Convex Model Predictive Control for Vehicular Systems
This method addresses control challenges for aeronautical and vehicular systems by eliminating transcendental trigonometric terms, offering a potential improvement over conventional linearization techniques.
The authors tackled the problem of Model Predictive Control (MPC) for systems with states in SO(2) or SO(3) by operating over the orbitope of rotation matrices, avoiding charts or linearization, and resulting in a scheme requiring only second-order cone or semidefinite constraints beyond typical QP schemes.
In this work, we present a method to perform Model Predictive Control (MPC) over systems whose state is an element of $SO(n)$ for $n=2,3$. This is done without charts or any local linearization, and instead is performed by operating over the orbitope of rotation matrices. This results in a novel MPC scheme without the drawbacks associated with conventional linearization techniques. Instead, second order cone- or semidefinite-constraints on state variables are the only requirement beyond those of a QP-scheme typical for MPC of linear systems. Of particular emphasis is the application to aeronautical and vehicular systems, wherein the method removes many of the transcendental trigonometric terms associated with these systems' state space equations. Furthermore, the method is shown to be compatible with many existing variants of MPC, including obstacle avoidance via Mixed Integer Linear Programming (MILP).