Efficiently Computable Constrained Optimal Feedback Controllers

Constrained optimal feedback controllers can be used to mitigate external perturbations and modeling errors in robot control. However, these controllers require extensive calculation that is one of their main limitations in real-time implementation. Here we present two locally optimal feedback controllers that can be efficiently computed online in real-time. These controllers are applicable to systems with nonlinear dynamics, nonlinear state and control dependent cost, and box constrained control inputs. The proposed locally optimal controllers differ from alternative feedback and re-computed feed-forward model predictive controllers which provide sub-optimal inputs and require significantly more online calculation in real-time implementation. Theoretical arguments, a numerical simulation, and a robot control experiment substantiate our claims, and show the applicability of the proposed efficiently computable constrained optimal feedback control method.