  We consider the problem of planning under observation and motion uncertainty
for nonlinear robotics systems. Determining the optimal solution to this
problem, generally formulated as a Partially Observed Markov Decision Process
(POMDP), is computationally intractable. We propose a Trajectory-optimized
Linear Quadratic Gaussian (T-LQG) approach that leads to quantifiably
near-optimal solutions for the POMDP problem. We provide a novel "separation
principle" for the design of an optimal nominal open-loop trajectory followed
by an optimal feedback control law, which provides a near-optimal feedback
control policy for belief space planning problems involving a polynomial order
of calculations of minimum order.
