Physically-Based Haptic Synthesis

The phrase “haptic rendering” was introduced by Salisbury et al. [1995] to designate a set of “algorithms for generating the force of interaction with virtual objects”. In this seminal paper many of the key issues associated with the implementation of virtual mechanical environments were first described. Here, we would like to comment on the concept of “haptic synthesis”, a set of algorithms designed to reduce the amount of online computations to a small and predictable amount, and yet able to synthesize signals which are physically accurate. The desire for a fixed, reduced amount of computation isn’t primarily motivated by the limitations of today’s microprocessors, but rather by basic facts about the physics of mechanical interaction between the macroscopic objects of interest in virtual reality simulations. This chapter discusses a set of algorithms to reconstruct interaction forces between virtual objects in a physically accurate manner. They must be fast enough to minimize the creation of spurious energy resulting from the discrete-time realization of displacement-to-force relationships. The most fundamental is an algorithm to compute the force of friction. Another algorithm is then described for sharp cutting, a close cousin of friction because of its dissipative nature. Synthesis of the nonlinear deformation response of arbitrary bodies is then considered. Textural effect are discussed in terms of small perturbations to the nominal signal. Finally, a simple shock synthesis technique based on Hertzian contacts is described. The haptic synthesis algorithms described in this chapter can be regarded as building blocks for a complete rendering system, and used together with other algorithms presented in this book. Long ago it was noticed that when simulating an elastic element with a haptic device where the manipulandum position is measured and the returned force is commanded,