Virtual fixture based haptic rendering of handwriting

Virtual fixture is widely used for motor skill assistance and training. For motor skills involving long and self-intersecting trajectories with variational curvatures, existing methods based on analytic representation of curves can not meet real time and stability requirements of haptic rendering. In this paper, a simple and efficient hierarchical structure is proposed to represent the time ordered geometry of the desired trajectory. The minimum distance from the position of the tool to the desired trajectory is calculated by filtering impossible segments while traversing the hierarchy. To avoid the force discontinuity caused by the singularity of the absolute minimum distance, a constraint conversion method is proposed. The experiments verified that the proposed method satisfied real time and stability requirements of haptic rendering. It enables applications of virtual fixture for assistance and training in handwriting, surgery operation and other skills involving complex trajectories.