T-PFC: A Trajectory-Optimized Perturbation Feedback Control Approach
For robotic control practitioners, this work offers a computationally cheaper alternative to NMPC with comparable performance, though it is an incremental improvement over existing perturbation feedback methods.
The paper derives a decoupling principle between open-loop plan and closed-loop feedback gains, leading to a perturbation feedback control approach that is near-optimal to third order under action uncertainty. It achieves near-identical performance to Nonlinear Model Predictive Control (NMPC) in robotic planning tasks while requiring significantly less computation.
Traditional stochastic optimal control methods that attempt to obtain an optimal feedback policy for nonlinear systems are computationally intractable. In this paper, we derive a decoupling principle between the open loop plan, and the closed loop feedback gains, that leads to a perturbation feedback control based solution to optimal control problems under action uncertainty, that is near-optimal to the third order. Extensive numerical simulations validate the theory, revealing a wide range of applicability, coping with medium levels of noise. The performance is compared with Nonlinear Model Predictive Control in several difficult robotic planning and control examples that show near identical performance to NMPC while requiring much lesser computational effort. It also leads us to raise the bigger question as to why NMPC should be used in robotic control as opposed to perturbation feedback approaches.