs and masses, these laws are analytically reduced to simple closed-form equations. The methodology is then generalized to the multivariable case. Several experiments are conducted including a 2-DOF coupled nonlinear VE example, and a scenario leading to a sequence of contacts with a virtual object. Besides the conceptual advantage, simulation and experimental results demonstrate some other advantages of the SC-LD over well-known time-domain passivity methods. These advantages include improved fidelity, simpler implementation, and less susceptibility to produce impulsive/chattering response.

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