Showing papers by "Zexiang Li published in 2000"

Stabilization of a 2-DOF spherical pendulum on X-Y table

Abstract: In this paper, a 2-DOF spherical pendulum system is constructed and balanced on a X-Y table. The pendulum is projected onto the x-z and y-z planes, which are parallel to the two motion directions of the X-Y table. These projections are treated independently to each other and are controlled separately. The stabilization control for a 1D inverted pendulum is proposed based on the state space approach and the Lie theoretic tools without resorting any direct approximation to each nonlinear term. A specially developed sensor system allows the contactless measurement of the inclination angles of the pendulum. The experimental results are reported.

A geometric method for computation of datum reference frames

Abstract: A datum reference frame (DRF) is a coordinate system used to locate and orient part features. Constructing a DRF from a set of datum features is a complicated process involving: a) specifying a valid combination and the precedence of the datum features which define the DRF; b) developing datum from datum features of the part; and c) determining the position and orientation of the DRF from the datums. We develop a geometric theory for establishing DRFs. The theory is based on the observation that a datum feature such as a plane, a cylinder or a sphere has a symmetry subgroup G/sub 0/ under the action by the group SE(3) of rigid motions in R/sup 3/. Thus, the configuration space of a datum feature can be identified with the homogeneous space SE(3)/G/sub 0/, and the problem of datum development can be posed as a minimization problem in SE(J)/G/sub 0/. We give conditions under which a datum feature qualifies to be a secondary or a tertiary datum. We present a sequential procedure that transforms the primary, secondary and tertiary datum problems as a minimization or a constrained minimization problem in the homogeneous spaces of SE(3). We develop simple algorithms to solve these problems, and give simulation results illustrating efficiency and simplicity of the approach.