Adjusting Output-Limiter for Stable Haptic Rendering in Virtual Environments

This paper presents a control method using an adjusting output-limiter for stable haptic rendering in virtual environments. In a simulation of force-reflecting interaction with deformable objects in the virtual environment, a quick computation of the accurate impedance of deformable objects is rare. This is particularly true when physics-based models, such as tensor-mass models or mass-spring models, are used. The problem is aggravated if the simulation involves changes in the geometry and/or impedance of the deformation model, such as cutting or suturing. The proposed control method guarantees stable haptic interaction with deformable objects of unknown and/or varying impedance. The method is based on the time-domain passivity theorem and the two-port network model. The controller adjusts the maximum permissible force to guarantee the passivity of the haptic system at every sampling instant. The controller notes only the magnitude of the reflective force, and does not depend on properties of the employed force model. This allows the proposed control method applicable to haptic systems involving deformable objects with unknown, nonlinear, and/or time-varying impedance. Designs of the controllers are presented for impedance-type and admittance-type haptic systems. The method is also extended for multiple degrees-of-freedom.