Convex Model Predictive Control for Vehicular Systems

TL;DR

This paper introduces a novel convex Model Predictive Control method for systems on SO(n), avoiding local linearization by operating over the orbitope, simplifying control of vehicular and aeronautical systems.

Contribution

It presents a convex MPC scheme that operates directly on rotation matrices without linearization, compatible with existing MPC variants and applicable to complex vehicular systems.

Findings

Eliminates trigonometric complexities in vehicle control models.

Compatible with obstacle avoidance techniques like MILP.

Demonstrates effectiveness on aeronautical and vehicular systems.

Abstract

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).