Haptic Rendering of Tool Contact

Virtual haptic interaction with simulated deformable bodies requires contact forces to be computed with reasonable approximations in real time. This paper makes use of St. Venant’s principle on concentrated loads, and Castigliano’s theory on deflection to show that when an elastic body is globally deformed, the point-force representation of a tool contact is a good approximation. However, when the deformation of the body is localized in a small region, the contact forces critically depend on the shape of the tool. Previously proposed approaches based on finite element and boundary element methods to predict deformation can not always be used to simulate tool contact. We propose a model for computing tool force-displacement responses which is efficiently calculated at run time by interpolation of pre-calculated force-deflection responses, each representing the response of a contact between a given tool and a body. The interpolation approach ensures the continuity of the rendered force, although this force is obtained from pre-calculated responses at a set of discrete surface points. The paper also describes how sliding contacts can be modeled by computing tangential friction forces in terms of pre-sliding displacements over the surface of the undeformed body. Tests involving two deformation types and various contact forms were performed on samples of rubber and of calf liver. A computer implementation is also described.