  We consider nonlinear stochastic systems that arise in path planning and
control of mobile robots. As is typical of almost all nonlinear stochastic
systems, the optimally solving problem is intractable. We provide a design
approach which yields a tractable design that is quantifiably near-optimal. We
exhibit a "separation" principle under a small noise assumption consisting of
the optimal open-loop design of nominal trajectory followed by an optimal
feedback law to track this trajectory, which is different from the usual effort
of separating estimation from control. As a corollary, we obtain a
trajectory-optimized linear quadratic regulator design for stochastic nonlinear
systems with Gaussian noise.
