  We present a locally optimal tracking controller for Cable Driven Parallel
Robot (CDPR) control based on a time-varying Linear Quadratic Gaussian (TV-LQG)
controller. In contrast to many methods which use fixed feedback gains, our
time-varying controller computes the optimal gains depending on the location in
the workspace and the future trajectory. Meanwhile, we rely heavily on offline
computation to reduce the burden of online implementation and feasibility
checking. Following the growing popularity of probabilistic graphical models
for optimal control, we use factor graphs as a tool to formulate our controller
for their efficiency, intuitiveness, and modularity. The topology of a factor
graph encodes the relevant structural properties of equations in a way that
facilitates insight and efficient computation using sparse linear algebra
solvers. We first use factor graph optimization to compute a nominal
trajectory, then linearize the graph and apply variable elimination to compute
the locally optimal, time varying linear feedback gains. Next, we leverage the
factor graph formulation to compute the locally optimal, time-varying Kalman
Filter gains, and finally combine the locally optimal linear control and
estimation laws to form a TV-LQG controller. We compare the tracking accuracy
of our TV-LQG controller to a state-of-the-art dual-space feed-forward
controller on a 2.9m x 2.3m, 4-cable planar robot and demonstrate improved
tracking accuracies of 0.8{\deg} and 11.6mm root mean square error in rotation
and translation respectively.
