Texture, roughness, and shape haptic perception of deformable virtual objects with constrained Lagrangian formulation

Haptic interaction with a virtual object establishes a kinesthetic sensation to the user. It is well accepted that to better perceive a given virtual object, it is relevant to yield some surface properties of the object, for instance the shape through the normal contact force, the roughness by the sliding friction, and the texture as a combination of both of them. On this problem, force control is the key issue. This problem has been highlighted three decades ago, when there was not available any good haptic display. Since then, a number of methods on force feedback have been proposed to convey these features, wherein the main scheme is based on the penalty method. However, when the object is deformable, the penalty method cannot compute properly the shape and roughness since the contact force ignores the inherent deformation of the object. In contrast, if the contact force is computed using the constrained Lagrangian, this force depends on the dynamic deformation of the object. In this paper, a constrained Lagrangian-based oriented framework is proposed to compute the contact force dynamically, in such a way that it can easily realize these effects over implicit dynamical objects. This powerful scheme can produce these effects seamlessly. Experimental results using PHANTOM on deformable and undeformable virtual objects are presented and discussed.