Professor Brent
Gillespie
Department of
Mechanical Engineering
University of
Michigan
Abstract
-- A vital piece of enabling technology for computer animation, CAD software,
and interactive virtual environments is a fast and reliable collision
detector—or even better, a fast and reliable closest point
algorithm. For parametric models,
closest point algorithms are usually based on NewtonÕs Iteration, enjoy only
local convergence, and possess rather touchy convergence rates. In this talk I will present a new
collision detector based on a re-formulation of the closest point algorithm as
a nonlinear control design problem.
Control design and analysis tools allow us to solve the problem with
considerable flair and to outfit the controller with attractive features like
global convergence. We time-differentiated the geometric minimization problem
to form the differential kinematics, then solved the inverse differential
kinematics with a feedback stabilized controller. The controller selects parametric speeds that drive any pair
of initialization points to the true closest points on two convex surfaces. Two
switching rules based on Voronoi diagrams extend the controller to objects made
of tiled-together surface patches.
Global uniform asymptotic stability of the hybrid dynamical system is
proved with a common Lyapunov function.
I
will also review work in our lab on a hybrid systems approach to other
applications in haptic rendering, including robot-assisted rehabilitation,
vehicle controls, and automated modeling.
We are particularly interested in hybrid system dynamics because the
human sensorimotor system seems to be keenly adept at exciting such dynamics
and extracting desired behavior from hybrid dynamical systems.
Friday, September 16,
2005
3:30 – 4:30
p.m.