Simulating sharp geometric features in six degrees-of-freedom haptic rendering.

It is a challenging problem to achieve six degree-of-freedom (DoF) haptic simulation of subtle force feelings caused by contacts at sharp geometric features in multi-region contact scenarios. We design a novel sphere-tree model for objects with sharp features and use a configuration-based optimization method to compute feedback force and torque. Given a triangle mesh of an object, a sphere-tree model is created based on dihedral angles between pairs of adjacent triangles. The model consists of a hierarchical sphere-tree for global shape and a linked-list of spheres for local areas with sharp features. In each local area with a sharp edge, we first identify those spheres with radii greater than an upper limit determined by the dihedral angle of the edge. Those spheres are further divided into a linear list of smaller spheres by a splitting method. The experiment results from a cylinder-cube interaction validate that the proposed method can simulate subtle force direction changes when an object slides across sharp edges. Perception-based experiments and a haptic-to-vision shape matching task are also used to compare the performance between our proposed method and other rendering methods. The comparison results show that our method is more effective in simulating sharp features both in terms of measured force signals and human subjective evaluation. Non-penetration among objects is maintained for multi-region contact scenarios. The haptic rendering rate is about 1 kHz, and the subtle force feeling of sliding along sharp features can be stably simulated.