A Near-Optimal Separation Principle for Nonlinear Stochastic Systems Arising in Robotic Path Planning and Control
This work addresses a fundamental challenge in robotics by providing a practical solution for path planning and control in stochastic environments, though it is incremental as it builds on existing separation principles with a new twist.
The paper tackles the intractable problem of optimal control for nonlinear stochastic systems in robotic path planning by proposing a tractable, near-optimal design approach based on a separation principle that combines open-loop trajectory planning with feedback tracking, achieving quantifiable near-optimality under small noise assumptions.
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.