A new approach to solve constraint forces of virtual fixtures in haptic rendering

International audienceWe present in this paper an iterative algorithm to solve constraint forces for haptic interactive simulation. The haptic forces are induced by interaction with guidance virtual fixtures having forbidden regions. In general, a haptic rendering based on an explicit formulation of the constraint forces (with virtual springs) can lead to severe numerical stability problems in case of hard constraint. The novelty of the proposed algorithm is based on an implicit formulation of these constraint forces from a Lagrangian augmented formulation. By using a UZAWA technique, it is possible to control the intensity of the constraint force in the force range of the haptic device. “Hard” and “Soft” constraints are considered and discussed through this new approach based on algorithms in computational mechanics. This paper is also among the first contribution to bridge two domains, the computational mechanics and the computational haptic rendering in the context of Virtual Fixtures