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

We consider nonlinear stochastic systems that arise in path planning and control of mobile robots. As is typical of almost all nonlinear stochastic systems, optimally solving the problem is intractable. Moreover, even if obtained it would require centralized control, while the path planning problem for mobile robots requires decentralized solutions. We provide a design approach which yields a tractable design that is quantifiably near-optimal. We exhibit a decoupling result under a small noise assumption consisting of the optimal open-loop design of nominal trajectory followed by decentralized feedback law to track this trajectory. As a corollary, we obtain a trajectory-optimized linear quadratic regulator design for stochastic nonlinear systems with Gaussian noise.