V.Patoglu, Closest Point Maintenance for Haptic Rendering of ...

Faculty of Engineering and Natural Sciences
FENS SEMINARS

Closest Point Maintenance for Haptic Rendering of Hybrid Dynamical Virtual Environments

Volkan Patoglu
Rice University, Department of Mechanical Engineering and Material Science

Unlike objects in the physical world, objects in the virtual world lack matter to detected and respond to collisions and to otherwise govern behavior. To shore things up, we employ various models and solvers to construct virtual environments. We are interested in environments that can be manipulated and explored through a haptic interface. Many tools are available for the production and solution of dynamical models. Production of geometric models is generously served by tools from differential geometry and CAD. Solution of geometric models, on the other hand, is generally a rather ad hoc affair in virtual environment simulators. Determination of the closest points on two parametric surfaces, for example, is usually performed by Newton iteration and remains quite sensitive to initialization errors and step size selection. We have re-formulated the closest point problem for parametric surfaces in a differential kinematic form, to be solved with the design of a stabilizing controller. Control design and analysis tools allow us to solve the problem with considerable flair and to accompany the solution with convergence proofs. Our design is based on a control Lyapunov function that together with a top-level switching algorithm based on Voronoi diagrams, accounts for the combined and interacting effects of object shape and object motion while achieving global uniform asymptotic stability for the pair of closest points. I will also present some of our work in haptic rendering of hybrid dynamical systems that uses our collision detector along with a general-purpose symbolic/numerical dynamics engine for interactive simulation.

December 26, 2005, 10:40, FENS L030