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

A Near-Optimal Separation Principle for Nonlinear Stochastic Systems Arising in Robotic Path Planning and Control