In this project, we used Optimal Control Theory to calculate trajectories
that are best from an estimation point of view. We start from a dynamic
model of an object whose position and velocity coordinates are to be estimated.
Camera observations are seen to be 2D projections of a number of object
feature points on a plane; the image points are dependent in a known manner
on object and camera locations, i.e. are related to these by known equations.
These observation equations, and the observation noise, depend on such
variables as zoom and position. It is possible to formulate an optimization
problem where the control variables are the forces acting on the cameras,
and the performance index is a function of the covariance of the errors
in the estimates generated by a Kalman filter. The outcome is a trajectory
designed for optimum estimation of object position and velocity. We have
used the results also to study the grasping of a moving object, where a
compromise is needed between control and estimation.