Common approaches for the haptic rendering of complex scenarios employ multi-rate simulation schemes. Here, the collision queries or the simulation of a complex deformable object are often performed asynchronously at a lower frequency, while some kind of intermediate contact representation is used to simulate interactions at the haptic rate. However, this can produce artifacts in the haptic rendering when the contact situation quickly changes and the intermediate representation is not able to reflect the changes due to the lower update rate.
We address this problem utilizing a novel contact model. It facilitates the creation of contact representations that are accurate for a large range of motions and multiple simulation time-steps. We handle problematic geometrically convex contact regions using a local convex decomposition and special constraints for convex areas. We combine our accurate contact model with an implicit temporal integration scheme to create an intermediate mechanical contact representation, which reflects the dynamic behavior of the simulated objects. To maintain a haptic real time simulation, the size of the region modeled by the contact representation is automatically adapted to the complexity of the geometry in contact. Moreover, we propose a new iterative solving scheme for the involved constrained dynamics problems. We increase the robustness of our method using techniques from trust region-based optimization. Our approach can be combined with standard methods for the modeling of deformable objects or constraint-based approaches for the modeling of, for instance, friction or joints. We demonstrate its benefits with respect to the simulation accuracy and the quality of the rendered haptic forces in several scenarios with one or more haptic proxies.